auto import from //depot/cupcake/@135843
diff --git a/libtommath/Android.mk b/libtommath/Android.mk
new file mode 100644
index 0000000..fed8e39
--- /dev/null
+++ b/libtommath/Android.mk
@@ -0,0 +1,34 @@
+LOCAL_PATH:= $(call my-dir)
+include $(CLEAR_VARS)
+
+LOCAL_MODULE := libtommath
+LOCAL_SRC_FILES := \
+bncore.c bn_mp_init.c bn_mp_clear.c bn_mp_exch.c bn_mp_grow.c bn_mp_shrink.c \
+bn_mp_clamp.c bn_mp_zero.c bn_mp_set.c bn_mp_set_int.c bn_mp_init_size.c bn_mp_copy.c \
+bn_mp_init_copy.c bn_mp_abs.c bn_mp_neg.c bn_mp_cmp_mag.c bn_mp_cmp.c bn_mp_cmp_d.c \
+bn_mp_rshd.c bn_mp_lshd.c bn_mp_mod_2d.c bn_mp_div_2d.c bn_mp_mul_2d.c bn_mp_div_2.c \
+bn_mp_mul_2.c bn_s_mp_add.c bn_s_mp_sub.c bn_fast_s_mp_mul_digs.c bn_s_mp_mul_digs.c \
+bn_fast_s_mp_mul_high_digs.c bn_s_mp_mul_high_digs.c bn_fast_s_mp_sqr.c bn_s_mp_sqr.c \
+bn_mp_add.c bn_mp_sub.c bn_mp_karatsuba_mul.c bn_mp_mul.c bn_mp_karatsuba_sqr.c \
+bn_mp_sqr.c bn_mp_div.c bn_mp_mod.c bn_mp_add_d.c bn_mp_sub_d.c bn_mp_mul_d.c \
+bn_mp_div_d.c bn_mp_mod_d.c bn_mp_expt_d.c bn_mp_addmod.c bn_mp_submod.c \
+bn_mp_mulmod.c bn_mp_sqrmod.c bn_mp_gcd.c bn_mp_lcm.c bn_fast_mp_invmod.c bn_mp_invmod.c \
+bn_mp_reduce.c bn_mp_montgomery_setup.c bn_fast_mp_montgomery_reduce.c bn_mp_montgomery_reduce.c \
+bn_mp_exptmod_fast.c bn_mp_exptmod.c bn_mp_2expt.c bn_mp_n_root.c bn_mp_jacobi.c bn_reverse.c \
+bn_mp_count_bits.c bn_mp_read_unsigned_bin.c bn_mp_read_signed_bin.c bn_mp_to_unsigned_bin.c \
+bn_mp_to_signed_bin.c bn_mp_unsigned_bin_size.c bn_mp_signed_bin_size.c \
+bn_mp_xor.c bn_mp_and.c bn_mp_or.c bn_mp_rand.c bn_mp_montgomery_calc_normalization.c \
+bn_mp_prime_is_divisible.c bn_prime_tab.c bn_mp_prime_fermat.c bn_mp_prime_miller_rabin.c \
+bn_mp_prime_is_prime.c bn_mp_prime_next_prime.c bn_mp_dr_reduce.c \
+bn_mp_dr_is_modulus.c bn_mp_dr_setup.c bn_mp_reduce_setup.c \
+bn_mp_toom_mul.c bn_mp_toom_sqr.c bn_mp_div_3.c bn_s_mp_exptmod.c \
+bn_mp_reduce_2k.c bn_mp_reduce_is_2k.c bn_mp_reduce_2k_setup.c \
+bn_mp_reduce_2k_l.c bn_mp_reduce_is_2k_l.c bn_mp_reduce_2k_setup_l.c \
+bn_mp_radix_smap.c bn_mp_read_radix.c bn_mp_toradix.c bn_mp_radix_size.c \
+bn_mp_fread.c bn_mp_fwrite.c bn_mp_cnt_lsb.c bn_error.c \
+bn_mp_init_multi.c bn_mp_clear_multi.c bn_mp_exteuclid.c bn_mp_toradix_n.c \
+bn_mp_prime_random_ex.c bn_mp_get_int.c bn_mp_sqrt.c bn_mp_is_square.c bn_mp_init_set.c \
+bn_mp_init_set_int.c bn_mp_invmod_slow.c bn_mp_prime_rabin_miller_trials.c \
+bn_mp_to_signed_bin_n.c bn_mp_to_unsigned_bin_n.c
+
+include $(BUILD_STATIC_LIBRARY)
diff --git a/libtommath/LICENSE b/libtommath/LICENSE
new file mode 100644
index 0000000..5baa792
--- /dev/null
+++ b/libtommath/LICENSE
@@ -0,0 +1,4 @@
+LibTomMath is hereby released into the Public Domain.
+
+-- Tom St Denis
+
diff --git a/libtommath/Makefile.in b/libtommath/Makefile.in
new file mode 100644
index 0000000..961b92a
--- /dev/null
+++ b/libtommath/Makefile.in
@@ -0,0 +1,188 @@
+#Makefile for GCC
+#
+#Tom St Denis
+
+#version of library
+VERSION=0.40
+
+VPATH=@srcdir@
+srcdir=@srcdir@
+
+# Dropbear takes flags from the toplevel makefile
+CFLAGS += -I$(srcdir)
+
+#CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare
+
+ifndef IGNORE_SPEED
+
+#for speed
+#CFLAGS += -O3 -funroll-all-loops
+
+#for size
+#CFLAGS += -Os
+
+#x86 optimizations [should be valid for any GCC install though]
+#CFLAGS += -fomit-frame-pointer
+
+#debug
+#CFLAGS += -g3
+
+endif
+
+#install as this user
+ifndef INSTALL_GROUP
+ GROUP=wheel
+else
+ GROUP=$(INSTALL_GROUP)
+endif
+
+ifndef INSTALL_USER
+ USER=root
+else
+ USER=$(INSTALL_USER)
+endif
+
+#default files to install
+ifndef LIBNAME
+ LIBNAME=libtommath.a
+endif
+
+default: ${LIBNAME}
+
+HEADERS=tommath.h tommath_class.h tommath_superclass.h
+
+#LIBPATH-The directory for libtommath to be installed to.
+#INCPATH-The directory to install the header files for libtommath.
+#DATAPATH-The directory to install the pdf docs.
+DESTDIR=
+LIBPATH=/usr/lib
+INCPATH=/usr/include
+DATAPATH=/usr/share/doc/libtommath/pdf
+
+OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
+bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
+bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
+bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
+bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
+bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
+bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
+bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
+bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
+bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
+bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
+bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \
+bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
+bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
+bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
+bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
+bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
+bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
+bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
+bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+
+$(LIBNAME): $(OBJECTS)
+ $(AR) $(ARFLAGS) $@ $(OBJECTS)
+ $(RANLIB) $@
+
+#make a profiled library (takes a while!!!)
+#
+# This will build the library with profile generation
+# then run the test demo and rebuild the library.
+#
+# So far I've seen improvements in the MP math
+profiled:
+ make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing
+ ./ltmtest
+ rm -f *.a *.o ltmtest
+ make CFLAGS="$(CFLAGS) -fbranch-probabilities"
+
+#make a single object profiled library
+profiled_single:
+ perl gen.pl
+ $(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o
+ $(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest
+ ./ltmtest
+ rm -f *.o ltmtest
+ $(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o
+ $(AR) $(ARFLAGS) $(LIBNAME) mpi.o
+ $(RANLIB) $(LIBNAME)
+
+install: $(LIBNAME)
+ install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
+ install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
+ install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
+ install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
+
+test: $(LIBNAME) demo/demo.o
+ $(CC) $(CFLAGS) demo/demo.o $(LIBNAME) -o test
+
+mtest: test
+ cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
+
+timing: $(LIBNAME)
+ $(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest
+
+# makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
+docdvi: tommath.src
+ cd pics ; MAKE=${MAKE} ${MAKE}
+ echo "hello" > tommath.ind
+ perl booker.pl
+ latex tommath > /dev/null
+ latex tommath > /dev/null
+ makeindex tommath
+ latex tommath > /dev/null
+
+# poster, makes the single page PDF poster
+poster: poster.tex
+ pdflatex poster
+ rm -f poster.aux poster.log
+
+# makes the LTM book PDF file, requires tetex, cleans up the LaTeX temp files
+docs: docdvi
+ dvipdf tommath
+ rm -f tommath.log tommath.aux tommath.dvi tommath.idx tommath.toc tommath.lof tommath.ind tommath.ilg
+ cd pics ; MAKE=${MAKE} ${MAKE} clean
+
+#LTM user manual
+mandvi: bn.tex
+ echo "hello" > bn.ind
+ latex bn > /dev/null
+ latex bn > /dev/null
+ makeindex bn
+ latex bn > /dev/null
+
+#LTM user manual [pdf]
+manual: mandvi
+ pdflatex bn >/dev/null
+ rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc
+
+pretty:
+ perl pretty.build
+
+clean:
+ rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
+ *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la
+ rm -rf .libs
+ cd etc ; MAKE=${MAKE} ${MAKE} clean
+ cd pics ; MAKE=${MAKE} ${MAKE} clean
+
+#zipup the project (take that!)
+no_oops: clean
+ cd .. ; cvs commit
+ echo Scanning for scratch/dirty files
+ find . -type f | grep -v CVS | xargs -n 1 bash mess.sh
+
+zipup: clean manual poster docs
+ perl gen.pl ; mv mpi.c pre_gen/ ; \
+ cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \
+ cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; \
+ tar -c libtommath-$(VERSION)/* | bzip2 -9vvc > ltm-$(VERSION).tar.bz2 ; \
+ zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* ; \
+ mv -f ltm* ~ ; rm -rf libtommath-$(VERSION)
diff --git a/libtommath/bn.tex b/libtommath/bn.tex
new file mode 100644
index 0000000..38ece04
--- /dev/null
+++ b/libtommath/bn.tex
@@ -0,0 +1,1835 @@
+\documentclass[synpaper]{book}
+\usepackage{hyperref}
+\usepackage{makeidx}
+\usepackage{amssymb}
+\usepackage{color}
+\usepackage{alltt}
+\usepackage{graphicx}
+\usepackage{layout}
+\def\union{\cup}
+\def\intersect{\cap}
+\def\getsrandom{\stackrel{\rm R}{\gets}}
+\def\cross{\times}
+\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
+\def\catn{$\|$}
+\def\divides{\hspace{0.3em} | \hspace{0.3em}}
+\def\nequiv{\not\equiv}
+\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
+\def\lcm{{\rm lcm}}
+\def\gcd{{\rm gcd}}
+\def\log{{\rm log}}
+\def\ord{{\rm ord}}
+\def\abs{{\mathit abs}}
+\def\rep{{\mathit rep}}
+\def\mod{{\mathit\ mod\ }}
+\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
+\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
+\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
+\def\Or{{\rm\ or\ }}
+\def\And{{\rm\ and\ }}
+\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
+\def\implies{\Rightarrow}
+\def\undefined{{\rm ``undefined"}}
+\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
+\let\oldphi\phi
+\def\phi{\varphi}
+\def\Pr{{\rm Pr}}
+\newcommand{\str}[1]{{\mathbf{#1}}}
+\def\F{{\mathbb F}}
+\def\N{{\mathbb N}}
+\def\Z{{\mathbb Z}}
+\def\R{{\mathbb R}}
+\def\C{{\mathbb C}}
+\def\Q{{\mathbb Q}}
+\definecolor{DGray}{gray}{0.5}
+\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
+\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
+\def\gap{\vspace{0.5ex}}
+\makeindex
+\begin{document}
+\frontmatter
+\pagestyle{empty}
+\title{LibTomMath User Manual \\ v0.40}
+\author{Tom St Denis \\ tomstdenis@gmail.com}
+\maketitle
+This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been
+formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package.
+
+\vspace{10cm}
+
+\begin{flushright}Open Source. Open Academia. Open Minds.
+
+\mbox{ }
+
+Tom St Denis,
+
+Ontario, Canada
+\end{flushright}
+
+\tableofcontents
+\listoffigures
+\mainmatter
+\pagestyle{headings}
+\chapter{Introduction}
+\section{What is LibTomMath?}
+LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating
+large integer numbers. It was written in portable ISO C source code so that it will build on any platform with a conforming
+C compiler.
+
+In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how
+to implement ``bignum'' math. However, the resulting code has proven to be very useful. It has been used by numerous
+universities, commercial and open source software developers. It has been used on a variety of platforms ranging from
+Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines.
+
+\section{License}
+As of the v0.25 the library source code has been placed in the public domain with every new release. As of the v0.28
+release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new
+release as well. This textbook is meant to compliment the project by providing a more solid walkthrough of the development
+algorithms used in the library.
+
+Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger. They are not required to use LibTomMath.} are in the
+public domain everyone is entitled to do with them as they see fit.
+
+\section{Building LibTomMath}
+
+LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC. However, the library will
+also build in MSVC, Borland C out of the box. For any other ISO C compiler a makefile will have to be made by the end
+developer.
+
+\subsection{Static Libraries}
+To build as a static library for GCC issue the following
+\begin{alltt}
+make
+\end{alltt}
+
+command. This will build the library and archive the object files in ``libtommath.a''. Now you link against
+that and include ``tommath.h'' within your programs. Alternatively to build with MSVC issue the following
+\begin{alltt}
+nmake -f makefile.msvc
+\end{alltt}
+
+This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC
+version 6.00 with service pack 5.
+
+\subsection{Shared Libraries}
+To build as a shared library for GCC issue the following
+\begin{alltt}
+make -f makefile.shared
+\end{alltt}
+This requires the ``libtool'' package (common on most Linux/BSD systems). It will build LibTomMath as both shared
+and static then install (by default) into /usr/lib as well as install the header files in /usr/include. The shared
+library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''. Generally
+you use libtool to link your application against the shared object.
+
+There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires
+Cygwin to work with since it requires the auto-export/import functionality. The resulting DLL and import library
+``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.
+
+\subsection{Testing}
+To build the library and the test harness type
+
+\begin{alltt}
+make test
+\end{alltt}
+
+This will build the library, ``test'' and ``mtest/mtest''. The ``test'' program will accept test vectors and verify the
+results. ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI
+is included in the package}. Simply pipe mtest into test using
+
+\begin{alltt}
+mtest/mtest | test
+\end{alltt}
+
+If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into
+mtest. For example, if your PRNG program is called ``myprng'' simply invoke
+
+\begin{alltt}
+myprng | mtest/mtest | test
+\end{alltt}
+
+This will output a row of numbers that are increasing. Each column is a different test (such as addition, multiplication, etc)
+that is being performed. The numbers represent how many times the test was invoked. If an error is detected the program
+will exit with a dump of the relevent numbers it was working with.
+
+\section{Build Configuration}
+LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.
+Each phase changes how the library is built and they are applied one after another respectively.
+
+To make the system more powerful you can tweak the build process. Classes are defined in the file
+``tommath\_superclass.h''. By default, the symbol ``LTM\_ALL'' shall be defined which simply
+instructs the system to build all of the functions. This is how LibTomMath used to be packaged. This will give you
+access to every function LibTomMath offers.
+
+However, there are cases where such a build is not optional. For instance, you want to perform RSA operations. You
+don't need the vast majority of the library to perform these operations. Aside from LTM\_ALL there is
+another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt. Additional
+classes can be defined base on the need of the user.
+
+\subsection{Build Depends}
+In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
+which further define symbols. All of the symbols (technically they're macros $\ldots$) represent a given C source
+file. For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''. When a define has been enabled the
+function in the respective file will be compiled and linked into the library. Accordingly when the define
+is absent the file will not be compiled and not contribute any size to the library.
+
+You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).
+This is to help resolve as many dependencies as possible. In the last pass the symbol LTM\_LAST will be defined.
+This is useful for ``trims''.
+
+\subsection{Build Tweaks}
+A tweak is an algorithm ``alternative''. For example, to provide tradeoffs (usually between size and space).
+They can be enabled at any pass of the configuration phase.
+
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Define} & \textbf{Purpose} \\
+\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
+ & functional mp\_div() function \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsection{Build Trims}
+A trim is a manner of removing functionality from a function that is not required. For instance, to perform
+RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.
+Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
+only if LTM\_LAST has been defined.
+
+\subsubsection{Moduli Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
+ & BN\_MP\_REDUCE\_C \\
+ & BN\_MP\_REDUCE\_SETUP\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+\hline Exponentiation with random odd moduli & (The above plus the following) \\
+ & BN\_MP\_REDUCE\_2K\_C \\
+ & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
+ & BN\_MP\_REDUCE\_IS\_2K\_C \\
+ & BN\_MP\_DR\_IS\_MODULUS\_C \\
+ & BN\_MP\_DR\_REDUCE\_C \\
+ & BN\_MP\_DR\_SETUP\_C \\
+\hline Modular inverse odd moduli only & BN\_MP\_INVMOD\_SLOW\_C \\
+\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsubsection{Operand Size Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Moduli $\le 2560$ bits & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
+ & BN\_S\_MP\_MUL\_DIGS\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_S\_MP\_SQR\_C \\
+\hline Polynomial Schmolynomial & BN\_MP\_KARATSUBA\_MUL\_C \\
+ & BN\_MP\_KARATSUBA\_SQR\_C \\
+ & BN\_MP\_TOOM\_MUL\_C \\
+ & BN\_MP\_TOOM\_SQR\_C \\
+
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+
+\section{Purpose of LibTomMath}
+Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
+bleeding edge performance in mind. First and foremost LibTomMath was written to be entirely open. Not only is the
+source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the
+source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
+arithmetic techniques.
+
+LibTomMath was written to be an instructive collection of source code. This is why there are many comments, only one
+function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed
+increase.
+
+Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies
+the library (beat that!).
+
+So you may be thinking ``should I use LibTomMath?'' and the answer is a definite maybe. Let me tabulate what I think
+are the pros and cons of LibTomMath by comparing it to the math routines from GnuPG\footnote{GnuPG v1.2.3 versus LibTomMath v0.28}.
+
+\newpage\begin{figure}[here]
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|c|c|l|}
+\hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\
+\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath $ = 71.97$ \\
+\hline Commented function prototypes & X && GnuPG function names are cryptic. \\
+\hline Speed && X & LibTomMath is slower. \\
+\hline Totally free & X & & GPL has unfavourable restrictions.\\
+\hline Large function base & X & & GnuPG is barebones. \\
+\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\
+\hline Portable & X & & GnuPG requires configuration to build. \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+\caption{LibTomMath Valuation}
+\end{figure}
+
+It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application.
+However, LibTomMath was written with cryptography in mind. It provides essentially all of the functions a cryptosystem
+would require when working with large integers.
+
+So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
+own application but I think there are reasons not to. While LibTomMath is slower than libraries such as GnuMP it is
+not normally significantly slower. On x86 machines the difference is normally a factor of two when performing modular
+exponentiations. It depends largely on the processor, compiler and the moduli being used.
+
+Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern. However,
+on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
+that is very flexible, complete and performs well in resource contrained environments. Fast RSA for example can
+be performed with as little as 8KB of ram for data (again depending on build options).
+
+\chapter{Getting Started with LibTomMath}
+\section{Building Programs}
+In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically
+libtommath.a). There is no library initialization required and the entire library is thread safe.
+
+\section{Return Codes}
+There are three possible return codes a function may return.
+
+\index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM}
+\begin{figure}[here!]
+\begin{center}
+\begin{small}
+\begin{tabular}{|l|l|}
+\hline \textbf{Code} & \textbf{Meaning} \\
+\hline MP\_OKAY & The function succeeded. \\
+\hline MP\_VAL & The function input was invalid. \\
+\hline MP\_MEM & Heap memory exhausted. \\
+\hline &\\
+\hline MP\_YES & Response is yes. \\
+\hline MP\_NO & Response is no. \\
+\hline
+\end{tabular}
+\end{small}
+\end{center}
+\caption{Return Codes}
+\end{figure}
+
+The last two codes listed are not actually ``return'ed'' by a function. They are placed in an integer (the caller must
+provide the address of an integer it can store to) which the caller can access. To convert one of the three return codes
+to a string use the following function.
+
+\index{mp\_error\_to\_string}
+\begin{alltt}
+char *mp_error_to_string(int code);
+\end{alltt}
+
+This will return a pointer to a string which describes the given error code. It will not work for the return codes
+MP\_YES and MP\_NO.
+
+\section{Data Types}
+The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath. This data type is used to
+organize all of the data required to manipulate the integer it represents. Within LibTomMath it has been prototyped
+as the following.
+
+\index{mp\_int}
+\begin{alltt}
+typedef struct \{
+ int used, alloc, sign;
+ mp_digit *dp;
+\} mp_int;
+\end{alltt}
+
+Where ``mp\_digit'' is a data type that represents individual digits of the integer. By default, an mp\_digit is the
+ISO C ``unsigned long'' data type and each digit is $28-$bits long. The mp\_digit type can be configured to suit other
+platforms by defining the appropriate macros.
+
+All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure. You must allocate memory to
+hold the structure itself by yourself (whether off stack or heap it doesn't matter). The very first thing that must be
+done to use an mp\_int is that it must be initialized.
+
+\section{Function Organization}
+
+The arithmetic functions of the library are all organized to have the same style prototype. That is source operands
+are passed on the left and the destination is on the right. For instance,
+
+\begin{alltt}
+mp_add(&a, &b, &c); /* c = a + b */
+mp_mul(&a, &a, &c); /* c = a * a */
+mp_div(&a, &b, &c, &d); /* c = [a/b], d = a mod b */
+\end{alltt}
+
+Another feature of the way the functions have been implemented is that source operands can be destination operands as well.
+For instance,
+
+\begin{alltt}
+mp_add(&a, &b, &b); /* b = a + b */
+mp_div(&a, &b, &a, &c); /* a = [a/b], c = a mod b */
+\end{alltt}
+
+This allows operands to be re-used which can make programming simpler.
+
+\section{Initialization}
+\subsection{Single Initialization}
+A single mp\_int can be initialized with the ``mp\_init'' function.
+
+\index{mp\_init}
+\begin{alltt}
+int mp_init (mp_int * a);
+\end{alltt}
+
+This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int
+represents the default integer which is zero. If the functions returns MP\_OKAY then the mp\_int is ready to be used
+by the other LibTomMath functions.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Single Free}
+When you are finished with an mp\_int it is ideal to return the heap it used back to the system. The following function
+provides this functionality.
+
+\index{mp\_clear}
+\begin{alltt}
+void mp_clear (mp_int * a);
+\end{alltt}
+
+The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses. It sets the
+pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations.
+Is is legal to call mp\_clear() twice on the same mp\_int in a row.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ /* We're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Multiple Initializations}
+Certain algorithms require more than one large integer. In these instances it is ideal to initialize all of the mp\_int
+variables in an ``all or nothing'' fashion. That is, they are either all initialized successfully or they are all
+not initialized.
+
+The mp\_init\_multi() function provides this functionality.
+
+\index{mp\_init\_multi} \index{mp\_clear\_multi}
+\begin{alltt}
+int mp_init_multi(mp_int *mp, ...);
+\end{alltt}
+
+It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures. It will attempt to initialize them all
+at once. If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them
+are available for use. A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd
+from the heap at the same time.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int num1, num2, num3;
+ int result;
+
+ if ((result = mp_init_multi(&num1,
+ &num2,
+ &num3, NULL)) != MP\_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the numbers */
+
+ /* We're done with them. */
+ mp_clear_multi(&num1, &num2, &num3, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Other Initializers}
+To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided.
+
+\index{mp\_init\_copy}
+\begin{alltt}
+int mp_init_copy (mp_int * a, mp_int * b);
+\end{alltt}
+
+This function will initialize $a$ and make it a copy of $b$ if all goes well.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int num1, num2;
+ int result;
+
+ /* initialize and do work on num1 ... */
+
+ /* We want a copy of num1 in num2 now */
+ if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{
+ printf("Error initializing the copy. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now num2 is ready and contains a copy of num1 */
+
+ /* We're done with them. */
+ mp_clear_multi(&num1, &num2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+Another less common initializer is mp\_init\_size() which allows the user to initialize an mp\_int with a given
+default number of digits. By default, all initializers allocate \textbf{MP\_PREC} digits. This function lets
+you override this behaviour.
+
+\index{mp\_init\_size}
+\begin{alltt}
+int mp_init_size (mp_int * a, int size);
+\end{alltt}
+
+The $size$ parameter must be greater than zero. If the function succeeds the mp\_int $a$ will be initialized
+to have $size$ digits (which are all initially zero).
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ /* we need a 60-digit number */
+ if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\section{Maintenance Functions}
+
+\subsection{Reducing Memory Usage}
+When an mp\_int is in a state where it won't be changed again\footnote{A Diffie-Hellman modulus for instance.} excess
+digits can be removed to return memory to the heap with the mp\_shrink() function.
+
+\index{mp\_shrink}
+\begin{alltt}
+int mp_shrink (mp_int * a);
+\end{alltt}
+
+This will remove excess digits of the mp\_int $a$. If the operation fails the mp\_int should be intact without the
+excess digits being removed. Note that you can use a shrunk mp\_int in further computations, however, such operations
+will require heap operations which can be slow. It is not ideal to shrink mp\_int variables that you will further
+modify in the system (unless you are seriously low on memory).
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number [e.g. pre-computation] */
+
+ /* We're done with it for now. */
+ if ((result = mp_shrink(&number)) != MP_OKAY) \{
+ printf("Error shrinking the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use it .... */
+
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Adding additional digits}
+
+Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
+the integer the mp\_int is meant to equal. The \textit{used} parameter dictates how many digits are significant, that is,
+contribute to the value of the mp\_int. The \textit{alloc} parameter dictates how many digits are currently available in
+the array. If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
+your desired size.
+
+\index{mp\_grow}
+\begin{alltt}
+int mp_grow (mp_int * a, int size);
+\end{alltt}
+
+This will grow the array of digits of $a$ to $size$. If the \textit{alloc} parameter is already bigger than
+$size$ the function will not do anything.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* use the number */
+
+ /* We need to add 20 digits to the number */
+ if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{
+ printf("Error growing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+
+ /* use the number */
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\chapter{Basic Operations}
+\section{Small Constants}
+Setting mp\_ints to small constants is a relatively common operation. To accomodate these instances there are two
+small constant assignment functions. The first function is used to set a single digit constant while the second sets
+an ISO C style ``unsigned long'' constant. The reason for both functions is efficiency. Setting a single digit is quick but the
+domain of a digit can change (it's always at least $0 \ldots 127$).
+
+\subsection{Single Digit}
+
+Setting a single digit can be accomplished with the following function.
+
+\index{mp\_set}
+\begin{alltt}
+void mp_set (mp_int * a, mp_digit b);
+\end{alltt}
+
+This will zero the contents of $a$ and make it represent an integer equal to the value of $b$. Note that this
+function has a return type of \textbf{void}. It cannot cause an error so it is safe to assume the function
+succeeded.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 5 */
+ mp_set(&number, 5);
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+\subsection{Long Constants}
+
+To set a constant that is the size of an ISO C ``unsigned long'' and larger than a single digit the following function
+can be used.
+
+\index{mp\_set\_int}
+\begin{alltt}
+int mp_set_int (mp_int * a, unsigned long b);
+\end{alltt}
+
+This will assign the value of the 32-bit variable $b$ to the mp\_int $a$. Unlike mp\_set() this function will always
+accept a 32-bit input regardless of the size of a single digit. However, since the value may span several digits
+this function can fail if it runs out of heap memory.
+
+To get the ``unsigned long'' copy of an mp\_int the following function can be used.
+
+\index{mp\_get\_int}
+\begin{alltt}
+unsigned long mp_get_int (mp_int * a);
+\end{alltt}
+
+This will return the 32 least significant bits of the mp\_int $a$.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 654321 (note this is bigger than 127) */
+ if ((result = mp_set_int(&number, 654321)) != MP_OKAY) \{
+ printf("Error setting the value of the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ printf("number == \%lu", mp_get_int(&number));
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+This should output the following if the program succeeds.
+
+\begin{alltt}
+number == 654321
+\end{alltt}
+
+\subsection{Initialize and Setting Constants}
+To both initialize and set small constants the following two functions are available.
+\index{mp\_init\_set} \index{mp\_init\_set\_int}
+\begin{alltt}
+int mp_init_set (mp_int * a, mp_digit b);
+int mp_init_set_int (mp_int * a, unsigned long b);
+\end{alltt}
+
+Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ /* initialize and set a single digit */
+ if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{
+ printf("Error setting number1: \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* initialize and set a long */
+ if ((result = mp_init_set_int(&number2, 1023)) != MP_OKAY) \{
+ printf("Error setting number2: \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* display */
+ printf("Number1, Number2 == \%lu, \%lu",
+ mp_get_int(&number1), mp_get_int(&number2));
+
+ /* clear */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+If this program succeeds it shall output.
+\begin{alltt}
+Number1, Number2 == 100, 1023
+\end{alltt}
+
+\section{Comparisons}
+
+Comparisons in LibTomMath are always performed in a ``left to right'' fashion. There are three possible return codes
+for any comparison.
+
+\index{MP\_GT} \index{MP\_EQ} \index{MP\_LT}
+\begin{figure}[here]
+\begin{center}
+\begin{tabular}{|c|c|}
+\hline \textbf{Result Code} & \textbf{Meaning} \\
+\hline MP\_GT & $a > b$ \\
+\hline MP\_EQ & $a = b$ \\
+\hline MP\_LT & $a < b$ \\
+\hline
+\end{tabular}
+\end{center}
+\caption{Comparison Codes for $a, b$}
+\label{fig:CMP}
+\end{figure}
+
+In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared. In this case $a$ is said to be ``to the left'' of
+$b$.
+
+\subsection{Unsigned comparison}
+
+An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the
+mp\_int structures. This is analogous to an absolute comparison. The function mp\_cmp\_mag() will compare two
+mp\_int variables based on their digits only.
+
+\index{mp\_cmp\_mag}
+\begin{alltt}
+int mp_cmp_mag(mp_int * a, mp_int * b);
+\end{alltt}
+This will compare $a$ to $b$ placing $a$ to the left of $b$. This function cannot fail and will return one of the
+three compare codes listed in figure \ref{fig:CMP}.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number1 to 5 */
+ mp_set(&number1, 5);
+
+ /* set the number2 to -6 */
+ mp_set(&number2, 6);
+ if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
+ printf("Error negating number2. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ switch(mp_cmp_mag(&number1, &number2)) \{
+ case MP_GT: printf("|number1| > |number2|"); break;
+ case MP_EQ: printf("|number1| = |number2|"); break;
+ case MP_LT: printf("|number1| < |number2|"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
+successfully it should print the following.
+
+\begin{alltt}
+|number1| < |number2|
+\end{alltt}
+
+This is because $\vert -6 \vert = 6$ and obviously $5 < 6$.
+
+\subsection{Signed comparison}
+
+To compare two mp\_int variables based on their signed value the mp\_cmp() function is provided.
+
+\index{mp\_cmp}
+\begin{alltt}
+int mp_cmp(mp_int * a, mp_int * b);
+\end{alltt}
+
+This will compare $a$ to the left of $b$. It will first compare the signs of the two mp\_int variables. If they
+differ it will return immediately based on their signs. If the signs are equal then it will compare the digits
+individually. This function will return one of the compare conditions codes listed in figure \ref{fig:CMP}.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number1 to 5 */
+ mp_set(&number1, 5);
+
+ /* set the number2 to -6 */
+ mp_set(&number2, 6);
+ if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
+ printf("Error negating number2. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ switch(mp_cmp(&number1, &number2)) \{
+ case MP_GT: printf("number1 > number2"); break;
+ case MP_EQ: printf("number1 = number2"); break;
+ case MP_LT: printf("number1 < number2"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
+successfully it should print the following.
+
+\begin{alltt}
+number1 > number2
+\end{alltt}
+
+\subsection{Single Digit}
+
+To compare a single digit against an mp\_int the following function has been provided.
+
+\index{mp\_cmp\_d}
+\begin{alltt}
+int mp_cmp_d(mp_int * a, mp_digit b);
+\end{alltt}
+
+This will compare $a$ to the left of $b$ using a signed comparison. Note that it will always treat $b$ as
+positive. This function is rather handy when you have to compare against small values such as $1$ (which often
+comes up in cryptography). The function cannot fail and will return one of the tree compare condition codes
+listed in figure \ref{fig:CMP}.
+
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 5 */
+ mp_set(&number, 5);
+
+ switch(mp_cmp_d(&number, 7)) \{
+ case MP_GT: printf("number > 7"); break;
+ case MP_EQ: printf("number = 7"); break;
+ case MP_LT: printf("number < 7"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program functions properly it will print out the following.
+
+\begin{alltt}
+number < 7
+\end{alltt}
+
+\section{Logical Operations}
+
+Logical operations are operations that can be performed either with simple shifts or boolean operators such as
+AND, XOR and OR directly. These operations are very quick.
+
+\subsection{Multiplication by two}
+
+Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
+right depending on the operation.
+
+When multiplying or dividing by two a special case routine can be used which are as follows.
+\index{mp\_mul\_2} \index{mp\_div\_2}
+\begin{alltt}
+int mp_mul_2(mp_int * a, mp_int * b);
+int mp_div_2(mp_int * a, mp_int * b);
+\end{alltt}
+
+The former will assign twice $a$ to $b$ while the latter will assign half $a$ to $b$. These functions are fast
+since the shift counts and maskes are hardcoded into the routines.
+
+\begin{small} \begin{alltt}
+int main(void)
+\{
+ mp_int number;
+ int result;
+
+ if ((result = mp_init(&number)) != MP_OKAY) \{
+ printf("Error initializing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the number to 5 */
+ mp_set(&number, 5);
+
+ /* multiply by two */
+ if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{
+ printf("Error multiplying the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+ switch(mp_cmp_d(&number, 7)) \{
+ case MP_GT: printf("2*number > 7"); break;
+ case MP_EQ: printf("2*number = 7"); break;
+ case MP_LT: printf("2*number < 7"); break;
+ \}
+
+ /* now divide by two */
+ if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{
+ printf("Error dividing the number. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+ switch(mp_cmp_d(&number, 7)) \{
+ case MP_GT: printf("2*number/2 > 7"); break;
+ case MP_EQ: printf("2*number/2 = 7"); break;
+ case MP_LT: printf("2*number/2 < 7"); break;
+ \}
+
+ /* we're done with it. */
+ mp_clear(&number);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt} \end{small}
+
+If this program is successful it will print out the following text.
+
+\begin{alltt}
+2*number > 7
+2*number/2 < 7
+\end{alltt}
+
+Since $10 > 7$ and $5 < 7$. To multiply by a power of two the following function can be used.
+
+\index{mp\_mul\_2d}
+\begin{alltt}
+int mp_mul_2d(mp_int * a, int b, mp_int * c);
+\end{alltt}
+
+This will multiply $a$ by $2^b$ and store the result in ``c''. If the value of $b$ is less than or equal to
+zero the function will copy $a$ to ``c'' without performing any further actions.
+
+To divide by a power of two use the following.
+
+\index{mp\_div\_2d}
+\begin{alltt}
+int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
+\end{alltt}
+Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'. If $b \le 0$ then the
+function simply copies $a$ over to ``c'' and zeroes $d$. The variable $d$ may be passed as a \textbf{NULL}
+value to signal that the remainder is not desired.
+
+\subsection{Polynomial Basis Operations}
+
+Strictly speaking the organization of the integers within the mp\_int structures is what is known as a
+``polynomial basis''. This simply means a field element is stored by divisions of a radix. For example, if
+$f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be
+the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$.
+
+To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place. The
+following function provides this operation.
+
+\index{mp\_lshd}
+\begin{alltt}
+int mp_lshd (mp_int * a, int b);
+\end{alltt}
+
+This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes
+in the least significant digits. Similarly to divide by a power of $x$ the following function is provided.
+
+\index{mp\_rshd}
+\begin{alltt}
+void mp_rshd (mp_int * a, int b)
+\end{alltt}
+This will divide $a$ in place by $x^b$ and discard the remainder. This function cannot fail as it performs the operations
+in place and no new digits are required to complete it.
+
+\subsection{AND, OR and XOR Operations}
+
+While AND, OR and XOR operations are not typical ``bignum functions'' they can be useful in several instances. The
+three functions are prototyped as follows.
+
+\index{mp\_or} \index{mp\_and} \index{mp\_xor}
+\begin{alltt}
+int mp_or (mp_int * a, mp_int * b, mp_int * c);
+int mp_and (mp_int * a, mp_int * b, mp_int * c);
+int mp_xor (mp_int * a, mp_int * b, mp_int * c);
+\end{alltt}
+
+Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.
+
+\section{Addition and Subtraction}
+
+To compute an addition or subtraction the following two functions can be used.
+
+\index{mp\_add} \index{mp\_sub}
+\begin{alltt}
+int mp_add (mp_int * a, mp_int * b, mp_int * c);
+int mp_sub (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+
+Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction. The operations are fully sign
+aware.
+
+\section{Sign Manipulation}
+\subsection{Negation}
+\label{sec:NEG}
+Simple integer negation can be performed with the following.
+
+\index{mp\_neg}
+\begin{alltt}
+int mp_neg (mp_int * a, mp_int * b);
+\end{alltt}
+
+Which assigns $-a$ to $b$.
+
+\subsection{Absolute}
+Simple integer absolutes can be performed with the following.
+
+\index{mp\_neg}
+\begin{alltt}
+int mp_abs (mp_int * a, mp_int * b);
+\end{alltt}
+
+Which assigns $\vert a \vert$ to $b$.
+
+\section{Integer Division and Remainder}
+To perform a complete and general integer division with remainder use the following function.
+
+\index{mp\_div}
+\begin{alltt}
+int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
+\end{alltt}
+
+This divides $a$ by $b$ and stores the quotient in $c$ and $d$. The signed quotient is computed such that
+$bc + d = a$. Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required. If
+$b$ is zero the function returns \textbf{MP\_VAL}.
+
+
+\chapter{Multiplication and Squaring}
+\section{Multiplication}
+A full signed integer multiplication can be performed with the following.
+\index{mp\_mul}
+\begin{alltt}
+int mp_mul (mp_int * a, mp_int * b, mp_int * c);
+\end{alltt}
+Which assigns the full signed product $ab$ to $c$. This function actually breaks into one of four cases which are
+specific multiplication routines optimized for given parameters. First there are the Toom-Cook multiplications which
+should only be used with very large inputs. This is followed by the Karatsuba multiplications which are for moderate
+sized inputs. Then followed by the Comba and baseline multipliers.
+
+Fortunately for the developer you don't really need to know this unless you really want to fine tune the system. mp\_mul()
+will determine on its own\footnote{Some tweaking may be required.} what routine to use automatically when it is called.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int number1, number2;
+ int result;
+
+ /* Initialize the numbers */
+ if ((result = mp_init_multi(&number1,
+ &number2, NULL)) != MP_OKAY) \{
+ printf("Error initializing the numbers. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* set the terms */
+ if ((result = mp_set_int(&number, 257)) != MP_OKAY) \{
+ printf("Error setting number1. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ if ((result = mp_set_int(&number2, 1023)) != MP_OKAY) \{
+ printf("Error setting number2. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* multiply them */
+ if ((result = mp_mul(&number1, &number2,
+ &number1)) != MP_OKAY) \{
+ printf("Error multiplying terms. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* display */
+ printf("number1 * number2 == \%lu", mp_get_int(&number1));
+
+ /* free terms and return */
+ mp_clear_multi(&number1, &number2, NULL);
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+If this program succeeds it shall output the following.
+
+\begin{alltt}
+number1 * number2 == 262911
+\end{alltt}
+
+\section{Squaring}
+Since squaring can be performed faster than multiplication it is performed it's own function instead of just using
+mp\_mul().
+
+\index{mp\_sqr}
+\begin{alltt}
+int mp_sqr (mp_int * a, mp_int * b);
+\end{alltt}
+
+Will square $a$ and store it in $b$. Like the case of multiplication there are four different squaring
+algorithms all which can be called from mp\_sqr(). It is ideal to use mp\_sqr over mp\_mul when squaring terms because
+of the speed difference.
+
+\section{Tuning Polynomial Basis Routines}
+
+Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
+the Comba and baseline algorithms use. At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require
+considerably less work. For example, a 10000-digit multiplication would take roughly 724,000 single precision
+multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
+of 138).
+
+So why not always use Karatsuba or Toom-Cook? The simple answer is that they have so much overhead that they're not
+actually faster than Comba until you hit distinct ``cutoff'' points. For Karatsuba with the default configuration,
+GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4). That is, at
+110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.
+
+Toom-Cook has incredible overhead and is probably only useful for very large inputs. So far no known cutoff points
+exist and for the most part I just set the cutoff points very high to make sure they're not called.
+
+A demo program in the ``etc/'' directory of the project called ``tune.c'' can be used to find the cutoff points. This
+can be built with GCC as follows
+
+\begin{alltt}
+make XXX
+\end{alltt}
+Where ``XXX'' is one of the following entries from the table \ref{fig:tuning}.
+
+\begin{figure}[here]
+\begin{center}
+\begin{small}
+\begin{tabular}{|l|l|}
+\hline \textbf{Value of XXX} & \textbf{Meaning} \\
+\hline tune & Builds portable tuning application \\
+\hline tune86 & Builds x86 (pentium and up) program for COFF \\
+\hline tune86c & Builds x86 program for Cygwin \\
+\hline tune86l & Builds x86 program for Linux (ELF format) \\
+\hline
+\end{tabular}
+\end{small}
+\end{center}
+\caption{Build Names for Tuning Programs}
+\label{fig:tuning}
+\end{figure}
+
+When the program is running it will output a series of measurements for different cutoff points. It will first find
+good Karatsuba squaring and multiplication points. Then it proceeds to find Toom-Cook points. Note that the Toom-Cook
+tuning takes a very long time as the cutoff points are likely to be very high.
+
+\chapter{Modular Reduction}
+
+Modular reduction is process of taking the remainder of one quantity divided by another. Expressed
+as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$.
+
+\begin{equation}
+a \equiv b \mbox{ (mod }c\mbox{)}
+\label{eqn:mod}
+\end{equation}
+
+Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly
+fast reduction algorithms can be written for the limited range.
+
+Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation
+algorithm mp\_exptmod when an appropriate modulus is detected.
+
+\section{Straight Division}
+In order to effect an arbitrary modular reduction the following algorithm is provided.
+
+\index{mp\_mod}
+\begin{alltt}
+int mp_mod(mp_int *a, mp_int *b, mp_int *c);
+\end{alltt}
+
+This reduces $a$ modulo $b$ and stores the result in $c$. The sign of $c$ shall agree with the sign
+of $b$. This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$.
+
+\section{Barrett Reduction}
+
+Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
+a decent speedup over straight division. First a $\mu$ value must be precomputed with the following function.
+
+\index{mp\_reduce\_setup}
+\begin{alltt}
+int mp_reduce_setup(mp_int *a, mp_int *b);
+\end{alltt}
+
+Given a modulus in $b$ this produces the required $\mu$ value in $a$. For any given modulus this only has to
+be computed once. Modular reduction can now be performed with the following.
+
+\index{mp\_reduce}
+\begin{alltt}
+int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
+\end{alltt}
+
+This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$. $a$ must be in the range
+$0 \le a < b^2$.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int a, b, c, mu;
+ int result;
+
+ /* initialize a,b to desired values, mp_init mu,
+ * c and set c to 1...we want to compute a^3 mod b
+ */
+
+ /* get mu value */
+ if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{
+ printf("Error getting mu. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* square a to get c = a^2 */
+ if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
+ printf("Error squaring. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' modulo b */
+ if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* multiply a to get c = a^3 */
+ if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' modulo b */
+ if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* c now equals a^3 mod b */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed.
+
+\section{Montgomery Reduction}
+
+Montgomery is a specialized reduction algorithm for any odd moduli. Like Barrett reduction a pre--computation
+step is required. This is accomplished with the following.
+
+\index{mp\_montgomery\_setup}
+\begin{alltt}
+int mp_montgomery_setup(mp_int *a, mp_digit *mp);
+\end{alltt}
+
+For the given odd moduli $a$ the precomputation value is placed in $mp$. The reduction is computed with the
+following.
+
+\index{mp\_montgomery\_reduce}
+\begin{alltt}
+int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
+\end{alltt}
+This reduces $a$ in place modulo $m$ with the pre--computed value $mp$. $a$ must be in the range
+$0 \le a < b^2$.
+
+Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit. With the default
+setup for instance, the limit is $127$ digits ($3556$--bits). Note that this function is not limited to
+$127$ digits just that it falls back to a baseline algorithm after that point.
+
+An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$
+where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).
+
+To quickly calculate $R$ the following function was provided.
+
+\index{mp\_montgomery\_calc\_normalization}
+\begin{alltt}
+int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
+\end{alltt}
+Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.
+
+The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system. For
+example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by
+multiplying it by $R$. Consider the following code snippet.
+
+\begin{alltt}
+int main(void)
+\{
+ mp_int a, b, c, R;
+ mp_digit mp;
+ int result;
+
+ /* initialize a,b to desired values,
+ * mp_init R, c and set c to 1....
+ */
+
+ /* get normalization */
+ if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{
+ printf("Error getting norm. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* get mp value */
+ if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{
+ printf("Error setting up montgomery. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* normalize `a' so now a is equal to aR */
+ if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{
+ printf("Error computing aR. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* square a to get c = a^2R^2 */
+ if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
+ printf("Error squaring. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */
+ if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* multiply a to get c = a^3R^2 */
+ if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */
+ if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */
+ if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
+ printf("Error reducing. \%s",
+ mp_error_to_string(result));
+ return EXIT_FAILURE;
+ \}
+
+ /* c now equals a^3 mod b */
+
+ return EXIT_SUCCESS;
+\}
+\end{alltt}
+
+This particular example does not look too efficient but it demonstrates the point of the algorithm. By
+normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$. This allows
+a single final reduction to correct for the normalization and the fast reduction used within the algorithm.
+
+For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}.
+
+\section{Restricted Dimminished Radix}
+
+``Dimminished Radix'' reduction refers to reduction with respect to moduli that are ameniable to simple
+digit shifting and small multiplications. In this case the ``restricted'' variant refers to moduli of the
+form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$).
+
+As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus.
+
+\index{mp\_dr\_setup}
+\begin{alltt}
+void mp_dr_setup(mp_int *a, mp_digit *d);
+\end{alltt}
+
+This computes the value required for the modulus $a$ and stores it in $d$. This function cannot fail
+and does not return any error codes. After the pre--computation a reduction can be performed with the
+following.
+
+\index{mp\_dr\_reduce}
+\begin{alltt}
+int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
+\end{alltt}
+
+This reduces $a$ in place modulo $b$ with the pre--computed value $mp$. $b$ must be of a restricted
+dimminished radix form and $a$ must be in the range $0 \le a < b^2$. Dimminished radix reductions are
+much faster than both Barrett and Montgomery reductions as they have a much lower asymtotic running time.
+
+Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
+BBS cryptographic purposes. This reduction algorithm is useful for Diffie-Hellman and ECC where fixed
+primes are acceptable.
+
+Note that unlike Montgomery reduction there is no normalization process. The result of this function is
+equal to the correct residue.
+
+\section{Unrestricted Dimminshed Radix}
+
+Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the
+form $2^k - p$ for $0 < p < \beta$. In this sense the unrestricted reductions are more flexible as they
+can be applied to a wider range of numbers.
+
+\index{mp\_reduce\_2k\_setup}
+\begin{alltt}
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
+\end{alltt}
+
+This will compute the required $d$ value for the given moduli $a$.
+
+\index{mp\_reduce\_2k}
+\begin{alltt}
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
+\end{alltt}
+
+This will reduce $a$ in place modulo $n$ with the pre--computed value $d$. From my experience this routine is
+slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction.
+
+\chapter{Exponentiation}
+\section{Single Digit Exponentiation}
+\index{mp\_expt\_d}
+\begin{alltt}
+int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
+\end{alltt}
+This computes $c = a^b$ using a simple binary left-to-right algorithm. It is faster than repeated multiplications by
+$a$ for all values of $b$ greater than three.
+
+\section{Modular Exponentiation}
+\index{mp\_exptmod}
+\begin{alltt}
+int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+\end{alltt}
+This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm. This function
+will automatically detect the fastest modular reduction technique to use during the operation. For negative values of
+$X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that
+$gcd(G, P) = 1$.
+
+This function is actually a shell around the two internal exponentiation functions. This routine will automatically
+detect when Barrett, Montgomery, Restricted and Unrestricted Dimminished Radix based exponentiation can be used. Generally
+moduli of the a ``restricted dimminished radix'' form lead to the fastest modular exponentiations. Followed by Montgomery
+and the other two algorithms.
+
+\section{Root Finding}
+\index{mp\_n\_root}
+\begin{alltt}
+int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+\end{alltt}
+This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$. The implementation of this function is not
+ideal for values of $b$ greater than three. It will work but become very slow. So unless you are working with very small
+numbers (less than 1000 bits) I'd avoid $b > 3$ situations. Will return a positive root only for even roots and return
+a root with the sign of the input for odd roots. For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$
+will return $-2$.
+
+This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly. Since
+the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
+values of $b$. If particularly large roots are required then a factor method could be used instead. For example,
+$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply
+$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$
+
+\chapter{Prime Numbers}
+\section{Trial Division}
+\index{mp\_prime\_is\_divisible}
+\begin{alltt}
+int mp_prime_is_divisible (mp_int * a, int *result)
+\end{alltt}
+This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the
+outcome in ``result''. That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is. Note that
+if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently
+the default is to set it to zero first.}.
+
+\section{Fermat Test}
+\index{mp\_prime\_fermat}
+\begin{alltt}
+int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
+\end{alltt}
+Performs a Fermat primality test to the base $b$. That is it computes $b^a \mbox{ mod }a$ and tests whether the value is
+equal to $b$ or not. If the values are equal then $a$ is probably prime and $result$ is set to one. Otherwise $result$
+is set to zero.
+
+\section{Miller-Rabin Test}
+\index{mp\_prime\_miller\_rabin}
+\begin{alltt}
+int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
+\end{alltt}
+Performs a Miller-Rabin test to the base $b$ of $a$. This test is much stronger than the Fermat test and is very hard to
+fool (besides with Carmichael numbers). If $a$ passes the test (therefore is probably prime) $result$ is set to one.
+Otherwise $result$ is set to zero.
+
+Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of
+Miller-Rabin are a subset of the failures of the Fermat test.
+
+\subsection{Required Number of Tests}
+Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen
+or so unique bases. However, it has been proven that the probability of failure goes down as the size of the input goes up.
+This is why a simple function has been provided to help out.
+
+\index{mp\_prime\_rabin\_miller\_trials}
+\begin{alltt}
+int mp_prime_rabin_miller_trials(int size)
+\end{alltt}
+This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
+in bits. This comes in handy specially since larger numbers are slower to test. For example, a 512-bit number would
+require ten tests whereas a 1024-bit number would only require four tests.
+
+You should always still perform a trial division before a Miller-Rabin test though.
+
+\section{Primality Testing}
+\index{mp\_prime\_is\_prime}
+\begin{alltt}
+int mp_prime_is_prime (mp_int * a, int t, int *result)
+\end{alltt}
+This will perform a trial division followed by $t$ rounds of Miller-Rabin tests on $a$ and store the result in $result$.
+If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero. Note that $t$ is bounded by
+$1 \le t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number of primes in the prime number table (by default this is $256$).
+
+\section{Next Prime}
+\index{mp\_prime\_next\_prime}
+\begin{alltt}
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
+\end{alltt}
+This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests. Set $bbs\_style$ to one if you
+want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime.
+
+\section{Random Primes}
+\index{mp\_prime\_random}
+\begin{alltt}
+int mp_prime_random(mp_int *a, int t, int size, int bbs,
+ ltm_prime_callback cb, void *dat)
+\end{alltt}
+This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
+$t$ rounds of tests. The ``ltm\_prime\_callback'' is a typedef for
+
+\begin{alltt}
+typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
+\end{alltt}
+
+Which is a function that must read $len$ bytes (and return the amount stored) into $dst$. The $dat$ variable is simply
+copied from the original input. It can be used to pass RNG context data to the callback. The function
+mp\_prime\_random() is more suitable for generating primes which must be secret (as in the case of RSA) since there
+is no skew on the least significant bits.
+
+\textit{Note:} As of v0.30 of the LibTomMath library this function has been deprecated. It is still available
+but users are encouraged to use the new mp\_prime\_random\_ex() function instead.
+
+\subsection{Extended Generation}
+\index{mp\_prime\_random\_ex}
+\begin{alltt}
+int mp_prime_random_ex(mp_int *a, int t,
+ int size, int flags,
+ ltm_prime_callback cb, void *dat);
+\end{alltt}
+This will generate a prime in $a$ using $t$ tests of the primality testing algorithms. The variable $size$
+specifies the bit length of the prime desired. The variable $flags$ specifies one of several options available
+(see fig. \ref{fig:primeopts}) which can be OR'ed together. The callback parameters are used as in
+mp\_prime\_random().
+
+\begin{figure}[here]
+\begin{center}
+\begin{small}
+\begin{tabular}{|r|l|}
+\hline \textbf{Flag} & \textbf{Meaning} \\
+\hline LTM\_PRIME\_BBS & Make the prime congruent to $3$ modulo $4$ \\
+\hline LTM\_PRIME\_SAFE & Make a prime $p$ such that $(p - 1)/2$ is also prime. \\
+ & This option implies LTM\_PRIME\_BBS as well. \\
+\hline LTM\_PRIME\_2MSB\_OFF & Makes sure that the bit adjacent to the most significant bit \\
+ & Is forced to zero. \\
+\hline LTM\_PRIME\_2MSB\_ON & Makes sure that the bit adjacent to the most significant bit \\
+ & Is forced to one. \\
+\hline
+\end{tabular}
+\end{small}
+\end{center}
+\caption{Primality Generation Options}
+\label{fig:primeopts}
+\end{figure}
+
+\chapter{Input and Output}
+\section{ASCII Conversions}
+\subsection{To ASCII}
+\index{mp\_toradix}
+\begin{alltt}
+int mp_toradix (mp_int * a, char *str, int radix);
+\end{alltt}
+This still store $a$ in ``str'' as a base-``radix'' string of ASCII chars. This function appends a NUL character
+to terminate the string. Valid values of ``radix'' line in the range $[2, 64]$. To determine the size (exact) required
+by the conversion before storing any data use the following function.
+
+\index{mp\_radix\_size}
+\begin{alltt}
+int mp_radix_size (mp_int * a, int radix, int *size)
+\end{alltt}
+This stores in ``size'' the number of characters (including space for the NUL terminator) required. Upon error this
+function returns an error code and ``size'' will be zero.
+
+\subsection{From ASCII}
+\index{mp\_read\_radix}
+\begin{alltt}
+int mp_read_radix (mp_int * a, char *str, int radix);
+\end{alltt}
+This will read the base-``radix'' NUL terminated string from ``str'' into $a$. It will stop reading when it reads a
+character it does not recognize (which happens to include th NUL char... imagine that...). A single leading $-$ sign
+can be used to denote a negative number.
+
+\section{Binary Conversions}
+
+Converting an mp\_int to and from binary is another keen idea.
+
+\index{mp\_unsigned\_bin\_size}
+\begin{alltt}
+int mp_unsigned_bin_size(mp_int *a);
+\end{alltt}
+
+This will return the number of bytes (octets) required to store the unsigned copy of the integer $a$.
+
+\index{mp\_to\_unsigned\_bin}
+\begin{alltt}
+int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
+\end{alltt}
+This will store $a$ into the buffer $b$ in big--endian format. Fortunately this is exactly what DER (or is it ASN?)
+requires. It does not store the sign of the integer.
+
+\index{mp\_read\_unsigned\_bin}
+\begin{alltt}
+int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
+\end{alltt}
+This will read in an unsigned big--endian array of bytes (octets) from $b$ of length $c$ into $a$. The resulting
+integer $a$ will always be positive.
+
+For those who acknowledge the existence of negative numbers (heretic!) there are ``signed'' versions of the
+previous functions.
+
+\begin{alltt}
+int mp_signed_bin_size(mp_int *a);
+int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
+int mp_to_signed_bin(mp_int *a, unsigned char *b);
+\end{alltt}
+They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
+byte depending on the sign. If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix
+is non--zero.
+
+\chapter{Algebraic Functions}
+\section{Extended Euclidean Algorithm}
+\index{mp\_exteuclid}
+\begin{alltt}
+int mp_exteuclid(mp_int *a, mp_int *b,
+ mp_int *U1, mp_int *U2, mp_int *U3);
+\end{alltt}
+
+This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds.
+
+\begin{equation}
+a \cdot U1 + b \cdot U2 = U3
+\end{equation}
+
+Any of the U1/U2/U3 paramters can be set to \textbf{NULL} if they are not desired.
+
+\section{Greatest Common Divisor}
+\index{mp\_gcd}
+\begin{alltt}
+int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+This will compute the greatest common divisor of $a$ and $b$ and store it in $c$.
+
+\section{Least Common Multiple}
+\index{mp\_lcm}
+\begin{alltt}
+int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+This will compute the least common multiple of $a$ and $b$ and store it in $c$.
+
+\section{Jacobi Symbol}
+\index{mp\_jacobi}
+\begin{alltt}
+int mp_jacobi (mp_int * a, mp_int * p, int *c)
+\end{alltt}
+This will compute the Jacobi symbol for $a$ with respect to $p$. If $p$ is prime this essentially computes the Legendre
+symbol. The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$. If $p$ is prime
+then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$. The result will be $0$ if $a$ divides $p$
+and the result will be $1$ if $a$ is a quadratic residue modulo $p$.
+
+\section{Modular Inverse}
+\index{mp\_invmod}
+\begin{alltt}
+int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+\end{alltt}
+Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.
+
+\section{Single Digit Functions}
+
+For those using small numbers (\textit{snicker snicker}) there are several ``helper'' functions
+
+\index{mp\_add\_d} \index{mp\_sub\_d} \index{mp\_mul\_d} \index{mp\_div\_d} \index{mp\_mod\_d}
+\begin{alltt}
+int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
+int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
+int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
+int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
+int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
+\end{alltt}
+
+These work like the full mp\_int capable variants except the second parameter $b$ is a mp\_digit. These
+functions fairly handy if you have to work with relatively small numbers since you will not have to allocate
+an entire mp\_int to store a number like $1$ or $2$.
+
+\input{bn.ind}
+
+\end{document}
diff --git a/libtommath/bn_error.c b/libtommath/bn_error.c
new file mode 100644
index 0000000..1ae6430
--- /dev/null
+++ b/libtommath/bn_error.c
@@ -0,0 +1,47 @@
+#include <tommath.h>
+#ifdef BN_ERROR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+static const struct {
+ int code;
+ char *msg;
+} msgs[] = {
+ { MP_OKAY, "Successful" },
+ { MP_MEM, "Out of heap" },
+ { MP_VAL, "Value out of range" }
+};
+
+/* return a char * string for a given code */
+char *mp_error_to_string(int code)
+{
+ int x;
+
+ /* scan the lookup table for the given message */
+ for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
+ if (msgs[x].code == code) {
+ return msgs[x].msg;
+ }
+ }
+
+ /* generic reply for invalid code */
+ return "Invalid error code";
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_error.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_fast_mp_invmod.c b/libtommath/bn_fast_mp_invmod.c
new file mode 100644
index 0000000..1974145
--- /dev/null
+++ b/libtommath/bn_fast_mp_invmod.c
@@ -0,0 +1,148 @@
+#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes the modular inverse via binary extended euclidean algorithm,
+ * that is c = 1/a mod b
+ *
+ * Based on slow invmod except this is optimized for the case where b is
+ * odd as per HAC Note 14.64 on pp. 610
+ */
+int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, B, D;
+ int res, neg;
+
+ /* 2. [modified] b must be odd */
+ if (mp_iseven (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init all our temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x == modulus, y == value to invert */
+ if ((res = mp_copy (b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* we need y = |a| */
+ if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 4.2 if B is odd then */
+ if (mp_isodd (&B) == 1) {
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* B = B/2 */
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 5.2 if D is odd then */
+ if (mp_isodd (&D) == 1) {
+ /* D = (D-x)/2 */
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* D = D/2 */
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ } else {
+ /* v - v - u, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0) {
+ goto top;
+ }
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* b is now the inverse */
+ neg = a->sign;
+ while (D.sign == MP_NEG) {
+ if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ mp_exch (&D, c);
+ c->sign = neg;
+ res = MP_OKAY;
+
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_fast_mp_montgomery_reduce.c b/libtommath/bn_fast_mp_montgomery_reduce.c
new file mode 100644
index 0000000..13538c8
--- /dev/null
+++ b/libtommath/bn_fast_mp_montgomery_reduce.c
@@ -0,0 +1,172 @@
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction
+ *
+ * This is an optimized implementation of montgomery_reduce
+ * which uses the comba method to quickly calculate the columns of the
+ * reduction.
+ *
+ * Based on Algorithm 14.32 on pp.601 of HAC.
+*/
+int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+ int ix, res, olduse;
+ mp_word W[MP_WARRAY];
+
+ /* get old used count */
+ olduse = x->used;
+
+ /* grow a as required */
+ if (x->alloc < n->used + 1) {
+ if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* first we have to get the digits of the input into
+ * an array of double precision words W[...]
+ */
+ {
+ register mp_word *_W;
+ register mp_digit *tmpx;
+
+ /* alias for the W[] array */
+ _W = W;
+
+ /* alias for the digits of x*/
+ tmpx = x->dp;
+
+ /* copy the digits of a into W[0..a->used-1] */
+ for (ix = 0; ix < x->used; ix++) {
+ *_W++ = *tmpx++;
+ }
+
+ /* zero the high words of W[a->used..m->used*2] */
+ for (; ix < n->used * 2 + 1; ix++) {
+ *_W++ = 0;
+ }
+ }
+
+ /* now we proceed to zero successive digits
+ * from the least significant upwards
+ */
+ for (ix = 0; ix < n->used; ix++) {
+ /* mu = ai * m' mod b
+ *
+ * We avoid a double precision multiplication (which isn't required)
+ * by casting the value down to a mp_digit. Note this requires
+ * that W[ix-1] have the carry cleared (see after the inner loop)
+ */
+ register mp_digit mu;
+ mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
+
+ /* a = a + mu * m * b**i
+ *
+ * This is computed in place and on the fly. The multiplication
+ * by b**i is handled by offseting which columns the results
+ * are added to.
+ *
+ * Note the comba method normally doesn't handle carries in the
+ * inner loop In this case we fix the carry from the previous
+ * column since the Montgomery reduction requires digits of the
+ * result (so far) [see above] to work. This is
+ * handled by fixing up one carry after the inner loop. The
+ * carry fixups are done in order so after these loops the
+ * first m->used words of W[] have the carries fixed
+ */
+ {
+ register int iy;
+ register mp_digit *tmpn;
+ register mp_word *_W;
+
+ /* alias for the digits of the modulus */
+ tmpn = n->dp;
+
+ /* Alias for the columns set by an offset of ix */
+ _W = W + ix;
+
+ /* inner loop */
+ for (iy = 0; iy < n->used; iy++) {
+ *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
+ }
+ }
+
+ /* now fix carry for next digit, W[ix+1] */
+ W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* now we have to propagate the carries and
+ * shift the words downward [all those least
+ * significant digits we zeroed].
+ */
+ {
+ register mp_digit *tmpx;
+ register mp_word *_W, *_W1;
+
+ /* nox fix rest of carries */
+
+ /* alias for current word */
+ _W1 = W + ix;
+
+ /* alias for next word, where the carry goes */
+ _W = W + ++ix;
+
+ for (; ix <= n->used * 2 + 1; ix++) {
+ *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* copy out, A = A/b**n
+ *
+ * The result is A/b**n but instead of converting from an
+ * array of mp_word to mp_digit than calling mp_rshd
+ * we just copy them in the right order
+ */
+
+ /* alias for destination word */
+ tmpx = x->dp;
+
+ /* alias for shifted double precision result */
+ _W = W + n->used;
+
+ for (ix = 0; ix < n->used + 1; ix++) {
+ *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
+ }
+
+ /* zero oldused digits, if the input a was larger than
+ * m->used+1 we'll have to clear the digits
+ */
+ for (; ix < olduse; ix++) {
+ *tmpx++ = 0;
+ }
+ }
+
+ /* set the max used and clamp */
+ x->used = n->used + 1;
+ mp_clamp (x);
+
+ /* if A >= m then A = A - m */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ return s_mp_sub (x, n, x);
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_fast_s_mp_mul_digs.c b/libtommath/bn_fast_s_mp_mul_digs.c
new file mode 100644
index 0000000..8e2e069
--- /dev/null
+++ b/libtommath/bn_fast_s_mp_mul_digs.c
@@ -0,0 +1,107 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Fast (comba) multiplier
+ *
+ * This is the fast column-array [comba] multiplier. It is
+ * designed to compute the columns of the product first
+ * then handle the carries afterwards. This has the effect
+ * of making the nested loops that compute the columns very
+ * simple and schedulable on super-scalar processors.
+ *
+ * This has been modified to produce a variable number of
+ * digits of output so if say only a half-product is required
+ * you don't have to compute the upper half (a feature
+ * required for fast Barrett reduction).
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ *
+ */
+int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
+
+ /* grow the destination as required */
+ if (c->alloc < digs) {
+ if ((res = mp_grow (c, digs)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
+
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
+
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+
+ }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = c->used;
+ c->used = pa;
+
+ {
+ register mp_digit *tmpc;
+ tmpc = c->dp;
+ for (ix = 0; ix < pa+1; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_digs.c,v $ */
+/* $Revision: 1.7 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_fast_s_mp_mul_high_digs.c b/libtommath/bn_fast_s_mp_mul_high_digs.c
new file mode 100644
index 0000000..4778b2f
--- /dev/null
+++ b/libtommath/bn_fast_s_mp_mul_high_digs.c
@@ -0,0 +1,98 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
+ * to see how it works.
+ *
+ * This is used in the Barrett reduction since for one of the multiplications
+ * only the higher digits were needed. This essentially halves the work.
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ */
+int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
+
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
+
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = c->used;
+ c->used = pa;
+
+ {
+ register mp_digit *tmpc;
+
+ tmpc = c->dp + digs;
+ for (ix = digs; ix < pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/11/14 03:46:25 $ */
diff --git a/libtommath/bn_fast_s_mp_sqr.c b/libtommath/bn_fast_s_mp_sqr.c
new file mode 100644
index 0000000..bb5974c
--- /dev/null
+++ b/libtommath/bn_fast_s_mp_sqr.c
@@ -0,0 +1,114 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* the jist of squaring...
+ * you do like mult except the offset of the tmpx [one that
+ * starts closer to zero] can't equal the offset of tmpy.
+ * So basically you set up iy like before then you min it with
+ * (ty-tx) so that it never happens. You double all those
+ * you add in the inner loop
+
+After that loop you do the squares and add them in.
+*/
+
+int fast_s_mp_sqr (mp_int * a, mp_int * b)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
+
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
+
+ /* clear counter */
+ _W = 0;
+
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
+
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
+
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+ }
+
+ /* store it */
+ W[ix] = (mp_digit)(_W & MP_MASK);
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = b->used;
+ b->used = a->used+a->used;
+
+ {
+ mp_digit *tmpb;
+ tmpb = b->dp;
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpb++ = 0;
+ }
+ }
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_2expt.c b/libtommath/bn_mp_2expt.c
new file mode 100644
index 0000000..9e5f32e
--- /dev/null
+++ b/libtommath/bn_mp_2expt.c
@@ -0,0 +1,48 @@
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes a = 2**b
+ *
+ * Simple algorithm which zeroes the int, grows it then just sets one bit
+ * as required.
+ */
+int
+mp_2expt (mp_int * a, int b)
+{
+ int res;
+
+ /* zero a as per default */
+ mp_zero (a);
+
+ /* grow a to accomodate the single bit */
+ if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* set the used count of where the bit will go */
+ a->used = b / DIGIT_BIT + 1;
+
+ /* put the single bit in its place */
+ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_2expt.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_abs.c b/libtommath/bn_mp_abs.c
new file mode 100644
index 0000000..9643c5e
--- /dev/null
+++ b/libtommath/bn_mp_abs.c
@@ -0,0 +1,43 @@
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = |a|
+ *
+ * Simple function copies the input and fixes the sign to positive
+ */
+int
+mp_abs (mp_int * a, mp_int * b)
+{
+ int res;
+
+ /* copy a to b */
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* force the sign of b to positive */
+ b->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_abs.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_add.c b/libtommath/bn_mp_add.c
new file mode 100644
index 0000000..a90eef6
--- /dev/null
+++ b/libtommath/bn_mp_add.c
@@ -0,0 +1,53 @@
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* high level addition (handles signs) */
+int mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ /* get sign of both inputs */
+ sa = a->sign;
+ sb = b->sign;
+
+ /* handle two cases, not four */
+ if (sa == sb) {
+ /* both positive or both negative */
+ /* add their magnitudes, copy the sign */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* one positive, the other negative */
+ /* subtract the one with the greater magnitude from */
+ /* the one of the lesser magnitude. The result gets */
+ /* the sign of the one with the greater magnitude. */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ c->sign = sb;
+ res = s_mp_sub (b, a, c);
+ } else {
+ c->sign = sa;
+ res = s_mp_sub (a, b, c);
+ }
+ }
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_add.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_add_d.c b/libtommath/bn_mp_add_d.c
new file mode 100644
index 0000000..5af5aa9
--- /dev/null
+++ b/libtommath/bn_mp_add_d.c
@@ -0,0 +1,112 @@
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* single digit addition */
+int
+mp_add_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ int res, ix, oldused;
+ mp_digit *tmpa, *tmpc, mu;
+
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* if a is negative and |a| >= b, call c = |a| - b */
+ if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
+ /* temporarily fix sign of a */
+ a->sign = MP_ZPOS;
+
+ /* c = |a| - b */
+ res = mp_sub_d(a, b, c);
+
+ /* fix sign */
+ a->sign = c->sign = MP_NEG;
+
+ /* clamp */
+ mp_clamp(c);
+
+ return res;
+ }
+
+ /* old number of used digits in c */
+ oldused = c->used;
+
+ /* sign always positive */
+ c->sign = MP_ZPOS;
+
+ /* source alias */
+ tmpa = a->dp;
+
+ /* destination alias */
+ tmpc = c->dp;
+
+ /* if a is positive */
+ if (a->sign == MP_ZPOS) {
+ /* add digit, after this we're propagating
+ * the carry.
+ */
+ *tmpc = *tmpa++ + b;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+
+ /* now handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ + mu;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+ }
+ /* set final carry */
+ ix++;
+ *tmpc++ = mu;
+
+ /* setup size */
+ c->used = a->used + 1;
+ } else {
+ /* a was negative and |a| < b */
+ c->used = 1;
+
+ /* the result is a single digit */
+ if (a->used == 1) {
+ *tmpc++ = b - a->dp[0];
+ } else {
+ *tmpc++ = b;
+ }
+
+ /* setup count so the clearing of oldused
+ * can fall through correctly
+ */
+ ix = 1;
+ }
+
+ /* now zero to oldused */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_add_d.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_addmod.c b/libtommath/bn_mp_addmod.c
new file mode 100644
index 0000000..d3b3ac4
--- /dev/null
+++ b/libtommath/bn_mp_addmod.c
@@ -0,0 +1,41 @@
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* d = a + b (mod c) */
+int
+mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_add (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_addmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_and.c b/libtommath/bn_mp_and.c
new file mode 100644
index 0000000..9a2c0ee
--- /dev/null
+++ b/libtommath/bn_mp_and.c
@@ -0,0 +1,57 @@
+#include <tommath.h>
+#ifdef BN_MP_AND_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* AND two ints together */
+int
+mp_and (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] &= x->dp[ix];
+ }
+
+ /* zero digits above the last from the smallest mp_int */
+ for (; ix < t.used; ix++) {
+ t.dp[ix] = 0;
+ }
+
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_and.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_clamp.c b/libtommath/bn_mp_clamp.c
new file mode 100644
index 0000000..da4e1ef
--- /dev/null
+++ b/libtommath/bn_mp_clamp.c
@@ -0,0 +1,44 @@
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* trim unused digits
+ *
+ * This is used to ensure that leading zero digits are
+ * trimed and the leading "used" digit will be non-zero
+ * Typically very fast. Also fixes the sign if there
+ * are no more leading digits
+ */
+void
+mp_clamp (mp_int * a)
+{
+ /* decrease used while the most significant digit is
+ * zero.
+ */
+ while (a->used > 0 && a->dp[a->used - 1] == 0) {
+ --(a->used);
+ }
+
+ /* reset the sign flag if used == 0 */
+ if (a->used == 0) {
+ a->sign = MP_ZPOS;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_clamp.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_clear.c b/libtommath/bn_mp_clear.c
new file mode 100644
index 0000000..000bd06
--- /dev/null
+++ b/libtommath/bn_mp_clear.c
@@ -0,0 +1,47 @@
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* clear one (frees) */
+void
+mp_clear (mp_int * a)
+{
+ volatile mp_digit *p;
+ int len;
+
+ /* only do anything if a hasn't been freed previously */
+ if (a->dp != NULL) {
+ /* first zero the digits */
+ len = a->alloc;
+ p = a->dp;
+ while (len--) {
+ *p++ = 0;
+ }
+
+ /* free ram */
+ XFREE(a->dp);
+
+ /* reset members to make debugging easier */
+ a->dp = NULL;
+ a->alloc = a->used = 0;
+ a->sign = MP_ZPOS;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_clear.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_clear_multi.c b/libtommath/bn_mp_clear_multi.c
new file mode 100644
index 0000000..e1859be
--- /dev/null
+++ b/libtommath/bn_mp_clear_multi.c
@@ -0,0 +1,34 @@
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+#include <stdarg.h>
+
+void mp_clear_multi(mp_int *mp, ...)
+{
+ mp_int* next_mp = mp;
+ va_list args;
+ va_start(args, mp);
+ while (next_mp != NULL) {
+ mp_clear(next_mp);
+ next_mp = va_arg(args, mp_int*);
+ }
+ va_end(args);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_clear_multi.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_cmp.c b/libtommath/bn_mp_cmp.c
new file mode 100644
index 0000000..f4e2af7
--- /dev/null
+++ b/libtommath/bn_mp_cmp.c
@@ -0,0 +1,43 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* compare two ints (signed)*/
+int
+mp_cmp (mp_int * a, mp_int * b)
+{
+ /* compare based on sign */
+ if (a->sign != b->sign) {
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ } else {
+ return MP_GT;
+ }
+ }
+
+ /* compare digits */
+ if (a->sign == MP_NEG) {
+ /* if negative compare opposite direction */
+ return mp_cmp_mag(b, a);
+ } else {
+ return mp_cmp_mag(a, b);
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cmp.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_cmp_d.c b/libtommath/bn_mp_cmp_d.c
new file mode 100644
index 0000000..20a19bc
--- /dev/null
+++ b/libtommath/bn_mp_cmp_d.c
@@ -0,0 +1,44 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* compare a digit */
+int mp_cmp_d(mp_int * a, mp_digit b)
+{
+ /* compare based on sign */
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ }
+
+ /* compare based on magnitude */
+ if (a->used > 1) {
+ return MP_GT;
+ }
+
+ /* compare the only digit of a to b */
+ if (a->dp[0] > b) {
+ return MP_GT;
+ } else if (a->dp[0] < b) {
+ return MP_LT;
+ } else {
+ return MP_EQ;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_cmp_mag.c b/libtommath/bn_mp_cmp_mag.c
new file mode 100644
index 0000000..5dc7a3f
--- /dev/null
+++ b/libtommath/bn_mp_cmp_mag.c
@@ -0,0 +1,55 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* compare maginitude of two ints (unsigned) */
+int mp_cmp_mag (mp_int * a, mp_int * b)
+{
+ int n;
+ mp_digit *tmpa, *tmpb;
+
+ /* compare based on # of non-zero digits */
+ if (a->used > b->used) {
+ return MP_GT;
+ }
+
+ if (a->used < b->used) {
+ return MP_LT;
+ }
+
+ /* alias for a */
+ tmpa = a->dp + (a->used - 1);
+
+ /* alias for b */
+ tmpb = b->dp + (a->used - 1);
+
+ /* compare based on digits */
+ for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
+ if (*tmpa > *tmpb) {
+ return MP_GT;
+ }
+
+ if (*tmpa < *tmpb) {
+ return MP_LT;
+ }
+ }
+ return MP_EQ;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_mag.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_cnt_lsb.c b/libtommath/bn_mp_cnt_lsb.c
new file mode 100644
index 0000000..017b990
--- /dev/null
+++ b/libtommath/bn_mp_cnt_lsb.c
@@ -0,0 +1,53 @@
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+static const int lnz[16] = {
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
+};
+
+/* Counts the number of lsbs which are zero before the first zero bit */
+int mp_cnt_lsb(mp_int *a)
+{
+ int x;
+ mp_digit q, qq;
+
+ /* easy out */
+ if (mp_iszero(a) == 1) {
+ return 0;
+ }
+
+ /* scan lower digits until non-zero */
+ for (x = 0; x < a->used && a->dp[x] == 0; x++);
+ q = a->dp[x];
+ x *= DIGIT_BIT;
+
+ /* now scan this digit until a 1 is found */
+ if ((q & 1) == 0) {
+ do {
+ qq = q & 15;
+ x += lnz[qq];
+ q >>= 4;
+ } while (qq == 0);
+ }
+ return x;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cnt_lsb.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_copy.c b/libtommath/bn_mp_copy.c
new file mode 100644
index 0000000..d820397
--- /dev/null
+++ b/libtommath/bn_mp_copy.c
@@ -0,0 +1,68 @@
+#include <tommath.h>
+#ifdef BN_MP_COPY_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* copy, b = a */
+int
+mp_copy (mp_int * a, mp_int * b)
+{
+ int res, n;
+
+ /* if dst == src do nothing */
+ if (a == b) {
+ return MP_OKAY;
+ }
+
+ /* grow dest */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero b and copy the parameters over */
+ {
+ register mp_digit *tmpa, *tmpb;
+
+ /* pointer aliases */
+
+ /* source */
+ tmpa = a->dp;
+
+ /* destination */
+ tmpb = b->dp;
+
+ /* copy all the digits */
+ for (n = 0; n < a->used; n++) {
+ *tmpb++ = *tmpa++;
+ }
+
+ /* clear high digits */
+ for (; n < b->used; n++) {
+ *tmpb++ = 0;
+ }
+ }
+
+ /* copy used count and sign */
+ b->used = a->used;
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_copy.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_count_bits.c b/libtommath/bn_mp_count_bits.c
new file mode 100644
index 0000000..ff4db22
--- /dev/null
+++ b/libtommath/bn_mp_count_bits.c
@@ -0,0 +1,45 @@
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* returns the number of bits in an int */
+int
+mp_count_bits (mp_int * a)
+{
+ int r;
+ mp_digit q;
+
+ /* shortcut */
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits and add that */
+ r = (a->used - 1) * DIGIT_BIT;
+
+ /* take the last digit and count the bits in it */
+ q = a->dp[a->used - 1];
+ while (q > ((mp_digit) 0)) {
+ ++r;
+ q >>= ((mp_digit) 1);
+ }
+ return r;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_count_bits.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_div.c b/libtommath/bn_mp_div.c
new file mode 100644
index 0000000..f4aa1aa
--- /dev/null
+++ b/libtommath/bn_mp_div.c
@@ -0,0 +1,294 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
+ ((res = mp_abs(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
+ }
+LBL_ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
+
+/* integer signed division.
+ * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+ * HAC pp.598 Algorithm 14.20
+ *
+ * Note that the description in HAC is horribly
+ * incomplete. For example, it doesn't consider
+ * the case where digits are removed from 'x' in
+ * the inner loop. It also doesn't consider the
+ * case that y has fewer than three digits, etc..
+ *
+ * The overall algorithm is as described as
+ * 14.20 from HAC but fixed to treat these cases.
+*/
+int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int q, x, y, t1, t2;
+ int res, n, t, i, norm, neg;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
+ return res;
+ }
+ q.used = a->used + 2;
+
+ if ((res = mp_init (&t1)) != MP_OKAY) {
+ goto LBL_Q;
+ }
+
+ if ((res = mp_init (&t2)) != MP_OKAY) {
+ goto LBL_T1;
+ }
+
+ if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
+ goto LBL_T2;
+ }
+
+ if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
+ goto LBL_X;
+ }
+
+ /* fix the sign */
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+ x.sign = y.sign = MP_ZPOS;
+
+ /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
+ norm = mp_count_bits(&y) % DIGIT_BIT;
+ if (norm < (int)(DIGIT_BIT-1)) {
+ norm = (DIGIT_BIT-1) - norm;
+ if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ } else {
+ norm = 0;
+ }
+
+ /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
+ n = x.used - 1;
+ t = y.used - 1;
+
+ /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
+ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
+ goto LBL_Y;
+ }
+
+ while (mp_cmp (&x, &y) != MP_LT) {
+ ++(q.dp[n - t]);
+ if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ }
+
+ /* reset y by shifting it back down */
+ mp_rshd (&y, n - t);
+
+ /* step 3. for i from n down to (t + 1) */
+ for (i = n; i >= (t + 1); i--) {
+ if (i > x.used) {
+ continue;
+ }
+
+ /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
+ * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
+ if (x.dp[i] == y.dp[t]) {
+ q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
+ } else {
+ mp_word tmp;
+ tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
+ tmp |= ((mp_word) x.dp[i - 1]);
+ tmp /= ((mp_word) y.dp[t]);
+ if (tmp > (mp_word) MP_MASK)
+ tmp = MP_MASK;
+ q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
+ }
+
+ /* while (q{i-t-1} * (yt * b + y{t-1})) >
+ xi * b**2 + xi-1 * b + xi-2
+
+ do q{i-t-1} -= 1;
+ */
+ q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
+ do {
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
+
+ /* find left hand */
+ mp_zero (&t1);
+ t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
+ t1.dp[1] = y.dp[t];
+ t1.used = 2;
+ if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* find right hand */
+ t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
+ t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
+ t2.dp[2] = x.dp[i];
+ t2.used = 3;
+ } while (mp_cmp_mag(&t1, &t2) == MP_GT);
+
+ /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
+ if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
+ if (x.sign == MP_NEG) {
+ if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
+ }
+ }
+
+ /* now q is the quotient and x is the remainder
+ * [which we have to normalize]
+ */
+
+ /* get sign before writing to c */
+ x.sign = x.used == 0 ? MP_ZPOS : a->sign;
+
+ if (c != NULL) {
+ mp_clamp (&q);
+ mp_exch (&q, c);
+ c->sign = neg;
+ }
+
+ if (d != NULL) {
+ if ((res = mp_div_2d (&x, norm, &x, NULL)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ mp_exch (&x, d);
+ }
+
+ res = MP_OKAY;
+
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+LBL_Q:mp_clear (&q);
+ return res;
+}
+
+#endif
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_div_2.c b/libtommath/bn_mp_div_2.c
new file mode 100644
index 0000000..0035e56
--- /dev/null
+++ b/libtommath/bn_mp_div_2.c
@@ -0,0 +1,68 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = a/2 */
+int mp_div_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* copy */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* source alias */
+ tmpa = a->dp + b->used - 1;
+
+ /* dest alias */
+ tmpb = b->dp + b->used - 1;
+
+ /* carry */
+ r = 0;
+ for (x = b->used - 1; x >= 0; x--) {
+ /* get the carry for the next iteration */
+ rr = *tmpa & 1;
+
+ /* shift the current digit, add in carry and store */
+ *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
+
+ /* forward carry to next iteration */
+ r = rr;
+ }
+
+ /* zero excess digits */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_2.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_div_2d.c b/libtommath/bn_mp_div_2d.c
new file mode 100644
index 0000000..6c18d80
--- /dev/null
+++ b/libtommath/bn_mp_div_2d.c
@@ -0,0 +1,97 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
+int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
+{
+ mp_digit D, r, rr;
+ int x, res;
+ mp_int t;
+
+
+ /* if the shift count is <= 0 then we do no work */
+ if (b <= 0) {
+ res = mp_copy (a, c);
+ if (d != NULL) {
+ mp_zero (d);
+ }
+ return res;
+ }
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ /* get the remainder */
+ if (d != NULL) {
+ if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ mp_rshd (c, b / DIGIT_BIT);
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ D = (mp_digit) (b % DIGIT_BIT);
+ if (D != 0) {
+ register mp_digit *tmpc, mask, shift;
+
+ /* mask */
+ mask = (((mp_digit)1) << D) - 1;
+
+ /* shift for lsb */
+ shift = DIGIT_BIT - D;
+
+ /* alias */
+ tmpc = c->dp + (c->used - 1);
+
+ /* carry */
+ r = 0;
+ for (x = c->used - 1; x >= 0; x--) {
+ /* get the lower bits of this word in a temp */
+ rr = *tmpc & mask;
+
+ /* shift the current word and mix in the carry bits from the previous word */
+ *tmpc = (*tmpc >> D) | (r << shift);
+ --tmpc;
+
+ /* set the carry to the carry bits of the current word found above */
+ r = rr;
+ }
+ }
+ mp_clamp (c);
+ if (d != NULL) {
+ mp_exch (&t, d);
+ }
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_2d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_div_3.c b/libtommath/bn_mp_div_3.c
new file mode 100644
index 0000000..c6090f4
--- /dev/null
+++ b/libtommath/bn_mp_div_3.c
@@ -0,0 +1,79 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* divide by three (based on routine from MPI and the GMP manual) */
+int
+mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
+{
+ mp_int q;
+ mp_word w, t;
+ mp_digit b;
+ int res, ix;
+
+ /* b = 2**DIGIT_BIT / 3 */
+ b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
+
+ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
+ return res;
+ }
+
+ q.used = a->used;
+ q.sign = a->sign;
+ w = 0;
+ for (ix = a->used - 1; ix >= 0; ix--) {
+ w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+
+ if (w >= 3) {
+ /* multiply w by [1/3] */
+ t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
+
+ /* now subtract 3 * [w/3] from w, to get the remainder */
+ w -= t+t+t;
+
+ /* fixup the remainder as required since
+ * the optimization is not exact.
+ */
+ while (w >= 3) {
+ t += 1;
+ w -= 3;
+ }
+ } else {
+ t = 0;
+ }
+ q.dp[ix] = (mp_digit)t;
+ }
+
+ /* [optional] store the remainder */
+ if (d != NULL) {
+ *d = (mp_digit)w;
+ }
+
+ /* [optional] store the quotient */
+ if (c != NULL) {
+ mp_clamp(&q);
+ mp_exch(&q, c);
+ }
+ mp_clear(&q);
+
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_3.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_div_d.c b/libtommath/bn_mp_div_d.c
new file mode 100644
index 0000000..771aa6a
--- /dev/null
+++ b/libtommath/bn_mp_div_d.c
@@ -0,0 +1,110 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+static int s_is_power_of_two(mp_digit b, int *p)
+{
+ int x;
+
+ for (x = 1; x < DIGIT_BIT; x++) {
+ if (b == (((mp_digit)1)<<x)) {
+ *p = x;
+ return 1;
+ }
+ }
+ return 0;
+}
+
+/* single digit division (based on routine from MPI) */
+int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
+{
+ mp_int q;
+ mp_word w;
+ mp_digit t;
+ int res, ix;
+
+ /* cannot divide by zero */
+ if (b == 0) {
+ return MP_VAL;
+ }
+
+ /* quick outs */
+ if (b == 1 || mp_iszero(a) == 1) {
+ if (d != NULL) {
+ *d = 0;
+ }
+ if (c != NULL) {
+ return mp_copy(a, c);
+ }
+ return MP_OKAY;
+ }
+
+ /* power of two ? */
+ if (s_is_power_of_two(b, &ix) == 1) {
+ if (d != NULL) {
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
+ }
+ if (c != NULL) {
+ return mp_div_2d(a, ix, c, NULL);
+ }
+ return MP_OKAY;
+ }
+
+#ifdef BN_MP_DIV_3_C
+ /* three? */
+ if (b == 3) {
+ return mp_div_3(a, c, d);
+ }
+#endif
+
+ /* no easy answer [c'est la vie]. Just division */
+ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
+ return res;
+ }
+
+ q.used = a->used;
+ q.sign = a->sign;
+ w = 0;
+ for (ix = a->used - 1; ix >= 0; ix--) {
+ w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+
+ if (w >= b) {
+ t = (mp_digit)(w / b);
+ w -= ((mp_word)t) * ((mp_word)b);
+ } else {
+ t = 0;
+ }
+ q.dp[ix] = (mp_digit)t;
+ }
+
+ if (d != NULL) {
+ *d = (mp_digit)w;
+ }
+
+ if (c != NULL) {
+ mp_clamp(&q);
+ mp_exch(&q, c);
+ }
+ mp_clear(&q);
+
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_dr_is_modulus.c b/libtommath/bn_mp_dr_is_modulus.c
new file mode 100644
index 0000000..e9223f3
--- /dev/null
+++ b/libtommath/bn_mp_dr_is_modulus.c
@@ -0,0 +1,43 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if a number is a valid DR modulus */
+int mp_dr_is_modulus(mp_int *a)
+{
+ int ix;
+
+ /* must be at least two digits */
+ if (a->used < 2) {
+ return 0;
+ }
+
+ /* must be of the form b**k - a [a <= b] so all
+ * but the first digit must be equal to -1 (mod b).
+ */
+ for (ix = 1; ix < a->used; ix++) {
+ if (a->dp[ix] != MP_MASK) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_dr_is_modulus.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_dr_reduce.c b/libtommath/bn_mp_dr_reduce.c
new file mode 100644
index 0000000..d2ef18f
--- /dev/null
+++ b/libtommath/bn_mp_dr_reduce.c
@@ -0,0 +1,94 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
+ *
+ * Based on algorithm from the paper
+ *
+ * "Generating Efficient Primes for Discrete Log Cryptosystems"
+ * Chae Hoon Lim, Pil Joong Lee,
+ * POSTECH Information Research Laboratories
+ *
+ * The modulus must be of a special format [see manual]
+ *
+ * Has been modified to use algorithm 7.10 from the LTM book instead
+ *
+ * Input x must be in the range 0 <= x <= (n-1)**2
+ */
+int
+mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
+{
+ int err, i, m;
+ mp_word r;
+ mp_digit mu, *tmpx1, *tmpx2;
+
+ /* m = digits in modulus */
+ m = n->used;
+
+ /* ensure that "x" has at least 2m digits */
+ if (x->alloc < m + m) {
+ if ((err = mp_grow (x, m + m)) != MP_OKAY) {
+ return err;
+ }
+ }
+
+/* top of loop, this is where the code resumes if
+ * another reduction pass is required.
+ */
+top:
+ /* aliases for digits */
+ /* alias for lower half of x */
+ tmpx1 = x->dp;
+
+ /* alias for upper half of x, or x/B**m */
+ tmpx2 = x->dp + m;
+
+ /* set carry to zero */
+ mu = 0;
+
+ /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
+ for (i = 0; i < m; i++) {
+ r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
+ *tmpx1++ = (mp_digit)(r & MP_MASK);
+ mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
+ }
+
+ /* set final carry */
+ *tmpx1++ = mu;
+
+ /* zero words above m */
+ for (i = m + 1; i < x->used; i++) {
+ *tmpx1++ = 0;
+ }
+
+ /* clamp, sub and return */
+ mp_clamp (x);
+
+ /* if x >= n then subtract and reduce again
+ * Each successive "recursion" makes the input smaller and smaller.
+ */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ s_mp_sub(x, n, x);
+ goto top;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_dr_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_dr_setup.c b/libtommath/bn_mp_dr_setup.c
new file mode 100644
index 0000000..3e82c9b
--- /dev/null
+++ b/libtommath/bn_mp_dr_setup.c
@@ -0,0 +1,32 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines the setup value */
+void mp_dr_setup(mp_int *a, mp_digit *d)
+{
+ /* the casts are required if DIGIT_BIT is one less than
+ * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
+ */
+ *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
+ ((mp_word)a->dp[0]));
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_dr_setup.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_exch.c b/libtommath/bn_mp_exch.c
new file mode 100644
index 0000000..81a42ac
--- /dev/null
+++ b/libtommath/bn_mp_exch.c
@@ -0,0 +1,34 @@
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* swap the elements of two integers, for cases where you can't simply swap the
+ * mp_int pointers around
+ */
+void
+mp_exch (mp_int * a, mp_int * b)
+{
+ mp_int t;
+
+ t = *a;
+ *a = *b;
+ *b = t;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exch.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_expt_d.c b/libtommath/bn_mp_expt_d.c
new file mode 100644
index 0000000..656cf68
--- /dev/null
+++ b/libtommath/bn_mp_expt_d.c
@@ -0,0 +1,57 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* calculate c = a**b using a square-multiply algorithm */
+int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ int res, x;
+ mp_int g;
+
+ if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* set initial result */
+ mp_set (c, 1);
+
+ for (x = 0; x < (int) DIGIT_BIT; x++) {
+ /* square */
+ if ((res = mp_sqr (c, c)) != MP_OKAY) {
+ mp_clear (&g);
+ return res;
+ }
+
+ /* if the bit is set multiply */
+ if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
+ if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
+ mp_clear (&g);
+ return res;
+ }
+ }
+
+ /* shift to next bit */
+ b <<= 1;
+ }
+
+ mp_clear (&g);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_expt_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_exptmod.c b/libtommath/bn_mp_exptmod.c
new file mode 100644
index 0000000..d72ab20
--- /dev/null
+++ b/libtommath/bn_mp_exptmod.c
@@ -0,0 +1,112 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+
+/* this is a shell function that calls either the normal or Montgomery
+ * exptmod functions. Originally the call to the montgomery code was
+ * embedded in the normal function but that wasted alot of stack space
+ * for nothing (since 99% of the time the Montgomery code would be called)
+ */
+int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+{
+ int dr;
+
+ /* modulus P must be positive */
+ if (P->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* if exponent X is negative we have to recurse */
+ if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
+ mp_int tmpG, tmpX;
+ int err;
+
+ /* first compute 1/G mod P */
+ if ((err = mp_init(&tmpG)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+
+ /* now get |X| */
+ if ((err = mp_init(&tmpX)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+ if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+ }
+
+ /* and now compute (1/G)**|X| instead of G**X [X < 0] */
+ err = mp_exptmod(&tmpG, &tmpX, P, Y);
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+#else
+ /* no invmod */
+ return MP_VAL;
+#endif
+ }
+
+/* modified diminished radix reduction */
+#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
+ if (mp_reduce_is_2k_l(P) == MP_YES) {
+ return s_mp_exptmod(G, X, P, Y, 1);
+ }
+#endif
+
+#ifdef BN_MP_DR_IS_MODULUS_C
+ /* is it a DR modulus? */
+ dr = mp_dr_is_modulus(P);
+#else
+ /* default to no */
+ dr = 0;
+#endif
+
+#ifdef BN_MP_REDUCE_IS_2K_C
+ /* if not, is it a unrestricted DR modulus? */
+ if (dr == 0) {
+ dr = mp_reduce_is_2k(P) << 1;
+ }
+#endif
+
+ /* if the modulus is odd or dr != 0 use the montgomery method */
+#ifdef BN_MP_EXPTMOD_FAST_C
+ if (mp_isodd (P) == 1 || dr != 0) {
+ return mp_exptmod_fast (G, X, P, Y, dr);
+ } else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
+ /* otherwise use the generic Barrett reduction technique */
+ return s_mp_exptmod (G, X, P, Y, 0);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
+ }
+#endif
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_exptmod_fast.c b/libtommath/bn_mp_exptmod_fast.c
new file mode 100644
index 0000000..32f8f16
--- /dev/null
+++ b/libtommath/bn_mp_exptmod_fast.c
@@ -0,0 +1,321 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
+ *
+ * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
+ * The value of k changes based on the size of the exponent.
+ *
+ * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
+ */
+
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res;
+ mp_digit buf, mp;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+
+ /* use a pointer to the reduction algorithm. This allows us to use
+ * one of many reduction algorithms without modding the guts of
+ * the code with if statements everywhere.
+ */
+ int (*redux)(mp_int*,mp_int*,mp_digit);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* determine and setup reduction code */
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+ /* now setup montgomery */
+ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+
+ /* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+ if (((P->used * 2 + 1) < MP_WARRAY) &&
+ P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ redux = fast_mp_montgomery_reduce;
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+ /* use slower baseline Montgomery method */
+ redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+ } else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
+ /* setup DR reduction for moduli of the form B**k - b */
+ mp_dr_setup(P, &mp);
+ redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ } else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
+ /* setup DR reduction for moduli of the form 2**k - b */
+ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+ redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ /* create M table
+ *
+
+ *
+ * The first half of the table is not computed though accept for M[0] and M[1]
+ */
+
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+ /* now we need R mod m */
+ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_RES;
+#endif
+
+ /* now set M[1] to G * R mod m */
+ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ } else {
+ mp_set(&res, 1);
+ if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* create upper table */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits so break */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int)DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* get next bit of the window */
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ if (redmode == 0) {
+ /* fixup result if Montgomery reduction is used
+ * recall that any value in a Montgomery system is
+ * actually multiplied by R mod n. So we have
+ * to reduce one more time to cancel out the factor
+ * of R.
+ */
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* swap res with Y */
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+#endif
+
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod_fast.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_exteuclid.c b/libtommath/bn_mp_exteuclid.c
new file mode 100644
index 0000000..25ccba9
--- /dev/null
+++ b/libtommath/bn_mp_exteuclid.c
@@ -0,0 +1,82 @@
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Extended euclidean algorithm of (a, b) produces
+ a*u1 + b*u2 = u3
+ */
+int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
+{
+ mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
+ int err;
+
+ if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* initialize, (u1,u2,u3) = (1,0,a) */
+ mp_set(&u1, 1);
+ if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* initialize, (v1,v2,v3) = (0,1,b) */
+ mp_set(&v2, 1);
+ if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; }
+
+ /* loop while v3 != 0 */
+ while (mp_iszero(&v3) == MP_NO) {
+ /* q = u3/v3 */
+ if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; }
+
+ /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
+ if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; }
+
+ /* (u1,u2,u3) = (v1,v2,v3) */
+ if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* (v1,v2,v3) = (t1,t2,t3) */
+ if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; }
+ }
+
+ /* make sure U3 >= 0 */
+ if (u3.sign == MP_NEG) {
+ mp_neg(&u1, &u1);
+ mp_neg(&u2, &u2);
+ mp_neg(&u3, &u3);
+ }
+
+ /* copy result out */
+ if (U1 != NULL) { mp_exch(U1, &u1); }
+ if (U2 != NULL) { mp_exch(U2, &u2); }
+ if (U3 != NULL) { mp_exch(U3, &u3); }
+
+ err = MP_OKAY;
+_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exteuclid.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_fread.c b/libtommath/bn_mp_fread.c
new file mode 100644
index 0000000..c3bd08d
--- /dev/null
+++ b/libtommath/bn_mp_fread.c
@@ -0,0 +1,67 @@
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* read a bigint from a file stream in ASCII */
+int mp_fread(mp_int *a, int radix, FILE *stream)
+{
+ int err, ch, neg, y;
+
+ /* clear a */
+ mp_zero(a);
+
+ /* if first digit is - then set negative */
+ ch = fgetc(stream);
+ if (ch == '-') {
+ neg = MP_NEG;
+ ch = fgetc(stream);
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ for (;;) {
+ /* find y in the radix map */
+ for (y = 0; y < radix; y++) {
+ if (mp_s_rmap[y] == ch) {
+ break;
+ }
+ }
+ if (y == radix) {
+ break;
+ }
+
+ /* shift up and add */
+ if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
+ return err;
+ }
+
+ ch = fgetc(stream);
+ }
+ if (mp_cmp_d(a, 0) != MP_EQ) {
+ a->sign = neg;
+ }
+
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_fread.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_fwrite.c b/libtommath/bn_mp_fwrite.c
new file mode 100644
index 0000000..006f923
--- /dev/null
+++ b/libtommath/bn_mp_fwrite.c
@@ -0,0 +1,52 @@
+#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+int mp_fwrite(mp_int *a, int radix, FILE *stream)
+{
+ char *buf;
+ int err, len, x;
+
+ if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
+ return err;
+ }
+
+ buf = OPT_CAST(char) XMALLOC (len);
+ if (buf == NULL) {
+ return MP_MEM;
+ }
+
+ if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
+ XFREE (buf);
+ return err;
+ }
+
+ for (x = 0; x < len; x++) {
+ if (fputc(buf[x], stream) == EOF) {
+ XFREE (buf);
+ return MP_VAL;
+ }
+ }
+
+ XFREE (buf);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_fwrite.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_gcd.c b/libtommath/bn_mp_gcd.c
new file mode 100644
index 0000000..23f6b02
--- /dev/null
+++ b/libtommath/bn_mp_gcd.c
@@ -0,0 +1,105 @@
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Greatest Common Divisor using the binary method */
+int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int u, v;
+ int k, u_lsb, v_lsb, res;
+
+ /* either zero than gcd is the largest */
+ if (mp_iszero (a) == MP_YES) {
+ return mp_abs (b, c);
+ }
+ if (mp_iszero (b) == MP_YES) {
+ return mp_abs (a, c);
+ }
+
+ /* get copies of a and b we can modify */
+ if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
+ goto LBL_U;
+ }
+
+ /* must be positive for the remainder of the algorithm */
+ u.sign = v.sign = MP_ZPOS;
+
+ /* B1. Find the common power of two for u and v */
+ u_lsb = mp_cnt_lsb(&u);
+ v_lsb = mp_cnt_lsb(&v);
+ k = MIN(u_lsb, v_lsb);
+
+ if (k > 0) {
+ /* divide the power of two out */
+ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ /* divide any remaining factors of two out */
+ if (u_lsb != k) {
+ if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ if (v_lsb != k) {
+ if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ while (mp_iszero(&v) == 0) {
+ /* make sure v is the largest */
+ if (mp_cmp_mag(&u, &v) == MP_GT) {
+ /* swap u and v to make sure v is >= u */
+ mp_exch(&u, &v);
+ }
+
+ /* subtract smallest from largest */
+ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ /* Divide out all factors of two */
+ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ /* multiply by 2**k which we divided out at the beginning */
+ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ c->sign = MP_ZPOS;
+ res = MP_OKAY;
+LBL_V:mp_clear (&u);
+LBL_U:mp_clear (&v);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_gcd.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_get_int.c b/libtommath/bn_mp_get_int.c
new file mode 100644
index 0000000..7948d46
--- /dev/null
+++ b/libtommath/bn_mp_get_int.c
@@ -0,0 +1,45 @@
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* get the lower 32-bits of an mp_int */
+unsigned long mp_get_int(mp_int * a)
+{
+ int i;
+ unsigned long res;
+
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits of the lsb we have to read */
+ i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
+
+ /* get most significant digit of result */
+ res = DIGIT(a,i);
+
+ while (--i >= 0) {
+ res = (res << DIGIT_BIT) | DIGIT(a,i);
+ }
+
+ /* force result to 32-bits always so it is consistent on non 32-bit platforms */
+ return res & 0xFFFFFFFFUL;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_get_int.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_grow.c b/libtommath/bn_mp_grow.c
new file mode 100644
index 0000000..2d50058
--- /dev/null
+++ b/libtommath/bn_mp_grow.c
@@ -0,0 +1,57 @@
+#include <tommath.h>
+#ifdef BN_MP_GROW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* grow as required */
+int mp_grow (mp_int * a, int size)
+{
+ int i;
+ mp_digit *tmp;
+
+ /* if the alloc size is smaller alloc more ram */
+ if (a->alloc < size) {
+ /* ensure there are always at least MP_PREC digits extra on top */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* reallocate the array a->dp
+ *
+ * We store the return in a temporary variable
+ * in case the operation failed we don't want
+ * to overwrite the dp member of a.
+ */
+ tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
+ if (tmp == NULL) {
+ /* reallocation failed but "a" is still valid [can be freed] */
+ return MP_MEM;
+ }
+
+ /* reallocation succeeded so set a->dp */
+ a->dp = tmp;
+
+ /* zero excess digits */
+ i = a->alloc;
+ a->alloc = size;
+ for (; i < a->alloc; i++) {
+ a->dp[i] = 0;
+ }
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_grow.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_init.c b/libtommath/bn_mp_init.c
new file mode 100644
index 0000000..565ea47
--- /dev/null
+++ b/libtommath/bn_mp_init.c
@@ -0,0 +1,46 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* init a new mp_int */
+int mp_init (mp_int * a)
+{
+ int i;
+
+ /* allocate memory required and clear it */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the digits to zero */
+ for (i = 0; i < MP_PREC; i++) {
+ a->dp[i] = 0;
+ }
+
+ /* set the used to zero, allocated digits to the default precision
+ * and sign to positive */
+ a->used = 0;
+ a->alloc = MP_PREC;
+ a->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_init_copy.c b/libtommath/bn_mp_init_copy.c
new file mode 100644
index 0000000..8e7329c
--- /dev/null
+++ b/libtommath/bn_mp_init_copy.c
@@ -0,0 +1,32 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* creates "a" then copies b into it */
+int mp_init_copy (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_init (a)) != MP_OKAY) {
+ return res;
+ }
+ return mp_copy (b, a);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_copy.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_init_multi.c b/libtommath/bn_mp_init_multi.c
new file mode 100644
index 0000000..d592f43
--- /dev/null
+++ b/libtommath/bn_mp_init_multi.c
@@ -0,0 +1,59 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+#include <stdarg.h>
+
+int mp_init_multi(mp_int *mp, ...)
+{
+ mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
+ int n = 0; /* Number of ok inits */
+ mp_int* cur_arg = mp;
+ va_list args;
+
+ va_start(args, mp); /* init args to next argument from caller */
+ while (cur_arg != NULL) {
+ if (mp_init(cur_arg) != MP_OKAY) {
+ /* Oops - error! Back-track and mp_clear what we already
+ succeeded in init-ing, then return error.
+ */
+ va_list clean_args;
+
+ /* end the current list */
+ va_end(args);
+
+ /* now start cleaning up */
+ cur_arg = mp;
+ va_start(clean_args, mp);
+ while (n--) {
+ mp_clear(cur_arg);
+ cur_arg = va_arg(clean_args, mp_int*);
+ }
+ va_end(clean_args);
+ res = MP_MEM;
+ break;
+ }
+ n++;
+ cur_arg = va_arg(args, mp_int*);
+ }
+ va_end(args);
+ return res; /* Assumed ok, if error flagged above. */
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_multi.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_init_set.c b/libtommath/bn_mp_init_set.c
new file mode 100644
index 0000000..a7ee8f7
--- /dev/null
+++ b/libtommath/bn_mp_init_set.c
@@ -0,0 +1,32 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* initialize and set a digit */
+int mp_init_set (mp_int * a, mp_digit b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ mp_set(a, b);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_set.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_init_set_int.c b/libtommath/bn_mp_init_set_int.c
new file mode 100644
index 0000000..7c9dd46
--- /dev/null
+++ b/libtommath/bn_mp_init_set_int.c
@@ -0,0 +1,31 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* initialize and set a digit */
+int mp_init_set_int (mp_int * a, unsigned long b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ return mp_set_int(a, b);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_set_int.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_init_size.c b/libtommath/bn_mp_init_size.c
new file mode 100644
index 0000000..4aebd1f
--- /dev/null
+++ b/libtommath/bn_mp_init_size.c
@@ -0,0 +1,48 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* init an mp_init for a given size */
+int mp_init_size (mp_int * a, int size)
+{
+ int x;
+
+ /* pad size so there are always extra digits */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* alloc mem */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the members */
+ a->used = 0;
+ a->alloc = size;
+ a->sign = MP_ZPOS;
+
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_size.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_invmod.c b/libtommath/bn_mp_invmod.c
new file mode 100644
index 0000000..3f5791f
--- /dev/null
+++ b/libtommath/bn_mp_invmod.c
@@ -0,0 +1,43 @@
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+#ifdef BN_FAST_MP_INVMOD_C
+ /* if the modulus is odd we can use a faster routine instead */
+ if (mp_isodd (b) == 1) {
+ return fast_mp_invmod (a, b, c);
+ }
+#endif
+
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
+
+ return MP_VAL;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_invmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_invmod_slow.c b/libtommath/bn_mp_invmod_slow.c
new file mode 100644
index 0000000..a4e4fbc
--- /dev/null
+++ b/libtommath/bn_mp_invmod_slow.c
@@ -0,0 +1,175 @@
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v,
+ &A, &B, &C, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x = a, y = b */
+ if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* 2. [modified] if x,y are both even then return an error! */
+ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ mp_set (&A, 1);
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 4.2 if A or B is odd then */
+ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
+ /* A = (A+y)/2, B = (B-x)/2 */
+ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* A = A/2, B = B/2 */
+ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 5.2 if C or D is odd then */
+ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
+ /* C = (C+y)/2, D = (D-x)/2 */
+ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* C = C/2, D = D/2 */
+ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, A = A - C, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ } else {
+ /* v - v - u, C = C - A, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0)
+ goto top;
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* if its too low */
+ while (mp_cmp_d(&C, 0) == MP_LT) {
+ if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* too big */
+ while (mp_cmp_mag(&C, b) != MP_LT) {
+ if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* C is now the inverse */
+ mp_exch (&C, c);
+ res = MP_OKAY;
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_invmod_slow.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_is_square.c b/libtommath/bn_mp_is_square.c
new file mode 100644
index 0000000..a235d97
--- /dev/null
+++ b/libtommath/bn_mp_is_square.c
@@ -0,0 +1,109 @@
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Check if remainders are possible squares - fast exclude non-squares */
+static const char rem_128[128] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
+};
+
+static const char rem_105[105] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
+ 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
+ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
+ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
+};
+
+/* Store non-zero to ret if arg is square, and zero if not */
+int mp_is_square(mp_int *arg,int *ret)
+{
+ int res;
+ mp_digit c;
+ mp_int t;
+ unsigned long r;
+
+ /* Default to Non-square :) */
+ *ret = MP_NO;
+
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* digits used? (TSD) */
+ if (arg->used == 0) {
+ return MP_OKAY;
+ }
+
+ /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
+ if (rem_128[127 & DIGIT(arg,0)] == 1) {
+ return MP_OKAY;
+ }
+
+ /* Next check mod 105 (3*5*7) */
+ if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
+ return res;
+ }
+ if (rem_105[c] == 1) {
+ return MP_OKAY;
+ }
+
+
+ if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ r = mp_get_int(&t);
+ /* Check for other prime modules, note it's not an ERROR but we must
+ * free "t" so the easiest way is to goto ERR. We know that res
+ * is already equal to MP_OKAY from the mp_mod call
+ */
+ if ( (1L<<(r%11)) & 0x5C4L ) goto ERR;
+ if ( (1L<<(r%13)) & 0x9E4L ) goto ERR;
+ if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR;
+ if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR;
+ if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR;
+ if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR;
+ if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR;
+
+ /* Final check - is sqr(sqrt(arg)) == arg ? */
+ if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
+ERR:mp_clear(&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_is_square.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_jacobi.c b/libtommath/bn_mp_jacobi.c
new file mode 100644
index 0000000..2e88fd4
--- /dev/null
+++ b/libtommath/bn_mp_jacobi.c
@@ -0,0 +1,105 @@
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes the jacobi c = (a | n) (or Legendre if n is prime)
+ * HAC pp. 73 Algorithm 2.149
+ */
+int mp_jacobi (mp_int * a, mp_int * p, int *c)
+{
+ mp_int a1, p1;
+ int k, s, r, res;
+ mp_digit residue;
+
+ /* if p <= 0 return MP_VAL */
+ if (mp_cmp_d(p, 0) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* step 1. if a == 0, return 0 */
+ if (mp_iszero (a) == 1) {
+ *c = 0;
+ return MP_OKAY;
+ }
+
+ /* step 2. if a == 1, return 1 */
+ if (mp_cmp_d (a, 1) == MP_EQ) {
+ *c = 1;
+ return MP_OKAY;
+ }
+
+ /* default */
+ s = 0;
+
+ /* step 3. write a = a1 * 2**k */
+ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&p1)) != MP_OKAY) {
+ goto LBL_A1;
+ }
+
+ /* divide out larger power of two */
+ k = mp_cnt_lsb(&a1);
+ if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+
+ /* step 4. if e is even set s=1 */
+ if ((k & 1) == 0) {
+ s = 1;
+ } else {
+ /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
+ residue = p->dp[0] & 7;
+
+ if (residue == 1 || residue == 7) {
+ s = 1;
+ } else if (residue == 3 || residue == 5) {
+ s = -1;
+ }
+ }
+
+ /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
+ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
+ s = -s;
+ }
+
+ /* if a1 == 1 we're done */
+ if (mp_cmp_d (&a1, 1) == MP_EQ) {
+ *c = s;
+ } else {
+ /* n1 = n mod a1 */
+ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ *c = s * r;
+ }
+
+ /* done */
+ res = MP_OKAY;
+LBL_P1:mp_clear (&p1);
+LBL_A1:mp_clear (&a1);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_karatsuba_mul.c b/libtommath/bn_mp_karatsuba_mul.c
new file mode 100644
index 0000000..35dc9a4
--- /dev/null
+++ b/libtommath/bn_mp_karatsuba_mul.c
@@ -0,0 +1,167 @@
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* c = |a| * |b| using Karatsuba Multiplication using
+ * three half size multiplications
+ *
+ * Let B represent the radix [e.g. 2**DIGIT_BIT] and
+ * let n represent half of the number of digits in
+ * the min(a,b)
+ *
+ * a = a1 * B**n + a0
+ * b = b1 * B**n + b0
+ *
+ * Then, a * b =>
+ a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
+ *
+ * Note that a1b1 and a0b0 are used twice and only need to be
+ * computed once. So in total three half size (half # of
+ * digit) multiplications are performed, a0b0, a1b1 and
+ * (a1+b1)(a0+b0)
+ *
+ * Note that a multiplication of half the digits requires
+ * 1/4th the number of single precision multiplications so in
+ * total after one call 25% of the single precision multiplications
+ * are saved. Note also that the call to mp_mul can end up back
+ * in this function if the a0, a1, b0, or b1 are above the threshold.
+ * This is known as divide-and-conquer and leads to the famous
+ * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
+ * the standard O(N**2) that the baseline/comba methods use.
+ * Generally though the overhead of this method doesn't pay off
+ * until a certain size (N ~ 80) is reached.
+ */
+int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
+ int B, err;
+
+ /* default the return code to an error */
+ err = MP_MEM;
+
+ /* min # of digits */
+ B = MIN (a->used, b->used);
+
+ /* now divide in two */
+ B = B >> 1;
+
+ /* init copy all the temps */
+ if (mp_init_size (&x0, B) != MP_OKAY)
+ goto ERR;
+ if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+ goto X0;
+ if (mp_init_size (&y0, B) != MP_OKAY)
+ goto X1;
+ if (mp_init_size (&y1, b->used - B) != MP_OKAY)
+ goto Y0;
+
+ /* init temps */
+ if (mp_init_size (&t1, B * 2) != MP_OKAY)
+ goto Y1;
+ if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
+ goto T1;
+ if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
+ goto X0Y0;
+
+ /* now shift the digits */
+ x0.used = y0.used = B;
+ x1.used = a->used - B;
+ y1.used = b->used - B;
+
+ {
+ register int x;
+ register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
+
+ /* we copy the digits directly instead of using higher level functions
+ * since we also need to shift the digits
+ */
+ tmpa = a->dp;
+ tmpb = b->dp;
+
+ tmpx = x0.dp;
+ tmpy = y0.dp;
+ for (x = 0; x < B; x++) {
+ *tmpx++ = *tmpa++;
+ *tmpy++ = *tmpb++;
+ }
+
+ tmpx = x1.dp;
+ for (x = B; x < a->used; x++) {
+ *tmpx++ = *tmpa++;
+ }
+
+ tmpy = y1.dp;
+ for (x = B; x < b->used; x++) {
+ *tmpy++ = *tmpb++;
+ }
+ }
+
+ /* only need to clamp the lower words since by definition the
+ * upper words x1/y1 must have a known number of digits
+ */
+ mp_clamp (&x0);
+ mp_clamp (&y0);
+
+ /* now calc the products x0y0 and x1y1 */
+ /* after this x0 is no longer required, free temp [x0==t2]! */
+ if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
+ goto X1Y1; /* x0y0 = x0*y0 */
+ if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
+ goto X1Y1; /* x1y1 = x1*y1 */
+
+ /* now calc x1+x0 and y1+y0 */
+ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = x1 - x0 */
+ if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
+ goto X1Y1; /* t2 = y1 - y0 */
+ if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
+
+ /* add x0y0 */
+ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
+ goto X1Y1; /* t2 = x0y0 + x1y1 */
+ if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
+
+ /* shift by B */
+ if (mp_lshd (&t1, B) != MP_OKAY)
+ goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+ if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
+ goto X1Y1; /* x1y1 = x1y1 << 2*B */
+
+ if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = x0y0 + t1 */
+ if (mp_add (&t1, &x1y1, c) != MP_OKAY)
+ goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
+
+ /* Algorithm succeeded set the return code to MP_OKAY */
+ err = MP_OKAY;
+
+X1Y1:mp_clear (&x1y1);
+X0Y0:mp_clear (&x0y0);
+T1:mp_clear (&t1);
+Y1:mp_clear (&y1);
+Y0:mp_clear (&y0);
+X1:mp_clear (&x1);
+X0:mp_clear (&x0);
+ERR:
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_mul.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_karatsuba_sqr.c b/libtommath/bn_mp_karatsuba_sqr.c
new file mode 100644
index 0000000..6d8ad6e
--- /dev/null
+++ b/libtommath/bn_mp_karatsuba_sqr.c
@@ -0,0 +1,121 @@
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Karatsuba squaring, computes b = a*a using three
+ * half size squarings
+ *
+ * See comments of karatsuba_mul for details. It
+ * is essentially the same algorithm but merely
+ * tuned to perform recursive squarings.
+ */
+int mp_karatsuba_sqr (mp_int * a, mp_int * b)
+{
+ mp_int x0, x1, t1, t2, x0x0, x1x1;
+ int B, err;
+
+ err = MP_MEM;
+
+ /* min # of digits */
+ B = a->used;
+
+ /* now divide in two */
+ B = B >> 1;
+
+ /* init copy all the temps */
+ if (mp_init_size (&x0, B) != MP_OKAY)
+ goto ERR;
+ if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+ goto X0;
+
+ /* init temps */
+ if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
+ goto X1;
+ if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
+ goto T1;
+ if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
+ goto T2;
+ if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
+ goto X0X0;
+
+ {
+ register int x;
+ register mp_digit *dst, *src;
+
+ src = a->dp;
+
+ /* now shift the digits */
+ dst = x0.dp;
+ for (x = 0; x < B; x++) {
+ *dst++ = *src++;
+ }
+
+ dst = x1.dp;
+ for (x = B; x < a->used; x++) {
+ *dst++ = *src++;
+ }
+ }
+
+ x0.used = B;
+ x1.used = a->used - B;
+
+ mp_clamp (&x0);
+
+ /* now calc the products x0*x0 and x1*x1 */
+ if (mp_sqr (&x0, &x0x0) != MP_OKAY)
+ goto X1X1; /* x0x0 = x0*x0 */
+ if (mp_sqr (&x1, &x1x1) != MP_OKAY)
+ goto X1X1; /* x1x1 = x1*x1 */
+
+ /* now calc (x1+x0)**2 */
+ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = x1 - x0 */
+ if (mp_sqr (&t1, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
+
+ /* add x0y0 */
+ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
+ goto X1X1; /* t2 = x0x0 + x1x1 */
+ if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
+
+ /* shift by B */
+ if (mp_lshd (&t1, B) != MP_OKAY)
+ goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
+ if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
+ goto X1X1; /* x1x1 = x1x1 << 2*B */
+
+ if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = x0x0 + t1 */
+ if (mp_add (&t1, &x1x1, b) != MP_OKAY)
+ goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
+
+ err = MP_OKAY;
+
+X1X1:mp_clear (&x1x1);
+X0X0:mp_clear (&x0x0);
+T2:mp_clear (&t2);
+T1:mp_clear (&t1);
+X1:mp_clear (&x1);
+X0:mp_clear (&x0);
+ERR:
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_sqr.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_lcm.c b/libtommath/bn_mp_lcm.c
new file mode 100644
index 0000000..48b2b63
--- /dev/null
+++ b/libtommath/bn_mp_lcm.c
@@ -0,0 +1,60 @@
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes least common multiple as |a*b|/(a, b) */
+int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res;
+ mp_int t1, t2;
+
+
+ if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* t1 = get the GCD of the two inputs */
+ if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
+ goto LBL_T;
+ }
+
+ /* divide the smallest by the GCD */
+ if (mp_cmp_mag(a, b) == MP_LT) {
+ /* store quotient in t2 such that t2 * b is the LCM */
+ if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(b, &t2, c);
+ } else {
+ /* store quotient in t2 such that t2 * a is the LCM */
+ if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(a, &t2, c);
+ }
+
+ /* fix the sign to positive */
+ c->sign = MP_ZPOS;
+
+LBL_T:
+ mp_clear_multi (&t1, &t2, NULL);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_lcm.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_lshd.c b/libtommath/bn_mp_lshd.c
new file mode 100644
index 0000000..ca9b853
--- /dev/null
+++ b/libtommath/bn_mp_lshd.c
@@ -0,0 +1,67 @@
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift left a certain amount of digits */
+int mp_lshd (mp_int * a, int b)
+{
+ int x, res;
+
+ /* if its less than zero return */
+ if (b <= 0) {
+ return MP_OKAY;
+ }
+
+ /* grow to fit the new digits */
+ if (a->alloc < a->used + b) {
+ if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ {
+ register mp_digit *top, *bottom;
+
+ /* increment the used by the shift amount then copy upwards */
+ a->used += b;
+
+ /* top */
+ top = a->dp + a->used - 1;
+
+ /* base */
+ bottom = a->dp + a->used - 1 - b;
+
+ /* much like mp_rshd this is implemented using a sliding window
+ * except the window goes the otherway around. Copying from
+ * the bottom to the top. see bn_mp_rshd.c for more info.
+ */
+ for (x = a->used - 1; x >= b; x--) {
+ *top-- = *bottom--;
+ }
+
+ /* zero the lower digits */
+ top = a->dp;
+ for (x = 0; x < b; x++) {
+ *top++ = 0;
+ }
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_lshd.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_mod.c b/libtommath/bn_mp_mod.c
new file mode 100644
index 0000000..be1f36d
--- /dev/null
+++ b/libtommath/bn_mp_mod.c
@@ -0,0 +1,48 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* c = a mod b, 0 <= c < b */
+int
+mp_mod (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int t;
+ int res;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ if (t.sign != b->sign) {
+ res = mp_add (b, &t, c);
+ } else {
+ res = MP_OKAY;
+ mp_exch (&t, c);
+ }
+
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_mod_2d.c b/libtommath/bn_mp_mod_2d.c
new file mode 100644
index 0000000..461b1b2
--- /dev/null
+++ b/libtommath/bn_mp_mod_2d.c
@@ -0,0 +1,55 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* calc a value mod 2**b */
+int
+mp_mod_2d (mp_int * a, int b, mp_int * c)
+{
+ int x, res;
+
+ /* if b is <= 0 then zero the int */
+ if (b <= 0) {
+ mp_zero (c);
+ return MP_OKAY;
+ }
+
+ /* if the modulus is larger than the value than return */
+ if (b >= (int) (a->used * DIGIT_BIT)) {
+ res = mp_copy (a, c);
+ return res;
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+
+ /* zero digits above the last digit of the modulus */
+ for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
+ c->dp[x] = 0;
+ }
+ /* clear the digit that is not completely outside/inside the modulus */
+ c->dp[b / DIGIT_BIT] &=
+ (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mod_2d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_mod_d.c b/libtommath/bn_mp_mod_d.c
new file mode 100644
index 0000000..8bc499b
--- /dev/null
+++ b/libtommath/bn_mp_mod_d.c
@@ -0,0 +1,27 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+int
+mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
+{
+ return mp_div_d(a, b, NULL, c);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mod_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_montgomery_calc_normalization.c b/libtommath/bn_mp_montgomery_calc_normalization.c
new file mode 100644
index 0000000..91eb5fe
--- /dev/null
+++ b/libtommath/bn_mp_montgomery_calc_normalization.c
@@ -0,0 +1,59 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/*
+ * shifts with subtractions when the result is greater than b.
+ *
+ * The method is slightly modified to shift B unconditionally upto just under
+ * the leading bit of b. This saves alot of multiple precision shifting.
+ */
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+{
+ int x, bits, res;
+
+ /* how many bits of last digit does b use */
+ bits = mp_count_bits (b) % DIGIT_BIT;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
+ }
+
+
+ /* now compute C = A * B mod b */
+ for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
+ if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
+ return res;
+ }
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
+ return res;
+ }
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_montgomery_reduce.c b/libtommath/bn_mp_montgomery_reduce.c
new file mode 100644
index 0000000..a121d2a
--- /dev/null
+++ b/libtommath/bn_mp_montgomery_reduce.c
@@ -0,0 +1,118 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction */
+int
+mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+ int ix, res, digs;
+ mp_digit mu;
+
+ /* can the fast reduction [comba] method be used?
+ *
+ * Note that unlike in mul you're safely allowed *less*
+ * than the available columns [255 per default] since carries
+ * are fixed up in the inner loop.
+ */
+ digs = n->used * 2 + 1;
+ if ((digs < MP_WARRAY) &&
+ n->used <
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_mp_montgomery_reduce (x, n, rho);
+ }
+
+ /* grow the input as required */
+ if (x->alloc < digs) {
+ if ((res = mp_grow (x, digs)) != MP_OKAY) {
+ return res;
+ }
+ }
+ x->used = digs;
+
+ for (ix = 0; ix < n->used; ix++) {
+ /* mu = ai * rho mod b
+ *
+ * The value of rho must be precalculated via
+ * montgomery_setup() such that
+ * it equals -1/n0 mod b this allows the
+ * following inner loop to reduce the
+ * input one digit at a time
+ */
+ mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
+
+ /* a = a + mu * m * b**i */
+ {
+ register int iy;
+ register mp_digit *tmpn, *tmpx, u;
+ register mp_word r;
+
+ /* alias for digits of the modulus */
+ tmpn = n->dp;
+
+ /* alias for the digits of x [the input] */
+ tmpx = x->dp + ix;
+
+ /* set the carry to zero */
+ u = 0;
+
+ /* Multiply and add in place */
+ for (iy = 0; iy < n->used; iy++) {
+ /* compute product and sum */
+ r = ((mp_word)mu) * ((mp_word)*tmpn++) +
+ ((mp_word) u) + ((mp_word) * tmpx);
+
+ /* get carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+
+ /* fix digit */
+ *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
+ }
+ /* At this point the ix'th digit of x should be zero */
+
+
+ /* propagate carries upwards as required*/
+ while (u) {
+ *tmpx += u;
+ u = *tmpx >> DIGIT_BIT;
+ *tmpx++ &= MP_MASK;
+ }
+ }
+ }
+
+ /* at this point the n.used'th least
+ * significant digits of x are all zero
+ * which means we can shift x to the
+ * right by n.used digits and the
+ * residue is unchanged.
+ */
+
+ /* x = x/b**n.used */
+ mp_clamp(x);
+ mp_rshd (x, n->used);
+
+ /* if x >= n then x = x - n */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ return s_mp_sub (x, n, x);
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_montgomery_setup.c b/libtommath/bn_mp_montgomery_setup.c
new file mode 100644
index 0000000..0dc800e
--- /dev/null
+++ b/libtommath/bn_mp_montgomery_setup.c
@@ -0,0 +1,59 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* setups the montgomery reduction stuff */
+int
+mp_montgomery_setup (mp_int * n, mp_digit * rho)
+{
+ mp_digit x, b;
+
+/* fast inversion mod 2**k
+ *
+ * Based on the fact that
+ *
+ * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
+ * => 2*X*A - X*X*A*A = 1
+ * => 2*(1) - (1) = 1
+ */
+ b = n->dp[0];
+
+ if ((b & 1) == 0) {
+ return MP_VAL;
+ }
+
+ x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
+ x *= 2 - b * x; /* here x*a==1 mod 2**8 */
+#if !defined(MP_8BIT)
+ x *= 2 - b * x; /* here x*a==1 mod 2**16 */
+#endif
+#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
+ x *= 2 - b * x; /* here x*a==1 mod 2**32 */
+#endif
+#ifdef MP_64BIT
+ x *= 2 - b * x; /* here x*a==1 mod 2**64 */
+#endif
+
+ /* rho = -1/m mod b */
+ *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/12/04 21:34:03 $ */
diff --git a/libtommath/bn_mp_mul.c b/libtommath/bn_mp_mul.c
new file mode 100644
index 0000000..f941a1a
--- /dev/null
+++ b/libtommath/bn_mp_mul.c
@@ -0,0 +1,66 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* high level multiplication (handles sign) */
+int mp_mul (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, neg;
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+
+ /* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
+ if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
+ res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
+ /* use Karatsuba? */
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ res = mp_karatsuba_mul (a, b, c);
+ } else
+#endif
+ {
+ /* can we use the fast multiplier?
+ *
+ * The fast multiplier can be used if the output will
+ * have less than MP_WARRAY digits and the number of
+ * digits won't affect carry propagation
+ */
+ int digs = a->used + b->used + 1;
+
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
+ if ((digs < MP_WARRAY) &&
+ MIN(a->used, b->used) <=
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ res = fast_s_mp_mul_digs (a, b, c, digs);
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
+
+ }
+ c->sign = (c->used > 0) ? neg : MP_ZPOS;
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_mul_2.c b/libtommath/bn_mp_mul_2.c
new file mode 100644
index 0000000..0d27a9d
--- /dev/null
+++ b/libtommath/bn_mp_mul_2.c
@@ -0,0 +1,82 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = a*2 */
+int mp_mul_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* grow to accomodate result */
+ if (b->alloc < a->used + 1) {
+ if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* alias for source */
+ tmpa = a->dp;
+
+ /* alias for dest */
+ tmpb = b->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < a->used; x++) {
+
+ /* get what will be the *next* carry bit from the
+ * MSB of the current digit
+ */
+ rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
+
+ /* now shift up this digit, add in the carry [from the previous] */
+ *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
+
+ /* copy the carry that would be from the source
+ * digit into the next iteration
+ */
+ r = rr;
+ }
+
+ /* new leading digit? */
+ if (r != 0) {
+ /* add a MSB which is always 1 at this point */
+ *tmpb = 1;
+ ++(b->used);
+ }
+
+ /* now zero any excess digits on the destination
+ * that we didn't write to
+ */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_mul_2d.c b/libtommath/bn_mp_mul_2d.c
new file mode 100644
index 0000000..d803bf4
--- /dev/null
+++ b/libtommath/bn_mp_mul_2d.c
@@ -0,0 +1,85 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift left by a certain bit count */
+int mp_mul_2d (mp_int * a, int b, mp_int * c)
+{
+ mp_digit d;
+ int res;
+
+ /* copy */
+ if (a != c) {
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
+ if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ d = (mp_digit) (b % DIGIT_BIT);
+ if (d != 0) {
+ register mp_digit *tmpc, shift, mask, r, rr;
+ register int x;
+
+ /* bitmask for carries */
+ mask = (((mp_digit)1) << d) - 1;
+
+ /* shift for msbs */
+ shift = DIGIT_BIT - d;
+
+ /* alias */
+ tmpc = c->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < c->used; x++) {
+ /* get the higher bits of the current word */
+ rr = (*tmpc >> shift) & mask;
+
+ /* shift the current word and OR in the carry */
+ *tmpc = ((*tmpc << d) | r) & MP_MASK;
+ ++tmpc;
+
+ /* set the carry to the carry bits of the current word */
+ r = rr;
+ }
+
+ /* set final carry */
+ if (r != 0) {
+ c->dp[(c->used)++] = r;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_mul_d.c b/libtommath/bn_mp_mul_d.c
new file mode 100644
index 0000000..a6324aa
--- /dev/null
+++ b/libtommath/bn_mp_mul_d.c
@@ -0,0 +1,79 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiply by a digit */
+int
+mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_digit u, *tmpa, *tmpc;
+ mp_word r;
+ int ix, res, olduse;
+
+ /* make sure c is big enough to hold a*b */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* get the original destinations used count */
+ olduse = c->used;
+
+ /* set the sign */
+ c->sign = a->sign;
+
+ /* alias for a->dp [source] */
+ tmpa = a->dp;
+
+ /* alias for c->dp [dest] */
+ tmpc = c->dp;
+
+ /* zero carry */
+ u = 0;
+
+ /* compute columns */
+ for (ix = 0; ix < a->used; ix++) {
+ /* compute product and carry sum for this term */
+ r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
+
+ /* mask off higher bits to get a single digit */
+ *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* send carry into next iteration */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+
+ /* store final carry [if any] and increment ix offset */
+ *tmpc++ = u;
+ ++ix;
+
+ /* now zero digits above the top */
+ while (ix++ < olduse) {
+ *tmpc++ = 0;
+ }
+
+ /* set used count */
+ c->used = a->used + 1;
+ mp_clamp(c);
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_mulmod.c b/libtommath/bn_mp_mulmod.c
new file mode 100644
index 0000000..46818b6
--- /dev/null
+++ b/libtommath/bn_mp_mulmod.c
@@ -0,0 +1,40 @@
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* d = a * b (mod c) */
+int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mulmod.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_n_root.c b/libtommath/bn_mp_n_root.c
new file mode 100644
index 0000000..c154016
--- /dev/null
+++ b/libtommath/bn_mp_n_root.c
@@ -0,0 +1,132 @@
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* find the n'th root of an integer
+ *
+ * Result found such that (c)**b <= a and (c+1)**b > a
+ *
+ * This algorithm uses Newton's approximation
+ * x[i+1] = x[i] - f(x[i])/f'(x[i])
+ * which will find the root in log(N) time where
+ * each step involves a fair bit. This is not meant to
+ * find huge roots [square and cube, etc].
+ */
+int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_int t1, t2, t3;
+ int res, neg;
+
+ /* input must be positive if b is even */
+ if ((b & 1) == 0 && a->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ if ((res = mp_init (&t1)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&t2)) != MP_OKAY) {
+ goto LBL_T1;
+ }
+
+ if ((res = mp_init (&t3)) != MP_OKAY) {
+ goto LBL_T2;
+ }
+
+ /* if a is negative fudge the sign but keep track */
+ neg = a->sign;
+ a->sign = MP_ZPOS;
+
+ /* t2 = 2 */
+ mp_set (&t2, 2);
+
+ do {
+ /* t1 = t2 */
+ if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+
+ /* t3 = t1**(b-1) */
+ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* numerator */
+ /* t2 = t1**b */
+ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t2 = t1**b - a */
+ if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* denominator */
+ /* t3 = t1**(b-1) * b */
+ if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t3 = (t1**b - a)/(b * t1**(b-1)) */
+ if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+ } while (mp_cmp (&t1, &t2) != MP_EQ);
+
+ /* result can be off by a few so check */
+ for (;;) {
+ if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ if (mp_cmp (&t2, a) == MP_GT) {
+ if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+ } else {
+ break;
+ }
+ }
+
+ /* reset the sign of a first */
+ a->sign = neg;
+
+ /* set the result */
+ mp_exch (&t1, c);
+
+ /* set the sign of the result */
+ c->sign = neg;
+
+ res = MP_OKAY;
+
+LBL_T3:mp_clear (&t3);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_n_root.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_neg.c b/libtommath/bn_mp_neg.c
new file mode 100644
index 0000000..0db9b40
--- /dev/null
+++ b/libtommath/bn_mp_neg.c
@@ -0,0 +1,40 @@
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = -a */
+int mp_neg (mp_int * a, mp_int * b)
+{
+ int res;
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (mp_iszero(b) != MP_YES) {
+ b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ } else {
+ b->sign = MP_ZPOS;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_neg.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_or.c b/libtommath/bn_mp_or.c
new file mode 100644
index 0000000..a9fc74a
--- /dev/null
+++ b/libtommath/bn_mp_or.c
@@ -0,0 +1,50 @@
+#include <tommath.h>
+#ifdef BN_MP_OR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* OR two ints together */
+int mp_or (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] |= x->dp[ix];
+ }
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_or.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_prime_fermat.c b/libtommath/bn_mp_prime_fermat.c
new file mode 100644
index 0000000..1869867
--- /dev/null
+++ b/libtommath/bn_mp_prime_fermat.c
@@ -0,0 +1,62 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* performs one Fermat test.
+ *
+ * If "a" were prime then b**a == b (mod a) since the order of
+ * the multiplicative sub-group would be phi(a) = a-1. That means
+ * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
+ *
+ * Sets result to 1 if the congruence holds, or zero otherwise.
+ */
+int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
+{
+ mp_int t;
+ int err;
+
+ /* default to composite */
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* init t */
+ if ((err = mp_init (&t)) != MP_OKAY) {
+ return err;
+ }
+
+ /* compute t = b**a mod a */
+ if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
+ goto LBL_T;
+ }
+
+ /* is it equal to b? */
+ if (mp_cmp (&t, b) == MP_EQ) {
+ *result = MP_YES;
+ }
+
+ err = MP_OKAY;
+LBL_T:mp_clear (&t);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_fermat.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_prime_is_divisible.c b/libtommath/bn_mp_prime_is_divisible.c
new file mode 100644
index 0000000..d065451
--- /dev/null
+++ b/libtommath/bn_mp_prime_is_divisible.c
@@ -0,0 +1,50 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if an integers is divisible by one
+ * of the first PRIME_SIZE primes or not
+ *
+ * sets result to 0 if not, 1 if yes
+ */
+int mp_prime_is_divisible (mp_int * a, int *result)
+{
+ int err, ix;
+ mp_digit res;
+
+ /* default to not */
+ *result = MP_NO;
+
+ for (ix = 0; ix < PRIME_SIZE; ix++) {
+ /* what is a mod LBL_prime_tab[ix] */
+ if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
+ return err;
+ }
+
+ /* is the residue zero? */
+ if (res == 0) {
+ *result = MP_YES;
+ return MP_OKAY;
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_divisible.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_prime_is_prime.c b/libtommath/bn_mp_prime_is_prime.c
new file mode 100644
index 0000000..d93d46a
--- /dev/null
+++ b/libtommath/bn_mp_prime_is_prime.c
@@ -0,0 +1,83 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* performs a variable number of rounds of Miller-Rabin
+ *
+ * Probability of error after t rounds is no more than
+
+ *
+ * Sets result to 1 if probably prime, 0 otherwise
+ */
+int mp_prime_is_prime (mp_int * a, int t, int *result)
+{
+ mp_int b;
+ int ix, err, res;
+
+ /* default to no */
+ *result = MP_NO;
+
+ /* valid value of t? */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* is the input equal to one of the primes in the table? */
+ for (ix = 0; ix < PRIME_SIZE; ix++) {
+ if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
+ *result = 1;
+ return MP_OKAY;
+ }
+ }
+
+ /* first perform trial division */
+ if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
+ return err;
+ }
+
+ /* return if it was trivially divisible */
+ if (res == MP_YES) {
+ return MP_OKAY;
+ }
+
+ /* now perform the miller-rabin rounds */
+ if ((err = mp_init (&b)) != MP_OKAY) {
+ return err;
+ }
+
+ for (ix = 0; ix < t; ix++) {
+ /* set the prime */
+ mp_set (&b, ltm_prime_tab[ix]);
+
+ if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
+ goto LBL_B;
+ }
+
+ if (res == MP_NO) {
+ goto LBL_B;
+ }
+ }
+
+ /* passed the test */
+ *result = MP_YES;
+LBL_B:mp_clear (&b);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_prime.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_prime_miller_rabin.c b/libtommath/bn_mp_prime_miller_rabin.c
new file mode 100644
index 0000000..9bd6ba1
--- /dev/null
+++ b/libtommath/bn_mp_prime_miller_rabin.c
@@ -0,0 +1,103 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Miller-Rabin test of "a" to the base of "b" as described in
+ * HAC pp. 139 Algorithm 4.24
+ *
+ * Sets result to 0 if definitely composite or 1 if probably prime.
+ * Randomly the chance of error is no more than 1/4 and often
+ * very much lower.
+ */
+int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
+{
+ mp_int n1, y, r;
+ int s, j, err;
+
+ /* default */
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* get n1 = a - 1 */
+ if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
+ goto LBL_N1;
+ }
+
+ /* set 2**s * r = n1 */
+ if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
+ goto LBL_N1;
+ }
+
+ /* count the number of least significant bits
+ * which are zero
+ */
+ s = mp_cnt_lsb(&r);
+
+ /* now divide n - 1 by 2**s */
+ if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
+ goto LBL_R;
+ }
+
+ /* compute y = b**r mod a */
+ if ((err = mp_init (&y)) != MP_OKAY) {
+ goto LBL_R;
+ }
+ if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if y != 1 and y != n1 do */
+ if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
+ j = 1;
+ /* while j <= s-1 and y != n1 */
+ while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
+ if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if y == 1 then composite */
+ if (mp_cmp_d (&y, 1) == MP_EQ) {
+ goto LBL_Y;
+ }
+
+ ++j;
+ }
+
+ /* if y != n1 then composite */
+ if (mp_cmp (&y, &n1) != MP_EQ) {
+ goto LBL_Y;
+ }
+ }
+
+ /* probably prime now */
+ *result = MP_YES;
+LBL_Y:mp_clear (&y);
+LBL_R:mp_clear (&r);
+LBL_N1:mp_clear (&n1);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_miller_rabin.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_prime_next_prime.c b/libtommath/bn_mp_prime_next_prime.c
new file mode 100644
index 0000000..a2da345
--- /dev/null
+++ b/libtommath/bn_mp_prime_next_prime.c
@@ -0,0 +1,170 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* finds the next prime after the number "a" using "t" trials
+ * of Miller-Rabin.
+ *
+ * bbs_style = 1 means the prime must be congruent to 3 mod 4
+ */
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
+{
+ int err, res, x, y;
+ mp_digit res_tab[PRIME_SIZE], step, kstep;
+ mp_int b;
+
+ /* ensure t is valid */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* force positive */
+ a->sign = MP_ZPOS;
+
+ /* simple algo if a is less than the largest prime in the table */
+ if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
+ /* find which prime it is bigger than */
+ for (x = PRIME_SIZE - 2; x >= 0; x--) {
+ if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
+ if (bbs_style == 1) {
+ /* ok we found a prime smaller or
+ * equal [so the next is larger]
+ *
+ * however, the prime must be
+ * congruent to 3 mod 4
+ */
+ if ((ltm_prime_tab[x + 1] & 3) != 3) {
+ /* scan upwards for a prime congruent to 3 mod 4 */
+ for (y = x + 1; y < PRIME_SIZE; y++) {
+ if ((ltm_prime_tab[y] & 3) == 3) {
+ mp_set(a, ltm_prime_tab[y]);
+ return MP_OKAY;
+ }
+ }
+ }
+ } else {
+ mp_set(a, ltm_prime_tab[x + 1]);
+ return MP_OKAY;
+ }
+ }
+ }
+ /* at this point a maybe 1 */
+ if (mp_cmp_d(a, 1) == MP_EQ) {
+ mp_set(a, 2);
+ return MP_OKAY;
+ }
+ /* fall through to the sieve */
+ }
+
+ /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
+ if (bbs_style == 1) {
+ kstep = 4;
+ } else {
+ kstep = 2;
+ }
+
+ /* at this point we will use a combination of a sieve and Miller-Rabin */
+
+ if (bbs_style == 1) {
+ /* if a mod 4 != 3 subtract the correct value to make it so */
+ if ((a->dp[0] & 3) != 3) {
+ if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
+ }
+ } else {
+ if (mp_iseven(a) == 1) {
+ /* force odd */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
+ return err;
+ }
+ }
+ }
+
+ /* generate the restable */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
+ return err;
+ }
+ }
+
+ /* init temp used for Miller-Rabin Testing */
+ if ((err = mp_init(&b)) != MP_OKAY) {
+ return err;
+ }
+
+ for (;;) {
+ /* skip to the next non-trivially divisible candidate */
+ step = 0;
+ do {
+ /* y == 1 if any residue was zero [e.g. cannot be prime] */
+ y = 0;
+
+ /* increase step to next candidate */
+ step += kstep;
+
+ /* compute the new residue without using division */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ /* add the step to each residue */
+ res_tab[x] += kstep;
+
+ /* subtract the modulus [instead of using division] */
+ if (res_tab[x] >= ltm_prime_tab[x]) {
+ res_tab[x] -= ltm_prime_tab[x];
+ }
+
+ /* set flag if zero */
+ if (res_tab[x] == 0) {
+ y = 1;
+ }
+ }
+ } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
+
+ /* add the step */
+ if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* if didn't pass sieve and step == MAX then skip test */
+ if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
+ continue;
+ }
+
+ /* is this prime? */
+ for (x = 0; x < t; x++) {
+ mp_set(&b, ltm_prime_tab[t]);
+ if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if (res == MP_NO) {
+ break;
+ }
+ }
+
+ if (res == MP_YES) {
+ break;
+ }
+ }
+
+ err = MP_OKAY;
+LBL_ERR:
+ mp_clear(&b);
+ return err;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_next_prime.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_prime_rabin_miller_trials.c b/libtommath/bn_mp_prime_rabin_miller_trials.c
new file mode 100644
index 0000000..140b254
--- /dev/null
+++ b/libtommath/bn_mp_prime_rabin_miller_trials.c
@@ -0,0 +1,52 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+
+static const struct {
+ int k, t;
+} sizes[] = {
+{ 128, 28 },
+{ 256, 16 },
+{ 384, 10 },
+{ 512, 7 },
+{ 640, 6 },
+{ 768, 5 },
+{ 896, 4 },
+{ 1024, 4 }
+};
+
+/* returns # of RM trials required for a given bit size */
+int mp_prime_rabin_miller_trials(int size)
+{
+ int x;
+
+ for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
+ if (sizes[x].k == size) {
+ return sizes[x].t;
+ } else if (sizes[x].k > size) {
+ return (x == 0) ? sizes[0].t : sizes[x - 1].t;
+ }
+ }
+ return sizes[x-1].t + 1;
+}
+
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_rabin_miller_trials.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_prime_random_ex.c b/libtommath/bn_mp_prime_random_ex.c
new file mode 100644
index 0000000..cde7a38
--- /dev/null
+++ b/libtommath/bn_mp_prime_random_ex.c
@@ -0,0 +1,125 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* makes a truly random prime of a given size (bits),
+ *
+ * Flags are as follows:
+ *
+ * LTM_PRIME_BBS - make prime congruent to 3 mod 4
+ * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
+ * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
+ * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
+ *
+ * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
+ * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
+ * so it can be NULL
+ *
+ */
+
+/* This is possibly the mother of all prime generation functions, muahahahahaha! */
+int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
+{
+ unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
+ int res, err, bsize, maskOR_msb_offset;
+
+ /* sanity check the input */
+ if (size <= 1 || t <= 0) {
+ return MP_VAL;
+ }
+
+ /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
+ if (flags & LTM_PRIME_SAFE) {
+ flags |= LTM_PRIME_BBS;
+ }
+
+ /* calc the byte size */
+ bsize = (size>>3) + ((size&7)?1:0);
+
+ /* we need a buffer of bsize bytes */
+ tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
+ if (tmp == NULL) {
+ return MP_MEM;
+ }
+
+ /* calc the maskAND value for the MSbyte*/
+ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));
+
+ /* calc the maskOR_msb */
+ maskOR_msb = 0;
+ maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
+ if (flags & LTM_PRIME_2MSB_ON) {
+ maskOR_msb |= 0x80 >> ((9 - size) & 7);
+ }
+
+ /* get the maskOR_lsb */
+ maskOR_lsb = 1;
+ if (flags & LTM_PRIME_BBS) {
+ maskOR_lsb |= 3;
+ }
+
+ do {
+ /* read the bytes */
+ if (cb(tmp, bsize, dat) != bsize) {
+ err = MP_VAL;
+ goto error;
+ }
+
+ /* work over the MSbyte */
+ tmp[0] &= maskAND;
+ tmp[0] |= 1 << ((size - 1) & 7);
+
+ /* mix in the maskORs */
+ tmp[maskOR_msb_offset] |= maskOR_msb;
+ tmp[bsize-1] |= maskOR_lsb;
+
+ /* read it in */
+ if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* see if (a-1)/2 is prime */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ }
+ } while (res == MP_NO);
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* restore a to the original value */
+ if ((err = mp_mul_2(a, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { goto error; }
+ }
+
+ err = MP_OKAY;
+error:
+ XFREE(tmp);
+ return err;
+}
+
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_random_ex.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_radix_size.c b/libtommath/bn_mp_radix_size.c
new file mode 100644
index 0000000..c9e8822
--- /dev/null
+++ b/libtommath/bn_mp_radix_size.c
@@ -0,0 +1,78 @@
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* returns size of ASCII reprensentation */
+int mp_radix_size (mp_int * a, int radix, int *size)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+
+ *size = 0;
+
+ /* special case for binary */
+ if (radix == 2) {
+ *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
+ return MP_OKAY;
+ }
+
+ /* make sure the radix is in range */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ if (mp_iszero(a) == MP_YES) {
+ *size = 2;
+ return MP_OKAY;
+ }
+
+ /* digs is the digit count */
+ digs = 0;
+
+ /* if it's negative add one for the sign */
+ if (a->sign == MP_NEG) {
+ ++digs;
+ }
+
+ /* init a copy of the input */
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* force temp to positive */
+ t.sign = MP_ZPOS;
+
+ /* fetch out all of the digits */
+ while (mp_iszero (&t) == MP_NO) {
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ ++digs;
+ }
+ mp_clear (&t);
+
+ /* return digs + 1, the 1 is for the NULL byte that would be required. */
+ *size = digs + 1;
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_radix_size.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_radix_smap.c b/libtommath/bn_mp_radix_smap.c
new file mode 100644
index 0000000..58c3a5e
--- /dev/null
+++ b/libtommath/bn_mp_radix_smap.c
@@ -0,0 +1,24 @@
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* chars used in radix conversions */
+const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_radix_smap.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_rand.c b/libtommath/bn_mp_rand.c
new file mode 100644
index 0000000..6c8f3b3
--- /dev/null
+++ b/libtommath/bn_mp_rand.c
@@ -0,0 +1,55 @@
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* makes a pseudo-random int of a given size */
+int
+mp_rand (mp_int * a, int digits)
+{
+ int res;
+ mp_digit d;
+
+ mp_zero (a);
+ if (digits <= 0) {
+ return MP_OKAY;
+ }
+
+ /* first place a random non-zero digit */
+ do {
+ d = ((mp_digit) abs (rand ())) & MP_MASK;
+ } while (d == 0);
+
+ if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
+ return res;
+ }
+
+ while (--digits > 0) {
+ if ((res = mp_lshd (a, 1)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_rand.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_read_radix.c b/libtommath/bn_mp_read_radix.c
new file mode 100644
index 0000000..d2119c1
--- /dev/null
+++ b/libtommath/bn_mp_read_radix.c
@@ -0,0 +1,85 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* read a string [ASCII] in a given radix */
+int mp_read_radix (mp_int * a, const char *str, int radix)
+{
+ int y, res, neg;
+ char ch;
+
+ /* zero the digit bignum */
+ mp_zero(a);
+
+ /* make sure the radix is ok */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* if the leading digit is a
+ * minus set the sign to negative.
+ */
+ if (*str == '-') {
+ ++str;
+ neg = MP_NEG;
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ /* set the integer to the default of zero */
+ mp_zero (a);
+
+ /* process each digit of the string */
+ while (*str) {
+ /* if the radix < 36 the conversion is case insensitive
+ * this allows numbers like 1AB and 1ab to represent the same value
+ * [e.g. in hex]
+ */
+ ch = (char) ((radix < 36) ? toupper (*str) : *str);
+ for (y = 0; y < 64; y++) {
+ if (ch == mp_s_rmap[y]) {
+ break;
+ }
+ }
+
+ /* if the char was found in the map
+ * and is less than the given radix add it
+ * to the number, otherwise exit the loop.
+ */
+ if (y < radix) {
+ if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ break;
+ }
+ ++str;
+ }
+
+ /* set the sign only if a != 0 */
+ if (mp_iszero(a) != 1) {
+ a->sign = neg;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_read_radix.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_read_signed_bin.c b/libtommath/bn_mp_read_signed_bin.c
new file mode 100644
index 0000000..e3df3c3
--- /dev/null
+++ b/libtommath/bn_mp_read_signed_bin.c
@@ -0,0 +1,41 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* read signed bin, big endian, first byte is 0==positive or 1==negative */
+int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
+{
+ int res;
+
+ /* read magnitude */
+ if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* first byte is 0 for positive, non-zero for negative */
+ if (b[0] == 0) {
+ a->sign = MP_ZPOS;
+ } else {
+ a->sign = MP_NEG;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_read_signed_bin.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_read_unsigned_bin.c b/libtommath/bn_mp_read_unsigned_bin.c
new file mode 100644
index 0000000..0c471ed
--- /dev/null
+++ b/libtommath/bn_mp_read_unsigned_bin.c
@@ -0,0 +1,55 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reads a unsigned char array, assumes the msb is stored first [big endian] */
+int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
+{
+ int res;
+
+ /* make sure there are at least two digits */
+ if (a->alloc < 2) {
+ if ((res = mp_grow(a, 2)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero the int */
+ mp_zero (a);
+
+ /* read the bytes in */
+ while (c-- > 0) {
+ if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
+ return res;
+ }
+
+#ifndef MP_8BIT
+ a->dp[0] |= *b++;
+ a->used += 1;
+#else
+ a->dp[0] = (*b & MP_MASK);
+ a->dp[1] |= ((*b++ >> 7U) & 1);
+ a->used += 2;
+#endif
+ }
+ mp_clamp (a);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_read_unsigned_bin.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce.c b/libtommath/bn_mp_reduce.c
new file mode 100644
index 0000000..3f7284a
--- /dev/null
+++ b/libtommath/bn_mp_reduce.c
@@ -0,0 +1,100 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduces x mod m, assumes 0 < x < m**2, mu is
+ * precomputed via mp_reduce_setup.
+ * From HAC pp.604 Algorithm 14.42
+ */
+int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
+{
+ mp_int q;
+ int res, um = m->used;
+
+ /* q = x */
+ if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
+ return res;
+ }
+
+ /* q1 = x / b**(k-1) */
+ mp_rshd (&q, um - 1);
+
+ /* according to HAC this optimization is ok */
+ if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
+ if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ } else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
+ if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
+ }
+
+ /* q3 = q2 / b**(k+1) */
+ mp_rshd (&q, um + 1);
+
+ /* x = x mod b**(k+1), quick (no division) */
+ if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* q = q * m mod b**(k+1), quick (no division) */
+ if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* x = x - q */
+ if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* If x < 0, add b**(k+1) to it */
+ if (mp_cmp_d (x, 0) == MP_LT) {
+ mp_set (&q, 1);
+ if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
+ goto CLEANUP;
+ if ((res = mp_add (x, &q, x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ /* Back off if it's too big */
+ while (mp_cmp (x, m) != MP_LT) {
+ if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ }
+
+CLEANUP:
+ mp_clear (&q);
+
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce_2k.c b/libtommath/bn_mp_reduce_2k.c
new file mode 100644
index 0000000..5810696
--- /dev/null
+++ b/libtommath/bn_mp_reduce_2k.c
@@ -0,0 +1,61 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d */
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (d != 1) {
+ /* q = q * d */
+ if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce_2k_l.c b/libtommath/bn_mp_reduce_2k_l.c
new file mode 100644
index 0000000..53b435f
--- /dev/null
+++ b/libtommath/bn_mp_reduce_2k_l.c
@@ -0,0 +1,62 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d
+ This differs from reduce_2k since "d" can be larger
+ than a single digit.
+*/
+int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* q = q * d */
+ if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_l.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce_2k_setup.c b/libtommath/bn_mp_reduce_2k_setup.c
new file mode 100644
index 0000000..07de0ec
--- /dev/null
+++ b/libtommath/bn_mp_reduce_2k_setup.c
@@ -0,0 +1,47 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
+{
+ int res, p;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(a);
+ if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ *d = tmp.dp[0];
+ mp_clear(&tmp);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce_2k_setup_l.c b/libtommath/bn_mp_reduce_2k_setup_l.c
new file mode 100644
index 0000000..05f0385
--- /dev/null
+++ b/libtommath/bn_mp_reduce_2k_setup_l.c
@@ -0,0 +1,44 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
+{
+ int res;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear(&tmp);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce_is_2k.c b/libtommath/bn_mp_reduce_is_2k.c
new file mode 100644
index 0000000..0897b0a
--- /dev/null
+++ b/libtommath/bn_mp_reduce_is_2k.c
@@ -0,0 +1,52 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if mp_reduce_2k can be used */
+int mp_reduce_is_2k(mp_int *a)
+{
+ int ix, iy, iw;
+ mp_digit iz;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ iy = mp_count_bits(a);
+ iz = 1;
+ iw = 1;
+
+ /* Test every bit from the second digit up, must be 1 */
+ for (ix = DIGIT_BIT; ix < iy; ix++) {
+ if ((a->dp[iw] & iz) == 0) {
+ return MP_NO;
+ }
+ iz <<= 1;
+ if (iz > (mp_digit)MP_MASK) {
+ ++iw;
+ iz = 1;
+ }
+ }
+ }
+ return MP_YES;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce_is_2k_l.c b/libtommath/bn_mp_reduce_is_2k_l.c
new file mode 100644
index 0000000..c4b42c9
--- /dev/null
+++ b/libtommath/bn_mp_reduce_is_2k_l.c
@@ -0,0 +1,44 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if reduce_2k_l can be used */
+int mp_reduce_is_2k_l(mp_int *a)
+{
+ int ix, iy;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ /* if more than half of the digits are -1 we're sold */
+ for (iy = ix = 0; ix < a->used; ix++) {
+ if (a->dp[ix] == MP_MASK) {
+ ++iy;
+ }
+ }
+ return (iy >= (a->used/2)) ? MP_YES : MP_NO;
+
+ }
+ return MP_NO;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k_l.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_reduce_setup.c b/libtommath/bn_mp_reduce_setup.c
new file mode 100644
index 0000000..5085af0
--- /dev/null
+++ b/libtommath/bn_mp_reduce_setup.c
@@ -0,0 +1,34 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* pre-calculate the value required for Barrett reduction
+ * For a given modulus "b" it calulates the value required in "a"
+ */
+int mp_reduce_setup (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ return mp_div (a, b, a, NULL);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_setup.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_rshd.c b/libtommath/bn_mp_rshd.c
new file mode 100644
index 0000000..534bd4d
--- /dev/null
+++ b/libtommath/bn_mp_rshd.c
@@ -0,0 +1,72 @@
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift right a certain amount of digits */
+void mp_rshd (mp_int * a, int b)
+{
+ int x;
+
+ /* if b <= 0 then ignore it */
+ if (b <= 0) {
+ return;
+ }
+
+ /* if b > used then simply zero it and return */
+ if (a->used <= b) {
+ mp_zero (a);
+ return;
+ }
+
+ {
+ register mp_digit *bottom, *top;
+
+ /* shift the digits down */
+
+ /* bottom */
+ bottom = a->dp;
+
+ /* top [offset into digits] */
+ top = a->dp + b;
+
+ /* this is implemented as a sliding window where
+ * the window is b-digits long and digits from
+ * the top of the window are copied to the bottom
+ *
+ * e.g.
+
+ b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
+ /\ | ---->
+ \-------------------/ ---->
+ */
+ for (x = 0; x < (a->used - b); x++) {
+ *bottom++ = *top++;
+ }
+
+ /* zero the top digits */
+ for (; x < a->used; x++) {
+ *bottom++ = 0;
+ }
+ }
+
+ /* remove excess digits */
+ a->used -= b;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_rshd.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_set.c b/libtommath/bn_mp_set.c
new file mode 100644
index 0000000..a1ebadb
--- /dev/null
+++ b/libtommath/bn_mp_set.c
@@ -0,0 +1,29 @@
+#include <tommath.h>
+#ifdef BN_MP_SET_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* set to a digit */
+void mp_set (mp_int * a, mp_digit b)
+{
+ mp_zero (a);
+ a->dp[0] = b & MP_MASK;
+ a->used = (a->dp[0] != 0) ? 1 : 0;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_set.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_set_int.c b/libtommath/bn_mp_set_int.c
new file mode 100644
index 0000000..35e844f
--- /dev/null
+++ b/libtommath/bn_mp_set_int.c
@@ -0,0 +1,48 @@
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* set a 32-bit const */
+int mp_set_int (mp_int * a, unsigned long b)
+{
+ int x, res;
+
+ mp_zero (a);
+
+ /* set four bits at a time */
+ for (x = 0; x < 8; x++) {
+ /* shift the number up four bits */
+ if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* OR in the top four bits of the source */
+ a->dp[0] |= (b >> 28) & 15;
+
+ /* shift the source up to the next four bits */
+ b <<= 4;
+
+ /* ensure that digits are not clamped off */
+ a->used += 1;
+ }
+ mp_clamp (a);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_set_int.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_shrink.c b/libtommath/bn_mp_shrink.c
new file mode 100644
index 0000000..e676068
--- /dev/null
+++ b/libtommath/bn_mp_shrink.c
@@ -0,0 +1,35 @@
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shrink a bignum */
+int mp_shrink (mp_int * a)
+{
+ mp_digit *tmp;
+ if (a->alloc != a->used && a->used > 0) {
+ if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * a->used)) == NULL) {
+ return MP_MEM;
+ }
+ a->dp = tmp;
+ a->alloc = a->used;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_shrink.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_signed_bin_size.c b/libtommath/bn_mp_signed_bin_size.c
new file mode 100644
index 0000000..8df0b78
--- /dev/null
+++ b/libtommath/bn_mp_signed_bin_size.c
@@ -0,0 +1,27 @@
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* get the size for an signed equivalent */
+int mp_signed_bin_size (mp_int * a)
+{
+ return 1 + mp_unsigned_bin_size (a);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_signed_bin_size.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_sqr.c b/libtommath/bn_mp_sqr.c
new file mode 100644
index 0000000..bff8a7d
--- /dev/null
+++ b/libtommath/bn_mp_sqr.c
@@ -0,0 +1,58 @@
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes b = a*a */
+int
+mp_sqr (mp_int * a, mp_int * b)
+{
+ int res;
+
+#ifdef BN_MP_TOOM_SQR_C
+ /* use Toom-Cook? */
+ if (a->used >= TOOM_SQR_CUTOFF) {
+ res = mp_toom_sqr(a, b);
+ /* Karatsuba? */
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ res = mp_karatsuba_sqr (a, b);
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
+ /* can we use the fast comba multiplier? */
+ if ((a->used * 2 + 1) < MP_WARRAY &&
+ a->used <
+ (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
+ res = fast_s_mp_sqr (a, b);
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
+ res = s_mp_sqr (a, b);
+#else
+ res = MP_VAL;
+#endif
+ }
+ b->sign = MP_ZPOS;
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_sqrmod.c b/libtommath/bn_mp_sqrmod.c
new file mode 100644
index 0000000..38cbc92
--- /dev/null
+++ b/libtommath/bn_mp_sqrmod.c
@@ -0,0 +1,41 @@
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* c = a * a (mod b) */
+int
+mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_sqr (a, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, b, c);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sqrmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_sqrt.c b/libtommath/bn_mp_sqrt.c
new file mode 100644
index 0000000..4449625
--- /dev/null
+++ b/libtommath/bn_mp_sqrt.c
@@ -0,0 +1,81 @@
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* this function is less generic than mp_n_root, simpler and faster */
+int mp_sqrt(mp_int *arg, mp_int *ret)
+{
+ int res;
+ mp_int t1,t2;
+
+ /* must be positive */
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* easy out */
+ if (mp_iszero(arg) == MP_YES) {
+ mp_zero(ret);
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init(&t2)) != MP_OKAY) {
+ goto E2;
+ }
+
+ /* First approx. (not very bad for large arg) */
+ mp_rshd (&t1,t1.used/2);
+
+ /* t1 > 0 */
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* And now t1 > sqrt(arg) */
+ do {
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* t1 >= sqrt(arg) >= t2 at this point */
+ } while (mp_cmp_mag(&t1,&t2) == MP_GT);
+
+ mp_exch(&t1,ret);
+
+E1: mp_clear(&t2);
+E2: mp_clear(&t1);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sqrt.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_sub.c b/libtommath/bn_mp_sub.c
new file mode 100644
index 0000000..a69d032
--- /dev/null
+++ b/libtommath/bn_mp_sub.c
@@ -0,0 +1,59 @@
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* high level subtraction (handles signs) */
+int
+mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ sa = a->sign;
+ sb = b->sign;
+
+ if (sa != sb) {
+ /* subtract a negative from a positive, OR */
+ /* subtract a positive from a negative. */
+ /* In either case, ADD their magnitudes, */
+ /* and use the sign of the first number. */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* subtract a positive from a positive, OR */
+ /* subtract a negative from a negative. */
+ /* First, take the difference between their */
+ /* magnitudes, then... */
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ /* Copy the sign from the first */
+ c->sign = sa;
+ /* The first has a larger or equal magnitude */
+ res = s_mp_sub (a, b, c);
+ } else {
+ /* The result has the *opposite* sign from */
+ /* the first number. */
+ c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ /* The second has a larger magnitude */
+ res = s_mp_sub (b, a, c);
+ }
+ }
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sub.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_sub_d.c b/libtommath/bn_mp_sub_d.c
new file mode 100644
index 0000000..ee77a5a
--- /dev/null
+++ b/libtommath/bn_mp_sub_d.c
@@ -0,0 +1,93 @@
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* single digit subtraction */
+int
+mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_digit *tmpa, *tmpc, mu;
+ int res, ix, oldused;
+
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* if a is negative just do an unsigned
+ * addition [with fudged signs]
+ */
+ if (a->sign == MP_NEG) {
+ a->sign = MP_ZPOS;
+ res = mp_add_d(a, b, c);
+ a->sign = c->sign = MP_NEG;
+
+ /* clamp */
+ mp_clamp(c);
+
+ return res;
+ }
+
+ /* setup regs */
+ oldused = c->used;
+ tmpa = a->dp;
+ tmpc = c->dp;
+
+ /* if a <= b simply fix the single digit */
+ if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
+ if (a->used == 1) {
+ *tmpc++ = b - *tmpa;
+ } else {
+ *tmpc++ = b;
+ }
+ ix = 1;
+
+ /* negative/1digit */
+ c->sign = MP_NEG;
+ c->used = 1;
+ } else {
+ /* positive/size */
+ c->sign = MP_ZPOS;
+ c->used = a->used;
+
+ /* subtract first digit */
+ *tmpc = *tmpa++ - b;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+
+ /* handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ - mu;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+ }
+ }
+
+ /* zero excess digits */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sub_d.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_submod.c b/libtommath/bn_mp_submod.c
new file mode 100644
index 0000000..bd24f25
--- /dev/null
+++ b/libtommath/bn_mp_submod.c
@@ -0,0 +1,42 @@
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* d = a - b (mod c) */
+int
+mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_submod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_to_signed_bin.c b/libtommath/bn_mp_to_signed_bin.c
new file mode 100644
index 0000000..9125d07
--- /dev/null
+++ b/libtommath/bn_mp_to_signed_bin.c
@@ -0,0 +1,33 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin (mp_int * a, unsigned char *b)
+{
+ int res;
+
+ if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
+ return res;
+ }
+ b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_to_signed_bin_n.c b/libtommath/bn_mp_to_signed_bin_n.c
new file mode 100644
index 0000000..4e9d217
--- /dev/null
+++ b/libtommath/bn_mp_to_signed_bin_n.c
@@ -0,0 +1,31 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+ if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_signed_bin_size(a);
+ return mp_to_signed_bin(a, b);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin_n.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_to_unsigned_bin.c b/libtommath/bn_mp_to_unsigned_bin.c
new file mode 100644
index 0000000..b25935d
--- /dev/null
+++ b/libtommath/bn_mp_to_unsigned_bin.c
@@ -0,0 +1,48 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
+{
+ int x, res;
+ mp_int t;
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ x = 0;
+ while (mp_iszero (&t) == 0) {
+#ifndef MP_8BIT
+ b[x++] = (unsigned char) (t.dp[0] & 255);
+#else
+ b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
+#endif
+ if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+ bn_reverse (b, x);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_to_unsigned_bin_n.c b/libtommath/bn_mp_to_unsigned_bin_n.c
new file mode 100644
index 0000000..4abf4e1
--- /dev/null
+++ b/libtommath/bn_mp_to_unsigned_bin_n.c
@@ -0,0 +1,31 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+ if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_unsigned_bin_size(a);
+ return mp_to_unsigned_bin(a, b);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin_n.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_toom_mul.c b/libtommath/bn_mp_toom_mul.c
new file mode 100644
index 0000000..fa29078
--- /dev/null
+++ b/libtommath/bn_mp_toom_mul.c
@@ -0,0 +1,284 @@
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower
+ * asymptotic running time of O(N**1.464). This algorithm is
+ * only particularly useful on VERY large inputs
+ * (we're talking 1000s of digits here...).
+*/
+int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
+ int res, B;
+
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* B */
+ B = MIN(a->used, b->used) / 3;
+
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* b = b2 * B**2 + b1 * B + b0 */
+ if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(b, &b1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b1, B);
+ mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+
+ if ((res = mp_copy(b, &b2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b2, B*2);
+
+ /* w0 = a0*b0 */
+ if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * b2 */
+ if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+
+
+ /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* now solve the matrix
+
+ 0 0 0 0 1
+ 1 2 4 8 16
+ 1 1 1 1 1
+ 16 8 4 2 1
+ 1 0 0 0 0
+
+ using 12 subtractions, 4 shifts,
+ 2 small divisions and 1 small multiplication
+ */
+
+ /* r1 - r4 */
+ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r0 */
+ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/2 */
+ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/2 */
+ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r2 - r0 - r4 */
+ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - 8r0 */
+ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - 8r4 */
+ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* 3r2 - r1 - r3 */
+ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/3 */
+ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/3 */
+ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* at this point shift W[n] by B*n */
+ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_toom_sqr.c b/libtommath/bn_mp_toom_sqr.c
new file mode 100644
index 0000000..093181a
--- /dev/null
+++ b/libtommath/bn_mp_toom_sqr.c
@@ -0,0 +1,226 @@
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* squaring using Toom-Cook 3-way algorithm */
+int
+mp_toom_sqr(mp_int *a, mp_int *b)
+{
+ mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
+ int res, B;
+
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* B */
+ B = a->used / 3;
+
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* w0 = a0*a0 */
+ if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * a2 */
+ if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))**2 */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))**2 */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+
+
+ /* w2 = (a2 + a1 + a0)**2 */
+ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* now solve the matrix
+
+ 0 0 0 0 1
+ 1 2 4 8 16
+ 1 1 1 1 1
+ 16 8 4 2 1
+ 1 0 0 0 0
+
+ using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
+ */
+
+ /* r1 - r4 */
+ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r0 */
+ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/2 */
+ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/2 */
+ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r2 - r0 - r4 */
+ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - 8r0 */
+ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - 8r4 */
+ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* 3r2 - r1 - r3 */
+ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/3 */
+ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/3 */
+ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* at this point shift W[n] by B*n */
+ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toom_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_toradix.c b/libtommath/bn_mp_toradix.c
new file mode 100644
index 0000000..c500832
--- /dev/null
+++ b/libtommath/bn_mp_toradix.c
@@ -0,0 +1,75 @@
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* stores a bignum as a ASCII string in a given radix (2..64) */
+int mp_toradix (mp_int * a, char *str, int radix)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+ char *_s = str;
+
+ /* check range of the radix */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* quick out if its zero */
+ if (mp_iszero(a) == 1) {
+ *str++ = '0';
+ *str = '\0';
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* if it is negative output a - */
+ if (t.sign == MP_NEG) {
+ ++_s;
+ *str++ = '-';
+ t.sign = MP_ZPOS;
+ }
+
+ digs = 0;
+ while (mp_iszero (&t) == 0) {
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ *str++ = mp_s_rmap[d];
+ ++digs;
+ }
+
+ /* reverse the digits of the string. In this case _s points
+ * to the first digit [exluding the sign] of the number]
+ */
+ bn_reverse ((unsigned char *)_s, digs);
+
+ /* append a NULL so the string is properly terminated */
+ *str = '\0';
+
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toradix.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_toradix_n.c b/libtommath/bn_mp_toradix_n.c
new file mode 100644
index 0000000..7c0f3bc
--- /dev/null
+++ b/libtommath/bn_mp_toradix_n.c
@@ -0,0 +1,88 @@
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* stores a bignum as a ASCII string in a given radix (2..64)
+ *
+ * Stores upto maxlen-1 chars and always a NULL byte
+ */
+int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+ char *_s = str;
+
+ /* check range of the maxlen, radix */
+ if (maxlen < 2 || radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* quick out if its zero */
+ if (mp_iszero(a) == MP_YES) {
+ *str++ = '0';
+ *str = '\0';
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* if it is negative output a - */
+ if (t.sign == MP_NEG) {
+ /* we have to reverse our digits later... but not the - sign!! */
+ ++_s;
+
+ /* store the flag and mark the number as positive */
+ *str++ = '-';
+ t.sign = MP_ZPOS;
+
+ /* subtract a char */
+ --maxlen;
+ }
+
+ digs = 0;
+ while (mp_iszero (&t) == 0) {
+ if (--maxlen < 1) {
+ /* no more room */
+ break;
+ }
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ *str++ = mp_s_rmap[d];
+ ++digs;
+ }
+
+ /* reverse the digits of the string. In this case _s points
+ * to the first digit [exluding the sign] of the number
+ */
+ bn_reverse ((unsigned char *)_s, digs);
+
+ /* append a NULL so the string is properly terminated */
+ *str = '\0';
+
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toradix_n.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_unsigned_bin_size.c b/libtommath/bn_mp_unsigned_bin_size.c
new file mode 100644
index 0000000..00d6aa0
--- /dev/null
+++ b/libtommath/bn_mp_unsigned_bin_size.c
@@ -0,0 +1,28 @@
+#include <tommath.h>
+#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* get the size for an unsigned equivalent */
+int mp_unsigned_bin_size (mp_int * a)
+{
+ int size = mp_count_bits (a);
+ return (size / 8 + ((size & 7) != 0 ? 1 : 0));
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_unsigned_bin_size.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_xor.c b/libtommath/bn_mp_xor.c
new file mode 100644
index 0000000..508c1a0
--- /dev/null
+++ b/libtommath/bn_mp_xor.c
@@ -0,0 +1,51 @@
+#include <tommath.h>
+#ifdef BN_MP_XOR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* XOR two ints together */
+int
+mp_xor (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] ^= x->dp[ix];
+ }
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_xor.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_mp_zero.c b/libtommath/bn_mp_zero.c
new file mode 100644
index 0000000..d8fd536
--- /dev/null
+++ b/libtommath/bn_mp_zero.c
@@ -0,0 +1,36 @@
+#include <tommath.h>
+#ifdef BN_MP_ZERO_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* set to zero */
+void mp_zero (mp_int * a)
+{
+ int n;
+ mp_digit *tmp;
+
+ a->sign = MP_ZPOS;
+ a->used = 0;
+
+ tmp = a->dp;
+ for (n = 0; n < a->alloc; n++) {
+ *tmp++ = 0;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_zero.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_prime_tab.c b/libtommath/bn_prime_tab.c
new file mode 100644
index 0000000..522d428
--- /dev/null
+++ b/libtommath/bn_prime_tab.c
@@ -0,0 +1,61 @@
+#include <tommath.h>
+#ifdef BN_PRIME_TAB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+const mp_digit ltm_prime_tab[] = {
+ 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
+ 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
+ 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
+ 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
+#ifndef MP_8BIT
+ 0x0083,
+ 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
+ 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
+ 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
+ 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
+
+ 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
+ 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
+ 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
+ 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
+ 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
+ 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
+ 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
+ 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
+
+ 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
+ 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
+ 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
+ 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
+ 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
+ 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
+ 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
+ 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
+
+ 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
+ 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
+ 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
+ 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
+ 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
+ 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
+ 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
+ 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
+#endif
+};
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_prime_tab.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_reverse.c b/libtommath/bn_reverse.c
new file mode 100644
index 0000000..ed19627
--- /dev/null
+++ b/libtommath/bn_reverse.c
@@ -0,0 +1,39 @@
+#include <tommath.h>
+#ifdef BN_REVERSE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reverse an array, used for radix code */
+void
+bn_reverse (unsigned char *s, int len)
+{
+ int ix, iy;
+ unsigned char t;
+
+ ix = 0;
+ iy = len - 1;
+ while (ix < iy) {
+ t = s[ix];
+ s[ix] = s[iy];
+ s[iy] = t;
+ ++ix;
+ --iy;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_reverse.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_s_mp_add.c b/libtommath/bn_s_mp_add.c
new file mode 100644
index 0000000..5d17f12
--- /dev/null
+++ b/libtommath/bn_s_mp_add.c
@@ -0,0 +1,109 @@
+#include <tommath.h>
+#ifdef BN_S_MP_ADD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* low level addition, based on HAC pp.594, Algorithm 14.7 */
+int
+s_mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int *x;
+ int olduse, res, min, max;
+
+ /* find sizes, we let |a| <= |b| which means we have to sort
+ * them. "x" will point to the input with the most digits
+ */
+ if (a->used > b->used) {
+ min = b->used;
+ max = a->used;
+ x = a;
+ } else {
+ min = a->used;
+ max = b->used;
+ x = b;
+ }
+
+ /* init result */
+ if (c->alloc < max + 1) {
+ if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* get old used digit count and set new one */
+ olduse = c->used;
+ c->used = max + 1;
+
+ {
+ register mp_digit u, *tmpa, *tmpb, *tmpc;
+ register int i;
+
+ /* alias for digit pointers */
+
+ /* first input */
+ tmpa = a->dp;
+
+ /* second input */
+ tmpb = b->dp;
+
+ /* destination */
+ tmpc = c->dp;
+
+ /* zero the carry */
+ u = 0;
+ for (i = 0; i < min; i++) {
+ /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
+ *tmpc = *tmpa++ + *tmpb++ + u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)DIGIT_BIT);
+
+ /* take away carry bit from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* now copy higher words if any, that is in A+B
+ * if A or B has more digits add those in
+ */
+ if (min != max) {
+ for (; i < max; i++) {
+ /* T[i] = X[i] + U */
+ *tmpc = x->dp[i] + u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)DIGIT_BIT);
+
+ /* take away carry bit from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+ }
+
+ /* add carry */
+ *tmpc++ = u;
+
+ /* clear digits above oldused */
+ for (i = c->used; i < olduse; i++) {
+ *tmpc++ = 0;
+ }
+ }
+
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_add.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_s_mp_exptmod.c b/libtommath/bn_s_mp_exptmod.c
new file mode 100644
index 0000000..189197c
--- /dev/null
+++ b/libtommath/bn_s_mp_exptmod.c
@@ -0,0 +1,252 @@
+#include <tommath.h>
+#ifdef BN_S_MP_EXPTMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res, mu;
+ mp_digit buf;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+ int (*redux)(mp_int*,mp_int*,mp_int*);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* create mu, used for Barrett reduction */
+ if ((err = mp_init (&mu)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ if (redmode == 0) {
+ if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce;
+ } else {
+ if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce_2k_l;
+ }
+
+ /* create M table
+ *
+ * The M table contains powers of the base,
+ * e.g. M[x] = G**x mod P
+ *
+ * The first half of the table is not
+ * computed though accept for M[0] and M[1]
+ */
+ if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring
+ * M[1] (winsize-1) times
+ */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ /* square it */
+ if ((err = mp_sqr (&M[1 << (winsize - 1)],
+ &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* reduce modulo P */
+ if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
+ * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
+ */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ mp_set (&res, 1);
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset the bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int) DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_MU:mp_clear (&mu);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_exptmod.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_s_mp_mul_digs.c b/libtommath/bn_s_mp_mul_digs.c
new file mode 100644
index 0000000..7d55b81
--- /dev/null
+++ b/libtommath/bn_s_mp_mul_digs.c
@@ -0,0 +1,90 @@
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiplies |a| * |b| and only computes upto digs digits of result
+ * HAC pp. 595, Algorithm 14.12 Modified so you can control how
+ * many digits of output are created.
+ */
+int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ mp_int t;
+ int res, pa, pb, ix, iy;
+ mp_digit u;
+ mp_word r;
+ mp_digit tmpx, *tmpt, *tmpy;
+
+ /* can we use the fast multiplier? */
+ if (((digs) < MP_WARRAY) &&
+ MIN (a->used, b->used) <
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_s_mp_mul_digs (a, b, c, digs);
+ }
+
+ if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
+ return res;
+ }
+ t.used = digs;
+
+ /* compute the digits of the product directly */
+ pa = a->used;
+ for (ix = 0; ix < pa; ix++) {
+ /* set the carry to zero */
+ u = 0;
+
+ /* limit ourselves to making digs digits of output */
+ pb = MIN (b->used, digs - ix);
+
+ /* setup some aliases */
+ /* copy of the digit from a used within the nested loop */
+ tmpx = a->dp[ix];
+
+ /* an alias for the destination shifted ix places */
+ tmpt = t.dp + ix;
+
+ /* an alias for the digits of b */
+ tmpy = b->dp;
+
+ /* compute the columns of the output and propagate the carry */
+ for (iy = 0; iy < pb; iy++) {
+ /* compute the column as a mp_word */
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
+
+ /* the new column is the lower part of the result */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get the carry word from the result */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+ /* set carry if it is placed below digs */
+ if (ix + iy < digs) {
+ *tmpt = u;
+ }
+ }
+
+ mp_clamp (&t);
+ mp_exch (&t, c);
+
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_digs.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_s_mp_mul_high_digs.c b/libtommath/bn_s_mp_mul_high_digs.c
new file mode 100644
index 0000000..1c0aae4
--- /dev/null
+++ b/libtommath/bn_s_mp_mul_high_digs.c
@@ -0,0 +1,81 @@
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiplies |a| * |b| and does not compute the lower digs digits
+ * [meant to get the higher part of the product]
+ */
+int
+s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ mp_int t;
+ int res, pa, pb, ix, iy;
+ mp_digit u;
+ mp_word r;
+ mp_digit tmpx, *tmpt, *tmpy;
+
+ /* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ if (((a->used + b->used + 1) < MP_WARRAY)
+ && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_s_mp_mul_high_digs (a, b, c, digs);
+ }
+#endif
+
+ if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ t.used = a->used + b->used + 1;
+
+ pa = a->used;
+ pb = b->used;
+ for (ix = 0; ix < pa; ix++) {
+ /* clear the carry */
+ u = 0;
+
+ /* left hand side of A[ix] * B[iy] */
+ tmpx = a->dp[ix];
+
+ /* alias to the address of where the digits will be stored */
+ tmpt = &(t.dp[digs]);
+
+ /* alias for where to read the right hand side from */
+ tmpy = b->dp + (digs - ix);
+
+ for (iy = digs - ix; iy < pb; iy++) {
+ /* calculate the double precision result */
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
+
+ /* get the lower part */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* carry the carry */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+ *tmpt = u;
+ }
+ mp_clamp (&t);
+ mp_exch (&t, c);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_high_digs.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_s_mp_sqr.c b/libtommath/bn_s_mp_sqr.c
new file mode 100644
index 0000000..b0063bc
--- /dev/null
+++ b/libtommath/bn_s_mp_sqr.c
@@ -0,0 +1,84 @@
+#include <tommath.h>
+#ifdef BN_S_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
+int s_mp_sqr (mp_int * a, mp_int * b)
+{
+ mp_int t;
+ int res, ix, iy, pa;
+ mp_word r;
+ mp_digit u, tmpx, *tmpt;
+
+ pa = a->used;
+ if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* default used is maximum possible size */
+ t.used = 2*pa + 1;
+
+ for (ix = 0; ix < pa; ix++) {
+ /* first calculate the digit at 2*ix */
+ /* calculate double precision result */
+ r = ((mp_word) t.dp[2*ix]) +
+ ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
+
+ /* store lower part in result */
+ t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get the carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+
+ /* left hand side of A[ix] * A[iy] */
+ tmpx = a->dp[ix];
+
+ /* alias for where to store the results */
+ tmpt = t.dp + (2*ix + 1);
+
+ for (iy = ix + 1; iy < pa; iy++) {
+ /* first calculate the product */
+ r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
+
+ /* now calculate the double precision result, note we use
+ * addition instead of *2 since it's easier to optimize
+ */
+ r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
+
+ /* store lower part */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ }
+ /* propagate upwards */
+ while (u != ((mp_digit) 0)) {
+ r = ((mp_word) *tmpt) + ((mp_word) u);
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ }
+ }
+
+ mp_clamp (&t);
+ mp_exch (&t, b);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bn_s_mp_sub.c b/libtommath/bn_s_mp_sub.c
new file mode 100644
index 0000000..f5949f5
--- /dev/null
+++ b/libtommath/bn_s_mp_sub.c
@@ -0,0 +1,89 @@
+#include <tommath.h>
+#ifdef BN_S_MP_SUB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
+int
+s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int olduse, res, min, max;
+
+ /* find sizes */
+ min = b->used;
+ max = a->used;
+
+ /* init result */
+ if (c->alloc < max) {
+ if ((res = mp_grow (c, max)) != MP_OKAY) {
+ return res;
+ }
+ }
+ olduse = c->used;
+ c->used = max;
+
+ {
+ register mp_digit u, *tmpa, *tmpb, *tmpc;
+ register int i;
+
+ /* alias for digit pointers */
+ tmpa = a->dp;
+ tmpb = b->dp;
+ tmpc = c->dp;
+
+ /* set carry to zero */
+ u = 0;
+ for (i = 0; i < min; i++) {
+ /* T[i] = A[i] - B[i] - U */
+ *tmpc = *tmpa++ - *tmpb++ - u;
+
+ /* U = carry bit of T[i]
+ * Note this saves performing an AND operation since
+ * if a carry does occur it will propagate all the way to the
+ * MSB. As a result a single shift is enough to get the carry
+ */
+ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+
+ /* Clear carry from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* now copy higher words if any, e.g. if A has more digits than B */
+ for (; i < max; i++) {
+ /* T[i] = A[i] - U */
+ *tmpc = *tmpa++ - u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+
+ /* Clear carry from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* clear digits above used (since we may not have grown result above) */
+ for (i = c->used; i < olduse; i++) {
+ *tmpc++ = 0;
+ }
+ }
+
+ mp_clamp (c);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_sub.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/bncore.c b/libtommath/bncore.c
new file mode 100644
index 0000000..989a1dd
--- /dev/null
+++ b/libtommath/bncore.c
@@ -0,0 +1,36 @@
+#include <tommath.h>
+#ifdef BNCORE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Known optimal configurations
+
+ CPU /Compiler /MUL CUTOFF/SQR CUTOFF
+-------------------------------------------------------------
+ Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
+ AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35
+
+*/
+
+int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */
+ KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */
+
+ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
+ TOOM_SQR_CUTOFF = 400;
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bncore.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/booker.pl b/libtommath/booker.pl
new file mode 100644
index 0000000..49f1889
--- /dev/null
+++ b/libtommath/booker.pl
@@ -0,0 +1,265 @@
+#!/bin/perl
+#
+#Used to prepare the book "tommath.src" for LaTeX by pre-processing it into a .tex file
+#
+#Essentially you write the "tommath.src" as normal LaTex except where you want code snippets you put
+#
+#EXAM,file
+#
+#This preprocessor will then open "file" and insert it as a verbatim copy.
+#
+#Tom St Denis
+
+#get graphics type
+if (shift =~ /PDF/) {
+ $graph = "";
+} else {
+ $graph = ".ps";
+}
+
+open(IN,"<tommath.src") or die "Can't open source file";
+open(OUT,">tommath.tex") or die "Can't open destination file";
+
+print "Scanning for sections\n";
+$chapter = $section = $subsection = 0;
+$x = 0;
+while (<IN>) {
+ print ".";
+ if (!(++$x % 80)) { print "\n"; }
+ #update the headings
+ if (~($_ =~ /\*/)) {
+ if ($_ =~ /\\chapter{.+}/) {
+ ++$chapter;
+ $section = $subsection = 0;
+ } elsif ($_ =~ /\\section{.+}/) {
+ ++$section;
+ $subsection = 0;
+ } elsif ($_ =~ /\\subsection{.+}/) {
+ ++$subsection;
+ }
+ }
+
+ if ($_ =~ m/MARK/) {
+ @m = split(",",$_);
+ chomp(@m[1]);
+ $index1{@m[1]} = $chapter;
+ $index2{@m[1]} = $section;
+ $index3{@m[1]} = $subsection;
+ }
+}
+close(IN);
+
+open(IN,"<tommath.src") or die "Can't open source file";
+$readline = $wroteline = 0;
+$srcline = 0;
+
+while (<IN>) {
+ ++$readline;
+ ++$srcline;
+
+ if ($_ =~ m/MARK/) {
+ } elsif ($_ =~ m/EXAM/ || $_ =~ m/LIST/) {
+ if ($_ =~ m/EXAM/) {
+ $skipheader = 1;
+ } else {
+ $skipheader = 0;
+ }
+
+ # EXAM,file
+ chomp($_);
+ @m = split(",",$_);
+ open(SRC,"<$m[1]") or die "Error:$srcline:Can't open source file $m[1]";
+
+ print "$srcline:Inserting $m[1]:";
+
+ $line = 0;
+ $tmp = $m[1];
+ $tmp =~ s/_/"\\_"/ge;
+ print OUT "\\vspace{+3mm}\\begin{small}\n\\hspace{-5.1mm}{\\bf File}: $tmp\n\\vspace{-3mm}\n\\begin{alltt}\n";
+ $wroteline += 5;
+
+ if ($skipheader == 1) {
+ # scan till next end of comment, e.g. skip license
+ while (<SRC>) {
+ $text[$line++] = $_;
+ last if ($_ =~ /math\.libtomcrypt\.com/);
+ }
+ <SRC>;
+ }
+
+ $inline = 0;
+ while (<SRC>) {
+ next if ($_ =~ /\$Source/);
+ next if ($_ =~ /\$Revision/);
+ next if ($_ =~ /\$Date/);
+ $text[$line++] = $_;
+ ++$inline;
+ chomp($_);
+ $_ =~ s/\t/" "/ge;
+ $_ =~ s/{/"^{"/ge;
+ $_ =~ s/}/"^}"/ge;
+ $_ =~ s/\\/'\symbol{92}'/ge;
+ $_ =~ s/\^/"\\"/ge;
+
+ printf OUT ("%03d ", $line);
+ for ($x = 0; $x < length($_); $x++) {
+ print OUT chr(vec($_, $x, 8));
+ if ($x == 75) {
+ print OUT "\n ";
+ ++$wroteline;
+ }
+ }
+ print OUT "\n";
+ ++$wroteline;
+ }
+ $totlines = $line;
+ print OUT "\\end{alltt}\n\\end{small}\n";
+ close(SRC);
+ print "$inline lines\n";
+ $wroteline += 2;
+ } elsif ($_ =~ m/@\d+,.+@/) {
+ # line contains [number,text]
+ # e.g. @14,for (ix = 0)@
+ $txt = $_;
+ while ($txt =~ m/@\d+,.+@/) {
+ @m = split("@",$txt); # splits into text, one, two
+ @parms = split(",",$m[1]); # splits one,two into two elements
+
+ # now search from $parms[0] down for $parms[1]
+ $found1 = 0;
+ $found2 = 0;
+ for ($i = $parms[0]; $i < $totlines && $found1 == 0; $i++) {
+ if ($text[$i] =~ m/\Q$parms[1]\E/) {
+ $foundline1 = $i + 1;
+ $found1 = 1;
+ }
+ }
+
+ # now search backwards
+ for ($i = $parms[0] - 1; $i >= 0 && $found2 == 0; $i--) {
+ if ($text[$i] =~ m/\Q$parms[1]\E/) {
+ $foundline2 = $i + 1;
+ $found2 = 1;
+ }
+ }
+
+ # now use the closest match or the first if tied
+ if ($found1 == 1 && $found2 == 0) {
+ $found = 1;
+ $foundline = $foundline1;
+ } elsif ($found1 == 0 && $found2 == 1) {
+ $found = 1;
+ $foundline = $foundline2;
+ } elsif ($found1 == 1 && $found2 == 1) {
+ $found = 1;
+ if (($foundline1 - $parms[0]) <= ($parms[0] - $foundline2)) {
+ $foundline = $foundline1;
+ } else {
+ $foundline = $foundline2;
+ }
+ } else {
+ $found = 0;
+ }
+
+ # if found replace
+ if ($found == 1) {
+ $delta = $parms[0] - $foundline;
+ print "Found replacement tag for \"$parms[1]\" on line $srcline which refers to line $foundline (delta $delta)\n";
+ $_ =~ s/@\Q$m[1]\E@/$foundline/;
+ } else {
+ print "ERROR: The tag \"$parms[1]\" on line $srcline was not found in the most recently parsed source!\n";
+ }
+
+ # remake the rest of the line
+ $cnt = @m;
+ $txt = "";
+ for ($i = 2; $i < $cnt; $i++) {
+ $txt = $txt . $m[$i] . "@";
+ }
+ }
+ print OUT $_;
+ ++$wroteline;
+ } elsif ($_ =~ /~.+~/) {
+ # line contains a ~text~ pair used to refer to indexing :-)
+ $txt = $_;
+ while ($txt =~ /~.+~/) {
+ @m = split("~", $txt);
+
+ # word is the second position
+ $word = @m[1];
+ $a = $index1{$word};
+ $b = $index2{$word};
+ $c = $index3{$word};
+
+ # if chapter (a) is zero it wasn't found
+ if ($a == 0) {
+ print "ERROR: the tag \"$word\" on line $srcline was not found previously marked.\n";
+ } else {
+ # format the tag as x, x.y or x.y.z depending on the values
+ $str = $a;
+ $str = $str . ".$b" if ($b != 0);
+ $str = $str . ".$c" if ($c != 0);
+
+ if ($b == 0 && $c == 0) {
+ # its a chapter
+ if ($a <= 10) {
+ if ($a == 1) {
+ $str = "chapter one";
+ } elsif ($a == 2) {
+ $str = "chapter two";
+ } elsif ($a == 3) {
+ $str = "chapter three";
+ } elsif ($a == 4) {
+ $str = "chapter four";
+ } elsif ($a == 5) {
+ $str = "chapter five";
+ } elsif ($a == 6) {
+ $str = "chapter six";
+ } elsif ($a == 7) {
+ $str = "chapter seven";
+ } elsif ($a == 8) {
+ $str = "chapter eight";
+ } elsif ($a == 9) {
+ $str = "chapter nine";
+ } elsif ($a == 10) {
+ $str = "chapter ten";
+ }
+ } else {
+ $str = "chapter " . $str;
+ }
+ } else {
+ $str = "section " . $str if ($b != 0 && $c == 0);
+ $str = "sub-section " . $str if ($b != 0 && $c != 0);
+ }
+
+ #substitute
+ $_ =~ s/~\Q$word\E~/$str/;
+
+ print "Found replacement tag for marker \"$word\" on line $srcline which refers to $str\n";
+ }
+
+ # remake rest of the line
+ $cnt = @m;
+ $txt = "";
+ for ($i = 2; $i < $cnt; $i++) {
+ $txt = $txt . $m[$i] . "~";
+ }
+ }
+ print OUT $_;
+ ++$wroteline;
+ } elsif ($_ =~ m/FIGU/) {
+ # FIGU,file,caption
+ chomp($_);
+ @m = split(",", $_);
+ print OUT "\\begin{center}\n\\begin{figure}[here]\n\\includegraphics{pics/$m[1]$graph}\n";
+ print OUT "\\caption{$m[2]}\n\\label{pic:$m[1]}\n\\end{figure}\n\\end{center}\n";
+ $wroteline += 4;
+ } else {
+ print OUT $_;
+ ++$wroteline;
+ }
+}
+print "Read $readline lines, wrote $wroteline lines\n";
+
+close (OUT);
+close (IN);
diff --git a/libtommath/changes.txt b/libtommath/changes.txt
new file mode 100644
index 0000000..aaaf69f
--- /dev/null
+++ b/libtommath/changes.txt
@@ -0,0 +1,393 @@
+December 24th, 2006
+v0.40 -- Updated makefile to properly support LIBNAME
+ -- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind!
+
+April 4th, 2006
+v0.39 -- Jim Wigginton pointed out my Montgomery examples in figures 6.4 and 6.6 were off by one, k should be 9 not 8
+ -- Bruce Guenter suggested I use --tag=CC for libtool builds where the compiler may think it's C++.
+ -- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book)
+ -- updated some of the @@ tags in tommath.src to reflect source changes.
+ -- updated email and url info in all source files
+
+Jan 26th, 2006
+v0.38 -- broken makefile.shared fixed
+ -- removed some carry stores that were not required [updated text]
+
+November 18th, 2005
+v0.37 -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs. Fixed.
+ -- [rinick@gmail.com] reported the makefile.bcc was messed up. Fixed.
+ -- [Kevin Kenny] reported some issues with mp_toradix_n(). Now it doesn't require a min of 3 chars of output.
+ -- Made the make command renamable. Wee
+
+August 1st, 2005
+v0.36 -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed.
+ -- [Peter LaDow] found a typo in the XREALLOC macro
+ -- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input
+ -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags]
+ -- Kevin Kenny pointed out a stray //
+ -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code]
+ -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use
+ unsigned operations in the routine.
+ -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix)
+ -- Updated makefiles to be way more flexible
+
+March 12th, 2005
+v0.35 -- Stupid XOR function missing line again... oops.
+ -- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt]
+ -- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ]
+ -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns. ;-)
+ -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
+ -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
+ -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs"
+ -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
+ -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!
+
+February 12th, 2005
+v0.34 -- Fixed two more small errors in mp_prime_random_ex()
+ -- Fixed overflow in mp_mul_d() [Kevin Kenny]
+ -- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size]
+ -- Added "large" diminished radix support. Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
+ Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
+ -- Updated the manual a bit
+ -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the
+ end of Feb/05. Once I get back I'll have tons of free time and I plan to go to town on the book.
+ As of this release the API will freeze. At least until the book catches up with all the changes. I welcome
+ bug reports but new algorithms will have to wait.
+
+December 23rd, 2004
+v0.33 -- Fixed "small" variant for mp_div() which would munge with negative dividends...
+ -- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when
+ no special flags were set
+ -- Fixed overflow [minor] bug in fast_s_mp_sqr()
+ -- Made the makefiles easier to configure the group/user that ltm will install as
+ -- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan)
+ -- Matt Johnston pointed out a missing semi-colon in mp_exptmod
+
+October 29th, 2004
+v0.32 -- Added "makefile.shared" for shared object support
+ -- Added more to the build options/configs in the manual
+ -- Started the Depends framework, wrote dep.pl to scan deps and
+ produce "callgraph.txt" ;-)
+ -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
+ RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
+ -- Merged in the small/slower mp_div replacement. You can now toggle which
+ you want to use as your mp_div() at build time. Saves roughly 8KB or so.
+ -- Renamed a few files and changed some comments to make depends system work better.
+ (No changes to function names)
+ -- Merged in new Combas that perform 2 reads per inner loop instead of the older
+ 3reads/2writes per inner loop of the old code. Really though if you want speed
+ learn to use TomsFastMath ;-)
+
+August 9th, 2004
+v0.31 -- "profiled" builds now :-) new timings for Intel Northwoods
+ -- Added "pretty" build target
+ -- Update mp_init() to actually assign 0's instead of relying on calloc()
+ -- "Wolfgang Ehrhardt" <Wolfgang.Ehrhardt@munich.netsurf.de> found a bug in mp_mul() where if
+ you multiply a negative by zero you get negative zero as the result. Oops.
+ -- J Harper from PeerSec let me toy with his AMD64 and I got 60-bit digits working properly
+ [this also means that I fixed a bug where if sizeof(int) < sizeof(mp_digit) it would bug]
+
+April 11th, 2004
+v0.30 -- Added "mp_toradix_n" which stores upto "n-1" least significant digits of an mp_int
+ -- Johan Lindh sent a patch so MSVC wouldn't whine about redefining malloc [in weird dll modes]
+ -- Henrik Goldman spotted a missing OPT_CAST in mp_fwrite()
+ -- Tuned tommath.h so that when MP_LOW_MEM is defined MP_PREC shall be reduced.
+ [I also allow MP_PREC to be externally defined now]
+ -- Sped up mp_cnt_lsb() by using a 4x4 table [e.g. 4x speedup]
+ -- Added mp_prime_random_ex() which is a more versatile prime generator accurate to
+ exact bit lengths (unlike the deprecated but still available mp_prime_random() which
+ is only accurate to byte lengths). See the new LTM_PRIME_* flags ;-)
+ -- Alex Polushin contributed an optimized mp_sqrt() as well as mp_get_int() and mp_is_square().
+ I've cleaned them all up to be a little more consistent [along with one bug fix] for this release.
+ -- Added mp_init_set and mp_init_set_int to initialize and set small constants with one function
+ call.
+ -- Removed /etclib directory [um LibTomPoly deprecates this].
+ -- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus.
+ ++ N.B. My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org
+ website.
+
+Jan 25th, 2004
+v0.29 ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-)
+ -- Added fix to mp_shrink to prevent a realloc when used == 0 [e.g. realloc zero bytes???]
+ -- Made the mp_prime_rabin_miller_trials() function internal table smaller and also
+ set the minimum number of tests to two (sounds a bit safer).
+ -- Added a mp_exteuclid() which computes the extended euclidean algorithm.
+ -- Fixed a memory leak in s_mp_exptmod() [called when Barrett reduction is to be used] which would arise
+ if a multiplication or subsequent reduction failed [would not free the temp result].
+ -- Made an API change to mp_radix_size(). It now returns an error code and stores the required size
+ through an "int star" passed to it.
+
+Dec 24th, 2003
+v0.28 -- Henrik Goldman suggested I add casts to the montomgery code [stores into mu...] so compilers wouldn't
+ spew [erroneous] diagnostics... fixed.
+ -- Henrik Goldman also spotted two typos. One in mp_radix_size() and another in mp_toradix().
+ -- Added fix to mp_shrink() to avoid a memory leak.
+ -- Added mp_prime_random() which requires a callback to make truly random primes of a given nature
+ (idea from chat with Niels Ferguson at Crypto'03)
+ -- Picked up a second wind. I'm filled with Gooo. Mission Gooo!
+ -- Removed divisions from mp_reduce_is_2k()
+ -- Sped up mp_div_d() [general case] to use only one division per digit instead of two.
+ -- Added the heap macros from LTC to LTM. Now you can easily [by editing four lines of tommath.h]
+ change the name of the heap functions used in LTM [also compatible with LTC via MPI mode]
+ -- Added bn_prime_rabin_miller_trials() which gives the number of Rabin-Miller trials to achieve
+ a failure rate of less than 2^-96
+ -- fixed bug in fast_mp_invmod(). The initial testing logic was wrong. An invalid input is not when
+ "a" and "b" are even it's when "b" is even [the algo is for odd moduli only].
+ -- Started a new manual [finally]. It is incomplete and will be finished as time goes on. I had to stop
+ adding full demos around half way in chapter three so I could at least get a good portion of the
+ manual done. If you really need help using the library you can always email me!
+ -- My Textbook is now included as part of the package [all Public Domain]
+
+Sept 19th, 2003
+v0.27 -- Removed changes.txt~ which was made by accident since "kate" decided it was
+ a good time to re-enable backups... [kde is fun!]
+ -- In mp_grow() "a->dp" is not overwritten by realloc call [re: memory leak]
+ Now if mp_grow() fails the mp_int is still valid and can be cleared via
+ mp_clear() to reclaim the memory.
+ -- Henrik Goldman found a buffer overflow bug in mp_add_d(). Fixed.
+ -- Cleaned up mp_mul_d() to be much easier to read and follow.
+
+Aug 29th, 2003
+v0.26 -- Fixed typo that caused warning with GCC 3.2
+ -- Martin Marcel noticed a bug in mp_neg() that allowed negative zeroes.
+ Also, Martin is the fellow who noted the bugs in mp_gcd() of 0.24/0.25.
+ -- Martin Marcel noticed an optimization [and slight bug] in mp_lcm().
+ -- Added fix to mp_read_unsigned_bin to prevent a buffer overflow.
+ -- Beefed up the comments in the baseline multipliers [and montgomery]
+ -- Added "mont" demo to the makefile.msvc in etc/
+ -- Optimized sign compares in mp_cmp from 4 to 2 cases.
+
+Aug 4th, 2003
+v0.25 -- Fix to mp_gcd again... oops (0,-a) == (-a, 0) == a
+ -- Fix to mp_clear which didn't reset the sign [Greg Rose]
+ -- Added mp_error_to_string() to convert return codes to strings. [Greg Rose]
+ -- Optimized fast_mp_invmod() to do the test for invalid inputs [both even]
+ first so temps don't have to be initialized if it's going to fail.
+ -- Optimized mp_gcd() by removing mp_div_2d calls for when one of the inputs
+ is odd.
+ -- Tons of new comments, some indentation fixups, etc.
+ -- mp_jacobi() returns MP_VAL if the modulus is less than or equal to zero.
+ -- fixed two typos in the header of each file :-)
+ -- LibTomMath is officially Public Domain [see LICENSE]
+
+July 15th, 2003
+v0.24 -- Optimized mp_add_d and mp_sub_d to not allocate temporary variables
+ -- Fixed mp_gcd() so the gcd of 0,0 is 0. Allows the gcd operation to be chained
+ e.g. (0,0,a) == a [instead of 1]
+ -- Should be one of the last release for a while. Working on LibTomMath book now.
+ -- optimized the pprime demo [/etc/pprime.c] to first make a huge table of single
+ digit primes then it reads them randomly instead of randomly choosing/testing single
+ digit primes.
+
+July 12th, 2003
+v0.23 -- Optimized mp_prime_next_prime() to not use mp_mod [via is_divisible()] in each
+ iteration. Instead now a smaller table is kept of the residues which can be updated
+ without division.
+ -- Fixed a bug in next_prime() where an input of zero would be treated as odd and
+ have two added to it [to move to the next odd].
+ -- fixed a bug in prime_fermat() and prime_miller_rabin() which allowed the base
+ to be negative, zero or one. Normally the test is only valid if the base is
+ greater than one.
+ -- changed the next_prime() prototype to accept a new parameter "bbs_style" which
+ will find the next prime congruent to 3 mod 4. The default [bbs_style==0] will
+ make primes which are either congruent to 1 or 3 mod 4.
+ -- fixed mp_read_unsigned_bin() so that it doesn't include both code for
+ the case DIGIT_BIT < 8 and >= 8
+ -- optimized div_d() to easy out on division by 1 [or if a == 0] and use
+ logical shifts if the divisor is a power of two.
+ -- the default DIGIT_BIT type was not int for non-default builds. Fixed.
+
+July 2nd, 2003
+v0.22 -- Fixed up mp_invmod so the result is properly in range now [was always congruent to the inverse...]
+ -- Fixed up s_mp_exptmod and mp_exptmod_fast so the lower half of the pre-computed table isn't allocated
+ which makes the algorithm use half as much ram.
+ -- Fixed the install script not to make the book :-) [which isn't included anyways]
+ -- added mp_cnt_lsb() which counts how many of the lsbs are zero
+ -- optimized mp_gcd() to use the new mp_cnt_lsb() to replace multiple divisions by two by a single division.
+ -- applied similar optimization to mp_prime_miller_rabin().
+ -- Fixed a bug in both mp_invmod() and fast_mp_invmod() which tested for odd
+ via "mp_iseven() == 0" which is not valid [since zero is not even either].
+
+June 19th, 2003
+v0.21 -- Fixed bug in mp_mul_d which would not handle sign correctly [would not always forward it]
+ -- Removed the #line lines from gen.pl [was in violation of ISO C]
+
+June 8th, 2003
+v0.20 -- Removed the book from the package. Added the TDCAL license document.
+ -- This release is officially pure-bred TDCAL again [last officially TDCAL based release was v0.16]
+
+June 6th, 2003
+v0.19 -- Fixed a bug in mp_montgomery_reduce() which was introduced when I tweaked mp_rshd() in the previous release.
+ Essentially the digits were not trimmed before the compare which cause a subtraction to occur all the time.
+ -- Fixed up etc/tune.c a bit to stop testing new cutoffs after 16 failures [to find more optimal points].
+ Brute force ho!
+
+
+May 29th, 2003
+v0.18 -- Fixed a bug in s_mp_sqr which would handle carries properly just not very elegantly.
+ (e.g. correct result, just bad looking code)
+ -- Fixed bug in mp_sqr which still had a 512 constant instead of MP_WARRAY
+ -- Added Toom-Cook multipliers [needs tuning!]
+ -- Added efficient divide by 3 algorithm mp_div_3
+ -- Re-wrote mp_div_d to be faster than calling mp_div
+ -- Added in a donated BCC makefile and a single page LTM poster (ahalhabsi@sbcglobal.net)
+ -- Added mp_reduce_2k which reduces an input modulo n = 2**p - k for any single digit k
+ -- Made the exptmod system be aware of the 2k reduction algorithms.
+ -- Rewrote mp_dr_reduce to be smaller, simpler and easier to understand.
+
+May 17th, 2003
+v0.17 -- Benjamin Goldberg submitted optimized mp_add and mp_sub routines. A new gen.pl as well
+ as several smaller suggestions. Thanks!
+ -- removed call to mp_cmp in inner loop of mp_div and put mp_cmp_mag in its place :-)
+ -- Fixed bug in mp_exptmod that would cause it to fail for odd moduli when DIGIT_BIT != 28
+ -- mp_exptmod now also returns errors if the modulus is negative and will handle negative exponents
+ -- mp_prime_is_prime will now return true if the input is one of the primes in the prime table
+ -- Damian M Gryski (dgryski@uwaterloo.ca) found a index out of bounds error in the
+ mp_fast_s_mp_mul_high_digs function which didn't come up before. (fixed)
+ -- Refactored the DR reduction code so there is only one function per file.
+ -- Fixed bug in the mp_mul() which would erroneously avoid the faster multiplier [comba] when it was
+ allowed. The bug would not cause the incorrect value to be produced just less efficient (fixed)
+ -- Fixed similar bug in the Montgomery reduction code.
+ -- Added tons of (mp_digit) casts so the 7/15/28/31 bit digit code will work flawlessly out of the box.
+ Also added limited support for 64-bit machines with a 60-bit digit. Both thanks to Tom Wu (tom@arcot.com)
+ -- Added new comments here and there, cleaned up some code [style stuff]
+ -- Fixed a lingering typo in mp_exptmod* that would set bitcnt to zero then one. Very silly stuff :-)
+ -- Fixed up mp_exptmod_fast so it would set "redux" to the comba Montgomery reduction if allowed. This
+ saves quite a few calls and if statements.
+ -- Added etc/mont.c a test of the Montgomery reduction [assuming all else works :-| ]
+ -- Fixed up etc/tune.c to use a wider test range [more appropriate] also added a x86 based addition which
+ uses RDTSC for high precision timing.
+ -- Updated demo/demo.c to remove MPI stuff [won't work anyways], made the tests run for 2 seconds each so its
+ not so insanely slow. Also made the output space delimited [and fixed up various errors]
+ -- Added logs directory, logs/graph.dem which will use gnuplot to make a series of PNG files
+ that go with the pre-made index.html. You have to build [via make timing] and run ltmtest first in the
+ root of the package.
+ -- Fixed a bug in mp_sub and mp_add where "-a - -a" or "-a + a" would produce -0 as the result [obviously invalid].
+ -- Fixed a bug in mp_rshd. If the count == a.used it should zero/return [instead of shifting]
+ -- Fixed a "off-by-one" bug in mp_mul2d. The initial size check on alloc would be off by one if the residue
+ shifting caused a carry.
+ -- Fixed a bug where s_mp_mul_digs() would not call the Comba based routine if allowed. This made Barrett reduction
+ slower than it had to be.
+
+Mar 29th, 2003
+v0.16 -- Sped up mp_div by making normalization one shift call
+ -- Sped up mp_mul_2d/mp_div_2d by aliasing pointers :-)
+ -- Cleaned up mp_gcd to use the macros for odd/even detection
+ -- Added comments here and there, mostly there but occasionally here too.
+
+Mar 22nd, 2003
+v0.15 -- Added series of prime testing routines to lib
+ -- Fixed up etc/tune.c
+ -- Added DR reduction algorithm
+ -- Beefed up the manual more.
+ -- Fixed up demo/demo.c so it doesn't have so many warnings and it does the full series of
+ tests
+ -- Added "pre-gen" directory which will hold a "gen.pl"'ed copy of the entire lib [done at
+ zipup time so its always the latest]
+ -- Added conditional casts for C++ users [boo!]
+
+Mar 15th, 2003
+v0.14 -- Tons of manual updates
+ -- cleaned up the directory
+ -- added MSVC makefiles
+ -- source changes [that I don't recall]
+ -- Fixed up the lshd/rshd code to use pointer aliasing
+ -- Fixed up the mul_2d and div_2d to not call rshd/lshd unless needed
+ -- Fixed up etc/tune.c a tad
+ -- fixed up demo/demo.c to output comma-delimited results of timing
+ also fixed up timing demo to use a finer granularity for various functions
+ -- fixed up demo/demo.c testing to pause during testing so my Duron won't catch on fire
+ [stays around 31-35C during testing :-)]
+
+Feb 13th, 2003
+v0.13 -- tons of minor speed-ups in low level add, sub, mul_2 and div_2 which propagate
+ to other functions like mp_invmod, mp_div, etc...
+ -- Sped up mp_exptmod_fast by using new code to find R mod m [e.g. B^n mod m]
+ -- minor fixes
+
+Jan 17th, 2003
+v0.12 -- re-wrote the majority of the makefile so its more portable and will
+ install via "make install" on most *nix platforms
+ -- Re-packaged all the source as seperate files. Means the library a single
+ file packagage any more. Instead of just adding "bn.c" you have to add
+ libtommath.a
+ -- Renamed "bn.h" to "tommath.h"
+ -- Changes to the manual to reflect all of this
+ -- Used GNU Indent to clean up the source
+
+Jan 15th, 2003
+v0.11 -- More subtle fixes
+ -- Moved to gentoo linux [hurrah!] so made *nix specific fixes to the make process
+ -- Sped up the montgomery reduction code quite a bit
+ -- fixed up demo so when building timing for the x86 it assumes ELF format now
+
+Jan 9th, 2003
+v0.10 -- Pekka Riikonen suggested fixes to the radix conversion code.
+ -- Added baseline montgomery and comba montgomery reductions, sped up exptmods
+ [to a point, see bn.h for MONTGOMERY_EXPT_CUTOFF]
+
+Jan 6th, 2003
+v0.09 -- Updated the manual to reflect recent changes. :-)
+ -- Added Jacobi function (mp_jacobi) to supplement the number theory side of the lib
+ -- Added a Mersenne prime finder demo in ./etc/mersenne.c
+
+Jan 2nd, 2003
+v0.08 -- Sped up the multipliers by moving the inner loop variables into a smaller scope
+ -- Corrected a bunch of small "warnings"
+ -- Added more comments
+ -- Made "mtest" be able to use /dev/random, /dev/urandom or stdin for RNG data
+ -- Corrected some bugs where error messages were potentially ignored
+ -- add etc/pprime.c program which makes numbers which are provably prime.
+
+Jan 1st, 2003
+v0.07 -- Removed alot of heap operations from core functions to speed them up
+ -- Added a root finding function [and mp_sqrt macro like from MPI]
+ -- Added more to manual
+
+Dec 31st, 2002
+v0.06 -- Sped up the s_mp_add, s_mp_sub which inturn sped up mp_invmod, mp_exptmod, etc...
+ -- Cleaned up the header a bit more
+
+Dec 30th, 2002
+v0.05 -- Builds with MSVC out of the box
+ -- Fixed a bug in mp_invmod w.r.t. even moduli
+ -- Made mp_toradix and mp_read_radix use char instead of unsigned char arrays
+ -- Fixed up exptmod to use fewer multiplications
+ -- Fixed up mp_init_size to use only one heap operation
+ -- Note there is a slight "off-by-one" bug in the library somewhere
+ without the padding (see the source for comment) the library
+ crashes in libtomcrypt. Anyways a reasonable workaround is to pad the
+ numbers which will always correct it since as the numbers grow the padding
+ will still be beyond the end of the number
+ -- Added more to the manual
+
+Dec 29th, 2002
+v0.04 -- Fixed a memory leak in mp_to_unsigned_bin
+ -- optimized invmod code
+ -- Fixed bug in mp_div
+ -- use exchange instead of copy for results
+ -- added a bit more to the manual
+
+Dec 27th, 2002
+v0.03 -- Sped up s_mp_mul_high_digs by not computing the carries of the lower digits
+ -- Fixed a bug where mp_set_int wouldn't zero the value first and set the used member.
+ -- fixed a bug in s_mp_mul_high_digs where the limit placed on the result digits was not calculated properly
+ -- fixed bugs in add/sub/mul/sqr_mod functions where if the modulus and dest were the same it wouldn't work
+ -- fixed a bug in mp_mod and mp_mod_d concerning negative inputs
+ -- mp_mul_d didn't preserve sign
+ -- Many many many many fixes
+ -- Works in LibTomCrypt now :-)
+ -- Added iterations to the timing demos... more accurate.
+ -- Tom needs a job.
+
+Dec 26th, 2002
+v0.02 -- Fixed a few "slips" in the manual. This is "LibTomMath" afterall :-)
+ -- Added mp_cmp_mag, mp_neg, mp_abs and mp_radix_size that were missing.
+ -- Sped up the fast [comba] multipliers more [yahoo!]
+
+Dec 25th,2002
+v0.01 -- Initial release. Gimme a break.
+ -- Todo list,
+ add details to manual [e.g. algorithms]
+ more comments in code
+ example programs
diff --git a/libtommath/demo/demo.c b/libtommath/demo/demo.c
new file mode 100644
index 0000000..bb5eb44
--- /dev/null
+++ b/libtommath/demo/demo.c
@@ -0,0 +1,740 @@
+#include <time.h>
+
+#ifdef IOWNANATHLON
+#include <unistd.h>
+#define SLEEP sleep(4)
+#else
+#define SLEEP
+#endif
+
+#include "tommath.h"
+
+void ndraw(mp_int * a, char *name)
+{
+ char buf[16000];
+
+ printf("%s: ", name);
+ mp_toradix(a, buf, 10);
+ printf("%s\n", buf);
+}
+
+static void draw(mp_int * a)
+{
+ ndraw(a, "");
+}
+
+
+unsigned long lfsr = 0xAAAAAAAAUL;
+
+int lbit(void)
+{
+ if (lfsr & 0x80000000UL) {
+ lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
+ return 1;
+ } else {
+ lfsr <<= 1;
+ return 0;
+ }
+}
+
+int myrng(unsigned char *dst, int len, void *dat)
+{
+ int x;
+
+ for (x = 0; x < len; x++)
+ dst[x] = rand() & 0xFF;
+ return len;
+}
+
+
+
+char cmd[4096], buf[4096];
+int main(void)
+{
+ mp_int a, b, c, d, e, f;
+ unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
+ gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n, t;
+ unsigned rr;
+ int i, n, err, cnt, ix, old_kara_m, old_kara_s;
+ mp_digit mp;
+
+
+ mp_init(&a);
+ mp_init(&b);
+ mp_init(&c);
+ mp_init(&d);
+ mp_init(&e);
+ mp_init(&f);
+
+ srand(time(NULL));
+
+#if 0
+ // test montgomery
+ printf("Testing montgomery...\n");
+ for (i = 1; i < 10; i++) {
+ printf("Testing digit size: %d\n", i);
+ for (n = 0; n < 1000; n++) {
+ mp_rand(&a, i);
+ a.dp[0] |= 1;
+
+ // let's see if R is right
+ mp_montgomery_calc_normalization(&b, &a);
+ mp_montgomery_setup(&a, &mp);
+
+ // now test a random reduction
+ for (ix = 0; ix < 100; ix++) {
+ mp_rand(&c, 1 + abs(rand()) % (2*i));
+ mp_copy(&c, &d);
+ mp_copy(&c, &e);
+
+ mp_mod(&d, &a, &d);
+ mp_montgomery_reduce(&c, &a, mp);
+ mp_mulmod(&c, &b, &a, &c);
+
+ if (mp_cmp(&c, &d) != MP_EQ) {
+printf("d = e mod a, c = e MOD a\n");
+mp_todecimal(&a, buf); printf("a = %s\n", buf);
+mp_todecimal(&e, buf); printf("e = %s\n", buf);
+mp_todecimal(&d, buf); printf("d = %s\n", buf);
+mp_todecimal(&c, buf); printf("c = %s\n", buf);
+printf("compare no compare!\n"); exit(EXIT_FAILURE); }
+ }
+ }
+ }
+ printf("done\n");
+
+ // test mp_get_int
+ printf("Testing: mp_get_int\n");
+ for (i = 0; i < 1000; ++i) {
+ t = ((unsigned long) rand() * rand() + 1) & 0xFFFFFFFF;
+ mp_set_int(&a, t);
+ if (t != mp_get_int(&a)) {
+ printf("mp_get_int() bad result!\n");
+ return 1;
+ }
+ }
+ mp_set_int(&a, 0);
+ if (mp_get_int(&a) != 0) {
+ printf("mp_get_int() bad result!\n");
+ return 1;
+ }
+ mp_set_int(&a, 0xffffffff);
+ if (mp_get_int(&a) != 0xffffffff) {
+ printf("mp_get_int() bad result!\n");
+ return 1;
+ }
+ // test mp_sqrt
+ printf("Testing: mp_sqrt\n");
+ for (i = 0; i < 1000; ++i) {
+ printf("%6d\r", i);
+ fflush(stdout);
+ n = (rand() & 15) + 1;
+ mp_rand(&a, n);
+ if (mp_sqrt(&a, &b) != MP_OKAY) {
+ printf("mp_sqrt() error!\n");
+ return 1;
+ }
+ mp_n_root(&a, 2, &a);
+ if (mp_cmp_mag(&b, &a) != MP_EQ) {
+ printf("mp_sqrt() bad result!\n");
+ return 1;
+ }
+ }
+
+ printf("\nTesting: mp_is_square\n");
+ for (i = 0; i < 1000; ++i) {
+ printf("%6d\r", i);
+ fflush(stdout);
+
+ /* test mp_is_square false negatives */
+ n = (rand() & 7) + 1;
+ mp_rand(&a, n);
+ mp_sqr(&a, &a);
+ if (mp_is_square(&a, &n) != MP_OKAY) {
+ printf("fn:mp_is_square() error!\n");
+ return 1;
+ }
+ if (n == 0) {
+ printf("fn:mp_is_square() bad result!\n");
+ return 1;
+ }
+
+ /* test for false positives */
+ mp_add_d(&a, 1, &a);
+ if (mp_is_square(&a, &n) != MP_OKAY) {
+ printf("fp:mp_is_square() error!\n");
+ return 1;
+ }
+ if (n == 1) {
+ printf("fp:mp_is_square() bad result!\n");
+ return 1;
+ }
+
+ }
+ printf("\n\n");
+
+ /* test for size */
+ for (ix = 10; ix < 128; ix++) {
+ printf("Testing (not safe-prime): %9d bits \r", ix);
+ fflush(stdout);
+ err =
+ mp_prime_random_ex(&a, 8, ix,
+ (rand() & 1) ? LTM_PRIME_2MSB_OFF :
+ LTM_PRIME_2MSB_ON, myrng, NULL);
+ if (err != MP_OKAY) {
+ printf("failed with err code %d\n", err);
+ return EXIT_FAILURE;
+ }
+ if (mp_count_bits(&a) != ix) {
+ printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
+ return EXIT_FAILURE;
+ }
+ }
+
+ for (ix = 16; ix < 128; ix++) {
+ printf("Testing ( safe-prime): %9d bits \r", ix);
+ fflush(stdout);
+ err =
+ mp_prime_random_ex(&a, 8, ix,
+ ((rand() & 1) ? LTM_PRIME_2MSB_OFF :
+ LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE, myrng,
+ NULL);
+ if (err != MP_OKAY) {
+ printf("failed with err code %d\n", err);
+ return EXIT_FAILURE;
+ }
+ if (mp_count_bits(&a) != ix) {
+ printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix);
+ return EXIT_FAILURE;
+ }
+ /* let's see if it's really a safe prime */
+ mp_sub_d(&a, 1, &a);
+ mp_div_2(&a, &a);
+ mp_prime_is_prime(&a, 8, &cnt);
+ if (cnt != MP_YES) {
+ printf("sub is not prime!\n");
+ return EXIT_FAILURE;
+ }
+ }
+
+ printf("\n\n");
+
+ mp_read_radix(&a, "123456", 10);
+ mp_toradix_n(&a, buf, 10, 3);
+ printf("a == %s\n", buf);
+ mp_toradix_n(&a, buf, 10, 4);
+ printf("a == %s\n", buf);
+ mp_toradix_n(&a, buf, 10, 30);
+ printf("a == %s\n", buf);
+
+
+#if 0
+ for (;;) {
+ fgets(buf, sizeof(buf), stdin);
+ mp_read_radix(&a, buf, 10);
+ mp_prime_next_prime(&a, 5, 1);
+ mp_toradix(&a, buf, 10);
+ printf("%s, %lu\n", buf, a.dp[0] & 3);
+ }
+#endif
+
+ /* test mp_cnt_lsb */
+ printf("testing mp_cnt_lsb...\n");
+ mp_set(&a, 1);
+ for (ix = 0; ix < 1024; ix++) {
+ if (mp_cnt_lsb(&a) != ix) {
+ printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a));
+ return 0;
+ }
+ mp_mul_2(&a, &a);
+ }
+
+/* test mp_reduce_2k */
+ printf("Testing mp_reduce_2k...\n");
+ for (cnt = 3; cnt <= 128; ++cnt) {
+ mp_digit tmp;
+
+ mp_2expt(&a, cnt);
+ mp_sub_d(&a, 2, &a); /* a = 2**cnt - 2 */
+
+
+ printf("\nTesting %4d bits", cnt);
+ printf("(%d)", mp_reduce_is_2k(&a));
+ mp_reduce_2k_setup(&a, &tmp);
+ printf("(%d)", tmp);
+ for (ix = 0; ix < 1000; ix++) {
+ if (!(ix & 127)) {
+ printf(".");
+ fflush(stdout);
+ }
+ mp_rand(&b, (cnt / DIGIT_BIT + 1) * 2);
+ mp_copy(&c, &b);
+ mp_mod(&c, &a, &c);
+ mp_reduce_2k(&b, &a, 2);
+ if (mp_cmp(&c, &b)) {
+ printf("FAILED\n");
+ exit(0);
+ }
+ }
+ }
+
+/* test mp_div_3 */
+ printf("Testing mp_div_3...\n");
+ mp_set(&d, 3);
+ for (cnt = 0; cnt < 10000;) {
+ mp_digit r1, r2;
+
+ if (!(++cnt & 127))
+ printf("%9d\r", cnt);
+ mp_rand(&a, abs(rand()) % 128 + 1);
+ mp_div(&a, &d, &b, &e);
+ mp_div_3(&a, &c, &r2);
+
+ if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
+ printf("\n\nmp_div_3 => Failure\n");
+ }
+ }
+ printf("\n\nPassed div_3 testing\n");
+
+/* test the DR reduction */
+ printf("testing mp_dr_reduce...\n");
+ for (cnt = 2; cnt < 32; cnt++) {
+ printf("%d digit modulus\n", cnt);
+ mp_grow(&a, cnt);
+ mp_zero(&a);
+ for (ix = 1; ix < cnt; ix++) {
+ a.dp[ix] = MP_MASK;
+ }
+ a.used = cnt;
+ a.dp[0] = 3;
+
+ mp_rand(&b, cnt - 1);
+ mp_copy(&b, &c);
+
+ rr = 0;
+ do {
+ if (!(rr & 127)) {
+ printf("%9lu\r", rr);
+ fflush(stdout);
+ }
+ mp_sqr(&b, &b);
+ mp_add_d(&b, 1, &b);
+ mp_copy(&b, &c);
+
+ mp_mod(&b, &a, &b);
+ mp_dr_reduce(&c, &a, (((mp_digit) 1) << DIGIT_BIT) - a.dp[0]);
+
+ if (mp_cmp(&b, &c) != MP_EQ) {
+ printf("Failed on trial %lu\n", rr);
+ exit(-1);
+
+ }
+ } while (++rr < 500);
+ printf("Passed DR test for %d digits\n", cnt);
+ }
+
+#endif
+
+/* test the mp_reduce_2k_l code */
+#if 0
+#if 0
+/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
+ mp_2expt(&a, 1024);
+ mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
+ mp_sub(&a, &b, &a);
+#elif 1
+/* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */
+ mp_2expt(&a, 2048);
+ mp_read_radix(&b,
+ "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
+ 16);
+ mp_sub(&a, &b, &a);
+#endif
+
+ mp_todecimal(&a, buf);
+ printf("p==%s\n", buf);
+/* now mp_reduce_is_2k_l() should return */
+ if (mp_reduce_is_2k_l(&a) != 1) {
+ printf("mp_reduce_is_2k_l() return 0, should be 1\n");
+ return EXIT_FAILURE;
+ }
+ mp_reduce_2k_setup_l(&a, &d);
+ /* now do a million square+1 to see if it varies */
+ mp_rand(&b, 64);
+ mp_mod(&b, &a, &b);
+ mp_copy(&b, &c);
+ printf("testing mp_reduce_2k_l...");
+ fflush(stdout);
+ for (cnt = 0; cnt < (1UL << 20); cnt++) {
+ mp_sqr(&b, &b);
+ mp_add_d(&b, 1, &b);
+ mp_reduce_2k_l(&b, &a, &d);
+ mp_sqr(&c, &c);
+ mp_add_d(&c, 1, &c);
+ mp_mod(&c, &a, &c);
+ if (mp_cmp(&b, &c) != MP_EQ) {
+ printf("mp_reduce_2k_l() failed at step %lu\n", cnt);
+ mp_tohex(&b, buf);
+ printf("b == %s\n", buf);
+ mp_tohex(&c, buf);
+ printf("c == %s\n", buf);
+ return EXIT_FAILURE;
+ }
+ }
+ printf("...Passed\n");
+#endif
+
+ div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
+ sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
+ sub_d_n = 0;
+
+ /* force KARA and TOOM to enable despite cutoffs */
+ KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
+ TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;
+
+ for (;;) {
+ /* randomly clear and re-init one variable, this has the affect of triming the alloc space */
+ switch (abs(rand()) % 7) {
+ case 0:
+ mp_clear(&a);
+ mp_init(&a);
+ break;
+ case 1:
+ mp_clear(&b);
+ mp_init(&b);
+ break;
+ case 2:
+ mp_clear(&c);
+ mp_init(&c);
+ break;
+ case 3:
+ mp_clear(&d);
+ mp_init(&d);
+ break;
+ case 4:
+ mp_clear(&e);
+ mp_init(&e);
+ break;
+ case 5:
+ mp_clear(&f);
+ mp_init(&f);
+ break;
+ case 6:
+ break; /* don't clear any */
+ }
+
+
+ printf
+ ("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
+ add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
+ expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
+ fgets(cmd, 4095, stdin);
+ cmd[strlen(cmd) - 1] = 0;
+ printf("%s ]\r", cmd);
+ fflush(stdout);
+ if (!strcmp(cmd, "mul2d")) {
+ ++mul2d_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ sscanf(buf, "%d", &rr);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+
+ mp_mul_2d(&a, rr, &a);
+ a.sign = b.sign;
+ if (mp_cmp(&a, &b) != MP_EQ) {
+ printf("mul2d failed, rr == %d\n", rr);
+ draw(&a);
+ draw(&b);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "div2d")) {
+ ++div2d_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ sscanf(buf, "%d", &rr);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+
+ mp_div_2d(&a, rr, &a, &e);
+ a.sign = b.sign;
+ if (a.used == b.used && a.used == 0) {
+ a.sign = b.sign = MP_ZPOS;
+ }
+ if (mp_cmp(&a, &b) != MP_EQ) {
+ printf("div2d failed, rr == %d\n", rr);
+ draw(&a);
+ draw(&b);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "add")) {
+ ++add_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ mp_copy(&a, &d);
+ mp_add(&d, &b, &d);
+ if (mp_cmp(&c, &d) != MP_EQ) {
+ printf("add %lu failure!\n", add_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ return 0;
+ }
+
+ /* test the sign/unsigned storage functions */
+
+ rr = mp_signed_bin_size(&c);
+ mp_to_signed_bin(&c, (unsigned char *) cmd);
+ memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
+ mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
+ if (mp_cmp(&c, &d) != MP_EQ) {
+ printf("mp_signed_bin failure!\n");
+ draw(&c);
+ draw(&d);
+ return 0;
+ }
+
+
+ rr = mp_unsigned_bin_size(&c);
+ mp_to_unsigned_bin(&c, (unsigned char *) cmd);
+ memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
+ mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
+ if (mp_cmp_mag(&c, &d) != MP_EQ) {
+ printf("mp_unsigned_bin failure!\n");
+ draw(&c);
+ draw(&d);
+ return 0;
+ }
+
+ } else if (!strcmp(cmd, "sub")) {
+ ++sub_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ mp_copy(&a, &d);
+ mp_sub(&d, &b, &d);
+ if (mp_cmp(&c, &d) != MP_EQ) {
+ printf("sub %lu failure!\n", sub_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "mul")) {
+ ++mul_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ mp_copy(&a, &d);
+ mp_mul(&d, &b, &d);
+ if (mp_cmp(&c, &d) != MP_EQ) {
+ printf("mul %lu failure!\n", mul_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "div")) {
+ ++div_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&d, buf, 64);
+
+ mp_div(&a, &b, &e, &f);
+ if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
+ printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
+ mp_cmp(&d, &f));
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ draw(&e);
+ draw(&f);
+ return 0;
+ }
+
+ } else if (!strcmp(cmd, "sqr")) {
+ ++sqr_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ mp_copy(&a, &c);
+ mp_sqr(&c, &c);
+ if (mp_cmp(&b, &c) != MP_EQ) {
+ printf("sqr %lu failure!\n", sqr_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "gcd")) {
+ ++gcd_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ mp_copy(&a, &d);
+ mp_gcd(&d, &b, &d);
+ d.sign = c.sign;
+ if (mp_cmp(&c, &d) != MP_EQ) {
+ printf("gcd %lu failure!\n", gcd_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "lcm")) {
+ ++lcm_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ mp_copy(&a, &d);
+ mp_lcm(&d, &b, &d);
+ d.sign = c.sign;
+ if (mp_cmp(&c, &d) != MP_EQ) {
+ printf("lcm %lu failure!\n", lcm_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "expt")) {
+ ++expt_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&d, buf, 64);
+ mp_copy(&a, &e);
+ mp_exptmod(&e, &b, &c, &e);
+ if (mp_cmp(&d, &e) != MP_EQ) {
+ printf("expt %lu failure!\n", expt_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ draw(&e);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "invmod")) {
+ ++inv_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&c, buf, 64);
+ mp_invmod(&a, &b, &d);
+ mp_mulmod(&d, &a, &b, &e);
+ if (mp_cmp_d(&e, 1) != MP_EQ) {
+ printf("inv [wrong value from MPI?!] failure\n");
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ draw(&d);
+ mp_gcd(&a, &b, &e);
+ draw(&e);
+ return 0;
+ }
+
+ } else if (!strcmp(cmd, "div2")) {
+ ++div2_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ mp_div_2(&a, &c);
+ if (mp_cmp(&c, &b) != MP_EQ) {
+ printf("div_2 %lu failure\n", div2_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "mul2")) {
+ ++mul2_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ mp_mul_2(&a, &c);
+ if (mp_cmp(&c, &b) != MP_EQ) {
+ printf("mul_2 %lu failure\n", mul2_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "add_d")) {
+ ++add_d_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ sscanf(buf, "%d", &ix);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ mp_add_d(&a, ix, &c);
+ if (mp_cmp(&b, &c) != MP_EQ) {
+ printf("add_d %lu failure\n", add_d_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ printf("d == %d\n", ix);
+ return 0;
+ }
+ } else if (!strcmp(cmd, "sub_d")) {
+ ++sub_d_n;
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&a, buf, 64);
+ fgets(buf, 4095, stdin);
+ sscanf(buf, "%d", &ix);
+ fgets(buf, 4095, stdin);
+ mp_read_radix(&b, buf, 64);
+ mp_sub_d(&a, ix, &c);
+ if (mp_cmp(&b, &c) != MP_EQ) {
+ printf("sub_d %lu failure\n", sub_d_n);
+ draw(&a);
+ draw(&b);
+ draw(&c);
+ printf("d == %d\n", ix);
+ return 0;
+ }
+ }
+ }
+ return 0;
+}
+
+/* $Source: /cvs/libtom/libtommath/demo/demo.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2005/06/24 11:32:07 $ */
diff --git a/libtommath/demo/timing.c b/libtommath/demo/timing.c
new file mode 100644
index 0000000..d4660a9
--- /dev/null
+++ b/libtommath/demo/timing.c
@@ -0,0 +1,319 @@
+#include <tommath.h>
+#include <time.h>
+
+ulong64 _tt;
+
+#ifdef IOWNANATHLON
+#include <unistd.h>
+#define SLEEP sleep(4)
+#else
+#define SLEEP
+#endif
+
+
+void ndraw(mp_int * a, char *name)
+{
+ char buf[4096];
+
+ printf("%s: ", name);
+ mp_toradix(a, buf, 64);
+ printf("%s\n", buf);
+}
+
+static void draw(mp_int * a)
+{
+ ndraw(a, "");
+}
+
+
+unsigned long lfsr = 0xAAAAAAAAUL;
+
+int lbit(void)
+{
+ if (lfsr & 0x80000000UL) {
+ lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
+ return 1;
+ } else {
+ lfsr <<= 1;
+ return 0;
+ }
+}
+
+/* RDTSC from Scott Duplichan */
+static ulong64 TIMFUNC(void)
+{
+#if defined __GNUC__
+#if defined(__i386__) || defined(__x86_64__)
+ unsigned long long a;
+ __asm__ __volatile__("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::
+ "m"(a):"%eax", "%edx");
+ return a;
+#else /* gcc-IA64 version */
+ unsigned long result;
+ __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");
+
+ while (__builtin_expect((int) result == -1, 0))
+ __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");
+
+ return result;
+#endif
+
+ // Microsoft and Intel Windows compilers
+#elif defined _M_IX86
+ __asm rdtsc
+#elif defined _M_AMD64
+ return __rdtsc();
+#elif defined _M_IA64
+#if defined __INTEL_COMPILER
+#include <ia64intrin.h>
+#endif
+ return __getReg(3116);
+#else
+#error need rdtsc function for this build
+#endif
+}
+
+#define DO(x) x; x;
+//#define DO4(x) DO2(x); DO2(x);
+//#define DO8(x) DO4(x); DO4(x);
+//#define DO(x) DO8(x); DO8(x);
+
+int main(void)
+{
+ ulong64 tt, gg, CLK_PER_SEC;
+ FILE *log, *logb, *logc, *logd;
+ mp_int a, b, c, d, e, f;
+ int n, cnt, ix, old_kara_m, old_kara_s;
+ unsigned rr;
+
+ mp_init(&a);
+ mp_init(&b);
+ mp_init(&c);
+ mp_init(&d);
+ mp_init(&e);
+ mp_init(&f);
+
+ srand(time(NULL));
+
+
+ /* temp. turn off TOOM */
+ TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;
+
+ CLK_PER_SEC = TIMFUNC();
+ sleep(1);
+ CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;
+
+ printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
+ goto exptmod;
+ log = fopen("logs/add.log", "w");
+ for (cnt = 8; cnt <= 128; cnt += 8) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_add(&a, &b, &c));
+ gg = (TIMFUNC() - gg) >> 1;
+ if (tt > gg)
+ tt = gg;
+ } while (++rr < 100000);
+ printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
+ mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+ fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
+ fflush(log);
+ }
+ fclose(log);
+
+ log = fopen("logs/sub.log", "w");
+ for (cnt = 8; cnt <= 128; cnt += 8) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_sub(&a, &b, &c));
+ gg = (TIMFUNC() - gg) >> 1;
+ if (tt > gg)
+ tt = gg;
+ } while (++rr < 100000);
+
+ printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
+ mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+ fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
+ fflush(log);
+ }
+ fclose(log);
+
+ /* do mult/square twice, first without karatsuba and second with */
+ multtest:
+ old_kara_m = KARATSUBA_MUL_CUTOFF;
+ old_kara_s = KARATSUBA_SQR_CUTOFF;
+ for (ix = 0; ix < 2; ix++) {
+ printf("With%s Karatsuba\n", (ix == 0) ? "out" : "");
+
+ KARATSUBA_MUL_CUTOFF = (ix == 0) ? 9999 : old_kara_m;
+ KARATSUBA_SQR_CUTOFF = (ix == 0) ? 9999 : old_kara_s;
+
+ log = fopen((ix == 0) ? "logs/mult.log" : "logs/mult_kara.log", "w");
+ for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_mul(&a, &b, &c));
+ gg = (TIMFUNC() - gg) >> 1;
+ if (tt > gg)
+ tt = gg;
+ } while (++rr < 100);
+ printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n",
+ mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+ fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
+ fflush(log);
+ }
+ fclose(log);
+
+ log = fopen((ix == 0) ? "logs/sqr.log" : "logs/sqr_kara.log", "w");
+ for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_sqr(&a, &b));
+ gg = (TIMFUNC() - gg) >> 1;
+ if (tt > gg)
+ tt = gg;
+ } while (++rr < 100);
+ printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n",
+ mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+ fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt);
+ fflush(log);
+ }
+ fclose(log);
+
+ }
+ exptmod:
+
+ {
+ char *primes[] = {
+ /* 2K large moduli */
+ "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217",
+ "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169",
+ "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283",
+ /* 2K moduli mersenne primes */
+ "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
+ "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
+ "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
+ "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
+ "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
+ "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",
+
+ /* DR moduli */
+ "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
+ "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
+ "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
+ "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
+ "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
+ "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
+ "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",
+
+ /* generic unrestricted moduli */
+ "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
+ "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
+ "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
+ "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
+ "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
+ "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
+ "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
+ NULL
+ };
+ log = fopen("logs/expt.log", "w");
+ logb = fopen("logs/expt_dr.log", "w");
+ logc = fopen("logs/expt_2k.log", "w");
+ logd = fopen("logs/expt_2kl.log", "w");
+ for (n = 0; primes[n]; n++) {
+ SLEEP;
+ mp_read_radix(&a, primes[n], 10);
+ mp_zero(&b);
+ for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) {
+ mp_mul_2(&b, &b);
+ b.dp[0] |= lbit();
+ b.used += 1;
+ }
+ mp_sub_d(&a, 1, &c);
+ mp_mod(&b, &c, &b);
+ mp_set(&c, 3);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_exptmod(&c, &b, &a, &d));
+ gg = (TIMFUNC() - gg) >> 1;
+ if (tt > gg)
+ tt = gg;
+ } while (++rr < 10);
+ mp_sub_d(&a, 1, &e);
+ mp_sub(&e, &b, &b);
+ mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */
+ mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */
+ if (mp_cmp_d(&d, 1)) {
+ printf("Different (%d)!!!\n", mp_count_bits(&a));
+ draw(&d);
+ exit(0);
+ }
+ printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n",
+ mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+ fprintf(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log,
+ "%d %9llu\n", mp_count_bits(&a), tt);
+ }
+ }
+ fclose(log);
+ fclose(logb);
+ fclose(logc);
+ fclose(logd);
+
+ log = fopen("logs/invmod.log", "w");
+ for (cnt = 4; cnt <= 128; cnt += 4) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+
+ do {
+ mp_add_d(&b, 1, &b);
+ mp_gcd(&a, &b, &c);
+ } while (mp_cmp_d(&c, 1) != MP_EQ);
+
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_invmod(&b, &a, &c));
+ gg = (TIMFUNC() - gg) >> 1;
+ if (tt > gg)
+ tt = gg;
+ } while (++rr < 1000);
+ mp_mulmod(&b, &c, &a, &d);
+ if (mp_cmp_d(&d, 1) != MP_EQ) {
+ printf("Failed to invert\n");
+ return 0;
+ }
+ printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n",
+ mp_count_bits(&a), CLK_PER_SEC / tt, tt);
+ fprintf(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
+ }
+ fclose(log);
+
+ return 0;
+}
+
+/* $Source: /cvs/libtom/libtommath/demo/timing.c,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/dep.pl b/libtommath/dep.pl
new file mode 100644
index 0000000..c39e27e
--- /dev/null
+++ b/libtommath/dep.pl
@@ -0,0 +1,123 @@
+#!/usr/bin/perl
+#
+# Walk through source, add labels and make classes
+#
+#use strict;
+
+my %deplist;
+
+#open class file and write preamble
+open(CLASS, ">tommath_class.h") or die "Couldn't open tommath_class.h for writing\n";
+print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined(LTM2)\n#define LTM3\n#endif\n#if defined(LTM1)\n#define LTM2\n#endif\n#define LTM1\n\n#if defined(LTM_ALL)\n";
+
+foreach my $filename (glob "bn*.c") {
+ my $define = $filename;
+
+print "Processing $filename\n";
+
+ # convert filename to upper case so we can use it as a define
+ $define =~ tr/[a-z]/[A-Z]/;
+ $define =~ tr/\./_/;
+ print CLASS "#define $define\n";
+
+ # now copy text and apply #ifdef as required
+ my $apply = 0;
+ open(SRC, "<$filename");
+ open(OUT, ">tmp");
+
+ # first line will be the #ifdef
+ my $line = <SRC>;
+ if ($line =~ /include/) {
+ print OUT $line;
+ } else {
+ print OUT "#include <tommath.h>\n#ifdef $define\n$line";
+ $apply = 1;
+ }
+ while (<SRC>) {
+ if (!($_ =~ /tommath\.h/)) {
+ print OUT $_;
+ }
+ }
+ if ($apply == 1) {
+ print OUT "#endif\n";
+ }
+ close SRC;
+ close OUT;
+
+ unlink($filename);
+ rename("tmp", $filename);
+}
+print CLASS "#endif\n\n";
+
+# now do classes
+
+foreach my $filename (glob "bn*.c") {
+ open(SRC, "<$filename") or die "Can't open source file!\n";
+
+ # convert filename to upper case so we can use it as a define
+ $filename =~ tr/[a-z]/[A-Z]/;
+ $filename =~ tr/\./_/;
+
+ print CLASS "#if defined($filename)\n";
+ my $list = $filename;
+
+ # scan for mp_* and make classes
+ while (<SRC>) {
+ my $line = $_;
+ while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) {
+ $line = $';
+ # now $& is the match, we want to skip over LTM keywords like
+ # mp_int, mp_word, mp_digit
+ if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int")) {
+ my $a = $&;
+ $a =~ tr/[a-z]/[A-Z]/;
+ $a = "BN_" . $a . "_C";
+ if (!($list =~ /$a/)) {
+ print CLASS " #define $a\n";
+ }
+ $list = $list . "," . $a;
+ }
+ }
+ }
+ @deplist{$filename} = $list;
+
+ print CLASS "#endif\n\n";
+ close SRC;
+}
+
+print CLASS "#ifdef LTM3\n#define LTM_LAST\n#endif\n#include <tommath_superclass.h>\n#include <tommath_class.h>\n#else\n#define LTM_LAST\n#endif\n";
+close CLASS;
+
+#now let's make a cool call graph...
+
+open(OUT,">callgraph.txt");
+$indent = 0;
+foreach (keys %deplist) {
+ $list = "";
+ draw_func(@deplist{$_});
+ print OUT "\n\n";
+}
+close(OUT);
+
+sub draw_func()
+{
+ my @funcs = split(",", $_[0]);
+ if ($list =~ /@funcs[0]/) {
+ return;
+ } else {
+ $list = $list . @funcs[0];
+ }
+ if ($indent == 0) { }
+ elsif ($indent >= 1) { print OUT "| " x ($indent - 1) . "+--->"; }
+ print OUT @funcs[0] . "\n";
+ shift @funcs;
+ my $temp = $list;
+ foreach my $i (@funcs) {
+ ++$indent;
+ draw_func(@deplist{$i});
+ --$indent;
+ }
+ $list = $temp;
+}
+
+
diff --git a/libtommath/etc/2kprime.1 b/libtommath/etc/2kprime.1
new file mode 100644
index 0000000..c41ded1
--- /dev/null
+++ b/libtommath/etc/2kprime.1
@@ -0,0 +1,2 @@
+256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823
+512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979
diff --git a/libtommath/etc/2kprime.c b/libtommath/etc/2kprime.c
new file mode 100644
index 0000000..c09818f
--- /dev/null
+++ b/libtommath/etc/2kprime.c
@@ -0,0 +1,84 @@
+/* Makes safe primes of a 2k nature */
+#include <tommath.h>
+#include <time.h>
+
+int sizes[] = {256, 512, 768, 1024, 1536, 2048, 3072, 4096};
+
+int main(void)
+{
+ char buf[2000];
+ int x, y;
+ mp_int q, p;
+ FILE *out;
+ clock_t t1;
+ mp_digit z;
+
+ mp_init_multi(&q, &p, NULL);
+
+ out = fopen("2kprime.1", "w");
+ for (x = 0; x < (int)(sizeof(sizes) / sizeof(sizes[0])); x++) {
+ top:
+ mp_2expt(&q, sizes[x]);
+ mp_add_d(&q, 3, &q);
+ z = -3;
+
+ t1 = clock();
+ for(;;) {
+ mp_sub_d(&q, 4, &q);
+ z += 4;
+
+ if (z > MP_MASK) {
+ printf("No primes of size %d found\n", sizes[x]);
+ break;
+ }
+
+ if (clock() - t1 > CLOCKS_PER_SEC) {
+ printf("."); fflush(stdout);
+// sleep((clock() - t1 + CLOCKS_PER_SEC/2)/CLOCKS_PER_SEC);
+ t1 = clock();
+ }
+
+ /* quick test on q */
+ mp_prime_is_prime(&q, 1, &y);
+ if (y == 0) {
+ continue;
+ }
+
+ /* find (q-1)/2 */
+ mp_sub_d(&q, 1, &p);
+ mp_div_2(&p, &p);
+ mp_prime_is_prime(&p, 3, &y);
+ if (y == 0) {
+ continue;
+ }
+
+ /* test on q */
+ mp_prime_is_prime(&q, 3, &y);
+ if (y == 0) {
+ continue;
+ }
+
+ break;
+ }
+
+ if (y == 0) {
+ ++sizes[x];
+ goto top;
+ }
+
+ mp_toradix(&q, buf, 10);
+ printf("\n\n%d-bits (k = %lu) = %s\n", sizes[x], z, buf);
+ fprintf(out, "%d-bits (k = %lu) = %s\n", sizes[x], z, buf); fflush(out);
+ }
+
+ return 0;
+}
+
+
+
+
+
+
+/* $Source: /cvs/libtom/libtommath/etc/2kprime.c,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/etc/drprime.c b/libtommath/etc/drprime.c
new file mode 100644
index 0000000..e413985
--- /dev/null
+++ b/libtommath/etc/drprime.c
@@ -0,0 +1,64 @@
+/* Makes safe primes of a DR nature */
+#include <tommath.h>
+
+int sizes[] = { 1+256/DIGIT_BIT, 1+512/DIGIT_BIT, 1+768/DIGIT_BIT, 1+1024/DIGIT_BIT, 1+2048/DIGIT_BIT, 1+4096/DIGIT_BIT };
+int main(void)
+{
+ int res, x, y;
+ char buf[4096];
+ FILE *out;
+ mp_int a, b;
+
+ mp_init(&a);
+ mp_init(&b);
+
+ out = fopen("drprimes.txt", "w");
+ for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) {
+ top:
+ printf("Seeking a %d-bit safe prime\n", sizes[x] * DIGIT_BIT);
+ mp_grow(&a, sizes[x]);
+ mp_zero(&a);
+ for (y = 1; y < sizes[x]; y++) {
+ a.dp[y] = MP_MASK;
+ }
+
+ /* make a DR modulus */
+ a.dp[0] = -1;
+ a.used = sizes[x];
+
+ /* now loop */
+ res = 0;
+ for (;;) {
+ a.dp[0] += 4;
+ if (a.dp[0] >= MP_MASK) break;
+ mp_prime_is_prime(&a, 1, &res);
+ if (res == 0) continue;
+ printf("."); fflush(stdout);
+ mp_sub_d(&a, 1, &b);
+ mp_div_2(&b, &b);
+ mp_prime_is_prime(&b, 3, &res);
+ if (res == 0) continue;
+ mp_prime_is_prime(&a, 3, &res);
+ if (res == 1) break;
+ }
+
+ if (res != 1) {
+ printf("Error not DR modulus\n"); sizes[x] += 1; goto top;
+ } else {
+ mp_toradix(&a, buf, 10);
+ printf("\n\np == %s\n\n", buf);
+ fprintf(out, "%d-bit prime:\np == %s\n\n", mp_count_bits(&a), buf); fflush(out);
+ }
+ }
+ fclose(out);
+
+ mp_clear(&a);
+ mp_clear(&b);
+
+ return 0;
+}
+
+
+/* $Source: /cvs/libtom/libtommath/etc/drprime.c,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/etc/drprimes.28 b/libtommath/etc/drprimes.28
new file mode 100644
index 0000000..9d438ad
--- /dev/null
+++ b/libtommath/etc/drprimes.28
@@ -0,0 +1,25 @@
+DR safe primes for 28-bit digits.
+
+224-bit prime:
+p == 26959946667150639794667015087019630673637144422540572481103341844143
+
+532-bit prime:
+p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747
+
+784-bit prime:
+p == 101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039
+
+1036-bit prime:
+p == 736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821798437127
+
+1540-bit prime:
+p == 38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783
+
+2072-bit prime:
+p == 542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147
+
+3080-bit prime:
+p == 1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503
+
+4116-bit prime:
+p == 1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679
diff --git a/libtommath/etc/drprimes.txt b/libtommath/etc/drprimes.txt
new file mode 100644
index 0000000..7c97f67
--- /dev/null
+++ b/libtommath/etc/drprimes.txt
@@ -0,0 +1,9 @@
+300-bit prime:
+p == 2037035976334486086268445688409378161051468393665936250636140449354381298610415201576637819
+
+540-bit prime:
+p == 3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206810991770626477344739
+
+780-bit prime:
+p == 6359114106063703798370219984742410466332205126109989319225557147754704702203399726411277962562135973685197744935448875852478791860694279747355800678568677946181447581781401213133886609947027230004277244697462656003655947791725966271167
+
diff --git a/libtommath/etc/makefile b/libtommath/etc/makefile
new file mode 100644
index 0000000..99154d8
--- /dev/null
+++ b/libtommath/etc/makefile
@@ -0,0 +1,50 @@
+CFLAGS += -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops -I../
+
+# default lib name (requires install with root)
+# LIBNAME=-ltommath
+
+# libname when you can't install the lib with install
+LIBNAME=../libtommath.a
+
+#provable primes
+pprime: pprime.o
+ $(CC) pprime.o $(LIBNAME) -o pprime
+
+# portable [well requires clock()] tuning app
+tune: tune.o
+ $(CC) tune.o $(LIBNAME) -o tune
+
+# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
+tune86: tune.c
+ nasm -f coff timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+# for cygwin
+tune86c: tune.c
+ nasm -f gnuwin32 timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+#make tune86 for linux or any ELF format
+tune86l: tune.c
+ nasm -f elf -DUSE_ELF timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
+
+# spits out mersenne primes
+mersenne: mersenne.o
+ $(CC) mersenne.o $(LIBNAME) -o mersenne
+
+# fines DR safe primes for the given config
+drprime: drprime.o
+ $(CC) drprime.o $(LIBNAME) -o drprime
+
+# fines 2k safe primes for the given config
+2kprime: 2kprime.o
+ $(CC) 2kprime.o $(LIBNAME) -o 2kprime
+
+mont: mont.o
+ $(CC) mont.o $(LIBNAME) -o mont
+
+
+clean:
+ rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat \
+ *.da *.dyn *.dpi *~
diff --git a/libtommath/etc/makefile.icc b/libtommath/etc/makefile.icc
new file mode 100644
index 0000000..8a1ffff
--- /dev/null
+++ b/libtommath/etc/makefile.icc
@@ -0,0 +1,67 @@
+CC = icc
+
+CFLAGS += -I../
+
+# optimize for SPEED
+#
+# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
+# -ax? specifies make code specifically for ? but compatible with IA-32
+# -x? specifies compile solely for ? [not specifically IA-32 compatible]
+#
+# where ? is
+# K - PIII
+# W - first P4 [Williamette]
+# N - P4 Northwood
+# P - P4 Prescott
+# B - Blend of P4 and PM [mobile]
+#
+# Default to just generic max opts
+CFLAGS += -O3 -xP -ip
+
+# default lib name (requires install with root)
+# LIBNAME=-ltommath
+
+# libname when you can't install the lib with install
+LIBNAME=../libtommath.a
+
+#provable primes
+pprime: pprime.o
+ $(CC) pprime.o $(LIBNAME) -o pprime
+
+# portable [well requires clock()] tuning app
+tune: tune.o
+ $(CC) tune.o $(LIBNAME) -o tune
+
+# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
+tune86: tune.c
+ nasm -f coff timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+# for cygwin
+tune86c: tune.c
+ nasm -f gnuwin32 timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+#make tune86 for linux or any ELF format
+tune86l: tune.c
+ nasm -f elf -DUSE_ELF timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
+
+# spits out mersenne primes
+mersenne: mersenne.o
+ $(CC) mersenne.o $(LIBNAME) -o mersenne
+
+# fines DR safe primes for the given config
+drprime: drprime.o
+ $(CC) drprime.o $(LIBNAME) -o drprime
+
+# fines 2k safe primes for the given config
+2kprime: 2kprime.o
+ $(CC) 2kprime.o $(LIBNAME) -o 2kprime
+
+mont: mont.o
+ $(CC) mont.o $(LIBNAME) -o mont
+
+
+clean:
+ rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il
diff --git a/libtommath/etc/makefile.msvc b/libtommath/etc/makefile.msvc
new file mode 100644
index 0000000..2833372
--- /dev/null
+++ b/libtommath/etc/makefile.msvc
@@ -0,0 +1,23 @@
+#MSVC Makefile
+#
+#Tom St Denis
+
+CFLAGS = /I../ /Ox /DWIN32 /W3
+
+pprime: pprime.obj
+ cl pprime.obj ../tommath.lib
+
+mersenne: mersenne.obj
+ cl mersenne.obj ../tommath.lib
+
+tune: tune.obj
+ cl tune.obj ../tommath.lib
+
+mont: mont.obj
+ cl mont.obj ../tommath.lib
+
+drprime: drprime.obj
+ cl drprime.obj ../tommath.lib
+
+2kprime: 2kprime.obj
+ cl 2kprime.obj ../tommath.lib
diff --git a/libtommath/etc/mersenne.c b/libtommath/etc/mersenne.c
new file mode 100644
index 0000000..6a6497a
--- /dev/null
+++ b/libtommath/etc/mersenne.c
@@ -0,0 +1,144 @@
+/* Finds Mersenne primes using the Lucas-Lehmer test
+ *
+ * Tom St Denis, tomstdenis@gmail.com
+ */
+#include <time.h>
+#include <tommath.h>
+
+int
+is_mersenne (long s, int *pp)
+{
+ mp_int n, u;
+ int res, k;
+
+ *pp = 0;
+
+ if ((res = mp_init (&n)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&u)) != MP_OKAY) {
+ goto LBL_N;
+ }
+
+ /* n = 2^s - 1 */
+ if ((res = mp_2expt(&n, s)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* set u=4 */
+ mp_set (&u, 4);
+
+ /* for k=1 to s-2 do */
+ for (k = 1; k <= s - 2; k++) {
+ /* u = u^2 - 2 mod n */
+ if ((res = mp_sqr (&u, &u)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* make sure u is positive */
+ while (u.sign == MP_NEG) {
+ if ((res = mp_add (&u, &n, &u)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* reduce */
+ if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* if u == 0 then its prime */
+ if (mp_iszero (&u) == 1) {
+ mp_prime_is_prime(&n, 8, pp);
+ if (*pp != 1) printf("FAILURE\n");
+ }
+
+ res = MP_OKAY;
+LBL_MU:mp_clear (&u);
+LBL_N:mp_clear (&n);
+ return res;
+}
+
+/* square root of a long < 65536 */
+long
+i_sqrt (long x)
+{
+ long x1, x2;
+
+ x2 = 16;
+ do {
+ x1 = x2;
+ x2 = x1 - ((x1 * x1) - x) / (2 * x1);
+ } while (x1 != x2);
+
+ if (x1 * x1 > x) {
+ --x1;
+ }
+
+ return x1;
+}
+
+/* is the long prime by brute force */
+int
+isprime (long k)
+{
+ long y, z;
+
+ y = i_sqrt (k);
+ for (z = 2; z <= y; z++) {
+ if ((k % z) == 0)
+ return 0;
+ }
+ return 1;
+}
+
+
+int
+main (void)
+{
+ int pp;
+ long k;
+ clock_t tt;
+
+ k = 3;
+
+ for (;;) {
+ /* start time */
+ tt = clock ();
+
+ /* test if 2^k - 1 is prime */
+ if (is_mersenne (k, &pp) != MP_OKAY) {
+ printf ("Whoa error\n");
+ return -1;
+ }
+
+ if (pp == 1) {
+ /* count time */
+ tt = clock () - tt;
+
+ /* display if prime */
+ printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt);
+ }
+
+ /* goto next odd exponent */
+ k += 2;
+
+ /* but make sure its prime */
+ while (isprime (k) == 0) {
+ k += 2;
+ }
+ }
+ return 0;
+}
+
+/* $Source: /cvs/libtom/libtommath/etc/mersenne.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:47 $ */
diff --git a/libtommath/etc/mont.c b/libtommath/etc/mont.c
new file mode 100644
index 0000000..393be4c
--- /dev/null
+++ b/libtommath/etc/mont.c
@@ -0,0 +1,50 @@
+/* tests the montgomery routines */
+#include <tommath.h>
+
+int main(void)
+{
+ mp_int modulus, R, p, pp;
+ mp_digit mp;
+ long x, y;
+
+ srand(time(NULL));
+ mp_init_multi(&modulus, &R, &p, &pp, NULL);
+
+ /* loop through various sizes */
+ for (x = 4; x < 256; x++) {
+ printf("DIGITS == %3ld...", x); fflush(stdout);
+
+ /* make up the odd modulus */
+ mp_rand(&modulus, x);
+ modulus.dp[0] |= 1;
+
+ /* now find the R value */
+ mp_montgomery_calc_normalization(&R, &modulus);
+ mp_montgomery_setup(&modulus, &mp);
+
+ /* now run through a bunch tests */
+ for (y = 0; y < 1000; y++) {
+ mp_rand(&p, x/2); /* p = random */
+ mp_mul(&p, &R, &pp); /* pp = R * p */
+ mp_montgomery_reduce(&pp, &modulus, mp);
+
+ /* should be equal to p */
+ if (mp_cmp(&pp, &p) != MP_EQ) {
+ printf("FAILURE!\n");
+ exit(-1);
+ }
+ }
+ printf("PASSED\n");
+ }
+
+ return 0;
+}
+
+
+
+
+
+
+/* $Source: /cvs/libtom/libtommath/etc/mont.c,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/etc/pprime.c b/libtommath/etc/pprime.c
new file mode 100644
index 0000000..317e2a0
--- /dev/null
+++ b/libtommath/etc/pprime.c
@@ -0,0 +1,400 @@
+/* Generates provable primes
+ *
+ * See http://gmail.com:8080/papers/pp.pdf for more info.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://tom.gmail.com
+ */
+#include <time.h>
+#include "tommath.h"
+
+int n_prime;
+FILE *primes;
+
+/* fast square root */
+static mp_digit
+i_sqrt (mp_word x)
+{
+ mp_word x1, x2;
+
+ x2 = x;
+ do {
+ x1 = x2;
+ x2 = x1 - ((x1 * x1) - x) / (2 * x1);
+ } while (x1 != x2);
+
+ if (x1 * x1 > x) {
+ --x1;
+ }
+
+ return x1;
+}
+
+
+/* generates a prime digit */
+static void gen_prime (void)
+{
+ mp_digit r, x, y, next;
+ FILE *out;
+
+ out = fopen("pprime.dat", "wb");
+
+ /* write first set of primes */
+ r = 3; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 5; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 7; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 11; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 13; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 17; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 19; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 23; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 29; fwrite(&r, 1, sizeof(mp_digit), out);
+ r = 31; fwrite(&r, 1, sizeof(mp_digit), out);
+
+ /* get square root, since if 'r' is composite its factors must be < than this */
+ y = i_sqrt (r);
+ next = (y + 1) * (y + 1);
+
+ for (;;) {
+ do {
+ r += 2; /* next candidate */
+ r &= MP_MASK;
+ if (r < 31) break;
+
+ /* update sqrt ? */
+ if (next <= r) {
+ ++y;
+ next = (y + 1) * (y + 1);
+ }
+
+ /* loop if divisible by 3,5,7,11,13,17,19,23,29 */
+ if ((r % 3) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 5) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 7) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 11) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 13) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 17) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 19) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 23) == 0) {
+ x = 0;
+ continue;
+ }
+ if ((r % 29) == 0) {
+ x = 0;
+ continue;
+ }
+
+ /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */
+ for (x = 30; x <= y; x += 30) {
+ if ((r % (x + 1)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 7)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 11)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 13)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 17)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 19)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 23)) == 0) {
+ x = 0;
+ break;
+ }
+ if ((r % (x + 29)) == 0) {
+ x = 0;
+ break;
+ }
+ }
+ } while (x == 0);
+ if (r > 31) { fwrite(&r, 1, sizeof(mp_digit), out); printf("%9d\r", r); fflush(stdout); }
+ if (r < 31) break;
+ }
+
+ fclose(out);
+}
+
+void load_tab(void)
+{
+ primes = fopen("pprime.dat", "rb");
+ if (primes == NULL) {
+ gen_prime();
+ primes = fopen("pprime.dat", "rb");
+ }
+ fseek(primes, 0, SEEK_END);
+ n_prime = ftell(primes) / sizeof(mp_digit);
+}
+
+mp_digit prime_digit(void)
+{
+ int n;
+ mp_digit d;
+
+ n = abs(rand()) % n_prime;
+ fseek(primes, n * sizeof(mp_digit), SEEK_SET);
+ fread(&d, 1, sizeof(mp_digit), primes);
+ return d;
+}
+
+
+/* makes a prime of at least k bits */
+int
+pprime (int k, int li, mp_int * p, mp_int * q)
+{
+ mp_int a, b, c, n, x, y, z, v;
+ int res, ii;
+ static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
+
+ /* single digit ? */
+ if (k <= (int) DIGIT_BIT) {
+ mp_set (p, prime_digit ());
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init (&c)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&v)) != MP_OKAY) {
+ goto LBL_C;
+ }
+
+ /* product of first 50 primes */
+ if ((res =
+ mp_read_radix (&v,
+ "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
+ 10)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ if ((res = mp_init (&a)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ /* set the prime */
+ mp_set (&a, prime_digit ());
+
+ if ((res = mp_init (&b)) != MP_OKAY) {
+ goto LBL_A;
+ }
+
+ if ((res = mp_init (&n)) != MP_OKAY) {
+ goto LBL_B;
+ }
+
+ if ((res = mp_init (&x)) != MP_OKAY) {
+ goto LBL_N;
+ }
+
+ if ((res = mp_init (&y)) != MP_OKAY) {
+ goto LBL_X;
+ }
+
+ if ((res = mp_init (&z)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* now loop making the single digit */
+ while (mp_count_bits (&a) < k) {
+ fprintf (stderr, "prime has %4d bits left\r", k - mp_count_bits (&a));
+ fflush (stderr);
+ top:
+ mp_set (&b, prime_digit ());
+
+ /* now compute z = a * b * 2 */
+ if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) { /* z = a * b */
+ goto LBL_Z;
+ }
+
+ if ((res = mp_copy (&z, &c)) != MP_OKAY) { /* c = a * b */
+ goto LBL_Z;
+ }
+
+ if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) { /* z = 2 * a * b */
+ goto LBL_Z;
+ }
+
+ /* n = z + 1 */
+ if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) { /* n = z + 1 */
+ goto LBL_Z;
+ }
+
+ /* check (n, v) == 1 */
+ if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */
+ goto LBL_Z;
+ }
+
+ if (mp_cmp_d (&y, 1) != MP_EQ)
+ goto top;
+
+ /* now try base x=bases[ii] */
+ for (ii = 0; ii < li; ii++) {
+ mp_set (&x, bases[ii]);
+
+ /* compute x^a mod n */
+ if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */
+ goto LBL_Z;
+ }
+
+ /* if y == 1 loop */
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* now x^2a mod n */
+ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */
+ goto LBL_Z;
+ }
+
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* compute x^b mod n */
+ if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */
+ goto LBL_Z;
+ }
+
+ /* if y == 1 loop */
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* now x^2b mod n */
+ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */
+ goto LBL_Z;
+ }
+
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* compute x^c mod n == x^ab mod n */
+ if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */
+ goto LBL_Z;
+ }
+
+ /* if y == 1 loop */
+ if (mp_cmp_d (&y, 1) == MP_EQ)
+ continue;
+
+ /* now compute (x^c mod n)^2 */
+ if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */
+ goto LBL_Z;
+ }
+
+ /* y should be 1 */
+ if (mp_cmp_d (&y, 1) != MP_EQ)
+ continue;
+ break;
+ }
+
+ /* no bases worked? */
+ if (ii == li)
+ goto top;
+
+{
+ char buf[4096];
+
+ mp_toradix(&n, buf, 10);
+ printf("Certificate of primality for:\n%s\n\n", buf);
+ mp_toradix(&a, buf, 10);
+ printf("A == \n%s\n\n", buf);
+ mp_toradix(&b, buf, 10);
+ printf("B == \n%s\n\nG == %d\n", buf, bases[ii]);
+ printf("----------------------------------------------------------------\n");
+}
+
+ /* a = n */
+ mp_copy (&n, &a);
+ }
+
+ /* get q to be the order of the large prime subgroup */
+ mp_sub_d (&n, 1, q);
+ mp_div_2 (q, q);
+ mp_div (q, &b, q, NULL);
+
+ mp_exch (&n, p);
+
+ res = MP_OKAY;
+LBL_Z:mp_clear (&z);
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_N:mp_clear (&n);
+LBL_B:mp_clear (&b);
+LBL_A:mp_clear (&a);
+LBL_V:mp_clear (&v);
+LBL_C:mp_clear (&c);
+ return res;
+}
+
+
+int
+main (void)
+{
+ mp_int p, q;
+ char buf[4096];
+ int k, li;
+ clock_t t1;
+
+ srand (time (NULL));
+ load_tab();
+
+ printf ("Enter # of bits: \n");
+ fgets (buf, sizeof (buf), stdin);
+ sscanf (buf, "%d", &k);
+
+ printf ("Enter number of bases to try (1 to 8):\n");
+ fgets (buf, sizeof (buf), stdin);
+ sscanf (buf, "%d", &li);
+
+
+ mp_init (&p);
+ mp_init (&q);
+
+ t1 = clock ();
+ pprime (k, li, &p, &q);
+ t1 = clock () - t1;
+
+ printf ("\n\nTook %ld ticks, %d bits\n", t1, mp_count_bits (&p));
+
+ mp_toradix (&p, buf, 10);
+ printf ("P == %s\n", buf);
+ mp_toradix (&q, buf, 10);
+ printf ("Q == %s\n", buf);
+
+ return 0;
+}
+
+/* $Source: /cvs/libtom/libtommath/etc/pprime.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:47 $ */
diff --git a/libtommath/etc/prime.1024 b/libtommath/etc/prime.1024
new file mode 100644
index 0000000..5636e2d
--- /dev/null
+++ b/libtommath/etc/prime.1024
@@ -0,0 +1,414 @@
+Enter # of bits:
+Enter number of bases to try (1 to 8):
+Certificate of primality for:
+36360080703173363
+
+A ==
+89963569
+
+B ==
+202082249
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+4851595597739856136987139
+
+A ==
+36360080703173363
+
+B ==
+66715963
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+19550639734462621430325731591027
+
+A ==
+4851595597739856136987139
+
+B ==
+2014867
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+10409036141344317165691858509923818734539
+
+A ==
+19550639734462621430325731591027
+
+B ==
+266207047
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1049829549988285012736475602118094726647504414203
+
+A ==
+10409036141344317165691858509923818734539
+
+B ==
+50428759
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+77194737385528288387712399596835459931920358844586615003
+
+A ==
+1049829549988285012736475602118094726647504414203
+
+B ==
+36765367
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+35663756695365208574443215955488689578374232732893628896541201763
+
+A ==
+77194737385528288387712399596835459931920358844586615003
+
+B ==
+230998627
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+16711831463502165169495622246023119698415848120292671294127567620396469803
+
+A ==
+35663756695365208574443215955488689578374232732893628896541201763
+
+B ==
+234297127
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+6163534781560285962890718925972249753147470953579266394395432475622345597103528739
+
+A ==
+16711831463502165169495622246023119698415848120292671294127567620396469803
+
+B ==
+184406323
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787
+
+A ==
+6163534781560285962890718925972249753147470953579266394395432475622345597103528739
+
+B ==
+66054487
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187
+
+A ==
+814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787
+
+B ==
+108362239
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419
+
+A ==
+176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187
+
+B ==
+127286707
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059
+
+A ==
+44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419
+
+B ==
+229284691
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979
+
+A ==
+20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059
+
+B ==
+152800771
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123
+
+A ==
+6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979
+
+B ==
+246595759
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499
+
+A ==
+3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123
+
+B ==
+4252063
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163
+
+A ==
+26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499
+
+B ==
+210605419
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187
+
+A ==
+11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163
+
+B ==
+74170111
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363
+
+A ==
+1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187
+
+B ==
+260016763
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283
+
+A ==
+857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363
+
+B ==
+102563707
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283
+
+A ==
+175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283
+
+B ==
+137747527
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403
+
+A ==
+48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283
+
+B ==
+135672847
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123
+
+A ==
+13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403
+
+B ==
+241523587
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083
+
+A ==
+6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123
+
+B ==
+248388667
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067
+
+A ==
+3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083
+
+B ==
+61849651
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739
+
+A ==
+390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067
+
+B ==
+62201707
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419
+
+A ==
+48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739
+
+B ==
+264832231
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387
+
+A ==
+25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419
+
+B ==
+54494047
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547
+
+A ==
+2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387
+
+B ==
+131594179
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683
+
+A ==
+738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547
+
+B ==
+266107603
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627
+
+A ==
+392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683
+
+B ==
+214408111
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643
+
+A ==
+168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627
+
+B ==
+44122723
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019
+
+A ==
+14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643
+
+B ==
+40808563
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843
+
+A ==
+1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019
+
+B ==
+77035759
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683
+
+A ==
+186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843
+
+B ==
+222383587
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
+
+A ==
+83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683
+
+B ==
+23407687
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723
+
+A ==
+3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
+
+B ==
+213701827
+
+G == 2
+----------------------------------------------------------------
+
+
+Took 33057 ticks, 1048 bits
+P == 1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723
+Q == 3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
diff --git a/libtommath/etc/prime.512 b/libtommath/etc/prime.512
new file mode 100644
index 0000000..cb6ec30
--- /dev/null
+++ b/libtommath/etc/prime.512
@@ -0,0 +1,205 @@
+Enter # of bits:
+Enter number of bases to try (1 to 8):
+Certificate of primality for:
+85933926807634727
+
+A ==
+253758023
+
+B ==
+169322581
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+23930198825086241462113799
+
+A ==
+85933926807634727
+
+B ==
+139236037
+
+G == 11
+----------------------------------------------------------------
+Certificate of primality for:
+6401844647261612602378676572510019
+
+A ==
+23930198825086241462113799
+
+B ==
+133760791
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+269731366027728777712034888684015329354259
+
+A ==
+6401844647261612602378676572510019
+
+B ==
+21066691
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+37942338209025571690075025099189467992329684223707
+
+A ==
+269731366027728777712034888684015329354259
+
+B ==
+70333567
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+15306904714258982484473490774101705363308327436988160248323
+
+A ==
+37942338209025571690075025099189467992329684223707
+
+B ==
+201712723
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1616744757018513392810355191503853040357155275733333124624513530099
+
+A ==
+15306904714258982484473490774101705363308327436988160248323
+
+B ==
+52810963
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+464222094814208047161771036072622485188658077940154689939306386289983787983
+
+A ==
+1616744757018513392810355191503853040357155275733333124624513530099
+
+B ==
+143566909
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+187429931674053784626487560729643601208757374994177258429930699354770049369025096447
+
+A ==
+464222094814208047161771036072622485188658077940154689939306386289983787983
+
+B ==
+201875281
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563
+
+A ==
+187429931674053784626487560729643601208757374994177258429930699354770049369025096447
+
+B ==
+268311523
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163
+
+A ==
+100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563
+
+B ==
+5834287
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623
+
+A ==
+1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163
+
+B ==
+81567097
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519
+
+A ==
+191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623
+
+B ==
+151095433
+
+G == 7
+----------------------------------------------------------------
+Certificate of primality for:
+13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803
+
+A ==
+57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519
+
+B ==
+119178679
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979
+
+A ==
+13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803
+
+B ==
+256552363
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463
+
+A ==
+7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979
+
+B ==
+86720989
+
+G == 5
+----------------------------------------------------------------
+Certificate of primality for:
+446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
+
+A ==
+1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463
+
+B ==
+182015287
+
+G == 2
+----------------------------------------------------------------
+Certificate of primality for:
+5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243
+
+A ==
+446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
+
+B ==
+5920567
+
+G == 2
+----------------------------------------------------------------
+
+
+Took 3454 ticks, 521 bits
+P == 5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243
+Q == 446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
diff --git a/libtommath/etc/timer.asm b/libtommath/etc/timer.asm
new file mode 100644
index 0000000..35890d9
--- /dev/null
+++ b/libtommath/etc/timer.asm
@@ -0,0 +1,37 @@
+; x86 timer in NASM
+;
+; Tom St Denis, tomstdenis@iahu.ca
+[bits 32]
+[section .data]
+time dd 0, 0
+
+[section .text]
+
+%ifdef USE_ELF
+[global t_start]
+t_start:
+%else
+[global _t_start]
+_t_start:
+%endif
+ push edx
+ push eax
+ rdtsc
+ mov [time+0],edx
+ mov [time+4],eax
+ pop eax
+ pop edx
+ ret
+
+%ifdef USE_ELF
+[global t_read]
+t_read:
+%else
+[global _t_read]
+_t_read:
+%endif
+ rdtsc
+ sub eax,[time+4]
+ sbb edx,[time+0]
+ ret
+
\ No newline at end of file
diff --git a/libtommath/etc/tune.c b/libtommath/etc/tune.c
new file mode 100644
index 0000000..d4a502c
--- /dev/null
+++ b/libtommath/etc/tune.c
@@ -0,0 +1,142 @@
+/* Tune the Karatsuba parameters
+ *
+ * Tom St Denis, tomstdenis@gmail.com
+ */
+#include <tommath.h>
+#include <time.h>
+
+/* how many times todo each size mult. Depends on your computer. For slow computers
+ * this can be low like 5 or 10. For fast [re: Athlon] should be 25 - 50 or so
+ */
+#define TIMES (1UL<<14UL)
+
+/* RDTSC from Scott Duplichan */
+static ulong64 TIMFUNC (void)
+ {
+ #if defined __GNUC__
+ #if defined(__i386__) || defined(__x86_64__)
+ unsigned long long a;
+ __asm__ __volatile__ ("rdtsc\nmovl %%eax,%0\nmovl %%edx,4+%0\n"::"m"(a):"%eax","%edx");
+ return a;
+ #else /* gcc-IA64 version */
+ unsigned long result;
+ __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+ while (__builtin_expect ((int) result == -1, 0))
+ __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+ return result;
+ #endif
+
+ // Microsoft and Intel Windows compilers
+ #elif defined _M_IX86
+ __asm rdtsc
+ #elif defined _M_AMD64
+ return __rdtsc ();
+ #elif defined _M_IA64
+ #if defined __INTEL_COMPILER
+ #include <ia64intrin.h>
+ #endif
+ return __getReg (3116);
+ #else
+ #error need rdtsc function for this build
+ #endif
+ }
+
+
+#ifndef X86_TIMER
+
+/* generic ISO C timer */
+ulong64 LBL_T;
+void t_start(void) { LBL_T = TIMFUNC(); }
+ulong64 t_read(void) { return TIMFUNC() - LBL_T; }
+
+#else
+extern void t_start(void);
+extern ulong64 t_read(void);
+#endif
+
+ulong64 time_mult(int size, int s)
+{
+ unsigned long x;
+ mp_int a, b, c;
+ ulong64 t1;
+
+ mp_init (&a);
+ mp_init (&b);
+ mp_init (&c);
+
+ mp_rand (&a, size);
+ mp_rand (&b, size);
+
+ if (s == 1) {
+ KARATSUBA_MUL_CUTOFF = size;
+ } else {
+ KARATSUBA_MUL_CUTOFF = 100000;
+ }
+
+ t_start();
+ for (x = 0; x < TIMES; x++) {
+ mp_mul(&a,&b,&c);
+ }
+ t1 = t_read();
+ mp_clear (&a);
+ mp_clear (&b);
+ mp_clear (&c);
+ return t1;
+}
+
+ulong64 time_sqr(int size, int s)
+{
+ unsigned long x;
+ mp_int a, b;
+ ulong64 t1;
+
+ mp_init (&a);
+ mp_init (&b);
+
+ mp_rand (&a, size);
+
+ if (s == 1) {
+ KARATSUBA_SQR_CUTOFF = size;
+ } else {
+ KARATSUBA_SQR_CUTOFF = 100000;
+ }
+
+ t_start();
+ for (x = 0; x < TIMES; x++) {
+ mp_sqr(&a,&b);
+ }
+ t1 = t_read();
+ mp_clear (&a);
+ mp_clear (&b);
+ return t1;
+}
+
+int
+main (void)
+{
+ ulong64 t1, t2;
+ int x, y;
+
+ for (x = 8; ; x += 2) {
+ t1 = time_mult(x, 0);
+ t2 = time_mult(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
+ }
+ y = x;
+
+ for (x = 8; ; x += 2) {
+ t1 = time_sqr(x, 0);
+ t2 = time_sqr(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
+ }
+ printf("KARATSUBA_MUL_CUTOFF = %d\n", y);
+ printf("KARATSUBA_SQR_CUTOFF = %d\n", x);
+
+ return 0;
+}
+
+/* $Source: /cvs/libtom/libtommath/etc/tune.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:47 $ */
diff --git a/libtommath/gen.pl b/libtommath/gen.pl
new file mode 100644
index 0000000..7236591
--- /dev/null
+++ b/libtommath/gen.pl
@@ -0,0 +1,17 @@
+#!/usr/bin/perl -w
+#
+# Generates a "single file" you can use to quickly
+# add the whole source without any makefile troubles
+#
+use strict;
+
+open( OUT, ">mpi.c" ) or die "Couldn't open mpi.c for writing: $!";
+foreach my $filename (glob "bn*.c") {
+ open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
+ print OUT "/* Start: $filename */\n";
+ print OUT while <SRC>;
+ print OUT "\n/* End: $filename */\n\n";
+ close SRC or die "Error closing $filename after reading: $!";
+}
+print OUT "\n/* EOF */\n";
+close OUT or die "Error closing mpi.c after writing: $!";
\ No newline at end of file
diff --git a/libtommath/logs/README b/libtommath/logs/README
new file mode 100644
index 0000000..ea20c81
--- /dev/null
+++ b/libtommath/logs/README
@@ -0,0 +1,13 @@
+To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package.
+Todo this type
+
+make timing ; ltmtest
+
+in the root. It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/.
+
+After doing that run "gnuplot graphs.dem" to make the PNGs. If you managed todo that all so far just open index.html to view
+them all :-)
+
+Have fun
+
+Tom
\ No newline at end of file
diff --git a/libtommath/logs/add.log b/libtommath/logs/add.log
new file mode 100644
index 0000000..43503ac
--- /dev/null
+++ b/libtommath/logs/add.log
@@ -0,0 +1,16 @@
+480 87
+960 111
+1440 135
+1920 159
+2400 200
+2880 224
+3360 248
+3840 272
+4320 296
+4800 320
+5280 344
+5760 368
+6240 392
+6720 416
+7200 440
+7680 464
diff --git a/libtommath/logs/addsub.png b/libtommath/logs/addsub.png
new file mode 100644
index 0000000..a5679ac
--- /dev/null
+++ b/libtommath/logs/addsub.png
Binary files differ
diff --git a/libtommath/logs/expt.log b/libtommath/logs/expt.log
new file mode 100644
index 0000000..70932ab
--- /dev/null
+++ b/libtommath/logs/expt.log
@@ -0,0 +1,7 @@
+513 1435869
+769 3544970
+1025 7791638
+2049 46902238
+2561 85334899
+3073 141451412
+4097 308770310
diff --git a/libtommath/logs/expt.png b/libtommath/logs/expt.png
new file mode 100644
index 0000000..9ee8bb7
--- /dev/null
+++ b/libtommath/logs/expt.png
Binary files differ
diff --git a/libtommath/logs/expt_2k.log b/libtommath/logs/expt_2k.log
new file mode 100644
index 0000000..97d325f
--- /dev/null
+++ b/libtommath/logs/expt_2k.log
@@ -0,0 +1,5 @@
+607 2109225
+1279 10148314
+2203 34126877
+3217 82716424
+4253 161569606
diff --git a/libtommath/logs/expt_2kl.log b/libtommath/logs/expt_2kl.log
new file mode 100644
index 0000000..d9ad4be
--- /dev/null
+++ b/libtommath/logs/expt_2kl.log
@@ -0,0 +1,4 @@
+1024 7705271
+2048 34286851
+4096 165207491
+521 1618631
diff --git a/libtommath/logs/expt_dr.log b/libtommath/logs/expt_dr.log
new file mode 100644
index 0000000..c6bbe07
--- /dev/null
+++ b/libtommath/logs/expt_dr.log
@@ -0,0 +1,7 @@
+532 1928550
+784 3763908
+1036 7564221
+1540 16566059
+2072 32283784
+3080 79851565
+4116 157843530
diff --git a/libtommath/logs/graphs.dem b/libtommath/logs/graphs.dem
new file mode 100644
index 0000000..dfaf613
--- /dev/null
+++ b/libtommath/logs/graphs.dem
@@ -0,0 +1,17 @@
+set terminal png
+set size 1.75
+set ylabel "Cycles per Operation"
+set xlabel "Operand size (bits)"
+
+set output "addsub.png"
+plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction"
+
+set output "mult.png"
+plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)"
+
+set output "expt.png"
+plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)"
+
+set output "invmod.png"
+plot 'invmod.log' smooth bezier title "Modular Inverse"
+
diff --git a/libtommath/logs/index.html b/libtommath/logs/index.html
new file mode 100644
index 0000000..4b68c25
--- /dev/null
+++ b/libtommath/logs/index.html
@@ -0,0 +1,27 @@
+<html>
+<head>
+<title>LibTomMath Log Plots</title>
+</head>
+<body>
+
+<h1>Addition and Subtraction</h1>
+<center><img src=addsub.png></center>
+<hr>
+
+<h1>Multipliers</h1>
+<center><img src=mult.png></center>
+<hr>
+
+<h1>Exptmod</h1>
+<center><img src=expt.png></center>
+<hr>
+
+<h1>Modular Inverse</h1>
+<center><img src=invmod.png></center>
+<hr>
+
+</body>
+</html>
+/* $Source: /cvs/libtom/libtommath/logs/index.html,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/logs/invmod.log b/libtommath/logs/invmod.log
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/libtommath/logs/invmod.log
diff --git a/libtommath/logs/invmod.png b/libtommath/logs/invmod.png
new file mode 100644
index 0000000..0a8a4ad
--- /dev/null
+++ b/libtommath/logs/invmod.png
Binary files differ
diff --git a/libtommath/logs/mult.log b/libtommath/logs/mult.log
new file mode 100644
index 0000000..33563fc
--- /dev/null
+++ b/libtommath/logs/mult.log
@@ -0,0 +1,84 @@
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diff --git a/libtommath/logs/mult.png b/libtommath/logs/mult.png
new file mode 100644
index 0000000..4f7a4ee
--- /dev/null
+++ b/libtommath/logs/mult.png
Binary files differ
diff --git a/libtommath/logs/mult_kara.log b/libtommath/logs/mult_kara.log
new file mode 100644
index 0000000..7136c79
--- /dev/null
+++ b/libtommath/logs/mult_kara.log
@@ -0,0 +1,84 @@
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diff --git a/libtommath/logs/sqr.log b/libtommath/logs/sqr.log
new file mode 100644
index 0000000..cd29fc5
--- /dev/null
+++ b/libtommath/logs/sqr.log
@@ -0,0 +1,84 @@
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diff --git a/libtommath/logs/sqr_kara.log b/libtommath/logs/sqr_kara.log
new file mode 100644
index 0000000..06355a7
--- /dev/null
+++ b/libtommath/logs/sqr_kara.log
@@ -0,0 +1,84 @@
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diff --git a/libtommath/logs/sub.log b/libtommath/logs/sub.log
new file mode 100644
index 0000000..9f84fa2
--- /dev/null
+++ b/libtommath/logs/sub.log
@@ -0,0 +1,16 @@
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diff --git a/libtommath/makefile.bcc b/libtommath/makefile.bcc
new file mode 100644
index 0000000..67743d9
--- /dev/null
+++ b/libtommath/makefile.bcc
@@ -0,0 +1,44 @@
+#
+# Borland C++Builder Makefile (makefile.bcc)
+#
+
+
+LIB = tlib
+CC = bcc32
+CFLAGS = -c -O2 -I.
+
+OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \
+bn_mp_clamp.obj bn_mp_zero.obj bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \
+bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
+bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \
+bn_mp_mul_2.obj bn_s_mp_add.obj bn_s_mp_sub.obj bn_fast_s_mp_mul_digs.obj bn_s_mp_mul_digs.obj \
+bn_fast_s_mp_mul_high_digs.obj bn_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_s_mp_sqr.obj \
+bn_mp_add.obj bn_mp_sub.obj bn_mp_karatsuba_mul.obj bn_mp_mul.obj bn_mp_karatsuba_sqr.obj \
+bn_mp_sqr.obj bn_mp_div.obj bn_mp_mod.obj bn_mp_add_d.obj bn_mp_sub_d.obj bn_mp_mul_d.obj \
+bn_mp_div_d.obj bn_mp_mod_d.obj bn_mp_expt_d.obj bn_mp_addmod.obj bn_mp_submod.obj \
+bn_mp_mulmod.obj bn_mp_sqrmod.obj bn_mp_gcd.obj bn_mp_lcm.obj bn_fast_mp_invmod.obj bn_mp_invmod.obj \
+bn_mp_reduce.obj bn_mp_montgomery_setup.obj bn_fast_mp_montgomery_reduce.obj bn_mp_montgomery_reduce.obj \
+bn_mp_exptmod_fast.obj bn_mp_exptmod.obj bn_mp_2expt.obj bn_mp_n_root.obj bn_mp_jacobi.obj bn_reverse.obj \
+bn_mp_count_bits.obj bn_mp_read_unsigned_bin.obj bn_mp_read_signed_bin.obj bn_mp_to_unsigned_bin.obj \
+bn_mp_to_signed_bin.obj bn_mp_unsigned_bin_size.obj bn_mp_signed_bin_size.obj \
+bn_mp_xor.obj bn_mp_and.obj bn_mp_or.obj bn_mp_rand.obj bn_mp_montgomery_calc_normalization.obj \
+bn_mp_prime_is_divisible.obj bn_prime_tab.obj bn_mp_prime_fermat.obj bn_mp_prime_miller_rabin.obj \
+bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
+bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
+bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
+bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
+bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \
+bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
+bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
+bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
+bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
+bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj
+
+TARGET = libtommath.lib
+
+$(TARGET): $(OBJECTS)
+
+.c.obj:
+ $(CC) $(CFLAGS) $<
+ $(LIB) $(TARGET) -+$@
diff --git a/libtommath/makefile.cygwin_dll b/libtommath/makefile.cygwin_dll
new file mode 100644
index 0000000..85a9b20
--- /dev/null
+++ b/libtommath/makefile.cygwin_dll
@@ -0,0 +1,55 @@
+#Makefile for Cygwin-GCC
+#
+#This makefile will build a Windows DLL [doesn't require cygwin to run] in the file
+#libtommath.dll. The import library is in libtommath.dll.a. Remember to add
+#"-Wl,--enable-auto-import" to your client build to avoid the auto-import warnings
+#
+#Tom St Denis
+CFLAGS += -I./ -Wall -W -Wshadow -O3 -funroll-loops -mno-cygwin
+
+#x86 optimizations [should be valid for any GCC install though]
+CFLAGS += -fomit-frame-pointer
+
+default: windll
+
+OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
+bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
+bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
+bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
+bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
+bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
+bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
+bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
+bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
+bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
+bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
+bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \
+bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
+bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
+bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
+bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
+bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
+bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
+bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
+bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+
+# make a Windows DLL via Cygwin
+windll: $(OBJECTS)
+ gcc -mno-cygwin -mdll -o libtommath.dll -Wl,--out-implib=libtommath.dll.a -Wl,--export-all-symbols *.o
+ ranlib libtommath.dll.a
+
+# build the test program using the windows DLL
+test: $(OBJECTS) windll
+ gcc $(CFLAGS) demo/demo.c libtommath.dll.a -Wl,--enable-auto-import -o test -s
+ cd mtest ; $(CC) -O3 -fomit-frame-pointer -funroll-loops mtest.c -o mtest -s
+
+/* $Source: /cvs/libtom/libtommath/makefile.cygwin_dll,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:45 $ */
diff --git a/libtommath/makefile.icc b/libtommath/makefile.icc
new file mode 100644
index 0000000..cf70ab0
--- /dev/null
+++ b/libtommath/makefile.icc
@@ -0,0 +1,116 @@
+#Makefile for ICC
+#
+#Tom St Denis
+CC=icc
+
+CFLAGS += -I./
+
+# optimize for SPEED
+#
+# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
+# -ax? specifies make code specifically for ? but compatible with IA-32
+# -x? specifies compile solely for ? [not specifically IA-32 compatible]
+#
+# where ? is
+# K - PIII
+# W - first P4 [Williamette]
+# N - P4 Northwood
+# P - P4 Prescott
+# B - Blend of P4 and PM [mobile]
+#
+# Default to just generic max opts
+CFLAGS += -O3 -xP -ip
+
+#install as this user
+USER=root
+GROUP=root
+
+default: libtommath.a
+
+#default files to install
+LIBNAME=libtommath.a
+HEADERS=tommath.h
+
+#LIBPATH-The directory for libtomcrypt to be installed to.
+#INCPATH-The directory to install the header files for libtommath.
+#DATAPATH-The directory to install the pdf docs.
+DESTDIR=
+LIBPATH=/usr/lib
+INCPATH=/usr/include
+DATAPATH=/usr/share/doc/libtommath/pdf
+
+OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
+bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
+bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
+bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
+bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
+bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
+bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
+bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
+bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
+bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
+bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
+bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \
+bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
+bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
+bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
+bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
+bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
+bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
+bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
+bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+
+libtommath.a: $(OBJECTS)
+ $(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
+ ranlib libtommath.a
+
+#make a profiled library (takes a while!!!)
+#
+# This will build the library with profile generation
+# then run the test demo and rebuild the library.
+#
+# So far I've seen improvements in the MP math
+profiled:
+ make -f makefile.icc CFLAGS="$(CFLAGS) -prof_gen -DTESTING" timing
+ ./ltmtest
+ rm -f *.a *.o ltmtest
+ make -f makefile.icc CFLAGS="$(CFLAGS) -prof_use"
+
+#make a single object profiled library
+profiled_single:
+ perl gen.pl
+ $(CC) $(CFLAGS) -prof_gen -DTESTING -c mpi.c -o mpi.o
+ $(CC) $(CFLAGS) -DTESTING -DTIMER demo/demo.c mpi.o -o ltmtest
+ ./ltmtest
+ rm -f *.o ltmtest
+ $(CC) $(CFLAGS) -prof_use -ip -DTESTING -c mpi.c -o mpi.o
+ $(AR) $(ARFLAGS) libtommath.a mpi.o
+ ranlib libtommath.a
+
+install: libtommath.a
+ install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
+ install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
+ install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
+ install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
+
+test: libtommath.a demo/demo.o
+ $(CC) demo/demo.o libtommath.a -o test
+
+mtest: test
+ cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
+
+timing: libtommath.a
+ $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest
+
+clean:
+ rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
+ *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.il etc/*.il *.dyn
+ cd etc ; make clean
+ cd pics ; make clean
diff --git a/libtommath/makefile.msvc b/libtommath/makefile.msvc
new file mode 100644
index 0000000..5edebec
--- /dev/null
+++ b/libtommath/makefile.msvc
@@ -0,0 +1,40 @@
+#MSVC Makefile
+#
+#Tom St Denis
+
+CFLAGS = /I. /Ox /DWIN32 /W3 /Fo$@
+
+default: library
+
+OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \
+bn_mp_clamp.obj bn_mp_zero.obj bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \
+bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
+bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \
+bn_mp_mul_2.obj bn_s_mp_add.obj bn_s_mp_sub.obj bn_fast_s_mp_mul_digs.obj bn_s_mp_mul_digs.obj \
+bn_fast_s_mp_mul_high_digs.obj bn_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_s_mp_sqr.obj \
+bn_mp_add.obj bn_mp_sub.obj bn_mp_karatsuba_mul.obj bn_mp_mul.obj bn_mp_karatsuba_sqr.obj \
+bn_mp_sqr.obj bn_mp_div.obj bn_mp_mod.obj bn_mp_add_d.obj bn_mp_sub_d.obj bn_mp_mul_d.obj \
+bn_mp_div_d.obj bn_mp_mod_d.obj bn_mp_expt_d.obj bn_mp_addmod.obj bn_mp_submod.obj \
+bn_mp_mulmod.obj bn_mp_sqrmod.obj bn_mp_gcd.obj bn_mp_lcm.obj bn_fast_mp_invmod.obj bn_mp_invmod.obj \
+bn_mp_reduce.obj bn_mp_montgomery_setup.obj bn_fast_mp_montgomery_reduce.obj bn_mp_montgomery_reduce.obj \
+bn_mp_exptmod_fast.obj bn_mp_exptmod.obj bn_mp_2expt.obj bn_mp_n_root.obj bn_mp_jacobi.obj bn_reverse.obj \
+bn_mp_count_bits.obj bn_mp_read_unsigned_bin.obj bn_mp_read_signed_bin.obj bn_mp_to_unsigned_bin.obj \
+bn_mp_to_signed_bin.obj bn_mp_unsigned_bin_size.obj bn_mp_signed_bin_size.obj \
+bn_mp_xor.obj bn_mp_and.obj bn_mp_or.obj bn_mp_rand.obj bn_mp_montgomery_calc_normalization.obj \
+bn_mp_prime_is_divisible.obj bn_prime_tab.obj bn_mp_prime_fermat.obj bn_mp_prime_miller_rabin.obj \
+bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
+bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
+bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
+bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
+bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \
+bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
+bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
+bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
+bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
+bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj
+
+HEADERS=tommath.h tommath_class.h tommath_superclass.h
+
+library: $(OBJECTS)
+ lib /out:tommath.lib $(OBJECTS)
diff --git a/libtommath/makefile.shared b/libtommath/makefile.shared
new file mode 100644
index 0000000..e230fb8
--- /dev/null
+++ b/libtommath/makefile.shared
@@ -0,0 +1,102 @@
+#Makefile for GCC
+#
+#Tom St Denis
+VERSION=0:40
+
+CC = libtool --mode=compile --tag=CC gcc
+
+CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare
+
+ifndef IGNORE_SPEED
+
+#for speed
+CFLAGS += -O3 -funroll-loops
+
+#for size
+#CFLAGS += -Os
+
+#x86 optimizations [should be valid for any GCC install though]
+CFLAGS += -fomit-frame-pointer
+
+endif
+
+#install as this user
+ifndef INSTALL_GROUP
+ GROUP=wheel
+else
+ GROUP=$(INSTALL_GROUP)
+endif
+
+ifndef INSTALL_USER
+ USER=root
+else
+ USER=$(INSTALL_USER)
+endif
+
+default: libtommath.la
+
+#default files to install
+ifndef LIBNAME
+ LIBNAME=libtommath.la
+endif
+ifndef LIBNAME_S
+ LIBNAME_S=libtommath.a
+endif
+HEADERS=tommath.h tommath_class.h tommath_superclass.h
+
+#LIBPATH-The directory for libtommath to be installed to.
+#INCPATH-The directory to install the header files for libtommath.
+#DATAPATH-The directory to install the pdf docs.
+DESTDIR=
+LIBPATH=/usr/lib
+INCPATH=/usr/include
+DATAPATH=/usr/share/doc/libtommath/pdf
+
+OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
+bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
+bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
+bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
+bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
+bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
+bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
+bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
+bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
+bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
+bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
+bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \
+bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
+bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
+bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
+bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
+bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
+bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
+bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
+bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+
+objs: $(OBJECTS)
+
+$(LIBNAME): $(OBJECTS)
+ libtool --mode=link gcc *.lo -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION)
+
+install: $(LIBNAME)
+ install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
+ libtool --mode=install install -c $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME)
+ install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
+ install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
+
+test: $(LIBNAME) demo/demo.o
+ gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o
+ libtool --mode=link gcc -o test demo/demo.o $(LIBNAME_S)
+
+mtest: test
+ cd mtest ; gcc $(CFLAGS) mtest.c -o mtest
+
+timing: $(LIBNAME)
+ gcc $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME_S) -o ltmtest
diff --git a/libtommath/mess.sh b/libtommath/mess.sh
new file mode 100644
index 0000000..bf639ce
--- /dev/null
+++ b/libtommath/mess.sh
@@ -0,0 +1,4 @@
+#!/bin/bash
+if cvs log $1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here" ; exit 1; fi
+
+
diff --git a/libtommath/mtest/logtab.h b/libtommath/mtest/logtab.h
new file mode 100644
index 0000000..bbefaef
--- /dev/null
+++ b/libtommath/mtest/logtab.h
@@ -0,0 +1,24 @@
+const float s_logv_2[] = {
+ 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* 0 1 2 3 */
+ 0.500000000, 0.430676558, 0.386852807, 0.356207187, /* 4 5 6 7 */
+ 0.333333333, 0.315464877, 0.301029996, 0.289064826, /* 8 9 10 11 */
+ 0.278942946, 0.270238154, 0.262649535, 0.255958025, /* 12 13 14 15 */
+ 0.250000000, 0.244650542, 0.239812467, 0.235408913, /* 16 17 18 19 */
+ 0.231378213, 0.227670249, 0.224243824, 0.221064729, /* 20 21 22 23 */
+ 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */
+ 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */
+ 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */
+ 0.193426404, 0.191958720, 0.190551412, 0.189200360, /* 36 37 38 39 */
+ 0.187901825, 0.186652411, 0.185449023, 0.184288833, /* 40 41 42 43 */
+ 0.183169251, 0.182087900, 0.181042597, 0.180031327, /* 44 45 46 47 */
+ 0.179052232, 0.178103594, 0.177183820, 0.176291434, /* 48 49 50 51 */
+ 0.175425064, 0.174583430, 0.173765343, 0.172969690, /* 52 53 54 55 */
+ 0.172195434, 0.171441601, 0.170707280, 0.169991616, /* 56 57 58 59 */
+ 0.169293808, 0.168613099, 0.167948779, 0.167300179, /* 60 61 62 63 */
+ 0.166666667
+};
+
+
+/* $Source: /cvs/libtom/libtommath/mtest/logtab.h,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/mtest/mpi-config.h b/libtommath/mtest/mpi-config.h
new file mode 100644
index 0000000..6049c25
--- /dev/null
+++ b/libtommath/mtest/mpi-config.h
@@ -0,0 +1,90 @@
+/* Default configuration for MPI library */
+/* $Id: mpi-config.h,v 1.2 2005/05/05 14:38:47 tom Exp $ */
+
+#ifndef MPI_CONFIG_H_
+#define MPI_CONFIG_H_
+
+/*
+ For boolean options,
+ 0 = no
+ 1 = yes
+
+ Other options are documented individually.
+
+ */
+
+#ifndef MP_IOFUNC
+#define MP_IOFUNC 0 /* include mp_print() ? */
+#endif
+
+#ifndef MP_MODARITH
+#define MP_MODARITH 1 /* include modular arithmetic ? */
+#endif
+
+#ifndef MP_NUMTH
+#define MP_NUMTH 1 /* include number theoretic functions? */
+#endif
+
+#ifndef MP_LOGTAB
+#define MP_LOGTAB 1 /* use table of logs instead of log()? */
+#endif
+
+#ifndef MP_MEMSET
+#define MP_MEMSET 1 /* use memset() to zero buffers? */
+#endif
+
+#ifndef MP_MEMCPY
+#define MP_MEMCPY 1 /* use memcpy() to copy buffers? */
+#endif
+
+#ifndef MP_CRYPTO
+#define MP_CRYPTO 1 /* erase memory on free? */
+#endif
+
+#ifndef MP_ARGCHK
+/*
+ 0 = no parameter checks
+ 1 = runtime checks, continue execution and return an error to caller
+ 2 = assertions; dump core on parameter errors
+ */
+#define MP_ARGCHK 2 /* how to check input arguments */
+#endif
+
+#ifndef MP_DEBUG
+#define MP_DEBUG 0 /* print diagnostic output? */
+#endif
+
+#ifndef MP_DEFPREC
+#define MP_DEFPREC 64 /* default precision, in digits */
+#endif
+
+#ifndef MP_MACRO
+#define MP_MACRO 1 /* use macros for frequent calls? */
+#endif
+
+#ifndef MP_SQUARE
+#define MP_SQUARE 1 /* use separate squaring code? */
+#endif
+
+#ifndef MP_PTAB_SIZE
+/*
+ When building mpprime.c, we build in a table of small prime
+ values to use for primality testing. The more you include,
+ the more space they take up. See primes.c for the possible
+ values (currently 16, 32, 64, 128, 256, and 6542)
+ */
+#define MP_PTAB_SIZE 128 /* how many built-in primes? */
+#endif
+
+#ifndef MP_COMPAT_MACROS
+#define MP_COMPAT_MACROS 1 /* define compatibility macros? */
+#endif
+
+#endif /* ifndef MPI_CONFIG_H_ */
+
+
+/* crc==3287762869, version==2, Sat Feb 02 06:43:53 2002 */
+
+/* $Source: /cvs/libtom/libtommath/mtest/mpi-config.h,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/mtest/mpi-types.h b/libtommath/mtest/mpi-types.h
new file mode 100644
index 0000000..026de58
--- /dev/null
+++ b/libtommath/mtest/mpi-types.h
@@ -0,0 +1,20 @@
+/* Type definitions generated by 'types.pl' */
+typedef char mp_sign;
+typedef unsigned short mp_digit; /* 2 byte type */
+typedef unsigned int mp_word; /* 4 byte type */
+typedef unsigned int mp_size;
+typedef int mp_err;
+
+#define MP_DIGIT_BIT (CHAR_BIT*sizeof(mp_digit))
+#define MP_DIGIT_MAX USHRT_MAX
+#define MP_WORD_BIT (CHAR_BIT*sizeof(mp_word))
+#define MP_WORD_MAX UINT_MAX
+
+#define MP_DIGIT_SIZE 2
+#define DIGIT_FMT "%04X"
+#define RADIX (MP_DIGIT_MAX+1)
+
+
+/* $Source: /cvs/libtom/libtommath/mtest/mpi-types.h,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/mtest/mpi.c b/libtommath/mtest/mpi.c
new file mode 100644
index 0000000..7c712dd
--- /dev/null
+++ b/libtommath/mtest/mpi.c
@@ -0,0 +1,3985 @@
+/*
+ mpi.c
+
+ by Michael J. Fromberger <sting@linguist.dartmouth.edu>
+ Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved
+
+ Arbitrary precision integer arithmetic library
+
+ $Id: mpi.c,v 1.2 2005/05/05 14:38:47 tom Exp $
+ */
+
+#include "mpi.h"
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+
+#if MP_DEBUG
+#include <stdio.h>
+
+#define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);}
+#else
+#define DIAG(T,V)
+#endif
+
+/*
+ If MP_LOGTAB is not defined, use the math library to compute the
+ logarithms on the fly. Otherwise, use the static table below.
+ Pick which works best for your system.
+ */
+#if MP_LOGTAB
+
+/* {{{ s_logv_2[] - log table for 2 in various bases */
+
+/*
+ A table of the logs of 2 for various bases (the 0 and 1 entries of
+ this table are meaningless and should not be referenced).
+
+ This table is used to compute output lengths for the mp_toradix()
+ function. Since a number n in radix r takes up about log_r(n)
+ digits, we estimate the output size by taking the least integer
+ greater than log_r(n), where:
+
+ log_r(n) = log_2(n) * log_r(2)
+
+ This table, therefore, is a table of log_r(2) for 2 <= r <= 36,
+ which are the output bases supported.
+ */
+
+#include "logtab.h"
+
+/* }}} */
+#define LOG_V_2(R) s_logv_2[(R)]
+
+#else
+
+#include <math.h>
+#define LOG_V_2(R) (log(2.0)/log(R))
+
+#endif
+
+/* Default precision for newly created mp_int's */
+static unsigned int s_mp_defprec = MP_DEFPREC;
+
+/* {{{ Digit arithmetic macros */
+
+/*
+ When adding and multiplying digits, the results can be larger than
+ can be contained in an mp_digit. Thus, an mp_word is used. These
+ macros mask off the upper and lower digits of the mp_word (the
+ mp_word may be more than 2 mp_digits wide, but we only concern
+ ourselves with the low-order 2 mp_digits)
+
+ If your mp_word DOES have more than 2 mp_digits, you need to
+ uncomment the first line, and comment out the second.
+ */
+
+/* #define CARRYOUT(W) (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */
+#define CARRYOUT(W) ((W)>>DIGIT_BIT)
+#define ACCUM(W) ((W)&MP_DIGIT_MAX)
+
+/* }}} */
+
+/* {{{ Comparison constants */
+
+#define MP_LT -1
+#define MP_EQ 0
+#define MP_GT 1
+
+/* }}} */
+
+/* {{{ Constant strings */
+
+/* Constant strings returned by mp_strerror() */
+static const char *mp_err_string[] = {
+ "unknown result code", /* say what? */
+ "boolean true", /* MP_OKAY, MP_YES */
+ "boolean false", /* MP_NO */
+ "out of memory", /* MP_MEM */
+ "argument out of range", /* MP_RANGE */
+ "invalid input parameter", /* MP_BADARG */
+ "result is undefined" /* MP_UNDEF */
+};
+
+/* Value to digit maps for radix conversion */
+
+/* s_dmap_1 - standard digits and letters */
+static const char *s_dmap_1 =
+ "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+
+#if 0
+/* s_dmap_2 - base64 ordering for digits */
+static const char *s_dmap_2 =
+ "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
+#endif
+
+/* }}} */
+
+/* {{{ Static function declarations */
+
+/*
+ If MP_MACRO is false, these will be defined as actual functions;
+ otherwise, suitable macro definitions will be used. This works
+ around the fact that ANSI C89 doesn't support an 'inline' keyword
+ (although I hear C9x will ... about bloody time). At present, the
+ macro definitions are identical to the function bodies, but they'll
+ expand in place, instead of generating a function call.
+
+ I chose these particular functions to be made into macros because
+ some profiling showed they are called a lot on a typical workload,
+ and yet they are primarily housekeeping.
+ */
+#if MP_MACRO == 0
+ void s_mp_setz(mp_digit *dp, mp_size count); /* zero digits */
+ void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy */
+ void *s_mp_alloc(size_t nb, size_t ni); /* general allocator */
+ void s_mp_free(void *ptr); /* general free function */
+#else
+
+ /* Even if these are defined as macros, we need to respect the settings
+ of the MP_MEMSET and MP_MEMCPY configuration options...
+ */
+ #if MP_MEMSET == 0
+ #define s_mp_setz(dp, count) \
+ {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;}
+ #else
+ #define s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit))
+ #endif /* MP_MEMSET */
+
+ #if MP_MEMCPY == 0
+ #define s_mp_copy(sp, dp, count) \
+ {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];}
+ #else
+ #define s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit))
+ #endif /* MP_MEMCPY */
+
+ #define s_mp_alloc(nb, ni) calloc(nb, ni)
+ #define s_mp_free(ptr) {if(ptr) free(ptr);}
+#endif /* MP_MACRO */
+
+mp_err s_mp_grow(mp_int *mp, mp_size min); /* increase allocated size */
+mp_err s_mp_pad(mp_int *mp, mp_size min); /* left pad with zeroes */
+
+void s_mp_clamp(mp_int *mp); /* clip leading zeroes */
+
+void s_mp_exch(mp_int *a, mp_int *b); /* swap a and b in place */
+
+mp_err s_mp_lshd(mp_int *mp, mp_size p); /* left-shift by p digits */
+void s_mp_rshd(mp_int *mp, mp_size p); /* right-shift by p digits */
+void s_mp_div_2d(mp_int *mp, mp_digit d); /* divide by 2^d in place */
+void s_mp_mod_2d(mp_int *mp, mp_digit d); /* modulo 2^d in place */
+mp_err s_mp_mul_2d(mp_int *mp, mp_digit d); /* multiply by 2^d in place*/
+void s_mp_div_2(mp_int *mp); /* divide by 2 in place */
+mp_err s_mp_mul_2(mp_int *mp); /* multiply by 2 in place */
+mp_digit s_mp_norm(mp_int *a, mp_int *b); /* normalize for division */
+mp_err s_mp_add_d(mp_int *mp, mp_digit d); /* unsigned digit addition */
+mp_err s_mp_sub_d(mp_int *mp, mp_digit d); /* unsigned digit subtract */
+mp_err s_mp_mul_d(mp_int *mp, mp_digit d); /* unsigned digit multiply */
+mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r);
+ /* unsigned digit divide */
+mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu);
+ /* Barrett reduction */
+mp_err s_mp_add(mp_int *a, mp_int *b); /* magnitude addition */
+mp_err s_mp_sub(mp_int *a, mp_int *b); /* magnitude subtract */
+mp_err s_mp_mul(mp_int *a, mp_int *b); /* magnitude multiply */
+#if 0
+void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len);
+ /* multiply buffers in place */
+#endif
+#if MP_SQUARE
+mp_err s_mp_sqr(mp_int *a); /* magnitude square */
+#else
+#define s_mp_sqr(a) s_mp_mul(a, a)
+#endif
+mp_err s_mp_div(mp_int *a, mp_int *b); /* magnitude divide */
+mp_err s_mp_2expt(mp_int *a, mp_digit k); /* a = 2^k */
+int s_mp_cmp(mp_int *a, mp_int *b); /* magnitude comparison */
+int s_mp_cmp_d(mp_int *a, mp_digit d); /* magnitude digit compare */
+int s_mp_ispow2(mp_int *v); /* is v a power of 2? */
+int s_mp_ispow2d(mp_digit d); /* is d a power of 2? */
+
+int s_mp_tovalue(char ch, int r); /* convert ch to value */
+char s_mp_todigit(int val, int r, int low); /* convert val to digit */
+int s_mp_outlen(int bits, int r); /* output length in bytes */
+
+/* }}} */
+
+/* {{{ Default precision manipulation */
+
+unsigned int mp_get_prec(void)
+{
+ return s_mp_defprec;
+
+} /* end mp_get_prec() */
+
+void mp_set_prec(unsigned int prec)
+{
+ if(prec == 0)
+ s_mp_defprec = MP_DEFPREC;
+ else
+ s_mp_defprec = prec;
+
+} /* end mp_set_prec() */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ mp_init(mp) */
+
+/*
+ mp_init(mp)
+
+ Initialize a new zero-valued mp_int. Returns MP_OKAY if successful,
+ MP_MEM if memory could not be allocated for the structure.
+ */
+
+mp_err mp_init(mp_int *mp)
+{
+ return mp_init_size(mp, s_mp_defprec);
+
+} /* end mp_init() */
+
+/* }}} */
+
+/* {{{ mp_init_array(mp[], count) */
+
+mp_err mp_init_array(mp_int mp[], int count)
+{
+ mp_err res;
+ int pos;
+
+ ARGCHK(mp !=NULL && count > 0, MP_BADARG);
+
+ for(pos = 0; pos < count; ++pos) {
+ if((res = mp_init(&mp[pos])) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ return MP_OKAY;
+
+ CLEANUP:
+ while(--pos >= 0)
+ mp_clear(&mp[pos]);
+
+ return res;
+
+} /* end mp_init_array() */
+
+/* }}} */
+
+/* {{{ mp_init_size(mp, prec) */
+
+/*
+ mp_init_size(mp, prec)
+
+ Initialize a new zero-valued mp_int with at least the given
+ precision; returns MP_OKAY if successful, or MP_MEM if memory could
+ not be allocated for the structure.
+ */
+
+mp_err mp_init_size(mp_int *mp, mp_size prec)
+{
+ ARGCHK(mp != NULL && prec > 0, MP_BADARG);
+
+ if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ SIGN(mp) = MP_ZPOS;
+ USED(mp) = 1;
+ ALLOC(mp) = prec;
+
+ return MP_OKAY;
+
+} /* end mp_init_size() */
+
+/* }}} */
+
+/* {{{ mp_init_copy(mp, from) */
+
+/*
+ mp_init_copy(mp, from)
+
+ Initialize mp as an exact copy of from. Returns MP_OKAY if
+ successful, MP_MEM if memory could not be allocated for the new
+ structure.
+ */
+
+mp_err mp_init_copy(mp_int *mp, mp_int *from)
+{
+ ARGCHK(mp != NULL && from != NULL, MP_BADARG);
+
+ if(mp == from)
+ return MP_OKAY;
+
+ if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ s_mp_copy(DIGITS(from), DIGITS(mp), USED(from));
+ USED(mp) = USED(from);
+ ALLOC(mp) = USED(from);
+ SIGN(mp) = SIGN(from);
+
+ return MP_OKAY;
+
+} /* end mp_init_copy() */
+
+/* }}} */
+
+/* {{{ mp_copy(from, to) */
+
+/*
+ mp_copy(from, to)
+
+ Copies the mp_int 'from' to the mp_int 'to'. It is presumed that
+ 'to' has already been initialized (if not, use mp_init_copy()
+ instead). If 'from' and 'to' are identical, nothing happens.
+ */
+
+mp_err mp_copy(mp_int *from, mp_int *to)
+{
+ ARGCHK(from != NULL && to != NULL, MP_BADARG);
+
+ if(from == to)
+ return MP_OKAY;
+
+ { /* copy */
+ mp_digit *tmp;
+
+ /*
+ If the allocated buffer in 'to' already has enough space to hold
+ all the used digits of 'from', we'll re-use it to avoid hitting
+ the memory allocater more than necessary; otherwise, we'd have
+ to grow anyway, so we just allocate a hunk and make the copy as
+ usual
+ */
+ if(ALLOC(to) >= USED(from)) {
+ s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from));
+ s_mp_copy(DIGITS(from), DIGITS(to), USED(from));
+
+ } else {
+ if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ s_mp_copy(DIGITS(from), tmp, USED(from));
+
+ if(DIGITS(to) != NULL) {
+#if MP_CRYPTO
+ s_mp_setz(DIGITS(to), ALLOC(to));
+#endif
+ s_mp_free(DIGITS(to));
+ }
+
+ DIGITS(to) = tmp;
+ ALLOC(to) = USED(from);
+ }
+
+ /* Copy the precision and sign from the original */
+ USED(to) = USED(from);
+ SIGN(to) = SIGN(from);
+ } /* end copy */
+
+ return MP_OKAY;
+
+} /* end mp_copy() */
+
+/* }}} */
+
+/* {{{ mp_exch(mp1, mp2) */
+
+/*
+ mp_exch(mp1, mp2)
+
+ Exchange mp1 and mp2 without allocating any intermediate memory
+ (well, unless you count the stack space needed for this call and the
+ locals it creates...). This cannot fail.
+ */
+
+void mp_exch(mp_int *mp1, mp_int *mp2)
+{
+#if MP_ARGCHK == 2
+ assert(mp1 != NULL && mp2 != NULL);
+#else
+ if(mp1 == NULL || mp2 == NULL)
+ return;
+#endif
+
+ s_mp_exch(mp1, mp2);
+
+} /* end mp_exch() */
+
+/* }}} */
+
+/* {{{ mp_clear(mp) */
+
+/*
+ mp_clear(mp)
+
+ Release the storage used by an mp_int, and void its fields so that
+ if someone calls mp_clear() again for the same int later, we won't
+ get tollchocked.
+ */
+
+void mp_clear(mp_int *mp)
+{
+ if(mp == NULL)
+ return;
+
+ if(DIGITS(mp) != NULL) {
+#if MP_CRYPTO
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+#endif
+ s_mp_free(DIGITS(mp));
+ DIGITS(mp) = NULL;
+ }
+
+ USED(mp) = 0;
+ ALLOC(mp) = 0;
+
+} /* end mp_clear() */
+
+/* }}} */
+
+/* {{{ mp_clear_array(mp[], count) */
+
+void mp_clear_array(mp_int mp[], int count)
+{
+ ARGCHK(mp != NULL && count > 0, MP_BADARG);
+
+ while(--count >= 0)
+ mp_clear(&mp[count]);
+
+} /* end mp_clear_array() */
+
+/* }}} */
+
+/* {{{ mp_zero(mp) */
+
+/*
+ mp_zero(mp)
+
+ Set mp to zero. Does not change the allocated size of the structure,
+ and therefore cannot fail (except on a bad argument, which we ignore)
+ */
+void mp_zero(mp_int *mp)
+{
+ if(mp == NULL)
+ return;
+
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+ USED(mp) = 1;
+ SIGN(mp) = MP_ZPOS;
+
+} /* end mp_zero() */
+
+/* }}} */
+
+/* {{{ mp_set(mp, d) */
+
+void mp_set(mp_int *mp, mp_digit d)
+{
+ if(mp == NULL)
+ return;
+
+ mp_zero(mp);
+ DIGIT(mp, 0) = d;
+
+} /* end mp_set() */
+
+/* }}} */
+
+/* {{{ mp_set_int(mp, z) */
+
+mp_err mp_set_int(mp_int *mp, long z)
+{
+ int ix;
+ unsigned long v = abs(z);
+ mp_err res;
+
+ ARGCHK(mp != NULL, MP_BADARG);
+
+ mp_zero(mp);
+ if(z == 0)
+ return MP_OKAY; /* shortcut for zero */
+
+ for(ix = sizeof(long) - 1; ix >= 0; ix--) {
+
+ if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
+ return res;
+
+ res = s_mp_add_d(mp,
+ (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX));
+ if(res != MP_OKAY)
+ return res;
+
+ }
+
+ if(z < 0)
+ SIGN(mp) = MP_NEG;
+
+ return MP_OKAY;
+
+} /* end mp_set_int() */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Digit arithmetic */
+
+/* {{{ mp_add_d(a, d, b) */
+
+/*
+ mp_add_d(a, d, b)
+
+ Compute the sum b = a + d, for a single digit d. Respects the sign of
+ its primary addend (single digits are unsigned anyway).
+ */
+
+mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b)
+{
+ mp_err res = MP_OKAY;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if(SIGN(b) == MP_ZPOS) {
+ res = s_mp_add_d(b, d);
+ } else if(s_mp_cmp_d(b, d) >= 0) {
+ res = s_mp_sub_d(b, d);
+ } else {
+ SIGN(b) = MP_ZPOS;
+
+ DIGIT(b, 0) = d - DIGIT(b, 0);
+ }
+
+ return res;
+
+} /* end mp_add_d() */
+
+/* }}} */
+
+/* {{{ mp_sub_d(a, d, b) */
+
+/*
+ mp_sub_d(a, d, b)
+
+ Compute the difference b = a - d, for a single digit d. Respects the
+ sign of its subtrahend (single digits are unsigned anyway).
+ */
+
+mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if(SIGN(b) == MP_NEG) {
+ if((res = s_mp_add_d(b, d)) != MP_OKAY)
+ return res;
+
+ } else if(s_mp_cmp_d(b, d) >= 0) {
+ if((res = s_mp_sub_d(b, d)) != MP_OKAY)
+ return res;
+
+ } else {
+ mp_neg(b, b);
+
+ DIGIT(b, 0) = d - DIGIT(b, 0);
+ SIGN(b) = MP_NEG;
+ }
+
+ if(s_mp_cmp_d(b, 0) == 0)
+ SIGN(b) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_sub_d() */
+
+/* }}} */
+
+/* {{{ mp_mul_d(a, d, b) */
+
+/*
+ mp_mul_d(a, d, b)
+
+ Compute the product b = a * d, for a single digit d. Respects the sign
+ of its multiplicand (single digits are unsigned anyway)
+ */
+
+mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if(d == 0) {
+ mp_zero(b);
+ return MP_OKAY;
+ }
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ res = s_mp_mul_d(b, d);
+
+ return res;
+
+} /* end mp_mul_d() */
+
+/* }}} */
+
+/* {{{ mp_mul_2(a, c) */
+
+mp_err mp_mul_2(mp_int *a, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ return s_mp_mul_2(c);
+
+} /* end mp_mul_2() */
+
+/* }}} */
+
+/* {{{ mp_div_d(a, d, q, r) */
+
+/*
+ mp_div_d(a, d, q, r)
+
+ Compute the quotient q = a / d and remainder r = a mod d, for a
+ single digit d. Respects the sign of its divisor (single digits are
+ unsigned anyway).
+ */
+
+mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r)
+{
+ mp_err res;
+ mp_digit rem;
+ int pow;
+
+ ARGCHK(a != NULL, MP_BADARG);
+
+ if(d == 0)
+ return MP_RANGE;
+
+ /* Shortcut for powers of two ... */
+ if((pow = s_mp_ispow2d(d)) >= 0) {
+ mp_digit mask;
+
+ mask = (1 << pow) - 1;
+ rem = DIGIT(a, 0) & mask;
+
+ if(q) {
+ mp_copy(a, q);
+ s_mp_div_2d(q, pow);
+ }
+
+ if(r)
+ *r = rem;
+
+ return MP_OKAY;
+ }
+
+ /*
+ If the quotient is actually going to be returned, we'll try to
+ avoid hitting the memory allocator by copying the dividend into it
+ and doing the division there. This can't be any _worse_ than
+ always copying, and will sometimes be better (since it won't make
+ another copy)
+
+ If it's not going to be returned, we need to allocate a temporary
+ to hold the quotient, which will just be discarded.
+ */
+ if(q) {
+ if((res = mp_copy(a, q)) != MP_OKAY)
+ return res;
+
+ res = s_mp_div_d(q, d, &rem);
+ if(s_mp_cmp_d(q, 0) == MP_EQ)
+ SIGN(q) = MP_ZPOS;
+
+ } else {
+ mp_int qp;
+
+ if((res = mp_init_copy(&qp, a)) != MP_OKAY)
+ return res;
+
+ res = s_mp_div_d(&qp, d, &rem);
+ if(s_mp_cmp_d(&qp, 0) == 0)
+ SIGN(&qp) = MP_ZPOS;
+
+ mp_clear(&qp);
+ }
+
+ if(r)
+ *r = rem;
+
+ return res;
+
+} /* end mp_div_d() */
+
+/* }}} */
+
+/* {{{ mp_div_2(a, c) */
+
+/*
+ mp_div_2(a, c)
+
+ Compute c = a / 2, disregarding the remainder.
+ */
+
+mp_err mp_div_2(mp_int *a, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ s_mp_div_2(c);
+
+ return MP_OKAY;
+
+} /* end mp_div_2() */
+
+/* }}} */
+
+/* {{{ mp_expt_d(a, d, b) */
+
+mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c)
+{
+ mp_int s, x;
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+ DIGIT(&s, 0) = 1;
+
+ while(d != 0) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ s_mp_exch(&s, c);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_expt_d() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Full arithmetic */
+
+/* {{{ mp_abs(a, b) */
+
+/*
+ mp_abs(a, b)
+
+ Compute b = |a|. 'a' and 'b' may be identical.
+ */
+
+mp_err mp_abs(mp_int *a, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ SIGN(b) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_abs() */
+
+/* }}} */
+
+/* {{{ mp_neg(a, b) */
+
+/*
+ mp_neg(a, b)
+
+ Compute b = -a. 'a' and 'b' may be identical.
+ */
+
+mp_err mp_neg(mp_int *a, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if(s_mp_cmp_d(b, 0) == MP_EQ)
+ SIGN(b) = MP_ZPOS;
+ else
+ SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG;
+
+ return MP_OKAY;
+
+} /* end mp_neg() */
+
+/* }}} */
+
+/* {{{ mp_add(a, b, c) */
+
+/*
+ mp_add(a, b, c)
+
+ Compute c = a + b. All parameters may be identical.
+ */
+
+mp_err mp_add(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ int cmp;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(SIGN(a) == SIGN(b)) { /* same sign: add values, keep sign */
+
+ /* Commutativity of addition lets us do this in either order,
+ so we avoid having to use a temporary even if the result
+ is supposed to replace the output
+ */
+ if(c == b) {
+ if((res = s_mp_add(c, a)) != MP_OKAY)
+ return res;
+ } else {
+ if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_add(c, b)) != MP_OKAY)
+ return res;
+ }
+
+ } else if((cmp = s_mp_cmp(a, b)) > 0) { /* different sign: a > b */
+
+ /* If the output is going to be clobbered, we will use a temporary
+ variable; otherwise, we'll do it without touching the memory
+ allocator at all, if possible
+ */
+ if(c == b) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+
+ if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(c, b)) != MP_OKAY)
+ return res;
+
+ }
+
+ } else if(cmp == 0) { /* different sign, a == b */
+
+ mp_zero(c);
+ return MP_OKAY;
+
+ } else { /* different sign: a < b */
+
+ /* See above... */
+ if(c == a) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+
+ if(c != b && (res = mp_copy(b, c)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(c, a)) != MP_OKAY)
+ return res;
+
+ }
+ }
+
+ if(USED(c) == 1 && DIGIT(c, 0) == 0)
+ SIGN(c) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_add() */
+
+/* }}} */
+
+/* {{{ mp_sub(a, b, c) */
+
+/*
+ mp_sub(a, b, c)
+
+ Compute c = a - b. All parameters may be identical.
+ */
+
+mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ int cmp;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(SIGN(a) != SIGN(b)) {
+ if(c == a) {
+ if((res = s_mp_add(c, b)) != MP_OKAY)
+ return res;
+ } else {
+ if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
+ return res;
+ if((res = s_mp_add(c, a)) != MP_OKAY)
+ return res;
+ SIGN(c) = SIGN(a);
+ }
+
+ } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */
+ if(c == b) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+ if(c != a && ((res = mp_copy(a, c)) != MP_OKAY))
+ return res;
+
+ if((res = s_mp_sub(c, b)) != MP_OKAY)
+ return res;
+ }
+
+ } else if(cmp == 0) { /* Same sign, equal magnitude */
+ mp_zero(c);
+ return MP_OKAY;
+
+ } else { /* Same sign, b > a */
+ if(c == a) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+ if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
+ return res;
+
+ if((res = s_mp_sub(c, a)) != MP_OKAY)
+ return res;
+ }
+
+ SIGN(c) = !SIGN(b);
+ }
+
+ if(USED(c) == 1 && DIGIT(c, 0) == 0)
+ SIGN(c) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_sub() */
+
+/* }}} */
+
+/* {{{ mp_mul(a, b, c) */
+
+/*
+ mp_mul(a, b, c)
+
+ Compute c = a * b. All parameters may be identical.
+ */
+
+mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ mp_sign sgn;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG;
+
+ if(c == b) {
+ if((res = s_mp_mul(c, a)) != MP_OKAY)
+ return res;
+
+ } else {
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_mul(c, b)) != MP_OKAY)
+ return res;
+ }
+
+ if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ)
+ SIGN(c) = MP_ZPOS;
+ else
+ SIGN(c) = sgn;
+
+ return MP_OKAY;
+
+} /* end mp_mul() */
+
+/* }}} */
+
+/* {{{ mp_mul_2d(a, d, c) */
+
+/*
+ mp_mul_2d(a, d, c)
+
+ Compute c = a * 2^d. a may be the same as c.
+ */
+
+mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if(d == 0)
+ return MP_OKAY;
+
+ return s_mp_mul_2d(c, d);
+
+} /* end mp_mul() */
+
+/* }}} */
+
+/* {{{ mp_sqr(a, b) */
+
+#if MP_SQUARE
+mp_err mp_sqr(mp_int *a, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_sqr(b)) != MP_OKAY)
+ return res;
+
+ SIGN(b) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_sqr() */
+#endif
+
+/* }}} */
+
+/* {{{ mp_div(a, b, q, r) */
+
+/*
+ mp_div(a, b, q, r)
+
+ Compute q = a / b and r = a mod b. Input parameters may be re-used
+ as output parameters. If q or r is NULL, that portion of the
+ computation will be discarded (although it will still be computed)
+
+ Pay no attention to the hacker behind the curtain.
+ */
+
+mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r)
+{
+ mp_err res;
+ mp_int qtmp, rtmp;
+ int cmp;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if(mp_cmp_z(b) == MP_EQ)
+ return MP_RANGE;
+
+ /* If a <= b, we can compute the solution without division, and
+ avoid any memory allocation
+ */
+ if((cmp = s_mp_cmp(a, b)) < 0) {
+ if(r) {
+ if((res = mp_copy(a, r)) != MP_OKAY)
+ return res;
+ }
+
+ if(q)
+ mp_zero(q);
+
+ return MP_OKAY;
+
+ } else if(cmp == 0) {
+
+ /* Set quotient to 1, with appropriate sign */
+ if(q) {
+ int qneg = (SIGN(a) != SIGN(b));
+
+ mp_set(q, 1);
+ if(qneg)
+ SIGN(q) = MP_NEG;
+ }
+
+ if(r)
+ mp_zero(r);
+
+ return MP_OKAY;
+ }
+
+ /* If we get here, it means we actually have to do some division */
+
+ /* Set up some temporaries... */
+ if((res = mp_init_copy(&qtmp, a)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&rtmp, b)) != MP_OKAY)
+ goto CLEANUP;
+
+ if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* Compute the signs for the output */
+ SIGN(&rtmp) = SIGN(a); /* Sr = Sa */
+ if(SIGN(a) == SIGN(b))
+ SIGN(&qtmp) = MP_ZPOS; /* Sq = MP_ZPOS if Sa = Sb */
+ else
+ SIGN(&qtmp) = MP_NEG; /* Sq = MP_NEG if Sa != Sb */
+
+ if(s_mp_cmp_d(&qtmp, 0) == MP_EQ)
+ SIGN(&qtmp) = MP_ZPOS;
+ if(s_mp_cmp_d(&rtmp, 0) == MP_EQ)
+ SIGN(&rtmp) = MP_ZPOS;
+
+ /* Copy output, if it is needed */
+ if(q)
+ s_mp_exch(&qtmp, q);
+
+ if(r)
+ s_mp_exch(&rtmp, r);
+
+CLEANUP:
+ mp_clear(&rtmp);
+ mp_clear(&qtmp);
+
+ return res;
+
+} /* end mp_div() */
+
+/* }}} */
+
+/* {{{ mp_div_2d(a, d, q, r) */
+
+mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL, MP_BADARG);
+
+ if(q) {
+ if((res = mp_copy(a, q)) != MP_OKAY)
+ return res;
+
+ s_mp_div_2d(q, d);
+ }
+
+ if(r) {
+ if((res = mp_copy(a, r)) != MP_OKAY)
+ return res;
+
+ s_mp_mod_2d(r, d);
+ }
+
+ return MP_OKAY;
+
+} /* end mp_div_2d() */
+
+/* }}} */
+
+/* {{{ mp_expt(a, b, c) */
+
+/*
+ mp_expt(a, b, c)
+
+ Compute c = a ** b, that is, raise a to the b power. Uses a
+ standard iterative square-and-multiply technique.
+ */
+
+mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_int s, x;
+ mp_err res;
+ mp_digit d;
+ int dig, bit;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(mp_cmp_z(b) < 0)
+ return MP_RANGE;
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+
+ mp_set(&s, 1);
+
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+ /* Loop over low-order digits in ascending order */
+ for(dig = 0; dig < (USED(b) - 1); dig++) {
+ d = DIGIT(b, dig);
+
+ /* Loop over bits of each non-maximal digit */
+ for(bit = 0; bit < DIGIT_BIT; bit++) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+ }
+
+ /* Consider now the last digit... */
+ d = DIGIT(b, dig);
+
+ while(d) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ if(mp_iseven(b))
+ SIGN(&s) = SIGN(a);
+
+ res = mp_copy(&s, c);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_expt() */
+
+/* }}} */
+
+/* {{{ mp_2expt(a, k) */
+
+/* Compute a = 2^k */
+
+mp_err mp_2expt(mp_int *a, mp_digit k)
+{
+ ARGCHK(a != NULL, MP_BADARG);
+
+ return s_mp_2expt(a, k);
+
+} /* end mp_2expt() */
+
+/* }}} */
+
+/* {{{ mp_mod(a, m, c) */
+
+/*
+ mp_mod(a, m, c)
+
+ Compute c = a (mod m). Result will always be 0 <= c < m.
+ */
+
+mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c)
+{
+ mp_err res;
+ int mag;
+
+ ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if(SIGN(m) == MP_NEG)
+ return MP_RANGE;
+
+ /*
+ If |a| > m, we need to divide to get the remainder and take the
+ absolute value.
+
+ If |a| < m, we don't need to do any division, just copy and adjust
+ the sign (if a is negative).
+
+ If |a| == m, we can simply set the result to zero.
+
+ This order is intended to minimize the average path length of the
+ comparison chain on common workloads -- the most frequent cases are
+ that |a| != m, so we do those first.
+ */
+ if((mag = s_mp_cmp(a, m)) > 0) {
+ if((res = mp_div(a, m, NULL, c)) != MP_OKAY)
+ return res;
+
+ if(SIGN(c) == MP_NEG) {
+ if((res = mp_add(c, m, c)) != MP_OKAY)
+ return res;
+ }
+
+ } else if(mag < 0) {
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if(mp_cmp_z(a) < 0) {
+ if((res = mp_add(c, m, c)) != MP_OKAY)
+ return res;
+
+ }
+
+ } else {
+ mp_zero(c);
+
+ }
+
+ return MP_OKAY;
+
+} /* end mp_mod() */
+
+/* }}} */
+
+/* {{{ mp_mod_d(a, d, c) */
+
+/*
+ mp_mod_d(a, d, c)
+
+ Compute c = a (mod d). Result will always be 0 <= c < d
+ */
+mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c)
+{
+ mp_err res;
+ mp_digit rem;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if(s_mp_cmp_d(a, d) > 0) {
+ if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY)
+ return res;
+
+ } else {
+ if(SIGN(a) == MP_NEG)
+ rem = d - DIGIT(a, 0);
+ else
+ rem = DIGIT(a, 0);
+ }
+
+ if(c)
+ *c = rem;
+
+ return MP_OKAY;
+
+} /* end mp_mod_d() */
+
+/* }}} */
+
+/* {{{ mp_sqrt(a, b) */
+
+/*
+ mp_sqrt(a, b)
+
+ Compute the integer square root of a, and store the result in b.
+ Uses an integer-arithmetic version of Newton's iterative linear
+ approximation technique to determine this value; the result has the
+ following two properties:
+
+ b^2 <= a
+ (b+1)^2 >= a
+
+ It is a range error to pass a negative value.
+ */
+mp_err mp_sqrt(mp_int *a, mp_int *b)
+{
+ mp_int x, t;
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ /* Cannot take square root of a negative value */
+ if(SIGN(a) == MP_NEG)
+ return MP_RANGE;
+
+ /* Special cases for zero and one, trivial */
+ if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ)
+ return mp_copy(a, b);
+
+ /* Initialize the temporaries we'll use below */
+ if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
+ return res;
+
+ /* Compute an initial guess for the iteration as a itself */
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+s_mp_rshd(&x, (USED(&x)/2)+1);
+mp_add_d(&x, 1, &x);
+
+ for(;;) {
+ /* t = (x * x) - a */
+ mp_copy(&x, &t); /* can't fail, t is big enough for original x */
+ if((res = mp_sqr(&t, &t)) != MP_OKAY ||
+ (res = mp_sub(&t, a, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* t = t / 2x */
+ s_mp_mul_2(&x);
+ if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY)
+ goto CLEANUP;
+ s_mp_div_2(&x);
+
+ /* Terminate the loop, if the quotient is zero */
+ if(mp_cmp_z(&t) == MP_EQ)
+ break;
+
+ /* x = x - t */
+ if((res = mp_sub(&x, &t, &x)) != MP_OKAY)
+ goto CLEANUP;
+
+ }
+
+ /* Copy result to output parameter */
+ mp_sub_d(&x, 1, &x);
+ s_mp_exch(&x, b);
+
+ CLEANUP:
+ mp_clear(&x);
+ X:
+ mp_clear(&t);
+
+ return res;
+
+} /* end mp_sqrt() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Modular arithmetic */
+
+#if MP_MODARITH
+/* {{{ mp_addmod(a, b, m, c) */
+
+/*
+ mp_addmod(a, b, m, c)
+
+ Compute c = (a + b) mod m
+ */
+
+mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_add(a, b, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+}
+
+/* }}} */
+
+/* {{{ mp_submod(a, b, m, c) */
+
+/*
+ mp_submod(a, b, m, c)
+
+ Compute c = (a - b) mod m
+ */
+
+mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_sub(a, b, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+}
+
+/* }}} */
+
+/* {{{ mp_mulmod(a, b, m, c) */
+
+/*
+ mp_mulmod(a, b, m, c)
+
+ Compute c = (a * b) mod m
+ */
+
+mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_mul(a, b, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+}
+
+/* }}} */
+
+/* {{{ mp_sqrmod(a, m, c) */
+
+#if MP_SQUARE
+mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_sqr(a, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+} /* end mp_sqrmod() */
+#endif
+
+/* }}} */
+
+/* {{{ mp_exptmod(a, b, m, c) */
+
+/*
+ mp_exptmod(a, b, m, c)
+
+ Compute c = (a ** b) mod m. Uses a standard square-and-multiply
+ method with modular reductions at each step. (This is basically the
+ same code as mp_expt(), except for the addition of the reductions)
+
+ The modular reductions are done using Barrett's algorithm (see
+ s_mp_reduce() below for details)
+ */
+
+mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_int s, x, mu;
+ mp_err res;
+ mp_digit d, *db = DIGITS(b);
+ mp_size ub = USED(b);
+ int dig, bit;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0)
+ return MP_RANGE;
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+ if((res = mp_mod(&x, m, &x)) != MP_OKAY ||
+ (res = mp_init(&mu)) != MP_OKAY)
+ goto MU;
+
+ mp_set(&s, 1);
+
+ /* mu = b^2k / m */
+ s_mp_add_d(&mu, 1);
+ s_mp_lshd(&mu, 2 * USED(m));
+ if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* Loop over digits of b in ascending order, except highest order */
+ for(dig = 0; dig < (ub - 1); dig++) {
+ d = *db++;
+
+ /* Loop over the bits of the lower-order digits */
+ for(bit = 0; bit < DIGIT_BIT; bit++) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+ }
+
+ /* Now do the last digit... */
+ d = *db;
+
+ while(d) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ s_mp_exch(&s, c);
+
+ CLEANUP:
+ mp_clear(&mu);
+ MU:
+ mp_clear(&x);
+ X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_exptmod() */
+
+/* }}} */
+
+/* {{{ mp_exptmod_d(a, d, m, c) */
+
+mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c)
+{
+ mp_int s, x;
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+ mp_set(&s, 1);
+
+ while(d != 0) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY ||
+ (res = mp_mod(&s, m, &s)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d /= 2;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY ||
+ (res = mp_mod(&x, m, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ s_mp_exch(&s, c);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_exptmod_d() */
+
+/* }}} */
+#endif /* if MP_MODARITH */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Comparison functions */
+
+/* {{{ mp_cmp_z(a) */
+
+/*
+ mp_cmp_z(a)
+
+ Compare a <=> 0. Returns <0 if a<0, 0 if a=0, >0 if a>0.
+ */
+
+int mp_cmp_z(mp_int *a)
+{
+ if(SIGN(a) == MP_NEG)
+ return MP_LT;
+ else if(USED(a) == 1 && DIGIT(a, 0) == 0)
+ return MP_EQ;
+ else
+ return MP_GT;
+
+} /* end mp_cmp_z() */
+
+/* }}} */
+
+/* {{{ mp_cmp_d(a, d) */
+
+/*
+ mp_cmp_d(a, d)
+
+ Compare a <=> d. Returns <0 if a<d, 0 if a=d, >0 if a>d
+ */
+
+int mp_cmp_d(mp_int *a, mp_digit d)
+{
+ ARGCHK(a != NULL, MP_EQ);
+
+ if(SIGN(a) == MP_NEG)
+ return MP_LT;
+
+ return s_mp_cmp_d(a, d);
+
+} /* end mp_cmp_d() */
+
+/* }}} */
+
+/* {{{ mp_cmp(a, b) */
+
+int mp_cmp(mp_int *a, mp_int *b)
+{
+ ARGCHK(a != NULL && b != NULL, MP_EQ);
+
+ if(SIGN(a) == SIGN(b)) {
+ int mag;
+
+ if((mag = s_mp_cmp(a, b)) == MP_EQ)
+ return MP_EQ;
+
+ if(SIGN(a) == MP_ZPOS)
+ return mag;
+ else
+ return -mag;
+
+ } else if(SIGN(a) == MP_ZPOS) {
+ return MP_GT;
+ } else {
+ return MP_LT;
+ }
+
+} /* end mp_cmp() */
+
+/* }}} */
+
+/* {{{ mp_cmp_mag(a, b) */
+
+/*
+ mp_cmp_mag(a, b)
+
+ Compares |a| <=> |b|, and returns an appropriate comparison result
+ */
+
+int mp_cmp_mag(mp_int *a, mp_int *b)
+{
+ ARGCHK(a != NULL && b != NULL, MP_EQ);
+
+ return s_mp_cmp(a, b);
+
+} /* end mp_cmp_mag() */
+
+/* }}} */
+
+/* {{{ mp_cmp_int(a, z) */
+
+/*
+ This just converts z to an mp_int, and uses the existing comparison
+ routines. This is sort of inefficient, but it's not clear to me how
+ frequently this wil get used anyway. For small positive constants,
+ you can always use mp_cmp_d(), and for zero, there is mp_cmp_z().
+ */
+int mp_cmp_int(mp_int *a, long z)
+{
+ mp_int tmp;
+ int out;
+
+ ARGCHK(a != NULL, MP_EQ);
+
+ mp_init(&tmp); mp_set_int(&tmp, z);
+ out = mp_cmp(a, &tmp);
+ mp_clear(&tmp);
+
+ return out;
+
+} /* end mp_cmp_int() */
+
+/* }}} */
+
+/* {{{ mp_isodd(a) */
+
+/*
+ mp_isodd(a)
+
+ Returns a true (non-zero) value if a is odd, false (zero) otherwise.
+ */
+int mp_isodd(mp_int *a)
+{
+ ARGCHK(a != NULL, 0);
+
+ return (DIGIT(a, 0) & 1);
+
+} /* end mp_isodd() */
+
+/* }}} */
+
+/* {{{ mp_iseven(a) */
+
+int mp_iseven(mp_int *a)
+{
+ return !mp_isodd(a);
+
+} /* end mp_iseven() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Number theoretic functions */
+
+#if MP_NUMTH
+/* {{{ mp_gcd(a, b, c) */
+
+/*
+ Like the old mp_gcd() function, except computes the GCD using the
+ binary algorithm due to Josef Stein in 1961 (via Knuth).
+ */
+mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ mp_int u, v, t;
+ mp_size k = 0;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ)
+ return MP_RANGE;
+ if(mp_cmp_z(a) == MP_EQ) {
+ return mp_copy(b, c);
+ } else if(mp_cmp_z(b) == MP_EQ) {
+ return mp_copy(a, c);
+ }
+
+ if((res = mp_init(&t)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&u, a)) != MP_OKAY)
+ goto U;
+ if((res = mp_init_copy(&v, b)) != MP_OKAY)
+ goto V;
+
+ SIGN(&u) = MP_ZPOS;
+ SIGN(&v) = MP_ZPOS;
+
+ /* Divide out common factors of 2 until at least 1 of a, b is even */
+ while(mp_iseven(&u) && mp_iseven(&v)) {
+ s_mp_div_2(&u);
+ s_mp_div_2(&v);
+ ++k;
+ }
+
+ /* Initialize t */
+ if(mp_isodd(&u)) {
+ if((res = mp_copy(&v, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* t = -v */
+ if(SIGN(&v) == MP_ZPOS)
+ SIGN(&t) = MP_NEG;
+ else
+ SIGN(&t) = MP_ZPOS;
+
+ } else {
+ if((res = mp_copy(&u, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ }
+
+ for(;;) {
+ while(mp_iseven(&t)) {
+ s_mp_div_2(&t);
+ }
+
+ if(mp_cmp_z(&t) == MP_GT) {
+ if((res = mp_copy(&t, &u)) != MP_OKAY)
+ goto CLEANUP;
+
+ } else {
+ if((res = mp_copy(&t, &v)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* v = -t */
+ if(SIGN(&t) == MP_ZPOS)
+ SIGN(&v) = MP_NEG;
+ else
+ SIGN(&v) = MP_ZPOS;
+ }
+
+ if((res = mp_sub(&u, &v, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ if(s_mp_cmp_d(&t, 0) == MP_EQ)
+ break;
+ }
+
+ s_mp_2expt(&v, k); /* v = 2^k */
+ res = mp_mul(&u, &v, c); /* c = u * v */
+
+ CLEANUP:
+ mp_clear(&v);
+ V:
+ mp_clear(&u);
+ U:
+ mp_clear(&t);
+
+ return res;
+
+} /* end mp_bgcd() */
+
+/* }}} */
+
+/* {{{ mp_lcm(a, b, c) */
+
+/* We compute the least common multiple using the rule:
+
+ ab = [a, b](a, b)
+
+ ... by computing the product, and dividing out the gcd.
+ */
+
+mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_int gcd, prod;
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ /* Set up temporaries */
+ if((res = mp_init(&gcd)) != MP_OKAY)
+ return res;
+ if((res = mp_init(&prod)) != MP_OKAY)
+ goto GCD;
+
+ if((res = mp_mul(a, b, &prod)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = mp_gcd(a, b, &gcd)) != MP_OKAY)
+ goto CLEANUP;
+
+ res = mp_div(&prod, &gcd, c, NULL);
+
+ CLEANUP:
+ mp_clear(&prod);
+ GCD:
+ mp_clear(&gcd);
+
+ return res;
+
+} /* end mp_lcm() */
+
+/* }}} */
+
+/* {{{ mp_xgcd(a, b, g, x, y) */
+
+/*
+ mp_xgcd(a, b, g, x, y)
+
+ Compute g = (a, b) and values x and y satisfying Bezout's identity
+ (that is, ax + by = g). This uses the extended binary GCD algorithm
+ based on the Stein algorithm used for mp_gcd()
+ */
+
+mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y)
+{
+ mp_int gx, xc, yc, u, v, A, B, C, D;
+ mp_int *clean[9];
+ mp_err res;
+ int last = -1;
+
+ if(mp_cmp_z(b) == 0)
+ return MP_RANGE;
+
+ /* Initialize all these variables we need */
+ if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &u;
+ if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &v;
+ if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &gx;
+ if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &A;
+ if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &B;
+ if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &C;
+ if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &D;
+ if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &xc;
+ mp_abs(&xc, &xc);
+ if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &yc;
+ mp_abs(&yc, &yc);
+
+ mp_set(&gx, 1);
+
+ /* Divide by two until at least one of them is even */
+ while(mp_iseven(&xc) && mp_iseven(&yc)) {
+ s_mp_div_2(&xc);
+ s_mp_div_2(&yc);
+ if((res = s_mp_mul_2(&gx)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ mp_copy(&xc, &u);
+ mp_copy(&yc, &v);
+ mp_set(&A, 1); mp_set(&D, 1);
+
+ /* Loop through binary GCD algorithm */
+ for(;;) {
+ while(mp_iseven(&u)) {
+ s_mp_div_2(&u);
+
+ if(mp_iseven(&A) && mp_iseven(&B)) {
+ s_mp_div_2(&A); s_mp_div_2(&B);
+ } else {
+ if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&A);
+ if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&B);
+ }
+ }
+
+ while(mp_iseven(&v)) {
+ s_mp_div_2(&v);
+
+ if(mp_iseven(&C) && mp_iseven(&D)) {
+ s_mp_div_2(&C); s_mp_div_2(&D);
+ } else {
+ if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&C);
+ if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&D);
+ }
+ }
+
+ if(mp_cmp(&u, &v) >= 0) {
+ if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP;
+
+ } else {
+ if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP;
+
+ }
+
+ /* If we're done, copy results to output */
+ if(mp_cmp_z(&u) == 0) {
+ if(x)
+ if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP;
+
+ if(y)
+ if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP;
+
+ if(g)
+ if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP;
+
+ break;
+ }
+ }
+
+ CLEANUP:
+ while(last >= 0)
+ mp_clear(clean[last--]);
+
+ return res;
+
+} /* end mp_xgcd() */
+
+/* }}} */
+
+/* {{{ mp_invmod(a, m, c) */
+
+/*
+ mp_invmod(a, m, c)
+
+ Compute c = a^-1 (mod m), if there is an inverse for a (mod m).
+ This is equivalent to the question of whether (a, m) = 1. If not,
+ MP_UNDEF is returned, and there is no inverse.
+ */
+
+mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c)
+{
+ mp_int g, x;
+ mp_err res;
+
+ ARGCHK(a && m && c, MP_BADARG);
+
+ if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
+ return MP_RANGE;
+
+ if((res = mp_init(&g)) != MP_OKAY)
+ return res;
+ if((res = mp_init(&x)) != MP_OKAY)
+ goto X;
+
+ if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY)
+ goto CLEANUP;
+
+ if(mp_cmp_d(&g, 1) != MP_EQ) {
+ res = MP_UNDEF;
+ goto CLEANUP;
+ }
+
+ res = mp_mod(&x, m, c);
+ SIGN(c) = SIGN(a);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&g);
+
+ return res;
+
+} /* end mp_invmod() */
+
+/* }}} */
+#endif /* if MP_NUMTH */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ mp_print(mp, ofp) */
+
+#if MP_IOFUNC
+/*
+ mp_print(mp, ofp)
+
+ Print a textual representation of the given mp_int on the output
+ stream 'ofp'. Output is generated using the internal radix.
+ */
+
+void mp_print(mp_int *mp, FILE *ofp)
+{
+ int ix;
+
+ if(mp == NULL || ofp == NULL)
+ return;
+
+ fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp);
+
+ for(ix = USED(mp) - 1; ix >= 0; ix--) {
+ fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix));
+ }
+
+} /* end mp_print() */
+
+#endif /* if MP_IOFUNC */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ More I/O Functions */
+
+/* {{{ mp_read_signed_bin(mp, str, len) */
+
+/*
+ mp_read_signed_bin(mp, str, len)
+
+ Read in a raw value (base 256) into the given mp_int
+ */
+
+mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len)
+{
+ mp_err res;
+
+ ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
+
+ if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) {
+ /* Get sign from first byte */
+ if(str[0])
+ SIGN(mp) = MP_NEG;
+ else
+ SIGN(mp) = MP_ZPOS;
+ }
+
+ return res;
+
+} /* end mp_read_signed_bin() */
+
+/* }}} */
+
+/* {{{ mp_signed_bin_size(mp) */
+
+int mp_signed_bin_size(mp_int *mp)
+{
+ ARGCHK(mp != NULL, 0);
+
+ return mp_unsigned_bin_size(mp) + 1;
+
+} /* end mp_signed_bin_size() */
+
+/* }}} */
+
+/* {{{ mp_to_signed_bin(mp, str) */
+
+mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str)
+{
+ ARGCHK(mp != NULL && str != NULL, MP_BADARG);
+
+ /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */
+ str[0] = (char)SIGN(mp);
+
+ return mp_to_unsigned_bin(mp, str + 1);
+
+} /* end mp_to_signed_bin() */
+
+/* }}} */
+
+/* {{{ mp_read_unsigned_bin(mp, str, len) */
+
+/*
+ mp_read_unsigned_bin(mp, str, len)
+
+ Read in an unsigned value (base 256) into the given mp_int
+ */
+
+mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len)
+{
+ int ix;
+ mp_err res;
+
+ ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
+
+ mp_zero(mp);
+
+ for(ix = 0; ix < len; ix++) {
+ if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
+ return res;
+
+ if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY)
+ return res;
+ }
+
+ return MP_OKAY;
+
+} /* end mp_read_unsigned_bin() */
+
+/* }}} */
+
+/* {{{ mp_unsigned_bin_size(mp) */
+
+int mp_unsigned_bin_size(mp_int *mp)
+{
+ mp_digit topdig;
+ int count;
+
+ ARGCHK(mp != NULL, 0);
+
+ /* Special case for the value zero */
+ if(USED(mp) == 1 && DIGIT(mp, 0) == 0)
+ return 1;
+
+ count = (USED(mp) - 1) * sizeof(mp_digit);
+ topdig = DIGIT(mp, USED(mp) - 1);
+
+ while(topdig != 0) {
+ ++count;
+ topdig >>= CHAR_BIT;
+ }
+
+ return count;
+
+} /* end mp_unsigned_bin_size() */
+
+/* }}} */
+
+/* {{{ mp_to_unsigned_bin(mp, str) */
+
+mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str)
+{
+ mp_digit *dp, *end, d;
+ unsigned char *spos;
+
+ ARGCHK(mp != NULL && str != NULL, MP_BADARG);
+
+ dp = DIGITS(mp);
+ end = dp + USED(mp) - 1;
+ spos = str;
+
+ /* Special case for zero, quick test */
+ if(dp == end && *dp == 0) {
+ *str = '\0';
+ return MP_OKAY;
+ }
+
+ /* Generate digits in reverse order */
+ while(dp < end) {
+ int ix;
+
+ d = *dp;
+ for(ix = 0; ix < sizeof(mp_digit); ++ix) {
+ *spos = d & UCHAR_MAX;
+ d >>= CHAR_BIT;
+ ++spos;
+ }
+
+ ++dp;
+ }
+
+ /* Now handle last digit specially, high order zeroes are not written */
+ d = *end;
+ while(d != 0) {
+ *spos = d & UCHAR_MAX;
+ d >>= CHAR_BIT;
+ ++spos;
+ }
+
+ /* Reverse everything to get digits in the correct order */
+ while(--spos > str) {
+ unsigned char t = *str;
+ *str = *spos;
+ *spos = t;
+
+ ++str;
+ }
+
+ return MP_OKAY;
+
+} /* end mp_to_unsigned_bin() */
+
+/* }}} */
+
+/* {{{ mp_count_bits(mp) */
+
+int mp_count_bits(mp_int *mp)
+{
+ int len;
+ mp_digit d;
+
+ ARGCHK(mp != NULL, MP_BADARG);
+
+ len = DIGIT_BIT * (USED(mp) - 1);
+ d = DIGIT(mp, USED(mp) - 1);
+
+ while(d != 0) {
+ ++len;
+ d >>= 1;
+ }
+
+ return len;
+
+} /* end mp_count_bits() */
+
+/* }}} */
+
+/* {{{ mp_read_radix(mp, str, radix) */
+
+/*
+ mp_read_radix(mp, str, radix)
+
+ Read an integer from the given string, and set mp to the resulting
+ value. The input is presumed to be in base 10. Leading non-digit
+ characters are ignored, and the function reads until a non-digit
+ character or the end of the string.
+ */
+
+mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix)
+{
+ int ix = 0, val = 0;
+ mp_err res;
+ mp_sign sig = MP_ZPOS;
+
+ ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX,
+ MP_BADARG);
+
+ mp_zero(mp);
+
+ /* Skip leading non-digit characters until a digit or '-' or '+' */
+ while(str[ix] &&
+ (s_mp_tovalue(str[ix], radix) < 0) &&
+ str[ix] != '-' &&
+ str[ix] != '+') {
+ ++ix;
+ }
+
+ if(str[ix] == '-') {
+ sig = MP_NEG;
+ ++ix;
+ } else if(str[ix] == '+') {
+ sig = MP_ZPOS; /* this is the default anyway... */
+ ++ix;
+ }
+
+ while((val = s_mp_tovalue(str[ix], radix)) >= 0) {
+ if((res = s_mp_mul_d(mp, radix)) != MP_OKAY)
+ return res;
+ if((res = s_mp_add_d(mp, val)) != MP_OKAY)
+ return res;
+ ++ix;
+ }
+
+ if(s_mp_cmp_d(mp, 0) == MP_EQ)
+ SIGN(mp) = MP_ZPOS;
+ else
+ SIGN(mp) = sig;
+
+ return MP_OKAY;
+
+} /* end mp_read_radix() */
+
+/* }}} */
+
+/* {{{ mp_radix_size(mp, radix) */
+
+int mp_radix_size(mp_int *mp, int radix)
+{
+ int len;
+ ARGCHK(mp != NULL, 0);
+
+ len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */
+
+ if(mp_cmp_z(mp) < 0)
+ ++len; /* for sign */
+
+ return len;
+
+} /* end mp_radix_size() */
+
+/* }}} */
+
+/* {{{ mp_value_radix_size(num, qty, radix) */
+
+/* num = number of digits
+ qty = number of bits per digit
+ radix = target base
+
+ Return the number of digits in the specified radix that would be
+ needed to express 'num' digits of 'qty' bits each.
+ */
+int mp_value_radix_size(int num, int qty, int radix)
+{
+ ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0);
+
+ return s_mp_outlen(num * qty, radix);
+
+} /* end mp_value_radix_size() */
+
+/* }}} */
+
+/* {{{ mp_toradix(mp, str, radix) */
+
+mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix)
+{
+ int ix, pos = 0;
+
+ ARGCHK(mp != NULL && str != NULL, MP_BADARG);
+ ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE);
+
+ if(mp_cmp_z(mp) == MP_EQ) {
+ str[0] = '0';
+ str[1] = '\0';
+ } else {
+ mp_err res;
+ mp_int tmp;
+ mp_sign sgn;
+ mp_digit rem, rdx = (mp_digit)radix;
+ char ch;
+
+ if((res = mp_init_copy(&tmp, mp)) != MP_OKAY)
+ return res;
+
+ /* Save sign for later, and take absolute value */
+ sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS;
+
+ /* Generate output digits in reverse order */
+ while(mp_cmp_z(&tmp) != 0) {
+ if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ /* Generate digits, use capital letters */
+ ch = s_mp_todigit(rem, radix, 0);
+
+ str[pos++] = ch;
+ }
+
+ /* Add - sign if original value was negative */
+ if(sgn == MP_NEG)
+ str[pos++] = '-';
+
+ /* Add trailing NUL to end the string */
+ str[pos--] = '\0';
+
+ /* Reverse the digits and sign indicator */
+ ix = 0;
+ while(ix < pos) {
+ char tmp = str[ix];
+
+ str[ix] = str[pos];
+ str[pos] = tmp;
+ ++ix;
+ --pos;
+ }
+
+ mp_clear(&tmp);
+ }
+
+ return MP_OKAY;
+
+} /* end mp_toradix() */
+
+/* }}} */
+
+/* {{{ mp_char2value(ch, r) */
+
+int mp_char2value(char ch, int r)
+{
+ return s_mp_tovalue(ch, r);
+
+} /* end mp_tovalue() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ mp_strerror(ec) */
+
+/*
+ mp_strerror(ec)
+
+ Return a string describing the meaning of error code 'ec'. The
+ string returned is allocated in static memory, so the caller should
+ not attempt to modify or free the memory associated with this
+ string.
+ */
+const char *mp_strerror(mp_err ec)
+{
+ int aec = (ec < 0) ? -ec : ec;
+
+ /* Code values are negative, so the senses of these comparisons
+ are accurate */
+ if(ec < MP_LAST_CODE || ec > MP_OKAY) {
+ return mp_err_string[0]; /* unknown error code */
+ } else {
+ return mp_err_string[aec + 1];
+ }
+
+} /* end mp_strerror() */
+
+/* }}} */
+
+/*========================================================================*/
+/*------------------------------------------------------------------------*/
+/* Static function definitions (internal use only) */
+
+/* {{{ Memory management */
+
+/* {{{ s_mp_grow(mp, min) */
+
+/* Make sure there are at least 'min' digits allocated to mp */
+mp_err s_mp_grow(mp_int *mp, mp_size min)
+{
+ if(min > ALLOC(mp)) {
+ mp_digit *tmp;
+
+ /* Set min to next nearest default precision block size */
+ min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec;
+
+ if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ s_mp_copy(DIGITS(mp), tmp, USED(mp));
+
+#if MP_CRYPTO
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+#endif
+ s_mp_free(DIGITS(mp));
+ DIGITS(mp) = tmp;
+ ALLOC(mp) = min;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_grow() */
+
+/* }}} */
+
+/* {{{ s_mp_pad(mp, min) */
+
+/* Make sure the used size of mp is at least 'min', growing if needed */
+mp_err s_mp_pad(mp_int *mp, mp_size min)
+{
+ if(min > USED(mp)) {
+ mp_err res;
+
+ /* Make sure there is room to increase precision */
+ if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY)
+ return res;
+
+ /* Increase precision; should already be 0-filled */
+ USED(mp) = min;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_pad() */
+
+/* }}} */
+
+/* {{{ s_mp_setz(dp, count) */
+
+#if MP_MACRO == 0
+/* Set 'count' digits pointed to by dp to be zeroes */
+void s_mp_setz(mp_digit *dp, mp_size count)
+{
+#if MP_MEMSET == 0
+ int ix;
+
+ for(ix = 0; ix < count; ix++)
+ dp[ix] = 0;
+#else
+ memset(dp, 0, count * sizeof(mp_digit));
+#endif
+
+} /* end s_mp_setz() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_copy(sp, dp, count) */
+
+#if MP_MACRO == 0
+/* Copy 'count' digits from sp to dp */
+void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count)
+{
+#if MP_MEMCPY == 0
+ int ix;
+
+ for(ix = 0; ix < count; ix++)
+ dp[ix] = sp[ix];
+#else
+ memcpy(dp, sp, count * sizeof(mp_digit));
+#endif
+
+} /* end s_mp_copy() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_alloc(nb, ni) */
+
+#if MP_MACRO == 0
+/* Allocate ni records of nb bytes each, and return a pointer to that */
+void *s_mp_alloc(size_t nb, size_t ni)
+{
+ return calloc(nb, ni);
+
+} /* end s_mp_alloc() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_free(ptr) */
+
+#if MP_MACRO == 0
+/* Free the memory pointed to by ptr */
+void s_mp_free(void *ptr)
+{
+ if(ptr)
+ free(ptr);
+
+} /* end s_mp_free() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_clamp(mp) */
+
+/* Remove leading zeroes from the given value */
+void s_mp_clamp(mp_int *mp)
+{
+ mp_size du = USED(mp);
+ mp_digit *zp = DIGITS(mp) + du - 1;
+
+ while(du > 1 && !*zp--)
+ --du;
+
+ USED(mp) = du;
+
+} /* end s_mp_clamp() */
+
+
+/* }}} */
+
+/* {{{ s_mp_exch(a, b) */
+
+/* Exchange the data for a and b; (b, a) = (a, b) */
+void s_mp_exch(mp_int *a, mp_int *b)
+{
+ mp_int tmp;
+
+ tmp = *a;
+ *a = *b;
+ *b = tmp;
+
+} /* end s_mp_exch() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Arithmetic helpers */
+
+/* {{{ s_mp_lshd(mp, p) */
+
+/*
+ Shift mp leftward by p digits, growing if needed, and zero-filling
+ the in-shifted digits at the right end. This is a convenient
+ alternative to multiplication by powers of the radix
+ */
+
+mp_err s_mp_lshd(mp_int *mp, mp_size p)
+{
+ mp_err res;
+ mp_size pos;
+ mp_digit *dp;
+ int ix;
+
+ if(p == 0)
+ return MP_OKAY;
+
+ if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY)
+ return res;
+
+ pos = USED(mp) - 1;
+ dp = DIGITS(mp);
+
+ /* Shift all the significant figures over as needed */
+ for(ix = pos - p; ix >= 0; ix--)
+ dp[ix + p] = dp[ix];
+
+ /* Fill the bottom digits with zeroes */
+ for(ix = 0; ix < p; ix++)
+ dp[ix] = 0;
+
+ return MP_OKAY;
+
+} /* end s_mp_lshd() */
+
+/* }}} */
+
+/* {{{ s_mp_rshd(mp, p) */
+
+/*
+ Shift mp rightward by p digits. Maintains the invariant that
+ digits above the precision are all zero. Digits shifted off the
+ end are lost. Cannot fail.
+ */
+
+void s_mp_rshd(mp_int *mp, mp_size p)
+{
+ mp_size ix;
+ mp_digit *dp;
+
+ if(p == 0)
+ return;
+
+ /* Shortcut when all digits are to be shifted off */
+ if(p >= USED(mp)) {
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+ USED(mp) = 1;
+ SIGN(mp) = MP_ZPOS;
+ return;
+ }
+
+ /* Shift all the significant figures over as needed */
+ dp = DIGITS(mp);
+ for(ix = p; ix < USED(mp); ix++)
+ dp[ix - p] = dp[ix];
+
+ /* Fill the top digits with zeroes */
+ ix -= p;
+ while(ix < USED(mp))
+ dp[ix++] = 0;
+
+ /* Strip off any leading zeroes */
+ s_mp_clamp(mp);
+
+} /* end s_mp_rshd() */
+
+/* }}} */
+
+/* {{{ s_mp_div_2(mp) */
+
+/* Divide by two -- take advantage of radix properties to do it fast */
+void s_mp_div_2(mp_int *mp)
+{
+ s_mp_div_2d(mp, 1);
+
+} /* end s_mp_div_2() */
+
+/* }}} */
+
+/* {{{ s_mp_mul_2(mp) */
+
+mp_err s_mp_mul_2(mp_int *mp)
+{
+ int ix;
+ mp_digit kin = 0, kout, *dp = DIGITS(mp);
+ mp_err res;
+
+ /* Shift digits leftward by 1 bit */
+ for(ix = 0; ix < USED(mp); ix++) {
+ kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1;
+ dp[ix] = (dp[ix] << 1) | kin;
+
+ kin = kout;
+ }
+
+ /* Deal with rollover from last digit */
+ if(kin) {
+ if(ix >= ALLOC(mp)) {
+ if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY)
+ return res;
+ dp = DIGITS(mp);
+ }
+
+ dp[ix] = kin;
+ USED(mp) += 1;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_mul_2() */
+
+/* }}} */
+
+/* {{{ s_mp_mod_2d(mp, d) */
+
+/*
+ Remainder the integer by 2^d, where d is a number of bits. This
+ amounts to a bitwise AND of the value, and does not require the full
+ division code
+ */
+void s_mp_mod_2d(mp_int *mp, mp_digit d)
+{
+ unsigned int ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT);
+ unsigned int ix;
+ mp_digit dmask, *dp = DIGITS(mp);
+
+ if(ndig >= USED(mp))
+ return;
+
+ /* Flush all the bits above 2^d in its digit */
+ dmask = (1 << nbit) - 1;
+ dp[ndig] &= dmask;
+
+ /* Flush all digits above the one with 2^d in it */
+ for(ix = ndig + 1; ix < USED(mp); ix++)
+ dp[ix] = 0;
+
+ s_mp_clamp(mp);
+
+} /* end s_mp_mod_2d() */
+
+/* }}} */
+
+/* {{{ s_mp_mul_2d(mp, d) */
+
+/*
+ Multiply by the integer 2^d, where d is a number of bits. This
+ amounts to a bitwise shift of the value, and does not require the
+ full multiplication code.
+ */
+mp_err s_mp_mul_2d(mp_int *mp, mp_digit d)
+{
+ mp_err res;
+ mp_digit save, next, mask, *dp;
+ mp_size used;
+ int ix;
+
+ if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY)
+ return res;
+
+ dp = DIGITS(mp); used = USED(mp);
+ d %= DIGIT_BIT;
+
+ mask = (1 << d) - 1;
+
+ /* If the shift requires another digit, make sure we've got one to
+ work with */
+ if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) {
+ if((res = s_mp_grow(mp, used + 1)) != MP_OKAY)
+ return res;
+ dp = DIGITS(mp);
+ }
+
+ /* Do the shifting... */
+ save = 0;
+ for(ix = 0; ix < used; ix++) {
+ next = (dp[ix] >> (DIGIT_BIT - d)) & mask;
+ dp[ix] = (dp[ix] << d) | save;
+ save = next;
+ }
+
+ /* If, at this point, we have a nonzero carryout into the next
+ digit, we'll increase the size by one digit, and store it...
+ */
+ if(save) {
+ dp[used] = save;
+ USED(mp) += 1;
+ }
+
+ s_mp_clamp(mp);
+ return MP_OKAY;
+
+} /* end s_mp_mul_2d() */
+
+/* }}} */
+
+/* {{{ s_mp_div_2d(mp, d) */
+
+/*
+ Divide the integer by 2^d, where d is a number of bits. This
+ amounts to a bitwise shift of the value, and does not require the
+ full division code (used in Barrett reduction, see below)
+ */
+void s_mp_div_2d(mp_int *mp, mp_digit d)
+{
+ int ix;
+ mp_digit save, next, mask, *dp = DIGITS(mp);
+
+ s_mp_rshd(mp, d / DIGIT_BIT);
+ d %= DIGIT_BIT;
+
+ mask = (1 << d) - 1;
+
+ save = 0;
+ for(ix = USED(mp) - 1; ix >= 0; ix--) {
+ next = dp[ix] & mask;
+ dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d));
+ save = next;
+ }
+
+ s_mp_clamp(mp);
+
+} /* end s_mp_div_2d() */
+
+/* }}} */
+
+/* {{{ s_mp_norm(a, b) */
+
+/*
+ s_mp_norm(a, b)
+
+ Normalize a and b for division, where b is the divisor. In order
+ that we might make good guesses for quotient digits, we want the
+ leading digit of b to be at least half the radix, which we
+ accomplish by multiplying a and b by a constant. This constant is
+ returned (so that it can be divided back out of the remainder at the
+ end of the division process).
+
+ We multiply by the smallest power of 2 that gives us a leading digit
+ at least half the radix. By choosing a power of 2, we simplify the
+ multiplication and division steps to simple shifts.
+ */
+mp_digit s_mp_norm(mp_int *a, mp_int *b)
+{
+ mp_digit t, d = 0;
+
+ t = DIGIT(b, USED(b) - 1);
+ while(t < (RADIX / 2)) {
+ t <<= 1;
+ ++d;
+ }
+
+ if(d != 0) {
+ s_mp_mul_2d(a, d);
+ s_mp_mul_2d(b, d);
+ }
+
+ return d;
+
+} /* end s_mp_norm() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive digit arithmetic */
+
+/* {{{ s_mp_add_d(mp, d) */
+
+/* Add d to |mp| in place */
+mp_err s_mp_add_d(mp_int *mp, mp_digit d) /* unsigned digit addition */
+{
+ mp_word w, k = 0;
+ mp_size ix = 1, used = USED(mp);
+ mp_digit *dp = DIGITS(mp);
+
+ w = dp[0] + d;
+ dp[0] = ACCUM(w);
+ k = CARRYOUT(w);
+
+ while(ix < used && k) {
+ w = dp[ix] + k;
+ dp[ix] = ACCUM(w);
+ k = CARRYOUT(w);
+ ++ix;
+ }
+
+ if(k != 0) {
+ mp_err res;
+
+ if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY)
+ return res;
+
+ DIGIT(mp, ix) = k;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_add_d() */
+
+/* }}} */
+
+/* {{{ s_mp_sub_d(mp, d) */
+
+/* Subtract d from |mp| in place, assumes |mp| > d */
+mp_err s_mp_sub_d(mp_int *mp, mp_digit d) /* unsigned digit subtract */
+{
+ mp_word w, b = 0;
+ mp_size ix = 1, used = USED(mp);
+ mp_digit *dp = DIGITS(mp);
+
+ /* Compute initial subtraction */
+ w = (RADIX + dp[0]) - d;
+ b = CARRYOUT(w) ? 0 : 1;
+ dp[0] = ACCUM(w);
+
+ /* Propagate borrows leftward */
+ while(b && ix < used) {
+ w = (RADIX + dp[ix]) - b;
+ b = CARRYOUT(w) ? 0 : 1;
+ dp[ix] = ACCUM(w);
+ ++ix;
+ }
+
+ /* Remove leading zeroes */
+ s_mp_clamp(mp);
+
+ /* If we have a borrow out, it's a violation of the input invariant */
+ if(b)
+ return MP_RANGE;
+ else
+ return MP_OKAY;
+
+} /* end s_mp_sub_d() */
+
+/* }}} */
+
+/* {{{ s_mp_mul_d(a, d) */
+
+/* Compute a = a * d, single digit multiplication */
+mp_err s_mp_mul_d(mp_int *a, mp_digit d)
+{
+ mp_word w, k = 0;
+ mp_size ix, max;
+ mp_err res;
+ mp_digit *dp = DIGITS(a);
+
+ /*
+ Single-digit multiplication will increase the precision of the
+ output by at most one digit. However, we can detect when this
+ will happen -- if the high-order digit of a, times d, gives a
+ two-digit result, then the precision of the result will increase;
+ otherwise it won't. We use this fact to avoid calling s_mp_pad()
+ unless absolutely necessary.
+ */
+ max = USED(a);
+ w = dp[max - 1] * d;
+ if(CARRYOUT(w) != 0) {
+ if((res = s_mp_pad(a, max + 1)) != MP_OKAY)
+ return res;
+ dp = DIGITS(a);
+ }
+
+ for(ix = 0; ix < max; ix++) {
+ w = (dp[ix] * d) + k;
+ dp[ix] = ACCUM(w);
+ k = CARRYOUT(w);
+ }
+
+ /* If there is a precision increase, take care of it here; the above
+ test guarantees we have enough storage to do this safely.
+ */
+ if(k) {
+ dp[max] = k;
+ USED(a) = max + 1;
+ }
+
+ s_mp_clamp(a);
+
+ return MP_OKAY;
+
+} /* end s_mp_mul_d() */
+
+/* }}} */
+
+/* {{{ s_mp_div_d(mp, d, r) */
+
+/*
+ s_mp_div_d(mp, d, r)
+
+ Compute the quotient mp = mp / d and remainder r = mp mod d, for a
+ single digit d. If r is null, the remainder will be discarded.
+ */
+
+mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r)
+{
+ mp_word w = 0, t;
+ mp_int quot;
+ mp_err res;
+ mp_digit *dp = DIGITS(mp), *qp;
+ int ix;
+
+ if(d == 0)
+ return MP_RANGE;
+
+ /* Make room for the quotient */
+ if((res = mp_init_size(", USED(mp))) != MP_OKAY)
+ return res;
+
+ USED(") = USED(mp); /* so clamping will work below */
+ qp = DIGITS(");
+
+ /* Divide without subtraction */
+ for(ix = USED(mp) - 1; ix >= 0; ix--) {
+ w = (w << DIGIT_BIT) | dp[ix];
+
+ if(w >= d) {
+ t = w / d;
+ w = w % d;
+ } else {
+ t = 0;
+ }
+
+ qp[ix] = t;
+ }
+
+ /* Deliver the remainder, if desired */
+ if(r)
+ *r = w;
+
+ s_mp_clamp(");
+ mp_exch(", mp);
+ mp_clear(");
+
+ return MP_OKAY;
+
+} /* end s_mp_div_d() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive full arithmetic */
+
+/* {{{ s_mp_add(a, b) */
+
+/* Compute a = |a| + |b| */
+mp_err s_mp_add(mp_int *a, mp_int *b) /* magnitude addition */
+{
+ mp_word w = 0;
+ mp_digit *pa, *pb;
+ mp_size ix, used = USED(b);
+ mp_err res;
+
+ /* Make sure a has enough precision for the output value */
+ if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY)
+ return res;
+
+ /*
+ Add up all digits up to the precision of b. If b had initially
+ the same precision as a, or greater, we took care of it by the
+ padding step above, so there is no problem. If b had initially
+ less precision, we'll have to make sure the carry out is duly
+ propagated upward among the higher-order digits of the sum.
+ */
+ pa = DIGITS(a);
+ pb = DIGITS(b);
+ for(ix = 0; ix < used; ++ix) {
+ w += *pa + *pb++;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w);
+ }
+
+ /* If we run out of 'b' digits before we're actually done, make
+ sure the carries get propagated upward...
+ */
+ used = USED(a);
+ while(w && ix < used) {
+ w += *pa;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w);
+ ++ix;
+ }
+
+ /* If there's an overall carry out, increase precision and include
+ it. We could have done this initially, but why touch the memory
+ allocator unless we're sure we have to?
+ */
+ if(w) {
+ if((res = s_mp_pad(a, used + 1)) != MP_OKAY)
+ return res;
+
+ DIGIT(a, ix) = w; /* pa may not be valid after s_mp_pad() call */
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_add() */
+
+/* }}} */
+
+/* {{{ s_mp_sub(a, b) */
+
+/* Compute a = |a| - |b|, assumes |a| >= |b| */
+mp_err s_mp_sub(mp_int *a, mp_int *b) /* magnitude subtract */
+{
+ mp_word w = 0;
+ mp_digit *pa, *pb;
+ mp_size ix, used = USED(b);
+
+ /*
+ Subtract and propagate borrow. Up to the precision of b, this
+ accounts for the digits of b; after that, we just make sure the
+ carries get to the right place. This saves having to pad b out to
+ the precision of a just to make the loops work right...
+ */
+ pa = DIGITS(a);
+ pb = DIGITS(b);
+
+ for(ix = 0; ix < used; ++ix) {
+ w = (RADIX + *pa) - w - *pb++;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w) ? 0 : 1;
+ }
+
+ used = USED(a);
+ while(ix < used) {
+ w = RADIX + *pa - w;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w) ? 0 : 1;
+ ++ix;
+ }
+
+ /* Clobber any leading zeroes we created */
+ s_mp_clamp(a);
+
+ /*
+ If there was a borrow out, then |b| > |a| in violation
+ of our input invariant. We've already done the work,
+ but we'll at least complain about it...
+ */
+ if(w)
+ return MP_RANGE;
+ else
+ return MP_OKAY;
+
+} /* end s_mp_sub() */
+
+/* }}} */
+
+mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu)
+{
+ mp_int q;
+ mp_err res;
+ mp_size um = USED(m);
+
+ if((res = mp_init_copy(&q, x)) != MP_OKAY)
+ return res;
+
+ s_mp_rshd(&q, um - 1); /* q1 = x / b^(k-1) */
+ s_mp_mul(&q, mu); /* q2 = q1 * mu */
+ s_mp_rshd(&q, um + 1); /* q3 = q2 / b^(k+1) */
+
+ /* x = x mod b^(k+1), quick (no division) */
+ s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1)));
+
+ /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */
+#ifndef SHRT_MUL
+ s_mp_mul(&q, m);
+ s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1)));
+#else
+ s_mp_mul_dig(&q, m, um + 1);
+#endif
+
+ /* x = x - q */
+ if((res = mp_sub(x, &q, x)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* If x < 0, add b^(k+1) to it */
+ if(mp_cmp_z(x) < 0) {
+ mp_set(&q, 1);
+ if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = mp_add(x, &q, x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ /* Back off if it's too big */
+ while(mp_cmp(x, m) >= 0) {
+ if((res = s_mp_sub(x, m)) != MP_OKAY)
+ break;
+ }
+
+ CLEANUP:
+ mp_clear(&q);
+
+ return res;
+
+} /* end s_mp_reduce() */
+
+
+
+/* {{{ s_mp_mul(a, b) */
+
+/* Compute a = |a| * |b| */
+mp_err s_mp_mul(mp_int *a, mp_int *b)
+{
+ mp_word w, k = 0;
+ mp_int tmp;
+ mp_err res;
+ mp_size ix, jx, ua = USED(a), ub = USED(b);
+ mp_digit *pa, *pb, *pt, *pbt;
+
+ if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY)
+ return res;
+
+ /* This has the effect of left-padding with zeroes... */
+ USED(&tmp) = ua + ub;
+
+ /* We're going to need the base value each iteration */
+ pbt = DIGITS(&tmp);
+
+ /* Outer loop: Digits of b */
+
+ pb = DIGITS(b);
+ for(ix = 0; ix < ub; ++ix, ++pb) {
+ if(*pb == 0)
+ continue;
+
+ /* Inner product: Digits of a */
+ pa = DIGITS(a);
+ for(jx = 0; jx < ua; ++jx, ++pa) {
+ pt = pbt + ix + jx;
+ w = *pb * *pa + k + *pt;
+ *pt = ACCUM(w);
+ k = CARRYOUT(w);
+ }
+
+ pbt[ix + jx] = k;
+ k = 0;
+ }
+
+ s_mp_clamp(&tmp);
+ s_mp_exch(&tmp, a);
+
+ mp_clear(&tmp);
+
+ return MP_OKAY;
+
+} /* end s_mp_mul() */
+
+/* }}} */
+
+/* {{{ s_mp_kmul(a, b, out, len) */
+
+#if 0
+void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len)
+{
+ mp_word w, k = 0;
+ mp_size ix, jx;
+ mp_digit *pa, *pt;
+
+ for(ix = 0; ix < len; ++ix, ++b) {
+ if(*b == 0)
+ continue;
+
+ pa = a;
+ for(jx = 0; jx < len; ++jx, ++pa) {
+ pt = out + ix + jx;
+ w = *b * *pa + k + *pt;
+ *pt = ACCUM(w);
+ k = CARRYOUT(w);
+ }
+
+ out[ix + jx] = k;
+ k = 0;
+ }
+
+} /* end s_mp_kmul() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_sqr(a) */
+
+/*
+ Computes the square of a, in place. This can be done more
+ efficiently than a general multiplication, because many of the
+ computation steps are redundant when squaring. The inner product
+ step is a bit more complicated, but we save a fair number of
+ iterations of the multiplication loop.
+ */
+#if MP_SQUARE
+mp_err s_mp_sqr(mp_int *a)
+{
+ mp_word w, k = 0;
+ mp_int tmp;
+ mp_err res;
+ mp_size ix, jx, kx, used = USED(a);
+ mp_digit *pa1, *pa2, *pt, *pbt;
+
+ if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY)
+ return res;
+
+ /* Left-pad with zeroes */
+ USED(&tmp) = 2 * used;
+
+ /* We need the base value each time through the loop */
+ pbt = DIGITS(&tmp);
+
+ pa1 = DIGITS(a);
+ for(ix = 0; ix < used; ++ix, ++pa1) {
+ if(*pa1 == 0)
+ continue;
+
+ w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1);
+
+ pbt[ix + ix] = ACCUM(w);
+ k = CARRYOUT(w);
+
+ /*
+ The inner product is computed as:
+
+ (C, S) = t[i,j] + 2 a[i] a[j] + C
+
+ This can overflow what can be represented in an mp_word, and
+ since C arithmetic does not provide any way to check for
+ overflow, we have to check explicitly for overflow conditions
+ before they happen.
+ */
+ for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) {
+ mp_word u = 0, v;
+
+ /* Store this in a temporary to avoid indirections later */
+ pt = pbt + ix + jx;
+
+ /* Compute the multiplicative step */
+ w = *pa1 * *pa2;
+
+ /* If w is more than half MP_WORD_MAX, the doubling will
+ overflow, and we need to record a carry out into the next
+ word */
+ u = (w >> (MP_WORD_BIT - 1)) & 1;
+
+ /* Double what we've got, overflow will be ignored as defined
+ for C arithmetic (we've already noted if it is to occur)
+ */
+ w *= 2;
+
+ /* Compute the additive step */
+ v = *pt + k;
+
+ /* If we do not already have an overflow carry, check to see
+ if the addition will cause one, and set the carry out if so
+ */
+ u |= ((MP_WORD_MAX - v) < w);
+
+ /* Add in the rest, again ignoring overflow */
+ w += v;
+
+ /* Set the i,j digit of the output */
+ *pt = ACCUM(w);
+
+ /* Save carry information for the next iteration of the loop.
+ This is why k must be an mp_word, instead of an mp_digit */
+ k = CARRYOUT(w) | (u << DIGIT_BIT);
+
+ } /* for(jx ...) */
+
+ /* Set the last digit in the cycle and reset the carry */
+ k = DIGIT(&tmp, ix + jx) + k;
+ pbt[ix + jx] = ACCUM(k);
+ k = CARRYOUT(k);
+
+ /* If we are carrying out, propagate the carry to the next digit
+ in the output. This may cascade, so we have to be somewhat
+ circumspect -- but we will have enough precision in the output
+ that we won't overflow
+ */
+ kx = 1;
+ while(k) {
+ k = pbt[ix + jx + kx] + 1;
+ pbt[ix + jx + kx] = ACCUM(k);
+ k = CARRYOUT(k);
+ ++kx;
+ }
+ } /* for(ix ...) */
+
+ s_mp_clamp(&tmp);
+ s_mp_exch(&tmp, a);
+
+ mp_clear(&tmp);
+
+ return MP_OKAY;
+
+} /* end s_mp_sqr() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_div(a, b) */
+
+/*
+ s_mp_div(a, b)
+
+ Compute a = a / b and b = a mod b. Assumes b > a.
+ */
+
+mp_err s_mp_div(mp_int *a, mp_int *b)
+{
+ mp_int quot, rem, t;
+ mp_word q;
+ mp_err res;
+ mp_digit d;
+ int ix;
+
+ if(mp_cmp_z(b) == 0)
+ return MP_RANGE;
+
+ /* Shortcut if b is power of two */
+ if((ix = s_mp_ispow2(b)) >= 0) {
+ mp_copy(a, b); /* need this for remainder */
+ s_mp_div_2d(a, (mp_digit)ix);
+ s_mp_mod_2d(b, (mp_digit)ix);
+
+ return MP_OKAY;
+ }
+
+ /* Allocate space to store the quotient */
+ if((res = mp_init_size(", USED(a))) != MP_OKAY)
+ return res;
+
+ /* A working temporary for division */
+ if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
+ goto T;
+
+ /* Allocate space for the remainder */
+ if((res = mp_init_size(&rem, USED(a))) != MP_OKAY)
+ goto REM;
+
+ /* Normalize to optimize guessing */
+ d = s_mp_norm(a, b);
+
+ /* Perform the division itself...woo! */
+ ix = USED(a) - 1;
+
+ while(ix >= 0) {
+ /* Find a partial substring of a which is at least b */
+ while(s_mp_cmp(&rem, b) < 0 && ix >= 0) {
+ if((res = s_mp_lshd(&rem, 1)) != MP_OKAY)
+ goto CLEANUP;
+
+ if((res = s_mp_lshd(", 1)) != MP_OKAY)
+ goto CLEANUP;
+
+ DIGIT(&rem, 0) = DIGIT(a, ix);
+ s_mp_clamp(&rem);
+ --ix;
+ }
+
+ /* If we didn't find one, we're finished dividing */
+ if(s_mp_cmp(&rem, b) < 0)
+ break;
+
+ /* Compute a guess for the next quotient digit */
+ q = DIGIT(&rem, USED(&rem) - 1);
+ if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1)
+ q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2);
+
+ q /= DIGIT(b, USED(b) - 1);
+
+ /* The guess can be as much as RADIX + 1 */
+ if(q >= RADIX)
+ q = RADIX - 1;
+
+ /* See what that multiplies out to */
+ mp_copy(b, &t);
+ if((res = s_mp_mul_d(&t, q)) != MP_OKAY)
+ goto CLEANUP;
+
+ /*
+ If it's too big, back it off. We should not have to do this
+ more than once, or, in rare cases, twice. Knuth describes a
+ method by which this could be reduced to a maximum of once, but
+ I didn't implement that here.
+ */
+ while(s_mp_cmp(&t, &rem) > 0) {
+ --q;
+ s_mp_sub(&t, b);
+ }
+
+ /* At this point, q should be the right next digit */
+ if((res = s_mp_sub(&rem, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ /*
+ Include the digit in the quotient. We allocated enough memory
+ for any quotient we could ever possibly get, so we should not
+ have to check for failures here
+ */
+ DIGIT(", 0) = q;
+ }
+
+ /* Denormalize remainder */
+ if(d != 0)
+ s_mp_div_2d(&rem, d);
+
+ s_mp_clamp(");
+ s_mp_clamp(&rem);
+
+ /* Copy quotient back to output */
+ s_mp_exch(", a);
+
+ /* Copy remainder back to output */
+ s_mp_exch(&rem, b);
+
+CLEANUP:
+ mp_clear(&rem);
+REM:
+ mp_clear(&t);
+T:
+ mp_clear(");
+
+ return res;
+
+} /* end s_mp_div() */
+
+/* }}} */
+
+/* {{{ s_mp_2expt(a, k) */
+
+mp_err s_mp_2expt(mp_int *a, mp_digit k)
+{
+ mp_err res;
+ mp_size dig, bit;
+
+ dig = k / DIGIT_BIT;
+ bit = k % DIGIT_BIT;
+
+ mp_zero(a);
+ if((res = s_mp_pad(a, dig + 1)) != MP_OKAY)
+ return res;
+
+ DIGIT(a, dig) |= (1 << bit);
+
+ return MP_OKAY;
+
+} /* end s_mp_2expt() */
+
+/* }}} */
+
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive comparisons */
+
+/* {{{ s_mp_cmp(a, b) */
+
+/* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b */
+int s_mp_cmp(mp_int *a, mp_int *b)
+{
+ mp_size ua = USED(a), ub = USED(b);
+
+ if(ua > ub)
+ return MP_GT;
+ else if(ua < ub)
+ return MP_LT;
+ else {
+ int ix = ua - 1;
+ mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix;
+
+ while(ix >= 0) {
+ if(*ap > *bp)
+ return MP_GT;
+ else if(*ap < *bp)
+ return MP_LT;
+
+ --ap; --bp; --ix;
+ }
+
+ return MP_EQ;
+ }
+
+} /* end s_mp_cmp() */
+
+/* }}} */
+
+/* {{{ s_mp_cmp_d(a, d) */
+
+/* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d */
+int s_mp_cmp_d(mp_int *a, mp_digit d)
+{
+ mp_size ua = USED(a);
+ mp_digit *ap = DIGITS(a);
+
+ if(ua > 1)
+ return MP_GT;
+
+ if(*ap < d)
+ return MP_LT;
+ else if(*ap > d)
+ return MP_GT;
+ else
+ return MP_EQ;
+
+} /* end s_mp_cmp_d() */
+
+/* }}} */
+
+/* {{{ s_mp_ispow2(v) */
+
+/*
+ Returns -1 if the value is not a power of two; otherwise, it returns
+ k such that v = 2^k, i.e. lg(v).
+ */
+int s_mp_ispow2(mp_int *v)
+{
+ mp_digit d, *dp;
+ mp_size uv = USED(v);
+ int extra = 0, ix;
+
+ d = DIGIT(v, uv - 1); /* most significant digit of v */
+
+ while(d && ((d & 1) == 0)) {
+ d >>= 1;
+ ++extra;
+ }
+
+ if(d == 1) {
+ ix = uv - 2;
+ dp = DIGITS(v) + ix;
+
+ while(ix >= 0) {
+ if(*dp)
+ return -1; /* not a power of two */
+
+ --dp; --ix;
+ }
+
+ return ((uv - 1) * DIGIT_BIT) + extra;
+ }
+
+ return -1;
+
+} /* end s_mp_ispow2() */
+
+/* }}} */
+
+/* {{{ s_mp_ispow2d(d) */
+
+int s_mp_ispow2d(mp_digit d)
+{
+ int pow = 0;
+
+ while((d & 1) == 0) {
+ ++pow; d >>= 1;
+ }
+
+ if(d == 1)
+ return pow;
+
+ return -1;
+
+} /* end s_mp_ispow2d() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive I/O helpers */
+
+/* {{{ s_mp_tovalue(ch, r) */
+
+/*
+ Convert the given character to its digit value, in the given radix.
+ If the given character is not understood in the given radix, -1 is
+ returned. Otherwise the digit's numeric value is returned.
+
+ The results will be odd if you use a radix < 2 or > 62, you are
+ expected to know what you're up to.
+ */
+int s_mp_tovalue(char ch, int r)
+{
+ int val, xch;
+
+ if(r > 36)
+ xch = ch;
+ else
+ xch = toupper(ch);
+
+ if(isdigit(xch))
+ val = xch - '0';
+ else if(isupper(xch))
+ val = xch - 'A' + 10;
+ else if(islower(xch))
+ val = xch - 'a' + 36;
+ else if(xch == '+')
+ val = 62;
+ else if(xch == '/')
+ val = 63;
+ else
+ return -1;
+
+ if(val < 0 || val >= r)
+ return -1;
+
+ return val;
+
+} /* end s_mp_tovalue() */
+
+/* }}} */
+
+/* {{{ s_mp_todigit(val, r, low) */
+
+/*
+ Convert val to a radix-r digit, if possible. If val is out of range
+ for r, returns zero. Otherwise, returns an ASCII character denoting
+ the value in the given radix.
+
+ The results may be odd if you use a radix < 2 or > 64, you are
+ expected to know what you're doing.
+ */
+
+char s_mp_todigit(int val, int r, int low)
+{
+ char ch;
+
+ if(val < 0 || val >= r)
+ return 0;
+
+ ch = s_dmap_1[val];
+
+ if(r <= 36 && low)
+ ch = tolower(ch);
+
+ return ch;
+
+} /* end s_mp_todigit() */
+
+/* }}} */
+
+/* {{{ s_mp_outlen(bits, radix) */
+
+/*
+ Return an estimate for how long a string is needed to hold a radix
+ r representation of a number with 'bits' significant bits.
+
+ Does not include space for a sign or a NUL terminator.
+ */
+int s_mp_outlen(int bits, int r)
+{
+ return (int)((double)bits * LOG_V_2(r));
+
+} /* end s_mp_outlen() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* HERE THERE BE DRAGONS */
+/* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */
+
+/* $Source: /cvs/libtom/libtommath/mtest/mpi.c,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/mtest/mpi.h b/libtommath/mtest/mpi.h
new file mode 100644
index 0000000..66ae873
--- /dev/null
+++ b/libtommath/mtest/mpi.h
@@ -0,0 +1,231 @@
+/*
+ mpi.h
+
+ by Michael J. Fromberger <sting@linguist.dartmouth.edu>
+ Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved
+
+ Arbitrary precision integer arithmetic library
+
+ $Id: mpi.h,v 1.2 2005/05/05 14:38:47 tom Exp $
+ */
+
+#ifndef _H_MPI_
+#define _H_MPI_
+
+#include "mpi-config.h"
+
+#define MP_LT -1
+#define MP_EQ 0
+#define MP_GT 1
+
+#if MP_DEBUG
+#undef MP_IOFUNC
+#define MP_IOFUNC 1
+#endif
+
+#if MP_IOFUNC
+#include <stdio.h>
+#include <ctype.h>
+#endif
+
+#include <limits.h>
+
+#define MP_NEG 1
+#define MP_ZPOS 0
+
+/* Included for compatibility... */
+#define NEG MP_NEG
+#define ZPOS MP_ZPOS
+
+#define MP_OKAY 0 /* no error, all is well */
+#define MP_YES 0 /* yes (boolean result) */
+#define MP_NO -1 /* no (boolean result) */
+#define MP_MEM -2 /* out of memory */
+#define MP_RANGE -3 /* argument out of range */
+#define MP_BADARG -4 /* invalid parameter */
+#define MP_UNDEF -5 /* answer is undefined */
+#define MP_LAST_CODE MP_UNDEF
+
+#include "mpi-types.h"
+
+/* Included for compatibility... */
+#define DIGIT_BIT MP_DIGIT_BIT
+#define DIGIT_MAX MP_DIGIT_MAX
+
+/* Macros for accessing the mp_int internals */
+#define SIGN(MP) ((MP)->sign)
+#define USED(MP) ((MP)->used)
+#define ALLOC(MP) ((MP)->alloc)
+#define DIGITS(MP) ((MP)->dp)
+#define DIGIT(MP,N) (MP)->dp[(N)]
+
+#if MP_ARGCHK == 1
+#define ARGCHK(X,Y) {if(!(X)){return (Y);}}
+#elif MP_ARGCHK == 2
+#include <assert.h>
+#define ARGCHK(X,Y) assert(X)
+#else
+#define ARGCHK(X,Y) /* */
+#endif
+
+/* This defines the maximum I/O base (minimum is 2) */
+#define MAX_RADIX 64
+
+typedef struct {
+ mp_sign sign; /* sign of this quantity */
+ mp_size alloc; /* how many digits allocated */
+ mp_size used; /* how many digits used */
+ mp_digit *dp; /* the digits themselves */
+} mp_int;
+
+/*------------------------------------------------------------------------*/
+/* Default precision */
+
+unsigned int mp_get_prec(void);
+void mp_set_prec(unsigned int prec);
+
+/*------------------------------------------------------------------------*/
+/* Memory management */
+
+mp_err mp_init(mp_int *mp);
+mp_err mp_init_array(mp_int mp[], int count);
+mp_err mp_init_size(mp_int *mp, mp_size prec);
+mp_err mp_init_copy(mp_int *mp, mp_int *from);
+mp_err mp_copy(mp_int *from, mp_int *to);
+void mp_exch(mp_int *mp1, mp_int *mp2);
+void mp_clear(mp_int *mp);
+void mp_clear_array(mp_int mp[], int count);
+void mp_zero(mp_int *mp);
+void mp_set(mp_int *mp, mp_digit d);
+mp_err mp_set_int(mp_int *mp, long z);
+mp_err mp_shrink(mp_int *a);
+
+
+/*------------------------------------------------------------------------*/
+/* Single digit arithmetic */
+
+mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b);
+mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b);
+mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b);
+mp_err mp_mul_2(mp_int *a, mp_int *c);
+mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r);
+mp_err mp_div_2(mp_int *a, mp_int *c);
+mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c);
+
+/*------------------------------------------------------------------------*/
+/* Sign manipulations */
+
+mp_err mp_abs(mp_int *a, mp_int *b);
+mp_err mp_neg(mp_int *a, mp_int *b);
+
+/*------------------------------------------------------------------------*/
+/* Full arithmetic */
+
+mp_err mp_add(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c);
+#if MP_SQUARE
+mp_err mp_sqr(mp_int *a, mp_int *b);
+#else
+#define mp_sqr(a, b) mp_mul(a, a, b)
+#endif
+mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r);
+mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r);
+mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_2expt(mp_int *a, mp_digit k);
+mp_err mp_sqrt(mp_int *a, mp_int *b);
+
+/*------------------------------------------------------------------------*/
+/* Modular arithmetic */
+
+#if MP_MODARITH
+mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c);
+mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c);
+mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+#if MP_SQUARE
+mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c);
+#else
+#define mp_sqrmod(a, m, c) mp_mulmod(a, a, m, c)
+#endif
+mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c);
+#endif /* MP_MODARITH */
+
+/*------------------------------------------------------------------------*/
+/* Comparisons */
+
+int mp_cmp_z(mp_int *a);
+int mp_cmp_d(mp_int *a, mp_digit d);
+int mp_cmp(mp_int *a, mp_int *b);
+int mp_cmp_mag(mp_int *a, mp_int *b);
+int mp_cmp_int(mp_int *a, long z);
+int mp_isodd(mp_int *a);
+int mp_iseven(mp_int *a);
+
+/*------------------------------------------------------------------------*/
+/* Number theoretic */
+
+#if MP_NUMTH
+mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y);
+mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c);
+#endif /* end MP_NUMTH */
+
+/*------------------------------------------------------------------------*/
+/* Input and output */
+
+#if MP_IOFUNC
+void mp_print(mp_int *mp, FILE *ofp);
+#endif /* end MP_IOFUNC */
+
+/*------------------------------------------------------------------------*/
+/* Base conversion */
+
+#define BITS 1
+#define BYTES CHAR_BIT
+
+mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len);
+int mp_signed_bin_size(mp_int *mp);
+mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str);
+
+mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len);
+int mp_unsigned_bin_size(mp_int *mp);
+mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str);
+
+int mp_count_bits(mp_int *mp);
+
+#if MP_COMPAT_MACROS
+#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
+#define mp_raw_size(mp) mp_signed_bin_size(mp)
+#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
+#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
+#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
+#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
+#endif
+
+mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix);
+int mp_radix_size(mp_int *mp, int radix);
+int mp_value_radix_size(int num, int qty, int radix);
+mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix);
+
+int mp_char2value(char ch, int r);
+
+#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
+#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
+#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
+#define mp_tohex(M, S) mp_toradix((M), (S), 16)
+
+/*------------------------------------------------------------------------*/
+/* Error strings */
+
+const char *mp_strerror(mp_err ec);
+
+#endif /* end _H_MPI_ */
+
+/* $Source: /cvs/libtom/libtommath/mtest/mpi.h,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/mtest/mtest.c b/libtommath/mtest/mtest.c
new file mode 100644
index 0000000..bdfe612
--- /dev/null
+++ b/libtommath/mtest/mtest.c
@@ -0,0 +1,308 @@
+/* makes a bignum test harness with NUM tests per operation
+ *
+ * the output is made in the following format [one parameter per line]
+
+operation
+operand1
+operand2
+[... operandN]
+result1
+result2
+[... resultN]
+
+So for example "a * b mod n" would be
+
+mulmod
+a
+b
+n
+a*b mod n
+
+e.g. if a=3, b=4 n=11 then
+
+mulmod
+3
+4
+11
+1
+
+ */
+
+#ifdef MP_8BIT
+#define THE_MASK 127
+#else
+#define THE_MASK 32767
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#include "mpi.c"
+
+FILE *rng;
+
+void rand_num(mp_int *a)
+{
+ int n, size;
+ unsigned char buf[2048];
+
+ size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 101;
+ buf[0] = (fgetc(rng)&1)?1:0;
+ fread(buf+1, 1, size, rng);
+ while (buf[1] == 0) buf[1] = fgetc(rng);
+ mp_read_raw(a, buf, 1+size);
+}
+
+void rand_num2(mp_int *a)
+{
+ int n, size;
+ unsigned char buf[2048];
+
+ size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 101;
+ buf[0] = (fgetc(rng)&1)?1:0;
+ fread(buf+1, 1, size, rng);
+ while (buf[1] == 0) buf[1] = fgetc(rng);
+ mp_read_raw(a, buf, 1+size);
+}
+
+#define mp_to64(a, b) mp_toradix(a, b, 64)
+
+int main(void)
+{
+ int n, tmp;
+ mp_int a, b, c, d, e;
+ clock_t t1;
+ char buf[4096];
+
+ mp_init(&a);
+ mp_init(&b);
+ mp_init(&c);
+ mp_init(&d);
+ mp_init(&e);
+
+
+ /* initial (2^n - 1)^2 testing, makes sure the comba multiplier works [it has the new carry code] */
+/*
+ mp_set(&a, 1);
+ for (n = 1; n < 8192; n++) {
+ mp_mul(&a, &a, &c);
+ printf("mul\n");
+ mp_to64(&a, buf);
+ printf("%s\n%s\n", buf, buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+
+ mp_add_d(&a, 1, &a);
+ mp_mul_2(&a, &a);
+ mp_sub_d(&a, 1, &a);
+ }
+*/
+
+ rng = fopen("/dev/urandom", "rb");
+ if (rng == NULL) {
+ rng = fopen("/dev/random", "rb");
+ if (rng == NULL) {
+ fprintf(stderr, "\nWarning: stdin used as random source\n\n");
+ rng = stdin;
+ }
+ }
+
+ t1 = clock();
+ for (;;) {
+#if 0
+ if (clock() - t1 > CLOCKS_PER_SEC) {
+ sleep(2);
+ t1 = clock();
+ }
+#endif
+ n = fgetc(rng) % 15;
+
+ if (n == 0) {
+ /* add tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_add(&a, &b, &c);
+ printf("add\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 1) {
+ /* sub tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_sub(&a, &b, &c);
+ printf("sub\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 2) {
+ /* mul tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_mul(&a, &b, &c);
+ printf("mul\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 3) {
+ /* div tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_div(&a, &b, &c, &d);
+ printf("div\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ mp_to64(&d, buf);
+ printf("%s\n", buf);
+ } else if (n == 4) {
+ /* sqr tests */
+ rand_num(&a);
+ mp_sqr(&a, &b);
+ printf("sqr\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 5) {
+ /* mul_2d test */
+ rand_num(&a);
+ mp_copy(&a, &b);
+ n = fgetc(rng) & 63;
+ mp_mul_2d(&b, n, &b);
+ mp_to64(&a, buf);
+ printf("mul2d\n");
+ printf("%s\n", buf);
+ printf("%d\n", n);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 6) {
+ /* div_2d test */
+ rand_num(&a);
+ mp_copy(&a, &b);
+ n = fgetc(rng) & 63;
+ mp_div_2d(&b, n, &b, NULL);
+ mp_to64(&a, buf);
+ printf("div2d\n");
+ printf("%s\n", buf);
+ printf("%d\n", n);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 7) {
+ /* gcd test */
+ rand_num(&a);
+ rand_num(&b);
+ a.sign = MP_ZPOS;
+ b.sign = MP_ZPOS;
+ mp_gcd(&a, &b, &c);
+ printf("gcd\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 8) {
+ /* lcm test */
+ rand_num(&a);
+ rand_num(&b);
+ a.sign = MP_ZPOS;
+ b.sign = MP_ZPOS;
+ mp_lcm(&a, &b, &c);
+ printf("lcm\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 9) {
+ /* exptmod test */
+ rand_num2(&a);
+ rand_num2(&b);
+ rand_num2(&c);
+// if (c.dp[0]&1) mp_add_d(&c, 1, &c);
+ a.sign = b.sign = c.sign = 0;
+ mp_exptmod(&a, &b, &c, &d);
+ printf("expt\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ mp_to64(&d, buf);
+ printf("%s\n", buf);
+ } else if (n == 10) {
+ /* invmod test */
+ rand_num2(&a);
+ rand_num2(&b);
+ b.sign = MP_ZPOS;
+ a.sign = MP_ZPOS;
+ mp_gcd(&a, &b, &c);
+ if (mp_cmp_d(&c, 1) != 0) continue;
+ if (mp_cmp_d(&b, 1) == 0) continue;
+ mp_invmod(&a, &b, &c);
+ printf("invmod\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 11) {
+ rand_num(&a);
+ mp_mul_2(&a, &a);
+ mp_div_2(&a, &b);
+ printf("div2\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 12) {
+ rand_num2(&a);
+ mp_mul_2(&a, &b);
+ printf("mul2\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 13) {
+ rand_num2(&a);
+ tmp = abs(rand()) & THE_MASK;
+ mp_add_d(&a, tmp, &b);
+ printf("add_d\n");
+ mp_to64(&a, buf);
+ printf("%s\n%d\n", buf, tmp);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 14) {
+ rand_num2(&a);
+ tmp = abs(rand()) & THE_MASK;
+ mp_sub_d(&a, tmp, &b);
+ printf("sub_d\n");
+ mp_to64(&a, buf);
+ printf("%s\n%d\n", buf, tmp);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ }
+ }
+ fclose(rng);
+ return 0;
+}
+
+/* $Source: /cvs/libtom/libtommath/mtest/mtest.c,v $ */
+/* $Revision: 1.2 $ */
+/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/pics/design_process.sxd b/libtommath/pics/design_process.sxd
new file mode 100644
index 0000000..7414dbb
--- /dev/null
+++ b/libtommath/pics/design_process.sxd
Binary files differ
diff --git a/libtommath/pics/design_process.tif b/libtommath/pics/design_process.tif
new file mode 100644
index 0000000..4a0c012
--- /dev/null
+++ b/libtommath/pics/design_process.tif
Binary files differ
diff --git a/libtommath/pics/expt_state.sxd b/libtommath/pics/expt_state.sxd
new file mode 100644
index 0000000..6518404
--- /dev/null
+++ b/libtommath/pics/expt_state.sxd
Binary files differ
diff --git a/libtommath/pics/expt_state.tif b/libtommath/pics/expt_state.tif
new file mode 100644
index 0000000..cb06e8e
--- /dev/null
+++ b/libtommath/pics/expt_state.tif
Binary files differ
diff --git a/libtommath/pics/makefile b/libtommath/pics/makefile
new file mode 100644
index 0000000..3ecb02f
--- /dev/null
+++ b/libtommath/pics/makefile
@@ -0,0 +1,35 @@
+# makes the images... yeah
+
+default: pses
+
+design_process.ps: design_process.tif
+ tiff2ps -s -e design_process.tif > design_process.ps
+
+sliding_window.ps: sliding_window.tif
+ tiff2ps -s -e sliding_window.tif > sliding_window.ps
+
+expt_state.ps: expt_state.tif
+ tiff2ps -s -e expt_state.tif > expt_state.ps
+
+primality.ps: primality.tif
+ tiff2ps -s -e primality.tif > primality.ps
+
+design_process.pdf: design_process.ps
+ epstopdf design_process.ps
+
+sliding_window.pdf: sliding_window.ps
+ epstopdf sliding_window.ps
+
+expt_state.pdf: expt_state.ps
+ epstopdf expt_state.ps
+
+primality.pdf: primality.ps
+ epstopdf primality.ps
+
+
+pses: sliding_window.ps expt_state.ps primality.ps design_process.ps
+pdfes: sliding_window.pdf expt_state.pdf primality.pdf design_process.pdf
+
+clean:
+ rm -rf *.ps *.pdf .xvpics
+
\ No newline at end of file
diff --git a/libtommath/pics/primality.tif b/libtommath/pics/primality.tif
new file mode 100644
index 0000000..76d6be3
--- /dev/null
+++ b/libtommath/pics/primality.tif
Binary files differ
diff --git a/libtommath/pics/radix.sxd b/libtommath/pics/radix.sxd
new file mode 100644
index 0000000..b9eb9a0
--- /dev/null
+++ b/libtommath/pics/radix.sxd
Binary files differ
diff --git a/libtommath/pics/sliding_window.sxd b/libtommath/pics/sliding_window.sxd
new file mode 100644
index 0000000..91e7c0d
--- /dev/null
+++ b/libtommath/pics/sliding_window.sxd
Binary files differ
diff --git a/libtommath/pics/sliding_window.tif b/libtommath/pics/sliding_window.tif
new file mode 100644
index 0000000..bb4cb96
--- /dev/null
+++ b/libtommath/pics/sliding_window.tif
Binary files differ
diff --git a/libtommath/poster.out b/libtommath/poster.out
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/libtommath/poster.out
diff --git a/libtommath/poster.tex b/libtommath/poster.tex
new file mode 100644
index 0000000..e7388f4
--- /dev/null
+++ b/libtommath/poster.tex
@@ -0,0 +1,35 @@
+\documentclass[landscape,11pt]{article}
+\usepackage{amsmath, amssymb}
+\usepackage{hyperref}
+\begin{document}
+\hspace*{-3in}
+\begin{tabular}{llllll}
+$c = a + b$ & {\tt mp\_add(\&a, \&b, \&c)} & $b = 2a$ & {\tt mp\_mul\_2(\&a, \&b)} & \\
+$c = a - b$ & {\tt mp\_sub(\&a, \&b, \&c)} & $b = a/2$ & {\tt mp\_div\_2(\&a, \&b)} & \\
+$c = ab $ & {\tt mp\_mul(\&a, \&b, \&c)} & $c = 2^ba$ & {\tt mp\_mul\_2d(\&a, b, \&c)} \\
+$b = a^2 $ & {\tt mp\_sqr(\&a, \&b)} & $c = a/2^b, d = a \mod 2^b$ & {\tt mp\_div\_2d(\&a, b, \&c, \&d)} \\
+$c = \lfloor a/b \rfloor, d = a \mod b$ & {\tt mp\_div(\&a, \&b, \&c, \&d)} & $c = a \mod 2^b $ & {\tt mp\_mod\_2d(\&a, b, \&c)} \\
+ && \\
+$a = b $ & {\tt mp\_set\_int(\&a, b)} & $c = a \vee b$ & {\tt mp\_or(\&a, \&b, \&c)} \\
+$b = a $ & {\tt mp\_copy(\&a, \&b)} & $c = a \wedge b$ & {\tt mp\_and(\&a, \&b, \&c)} \\
+ && $c = a \oplus b$ & {\tt mp\_xor(\&a, \&b, \&c)} \\
+ & \\
+$b = -a $ & {\tt mp\_neg(\&a, \&b)} & $d = a + b \mod c$ & {\tt mp\_addmod(\&a, \&b, \&c, \&d)} \\
+$b = |a| $ & {\tt mp\_abs(\&a, \&b)} & $d = a - b \mod c$ & {\tt mp\_submod(\&a, \&b, \&c, \&d)} \\
+ && $d = ab \mod c$ & {\tt mp\_mulmod(\&a, \&b, \&c, \&d)} \\
+Compare $a$ and $b$ & {\tt mp\_cmp(\&a, \&b)} & $c = a^2 \mod b$ & {\tt mp\_sqrmod(\&a, \&b, \&c)} \\
+Is Zero? & {\tt mp\_iszero(\&a)} & $c = a^{-1} \mod b$ & {\tt mp\_invmod(\&a, \&b, \&c)} \\
+Is Even? & {\tt mp\_iseven(\&a)} & $d = a^b \mod c$ & {\tt mp\_exptmod(\&a, \&b, \&c, \&d)} \\
+Is Odd ? & {\tt mp\_isodd(\&a)} \\
+&\\
+$\vert \vert a \vert \vert$ & {\tt mp\_unsigned\_bin\_size(\&a)} & $res$ = 1 if $a$ prime to $t$ rounds? & {\tt mp\_prime\_is\_prime(\&a, t, \&res)} \\
+$buf \leftarrow a$ & {\tt mp\_to\_unsigned\_bin(\&a, buf)} & Next prime after $a$ to $t$ rounds. & {\tt mp\_prime\_next\_prime(\&a, t, bbs\_style)} \\
+$a \leftarrow buf[0..len-1]$ & {\tt mp\_read\_unsigned\_bin(\&a, buf, len)} \\
+&\\
+$b = \sqrt{a}$ & {\tt mp\_sqrt(\&a, \&b)} & $c = \mbox{gcd}(a, b)$ & {\tt mp\_gcd(\&a, \&b, \&c)} \\
+$c = a^{1/b}$ & {\tt mp\_n\_root(\&a, b, \&c)} & $c = \mbox{lcm}(a, b)$ & {\tt mp\_lcm(\&a, \&b, \&c)} \\
+&\\
+Greater Than & MP\_GT & Equal To & MP\_EQ \\
+Less Than & MP\_LT & Bits per digit & DIGIT\_BIT \\
+\end{tabular}
+\end{document}
diff --git a/libtommath/pre_gen/mpi.c b/libtommath/pre_gen/mpi.c
new file mode 100644
index 0000000..f651138
--- /dev/null
+++ b/libtommath/pre_gen/mpi.c
@@ -0,0 +1,9514 @@
+/* Start: bn_error.c */
+#include <tommath.h>
+#ifdef BN_ERROR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+static const struct {
+ int code;
+ char *msg;
+} msgs[] = {
+ { MP_OKAY, "Successful" },
+ { MP_MEM, "Out of heap" },
+ { MP_VAL, "Value out of range" }
+};
+
+/* return a char * string for a given code */
+char *mp_error_to_string(int code)
+{
+ int x;
+
+ /* scan the lookup table for the given message */
+ for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
+ if (msgs[x].code == code) {
+ return msgs[x].msg;
+ }
+ }
+
+ /* generic reply for invalid code */
+ return "Invalid error code";
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_error.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_error.c */
+
+/* Start: bn_fast_mp_invmod.c */
+#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes the modular inverse via binary extended euclidean algorithm,
+ * that is c = 1/a mod b
+ *
+ * Based on slow invmod except this is optimized for the case where b is
+ * odd as per HAC Note 14.64 on pp. 610
+ */
+int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, B, D;
+ int res, neg;
+
+ /* 2. [modified] b must be odd */
+ if (mp_iseven (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init all our temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x == modulus, y == value to invert */
+ if ((res = mp_copy (b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* we need y = |a| */
+ if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 4.2 if B is odd then */
+ if (mp_isodd (&B) == 1) {
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* B = B/2 */
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 5.2 if D is odd then */
+ if (mp_isodd (&D) == 1) {
+ /* D = (D-x)/2 */
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* D = D/2 */
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ } else {
+ /* v - v - u, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0) {
+ goto top;
+ }
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* b is now the inverse */
+ neg = a->sign;
+ while (D.sign == MP_NEG) {
+ if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ mp_exch (&D, c);
+ c->sign = neg;
+ res = MP_OKAY;
+
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_fast_mp_invmod.c */
+
+/* Start: bn_fast_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction
+ *
+ * This is an optimized implementation of montgomery_reduce
+ * which uses the comba method to quickly calculate the columns of the
+ * reduction.
+ *
+ * Based on Algorithm 14.32 on pp.601 of HAC.
+*/
+int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+ int ix, res, olduse;
+ mp_word W[MP_WARRAY];
+
+ /* get old used count */
+ olduse = x->used;
+
+ /* grow a as required */
+ if (x->alloc < n->used + 1) {
+ if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* first we have to get the digits of the input into
+ * an array of double precision words W[...]
+ */
+ {
+ register mp_word *_W;
+ register mp_digit *tmpx;
+
+ /* alias for the W[] array */
+ _W = W;
+
+ /* alias for the digits of x*/
+ tmpx = x->dp;
+
+ /* copy the digits of a into W[0..a->used-1] */
+ for (ix = 0; ix < x->used; ix++) {
+ *_W++ = *tmpx++;
+ }
+
+ /* zero the high words of W[a->used..m->used*2] */
+ for (; ix < n->used * 2 + 1; ix++) {
+ *_W++ = 0;
+ }
+ }
+
+ /* now we proceed to zero successive digits
+ * from the least significant upwards
+ */
+ for (ix = 0; ix < n->used; ix++) {
+ /* mu = ai * m' mod b
+ *
+ * We avoid a double precision multiplication (which isn't required)
+ * by casting the value down to a mp_digit. Note this requires
+ * that W[ix-1] have the carry cleared (see after the inner loop)
+ */
+ register mp_digit mu;
+ mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
+
+ /* a = a + mu * m * b**i
+ *
+ * This is computed in place and on the fly. The multiplication
+ * by b**i is handled by offseting which columns the results
+ * are added to.
+ *
+ * Note the comba method normally doesn't handle carries in the
+ * inner loop In this case we fix the carry from the previous
+ * column since the Montgomery reduction requires digits of the
+ * result (so far) [see above] to work. This is
+ * handled by fixing up one carry after the inner loop. The
+ * carry fixups are done in order so after these loops the
+ * first m->used words of W[] have the carries fixed
+ */
+ {
+ register int iy;
+ register mp_digit *tmpn;
+ register mp_word *_W;
+
+ /* alias for the digits of the modulus */
+ tmpn = n->dp;
+
+ /* Alias for the columns set by an offset of ix */
+ _W = W + ix;
+
+ /* inner loop */
+ for (iy = 0; iy < n->used; iy++) {
+ *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
+ }
+ }
+
+ /* now fix carry for next digit, W[ix+1] */
+ W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* now we have to propagate the carries and
+ * shift the words downward [all those least
+ * significant digits we zeroed].
+ */
+ {
+ register mp_digit *tmpx;
+ register mp_word *_W, *_W1;
+
+ /* nox fix rest of carries */
+
+ /* alias for current word */
+ _W1 = W + ix;
+
+ /* alias for next word, where the carry goes */
+ _W = W + ++ix;
+
+ for (; ix <= n->used * 2 + 1; ix++) {
+ *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
+ }
+
+ /* copy out, A = A/b**n
+ *
+ * The result is A/b**n but instead of converting from an
+ * array of mp_word to mp_digit than calling mp_rshd
+ * we just copy them in the right order
+ */
+
+ /* alias for destination word */
+ tmpx = x->dp;
+
+ /* alias for shifted double precision result */
+ _W = W + n->used;
+
+ for (ix = 0; ix < n->used + 1; ix++) {
+ *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
+ }
+
+ /* zero oldused digits, if the input a was larger than
+ * m->used+1 we'll have to clear the digits
+ */
+ for (; ix < olduse; ix++) {
+ *tmpx++ = 0;
+ }
+ }
+
+ /* set the max used and clamp */
+ x->used = n->used + 1;
+ mp_clamp (x);
+
+ /* if A >= m then A = A - m */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ return s_mp_sub (x, n, x);
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_fast_mp_montgomery_reduce.c */
+
+/* Start: bn_fast_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Fast (comba) multiplier
+ *
+ * This is the fast column-array [comba] multiplier. It is
+ * designed to compute the columns of the product first
+ * then handle the carries afterwards. This has the effect
+ * of making the nested loops that compute the columns very
+ * simple and schedulable on super-scalar processors.
+ *
+ * This has been modified to produce a variable number of
+ * digits of output so if say only a half-product is required
+ * you don't have to compute the upper half (a feature
+ * required for fast Barrett reduction).
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ *
+ */
+int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
+
+ /* grow the destination as required */
+ if (c->alloc < digs) {
+ if ((res = mp_grow (c, digs)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
+
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
+
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+
+ }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = c->used;
+ c->used = pa;
+
+ {
+ register mp_digit *tmpc;
+ tmpc = c->dp;
+ for (ix = 0; ix < pa+1; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_digs.c,v $ */
+/* $Revision: 1.7 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_fast_s_mp_mul_digs.c */
+
+/* Start: bn_fast_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
+ * to see how it works.
+ *
+ * This is used in the Barrett reduction since for one of the multiplications
+ * only the higher digits were needed. This essentially halves the work.
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ */
+int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
+
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
+
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = c->used;
+ c->used = pa;
+
+ {
+ register mp_digit *tmpc;
+
+ tmpc = c->dp + digs;
+ for (ix = digs; ix < pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/11/14 03:46:25 $ */
+
+/* End: bn_fast_s_mp_mul_high_digs.c */
+
+/* Start: bn_fast_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* the jist of squaring...
+ * you do like mult except the offset of the tmpx [one that
+ * starts closer to zero] can't equal the offset of tmpy.
+ * So basically you set up iy like before then you min it with
+ * (ty-tx) so that it never happens. You double all those
+ * you add in the inner loop
+
+After that loop you do the squares and add them in.
+*/
+
+int fast_s_mp_sqr (mp_int * a, mp_int * b)
+{
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
+
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix < pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
+
+ /* clear counter */
+ _W = 0;
+
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
+
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
+
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+ }
+
+ /* store it */
+ W[ix] = (mp_digit)(_W & MP_MASK);
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
+ }
+
+ /* setup dest */
+ olduse = b->used;
+ b->used = a->used+a->used;
+
+ {
+ mp_digit *tmpb;
+ tmpb = b->dp;
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
+ }
+
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpb++ = 0;
+ }
+ }
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_fast_s_mp_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_fast_s_mp_sqr.c */
+
+/* Start: bn_mp_2expt.c */
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes a = 2**b
+ *
+ * Simple algorithm which zeroes the int, grows it then just sets one bit
+ * as required.
+ */
+int
+mp_2expt (mp_int * a, int b)
+{
+ int res;
+
+ /* zero a as per default */
+ mp_zero (a);
+
+ /* grow a to accomodate the single bit */
+ if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* set the used count of where the bit will go */
+ a->used = b / DIGIT_BIT + 1;
+
+ /* put the single bit in its place */
+ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_2expt.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_2expt.c */
+
+/* Start: bn_mp_abs.c */
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = |a|
+ *
+ * Simple function copies the input and fixes the sign to positive
+ */
+int
+mp_abs (mp_int * a, mp_int * b)
+{
+ int res;
+
+ /* copy a to b */
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* force the sign of b to positive */
+ b->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_abs.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_abs.c */
+
+/* Start: bn_mp_add.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* high level addition (handles signs) */
+int mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ /* get sign of both inputs */
+ sa = a->sign;
+ sb = b->sign;
+
+ /* handle two cases, not four */
+ if (sa == sb) {
+ /* both positive or both negative */
+ /* add their magnitudes, copy the sign */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* one positive, the other negative */
+ /* subtract the one with the greater magnitude from */
+ /* the one of the lesser magnitude. The result gets */
+ /* the sign of the one with the greater magnitude. */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ c->sign = sb;
+ res = s_mp_sub (b, a, c);
+ } else {
+ c->sign = sa;
+ res = s_mp_sub (a, b, c);
+ }
+ }
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_add.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_add.c */
+
+/* Start: bn_mp_add_d.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* single digit addition */
+int
+mp_add_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ int res, ix, oldused;
+ mp_digit *tmpa, *tmpc, mu;
+
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* if a is negative and |a| >= b, call c = |a| - b */
+ if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
+ /* temporarily fix sign of a */
+ a->sign = MP_ZPOS;
+
+ /* c = |a| - b */
+ res = mp_sub_d(a, b, c);
+
+ /* fix sign */
+ a->sign = c->sign = MP_NEG;
+
+ /* clamp */
+ mp_clamp(c);
+
+ return res;
+ }
+
+ /* old number of used digits in c */
+ oldused = c->used;
+
+ /* sign always positive */
+ c->sign = MP_ZPOS;
+
+ /* source alias */
+ tmpa = a->dp;
+
+ /* destination alias */
+ tmpc = c->dp;
+
+ /* if a is positive */
+ if (a->sign == MP_ZPOS) {
+ /* add digit, after this we're propagating
+ * the carry.
+ */
+ *tmpc = *tmpa++ + b;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+
+ /* now handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ + mu;
+ mu = *tmpc >> DIGIT_BIT;
+ *tmpc++ &= MP_MASK;
+ }
+ /* set final carry */
+ ix++;
+ *tmpc++ = mu;
+
+ /* setup size */
+ c->used = a->used + 1;
+ } else {
+ /* a was negative and |a| < b */
+ c->used = 1;
+
+ /* the result is a single digit */
+ if (a->used == 1) {
+ *tmpc++ = b - a->dp[0];
+ } else {
+ *tmpc++ = b;
+ }
+
+ /* setup count so the clearing of oldused
+ * can fall through correctly
+ */
+ ix = 1;
+ }
+
+ /* now zero to oldused */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_add_d.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_add_d.c */
+
+/* Start: bn_mp_addmod.c */
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* d = a + b (mod c) */
+int
+mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_add (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_addmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_addmod.c */
+
+/* Start: bn_mp_and.c */
+#include <tommath.h>
+#ifdef BN_MP_AND_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* AND two ints together */
+int
+mp_and (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] &= x->dp[ix];
+ }
+
+ /* zero digits above the last from the smallest mp_int */
+ for (; ix < t.used; ix++) {
+ t.dp[ix] = 0;
+ }
+
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_and.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_and.c */
+
+/* Start: bn_mp_clamp.c */
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* trim unused digits
+ *
+ * This is used to ensure that leading zero digits are
+ * trimed and the leading "used" digit will be non-zero
+ * Typically very fast. Also fixes the sign if there
+ * are no more leading digits
+ */
+void
+mp_clamp (mp_int * a)
+{
+ /* decrease used while the most significant digit is
+ * zero.
+ */
+ while (a->used > 0 && a->dp[a->used - 1] == 0) {
+ --(a->used);
+ }
+
+ /* reset the sign flag if used == 0 */
+ if (a->used == 0) {
+ a->sign = MP_ZPOS;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_clamp.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_clamp.c */
+
+/* Start: bn_mp_clear.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* clear one (frees) */
+void
+mp_clear (mp_int * a)
+{
+ int i;
+
+ /* only do anything if a hasn't been freed previously */
+ if (a->dp != NULL) {
+ /* first zero the digits */
+ for (i = 0; i < a->used; i++) {
+ a->dp[i] = 0;
+ }
+
+ /* free ram */
+ XFREE(a->dp);
+
+ /* reset members to make debugging easier */
+ a->dp = NULL;
+ a->alloc = a->used = 0;
+ a->sign = MP_ZPOS;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_clear.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_clear.c */
+
+/* Start: bn_mp_clear_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+#include <stdarg.h>
+
+void mp_clear_multi(mp_int *mp, ...)
+{
+ mp_int* next_mp = mp;
+ va_list args;
+ va_start(args, mp);
+ while (next_mp != NULL) {
+ mp_clear(next_mp);
+ next_mp = va_arg(args, mp_int*);
+ }
+ va_end(args);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_clear_multi.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_clear_multi.c */
+
+/* Start: bn_mp_cmp.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* compare two ints (signed)*/
+int
+mp_cmp (mp_int * a, mp_int * b)
+{
+ /* compare based on sign */
+ if (a->sign != b->sign) {
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ } else {
+ return MP_GT;
+ }
+ }
+
+ /* compare digits */
+ if (a->sign == MP_NEG) {
+ /* if negative compare opposite direction */
+ return mp_cmp_mag(b, a);
+ } else {
+ return mp_cmp_mag(a, b);
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cmp.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_cmp.c */
+
+/* Start: bn_mp_cmp_d.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* compare a digit */
+int mp_cmp_d(mp_int * a, mp_digit b)
+{
+ /* compare based on sign */
+ if (a->sign == MP_NEG) {
+ return MP_LT;
+ }
+
+ /* compare based on magnitude */
+ if (a->used > 1) {
+ return MP_GT;
+ }
+
+ /* compare the only digit of a to b */
+ if (a->dp[0] > b) {
+ return MP_GT;
+ } else if (a->dp[0] < b) {
+ return MP_LT;
+ } else {
+ return MP_EQ;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_cmp_d.c */
+
+/* Start: bn_mp_cmp_mag.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* compare maginitude of two ints (unsigned) */
+int mp_cmp_mag (mp_int * a, mp_int * b)
+{
+ int n;
+ mp_digit *tmpa, *tmpb;
+
+ /* compare based on # of non-zero digits */
+ if (a->used > b->used) {
+ return MP_GT;
+ }
+
+ if (a->used < b->used) {
+ return MP_LT;
+ }
+
+ /* alias for a */
+ tmpa = a->dp + (a->used - 1);
+
+ /* alias for b */
+ tmpb = b->dp + (a->used - 1);
+
+ /* compare based on digits */
+ for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
+ if (*tmpa > *tmpb) {
+ return MP_GT;
+ }
+
+ if (*tmpa < *tmpb) {
+ return MP_LT;
+ }
+ }
+ return MP_EQ;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cmp_mag.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_cmp_mag.c */
+
+/* Start: bn_mp_cnt_lsb.c */
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+static const int lnz[16] = {
+ 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
+};
+
+/* Counts the number of lsbs which are zero before the first zero bit */
+int mp_cnt_lsb(mp_int *a)
+{
+ int x;
+ mp_digit q, qq;
+
+ /* easy out */
+ if (mp_iszero(a) == 1) {
+ return 0;
+ }
+
+ /* scan lower digits until non-zero */
+ for (x = 0; x < a->used && a->dp[x] == 0; x++);
+ q = a->dp[x];
+ x *= DIGIT_BIT;
+
+ /* now scan this digit until a 1 is found */
+ if ((q & 1) == 0) {
+ do {
+ qq = q & 15;
+ x += lnz[qq];
+ q >>= 4;
+ } while (qq == 0);
+ }
+ return x;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_cnt_lsb.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_cnt_lsb.c */
+
+/* Start: bn_mp_copy.c */
+#include <tommath.h>
+#ifdef BN_MP_COPY_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* copy, b = a */
+int
+mp_copy (mp_int * a, mp_int * b)
+{
+ int res, n;
+
+ /* if dst == src do nothing */
+ if (a == b) {
+ return MP_OKAY;
+ }
+
+ /* grow dest */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero b and copy the parameters over */
+ {
+ register mp_digit *tmpa, *tmpb;
+
+ /* pointer aliases */
+
+ /* source */
+ tmpa = a->dp;
+
+ /* destination */
+ tmpb = b->dp;
+
+ /* copy all the digits */
+ for (n = 0; n < a->used; n++) {
+ *tmpb++ = *tmpa++;
+ }
+
+ /* clear high digits */
+ for (; n < b->used; n++) {
+ *tmpb++ = 0;
+ }
+ }
+
+ /* copy used count and sign */
+ b->used = a->used;
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_copy.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_copy.c */
+
+/* Start: bn_mp_count_bits.c */
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* returns the number of bits in an int */
+int
+mp_count_bits (mp_int * a)
+{
+ int r;
+ mp_digit q;
+
+ /* shortcut */
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits and add that */
+ r = (a->used - 1) * DIGIT_BIT;
+
+ /* take the last digit and count the bits in it */
+ q = a->dp[a->used - 1];
+ while (q > ((mp_digit) 0)) {
+ ++r;
+ q >>= ((mp_digit) 1);
+ }
+ return r;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_count_bits.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_count_bits.c */
+
+/* Start: bn_mp_div.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
+ ((res = mp_abs(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
+ }
+LBL_ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
+
+/* integer signed division.
+ * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+ * HAC pp.598 Algorithm 14.20
+ *
+ * Note that the description in HAC is horribly
+ * incomplete. For example, it doesn't consider
+ * the case where digits are removed from 'x' in
+ * the inner loop. It also doesn't consider the
+ * case that y has fewer than three digits, etc..
+ *
+ * The overall algorithm is as described as
+ * 14.20 from HAC but fixed to treat these cases.
+*/
+int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int q, x, y, t1, t2;
+ int res, n, t, i, norm, neg;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
+ return res;
+ }
+ q.used = a->used + 2;
+
+ if ((res = mp_init (&t1)) != MP_OKAY) {
+ goto LBL_Q;
+ }
+
+ if ((res = mp_init (&t2)) != MP_OKAY) {
+ goto LBL_T1;
+ }
+
+ if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
+ goto LBL_T2;
+ }
+
+ if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
+ goto LBL_X;
+ }
+
+ /* fix the sign */
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+ x.sign = y.sign = MP_ZPOS;
+
+ /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
+ norm = mp_count_bits(&y) % DIGIT_BIT;
+ if (norm < (int)(DIGIT_BIT-1)) {
+ norm = (DIGIT_BIT-1) - norm;
+ if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ } else {
+ norm = 0;
+ }
+
+ /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
+ n = x.used - 1;
+ t = y.used - 1;
+
+ /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
+ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
+ goto LBL_Y;
+ }
+
+ while (mp_cmp (&x, &y) != MP_LT) {
+ ++(q.dp[n - t]);
+ if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ }
+
+ /* reset y by shifting it back down */
+ mp_rshd (&y, n - t);
+
+ /* step 3. for i from n down to (t + 1) */
+ for (i = n; i >= (t + 1); i--) {
+ if (i > x.used) {
+ continue;
+ }
+
+ /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
+ * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
+ if (x.dp[i] == y.dp[t]) {
+ q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
+ } else {
+ mp_word tmp;
+ tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
+ tmp |= ((mp_word) x.dp[i - 1]);
+ tmp /= ((mp_word) y.dp[t]);
+ if (tmp > (mp_word) MP_MASK)
+ tmp = MP_MASK;
+ q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
+ }
+
+ /* while (q{i-t-1} * (yt * b + y{t-1})) >
+ xi * b**2 + xi-1 * b + xi-2
+
+ do q{i-t-1} -= 1;
+ */
+ q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
+ do {
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
+
+ /* find left hand */
+ mp_zero (&t1);
+ t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
+ t1.dp[1] = y.dp[t];
+ t1.used = 2;
+ if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* find right hand */
+ t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
+ t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
+ t2.dp[2] = x.dp[i];
+ t2.used = 3;
+ } while (mp_cmp_mag(&t1, &t2) == MP_GT);
+
+ /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
+ if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
+ if (x.sign == MP_NEG) {
+ if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+ if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
+ }
+ }
+
+ /* now q is the quotient and x is the remainder
+ * [which we have to normalize]
+ */
+
+ /* get sign before writing to c */
+ x.sign = x.used == 0 ? MP_ZPOS : a->sign;
+
+ if (c != NULL) {
+ mp_clamp (&q);
+ mp_exch (&q, c);
+ c->sign = neg;
+ }
+
+ if (d != NULL) {
+ mp_div_2d (&x, norm, &x, NULL);
+ mp_exch (&x, d);
+ }
+
+ res = MP_OKAY;
+
+LBL_Y:mp_clear (&y);
+LBL_X:mp_clear (&x);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+LBL_Q:mp_clear (&q);
+ return res;
+}
+
+#endif
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_div.c */
+
+/* Start: bn_mp_div_2.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = a/2 */
+int mp_div_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* copy */
+ if (b->alloc < a->used) {
+ if ((res = mp_grow (b, a->used)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* source alias */
+ tmpa = a->dp + b->used - 1;
+
+ /* dest alias */
+ tmpb = b->dp + b->used - 1;
+
+ /* carry */
+ r = 0;
+ for (x = b->used - 1; x >= 0; x--) {
+ /* get the carry for the next iteration */
+ rr = *tmpa & 1;
+
+ /* shift the current digit, add in carry and store */
+ *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
+
+ /* forward carry to next iteration */
+ r = rr;
+ }
+
+ /* zero excess digits */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ mp_clamp (b);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_2.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_div_2.c */
+
+/* Start: bn_mp_div_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
+int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
+{
+ mp_digit D, r, rr;
+ int x, res;
+ mp_int t;
+
+
+ /* if the shift count is <= 0 then we do no work */
+ if (b <= 0) {
+ res = mp_copy (a, c);
+ if (d != NULL) {
+ mp_zero (d);
+ }
+ return res;
+ }
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ /* get the remainder */
+ if (d != NULL) {
+ if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ mp_rshd (c, b / DIGIT_BIT);
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ D = (mp_digit) (b % DIGIT_BIT);
+ if (D != 0) {
+ register mp_digit *tmpc, mask, shift;
+
+ /* mask */
+ mask = (((mp_digit)1) << D) - 1;
+
+ /* shift for lsb */
+ shift = DIGIT_BIT - D;
+
+ /* alias */
+ tmpc = c->dp + (c->used - 1);
+
+ /* carry */
+ r = 0;
+ for (x = c->used - 1; x >= 0; x--) {
+ /* get the lower bits of this word in a temp */
+ rr = *tmpc & mask;
+
+ /* shift the current word and mix in the carry bits from the previous word */
+ *tmpc = (*tmpc >> D) | (r << shift);
+ --tmpc;
+
+ /* set the carry to the carry bits of the current word found above */
+ r = rr;
+ }
+ }
+ mp_clamp (c);
+ if (d != NULL) {
+ mp_exch (&t, d);
+ }
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_2d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_div_2d.c */
+
+/* Start: bn_mp_div_3.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* divide by three (based on routine from MPI and the GMP manual) */
+int
+mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
+{
+ mp_int q;
+ mp_word w, t;
+ mp_digit b;
+ int res, ix;
+
+ /* b = 2**DIGIT_BIT / 3 */
+ b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
+
+ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
+ return res;
+ }
+
+ q.used = a->used;
+ q.sign = a->sign;
+ w = 0;
+ for (ix = a->used - 1; ix >= 0; ix--) {
+ w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+
+ if (w >= 3) {
+ /* multiply w by [1/3] */
+ t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
+
+ /* now subtract 3 * [w/3] from w, to get the remainder */
+ w -= t+t+t;
+
+ /* fixup the remainder as required since
+ * the optimization is not exact.
+ */
+ while (w >= 3) {
+ t += 1;
+ w -= 3;
+ }
+ } else {
+ t = 0;
+ }
+ q.dp[ix] = (mp_digit)t;
+ }
+
+ /* [optional] store the remainder */
+ if (d != NULL) {
+ *d = (mp_digit)w;
+ }
+
+ /* [optional] store the quotient */
+ if (c != NULL) {
+ mp_clamp(&q);
+ mp_exch(&q, c);
+ }
+ mp_clear(&q);
+
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_3.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_div_3.c */
+
+/* Start: bn_mp_div_d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+static int s_is_power_of_two(mp_digit b, int *p)
+{
+ int x;
+
+ for (x = 1; x < DIGIT_BIT; x++) {
+ if (b == (((mp_digit)1)<<x)) {
+ *p = x;
+ return 1;
+ }
+ }
+ return 0;
+}
+
+/* single digit division (based on routine from MPI) */
+int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
+{
+ mp_int q;
+ mp_word w;
+ mp_digit t;
+ int res, ix;
+
+ /* cannot divide by zero */
+ if (b == 0) {
+ return MP_VAL;
+ }
+
+ /* quick outs */
+ if (b == 1 || mp_iszero(a) == 1) {
+ if (d != NULL) {
+ *d = 0;
+ }
+ if (c != NULL) {
+ return mp_copy(a, c);
+ }
+ return MP_OKAY;
+ }
+
+ /* power of two ? */
+ if (s_is_power_of_two(b, &ix) == 1) {
+ if (d != NULL) {
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
+ }
+ if (c != NULL) {
+ return mp_div_2d(a, ix, c, NULL);
+ }
+ return MP_OKAY;
+ }
+
+#ifdef BN_MP_DIV_3_C
+ /* three? */
+ if (b == 3) {
+ return mp_div_3(a, c, d);
+ }
+#endif
+
+ /* no easy answer [c'est la vie]. Just division */
+ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
+ return res;
+ }
+
+ q.used = a->used;
+ q.sign = a->sign;
+ w = 0;
+ for (ix = a->used - 1; ix >= 0; ix--) {
+ w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+
+ if (w >= b) {
+ t = (mp_digit)(w / b);
+ w -= ((mp_word)t) * ((mp_word)b);
+ } else {
+ t = 0;
+ }
+ q.dp[ix] = (mp_digit)t;
+ }
+
+ if (d != NULL) {
+ *d = (mp_digit)w;
+ }
+
+ if (c != NULL) {
+ mp_clamp(&q);
+ mp_exch(&q, c);
+ }
+ mp_clear(&q);
+
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_div_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_div_d.c */
+
+/* Start: bn_mp_dr_is_modulus.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if a number is a valid DR modulus */
+int mp_dr_is_modulus(mp_int *a)
+{
+ int ix;
+
+ /* must be at least two digits */
+ if (a->used < 2) {
+ return 0;
+ }
+
+ /* must be of the form b**k - a [a <= b] so all
+ * but the first digit must be equal to -1 (mod b).
+ */
+ for (ix = 1; ix < a->used; ix++) {
+ if (a->dp[ix] != MP_MASK) {
+ return 0;
+ }
+ }
+ return 1;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_dr_is_modulus.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_dr_is_modulus.c */
+
+/* Start: bn_mp_dr_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
+ *
+ * Based on algorithm from the paper
+ *
+ * "Generating Efficient Primes for Discrete Log Cryptosystems"
+ * Chae Hoon Lim, Pil Joong Lee,
+ * POSTECH Information Research Laboratories
+ *
+ * The modulus must be of a special format [see manual]
+ *
+ * Has been modified to use algorithm 7.10 from the LTM book instead
+ *
+ * Input x must be in the range 0 <= x <= (n-1)**2
+ */
+int
+mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
+{
+ int err, i, m;
+ mp_word r;
+ mp_digit mu, *tmpx1, *tmpx2;
+
+ /* m = digits in modulus */
+ m = n->used;
+
+ /* ensure that "x" has at least 2m digits */
+ if (x->alloc < m + m) {
+ if ((err = mp_grow (x, m + m)) != MP_OKAY) {
+ return err;
+ }
+ }
+
+/* top of loop, this is where the code resumes if
+ * another reduction pass is required.
+ */
+top:
+ /* aliases for digits */
+ /* alias for lower half of x */
+ tmpx1 = x->dp;
+
+ /* alias for upper half of x, or x/B**m */
+ tmpx2 = x->dp + m;
+
+ /* set carry to zero */
+ mu = 0;
+
+ /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
+ for (i = 0; i < m; i++) {
+ r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
+ *tmpx1++ = (mp_digit)(r & MP_MASK);
+ mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
+ }
+
+ /* set final carry */
+ *tmpx1++ = mu;
+
+ /* zero words above m */
+ for (i = m + 1; i < x->used; i++) {
+ *tmpx1++ = 0;
+ }
+
+ /* clamp, sub and return */
+ mp_clamp (x);
+
+ /* if x >= n then subtract and reduce again
+ * Each successive "recursion" makes the input smaller and smaller.
+ */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ s_mp_sub(x, n, x);
+ goto top;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_dr_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_dr_reduce.c */
+
+/* Start: bn_mp_dr_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines the setup value */
+void mp_dr_setup(mp_int *a, mp_digit *d)
+{
+ /* the casts are required if DIGIT_BIT is one less than
+ * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
+ */
+ *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
+ ((mp_word)a->dp[0]));
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_dr_setup.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_dr_setup.c */
+
+/* Start: bn_mp_exch.c */
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* swap the elements of two integers, for cases where you can't simply swap the
+ * mp_int pointers around
+ */
+void
+mp_exch (mp_int * a, mp_int * b)
+{
+ mp_int t;
+
+ t = *a;
+ *a = *b;
+ *b = t;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exch.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_exch.c */
+
+/* Start: bn_mp_expt_d.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* calculate c = a**b using a square-multiply algorithm */
+int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ int res, x;
+ mp_int g;
+
+ if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* set initial result */
+ mp_set (c, 1);
+
+ for (x = 0; x < (int) DIGIT_BIT; x++) {
+ /* square */
+ if ((res = mp_sqr (c, c)) != MP_OKAY) {
+ mp_clear (&g);
+ return res;
+ }
+
+ /* if the bit is set multiply */
+ if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
+ if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
+ mp_clear (&g);
+ return res;
+ }
+ }
+
+ /* shift to next bit */
+ b <<= 1;
+ }
+
+ mp_clear (&g);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_expt_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_expt_d.c */
+
+/* Start: bn_mp_exptmod.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+
+/* this is a shell function that calls either the normal or Montgomery
+ * exptmod functions. Originally the call to the montgomery code was
+ * embedded in the normal function but that wasted alot of stack space
+ * for nothing (since 99% of the time the Montgomery code would be called)
+ */
+int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
+{
+ int dr;
+
+ /* modulus P must be positive */
+ if (P->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* if exponent X is negative we have to recurse */
+ if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
+ mp_int tmpG, tmpX;
+ int err;
+
+ /* first compute 1/G mod P */
+ if ((err = mp_init(&tmpG)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+
+ /* now get |X| */
+ if ((err = mp_init(&tmpX)) != MP_OKAY) {
+ mp_clear(&tmpG);
+ return err;
+ }
+ if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+ }
+
+ /* and now compute (1/G)**|X| instead of G**X [X < 0] */
+ err = mp_exptmod(&tmpG, &tmpX, P, Y);
+ mp_clear_multi(&tmpG, &tmpX, NULL);
+ return err;
+#else
+ /* no invmod */
+ return MP_VAL;
+#endif
+ }
+
+/* modified diminished radix reduction */
+#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
+ if (mp_reduce_is_2k_l(P) == MP_YES) {
+ return s_mp_exptmod(G, X, P, Y, 1);
+ }
+#endif
+
+#ifdef BN_MP_DR_IS_MODULUS_C
+ /* is it a DR modulus? */
+ dr = mp_dr_is_modulus(P);
+#else
+ /* default to no */
+ dr = 0;
+#endif
+
+#ifdef BN_MP_REDUCE_IS_2K_C
+ /* if not, is it a unrestricted DR modulus? */
+ if (dr == 0) {
+ dr = mp_reduce_is_2k(P) << 1;
+ }
+#endif
+
+ /* if the modulus is odd or dr != 0 use the montgomery method */
+#ifdef BN_MP_EXPTMOD_FAST_C
+ if (mp_isodd (P) == 1 || dr != 0) {
+ return mp_exptmod_fast (G, X, P, Y, dr);
+ } else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
+ /* otherwise use the generic Barrett reduction technique */
+ return s_mp_exptmod (G, X, P, Y, 0);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
+ }
+#endif
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_exptmod.c */
+
+/* Start: bn_mp_exptmod_fast.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
+ *
+ * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
+ * The value of k changes based on the size of the exponent.
+ *
+ * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
+ */
+
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res;
+ mp_digit buf, mp;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+
+ /* use a pointer to the reduction algorithm. This allows us to use
+ * one of many reduction algorithms without modding the guts of
+ * the code with if statements everywhere.
+ */
+ int (*redux)(mp_int*,mp_int*,mp_digit);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* determine and setup reduction code */
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+ /* now setup montgomery */
+ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+
+ /* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
+ if (((P->used * 2 + 1) < MP_WARRAY) &&
+ P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ redux = fast_mp_montgomery_reduce;
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+ /* use slower baseline Montgomery method */
+ redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+ } else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
+ /* setup DR reduction for moduli of the form B**k - b */
+ mp_dr_setup(P, &mp);
+ redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ } else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
+ /* setup DR reduction for moduli of the form 2**k - b */
+ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
+ goto LBL_M;
+ }
+ redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto LBL_M;
+#endif
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ /* create M table
+ *
+
+ *
+ * The first half of the table is not computed though accept for M[0] and M[1]
+ */
+
+ if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+ /* now we need R mod m */
+ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+#else
+ err = MP_VAL;
+ goto LBL_RES;
+#endif
+
+ /* now set M[1] to G * R mod m */
+ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ } else {
+ mp_set(&res, 1);
+ if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* create upper table */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits so break */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int)DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* get next bit of the window */
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ if (redmode == 0) {
+ /* fixup result if Montgomery reduction is used
+ * recall that any value in a Montgomery system is
+ * actually multiplied by R mod n. So we have
+ * to reduce one more time to cancel out the factor
+ * of R.
+ */
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* swap res with Y */
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+#endif
+
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exptmod_fast.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_exptmod_fast.c */
+
+/* Start: bn_mp_exteuclid.c */
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Extended euclidean algorithm of (a, b) produces
+ a*u1 + b*u2 = u3
+ */
+int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
+{
+ mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
+ int err;
+
+ if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* initialize, (u1,u2,u3) = (1,0,a) */
+ mp_set(&u1, 1);
+ if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* initialize, (v1,v2,v3) = (0,1,b) */
+ mp_set(&v2, 1);
+ if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; }
+
+ /* loop while v3 != 0 */
+ while (mp_iszero(&v3) == MP_NO) {
+ /* q = u3/v3 */
+ if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; }
+
+ /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
+ if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; }
+
+ /* (u1,u2,u3) = (v1,v2,v3) */
+ if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; }
+
+ /* (v1,v2,v3) = (t1,t2,t3) */
+ if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; }
+ if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; }
+ }
+
+ /* make sure U3 >= 0 */
+ if (u3.sign == MP_NEG) {
+ mp_neg(&u1, &u1);
+ mp_neg(&u2, &u2);
+ mp_neg(&u3, &u3);
+ }
+
+ /* copy result out */
+ if (U1 != NULL) { mp_exch(U1, &u1); }
+ if (U2 != NULL) { mp_exch(U2, &u2); }
+ if (U3 != NULL) { mp_exch(U3, &u3); }
+
+ err = MP_OKAY;
+_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_exteuclid.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_exteuclid.c */
+
+/* Start: bn_mp_fread.c */
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* read a bigint from a file stream in ASCII */
+int mp_fread(mp_int *a, int radix, FILE *stream)
+{
+ int err, ch, neg, y;
+
+ /* clear a */
+ mp_zero(a);
+
+ /* if first digit is - then set negative */
+ ch = fgetc(stream);
+ if (ch == '-') {
+ neg = MP_NEG;
+ ch = fgetc(stream);
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ for (;;) {
+ /* find y in the radix map */
+ for (y = 0; y < radix; y++) {
+ if (mp_s_rmap[y] == ch) {
+ break;
+ }
+ }
+ if (y == radix) {
+ break;
+ }
+
+ /* shift up and add */
+ if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
+ return err;
+ }
+
+ ch = fgetc(stream);
+ }
+ if (mp_cmp_d(a, 0) != MP_EQ) {
+ a->sign = neg;
+ }
+
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_fread.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_fread.c */
+
+/* Start: bn_mp_fwrite.c */
+#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+int mp_fwrite(mp_int *a, int radix, FILE *stream)
+{
+ char *buf;
+ int err, len, x;
+
+ if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
+ return err;
+ }
+
+ buf = OPT_CAST(char) XMALLOC (len);
+ if (buf == NULL) {
+ return MP_MEM;
+ }
+
+ if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
+ XFREE (buf);
+ return err;
+ }
+
+ for (x = 0; x < len; x++) {
+ if (fputc(buf[x], stream) == EOF) {
+ XFREE (buf);
+ return MP_VAL;
+ }
+ }
+
+ XFREE (buf);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_fwrite.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_fwrite.c */
+
+/* Start: bn_mp_gcd.c */
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Greatest Common Divisor using the binary method */
+int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int u, v;
+ int k, u_lsb, v_lsb, res;
+
+ /* either zero than gcd is the largest */
+ if (mp_iszero (a) == MP_YES) {
+ return mp_abs (b, c);
+ }
+ if (mp_iszero (b) == MP_YES) {
+ return mp_abs (a, c);
+ }
+
+ /* get copies of a and b we can modify */
+ if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
+ goto LBL_U;
+ }
+
+ /* must be positive for the remainder of the algorithm */
+ u.sign = v.sign = MP_ZPOS;
+
+ /* B1. Find the common power of two for u and v */
+ u_lsb = mp_cnt_lsb(&u);
+ v_lsb = mp_cnt_lsb(&v);
+ k = MIN(u_lsb, v_lsb);
+
+ if (k > 0) {
+ /* divide the power of two out */
+ if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ /* divide any remaining factors of two out */
+ if (u_lsb != k) {
+ if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ if (v_lsb != k) {
+ if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ while (mp_iszero(&v) == 0) {
+ /* make sure v is the largest */
+ if (mp_cmp_mag(&u, &v) == MP_GT) {
+ /* swap u and v to make sure v is >= u */
+ mp_exch(&u, &v);
+ }
+
+ /* subtract smallest from largest */
+ if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
+ goto LBL_V;
+ }
+
+ /* Divide out all factors of two */
+ if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ }
+
+ /* multiply by 2**k which we divided out at the beginning */
+ if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
+ goto LBL_V;
+ }
+ c->sign = MP_ZPOS;
+ res = MP_OKAY;
+LBL_V:mp_clear (&u);
+LBL_U:mp_clear (&v);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_gcd.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_gcd.c */
+
+/* Start: bn_mp_get_int.c */
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* get the lower 32-bits of an mp_int */
+unsigned long mp_get_int(mp_int * a)
+{
+ int i;
+ unsigned long res;
+
+ if (a->used == 0) {
+ return 0;
+ }
+
+ /* get number of digits of the lsb we have to read */
+ i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
+
+ /* get most significant digit of result */
+ res = DIGIT(a,i);
+
+ while (--i >= 0) {
+ res = (res << DIGIT_BIT) | DIGIT(a,i);
+ }
+
+ /* force result to 32-bits always so it is consistent on non 32-bit platforms */
+ return res & 0xFFFFFFFFUL;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_get_int.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_get_int.c */
+
+/* Start: bn_mp_grow.c */
+#include <tommath.h>
+#ifdef BN_MP_GROW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* grow as required */
+int mp_grow (mp_int * a, int size)
+{
+ int i;
+ mp_digit *tmp;
+
+ /* if the alloc size is smaller alloc more ram */
+ if (a->alloc < size) {
+ /* ensure there are always at least MP_PREC digits extra on top */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* reallocate the array a->dp
+ *
+ * We store the return in a temporary variable
+ * in case the operation failed we don't want
+ * to overwrite the dp member of a.
+ */
+ tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
+ if (tmp == NULL) {
+ /* reallocation failed but "a" is still valid [can be freed] */
+ return MP_MEM;
+ }
+
+ /* reallocation succeeded so set a->dp */
+ a->dp = tmp;
+
+ /* zero excess digits */
+ i = a->alloc;
+ a->alloc = size;
+ for (; i < a->alloc; i++) {
+ a->dp[i] = 0;
+ }
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_grow.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_grow.c */
+
+/* Start: bn_mp_init.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* init a new mp_int */
+int mp_init (mp_int * a)
+{
+ int i;
+
+ /* allocate memory required and clear it */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the digits to zero */
+ for (i = 0; i < MP_PREC; i++) {
+ a->dp[i] = 0;
+ }
+
+ /* set the used to zero, allocated digits to the default precision
+ * and sign to positive */
+ a->used = 0;
+ a->alloc = MP_PREC;
+ a->sign = MP_ZPOS;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_init.c */
+
+/* Start: bn_mp_init_copy.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* creates "a" then copies b into it */
+int mp_init_copy (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_init (a)) != MP_OKAY) {
+ return res;
+ }
+ return mp_copy (b, a);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_copy.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_init_copy.c */
+
+/* Start: bn_mp_init_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+#include <stdarg.h>
+
+int mp_init_multi(mp_int *mp, ...)
+{
+ mp_err res = MP_OKAY; /* Assume ok until proven otherwise */
+ int n = 0; /* Number of ok inits */
+ mp_int* cur_arg = mp;
+ va_list args;
+
+ va_start(args, mp); /* init args to next argument from caller */
+ while (cur_arg != NULL) {
+ if (mp_init(cur_arg) != MP_OKAY) {
+ /* Oops - error! Back-track and mp_clear what we already
+ succeeded in init-ing, then return error.
+ */
+ va_list clean_args;
+
+ /* end the current list */
+ va_end(args);
+
+ /* now start cleaning up */
+ cur_arg = mp;
+ va_start(clean_args, mp);
+ while (n--) {
+ mp_clear(cur_arg);
+ cur_arg = va_arg(clean_args, mp_int*);
+ }
+ va_end(clean_args);
+ res = MP_MEM;
+ break;
+ }
+ n++;
+ cur_arg = va_arg(args, mp_int*);
+ }
+ va_end(args);
+ return res; /* Assumed ok, if error flagged above. */
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_multi.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_init_multi.c */
+
+/* Start: bn_mp_init_set.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* initialize and set a digit */
+int mp_init_set (mp_int * a, mp_digit b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ mp_set(a, b);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_set.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_init_set.c */
+
+/* Start: bn_mp_init_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* initialize and set a digit */
+int mp_init_set_int (mp_int * a, unsigned long b)
+{
+ int err;
+ if ((err = mp_init(a)) != MP_OKAY) {
+ return err;
+ }
+ return mp_set_int(a, b);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_set_int.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_init_set_int.c */
+
+/* Start: bn_mp_init_size.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* init an mp_init for a given size */
+int mp_init_size (mp_int * a, int size)
+{
+ int x;
+
+ /* pad size so there are always extra digits */
+ size += (MP_PREC * 2) - (size % MP_PREC);
+
+ /* alloc mem */
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
+ if (a->dp == NULL) {
+ return MP_MEM;
+ }
+
+ /* set the members */
+ a->used = 0;
+ a->alloc = size;
+ a->sign = MP_ZPOS;
+
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_init_size.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_init_size.c */
+
+/* Start: bn_mp_invmod.c */
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+#ifdef BN_FAST_MP_INVMOD_C
+ /* if the modulus is odd we can use a faster routine instead */
+ if (mp_isodd (b) == 1) {
+ return fast_mp_invmod (a, b, c);
+ }
+#endif
+
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
+
+ return MP_VAL;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_invmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_invmod.c */
+
+/* Start: bn_mp_invmod_slow.c */
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v,
+ &A, &B, &C, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x = a, y = b */
+ if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (b, &y)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* 2. [modified] if x,y are both even then return an error! */
+ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ mp_set (&A, 1);
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 4.2 if A or B is odd then */
+ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
+ /* A = (A+y)/2, B = (B-x)/2 */
+ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* A = A/2, B = B/2 */
+ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ /* 5.2 if C or D is odd then */
+ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
+ /* C = (C+y)/2, D = (D-x)/2 */
+ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+ /* C = C/2, D = D/2 */
+ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, A = A - C, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ } else {
+ /* v - v - u, C = C - A, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0)
+ goto top;
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto LBL_ERR;
+ }
+
+ /* if its too low */
+ while (mp_cmp_d(&C, 0) == MP_LT) {
+ if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* too big */
+ while (mp_cmp_mag(&C, b) != MP_LT) {
+ if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ }
+
+ /* C is now the inverse */
+ mp_exch (&C, c);
+ res = MP_OKAY;
+LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_invmod_slow.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_invmod_slow.c */
+
+/* Start: bn_mp_is_square.c */
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Check if remainders are possible squares - fast exclude non-squares */
+static const char rem_128[128] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
+};
+
+static const char rem_105[105] = {
+ 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
+ 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
+ 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
+ 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
+ 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
+ 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
+ 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
+};
+
+/* Store non-zero to ret if arg is square, and zero if not */
+int mp_is_square(mp_int *arg,int *ret)
+{
+ int res;
+ mp_digit c;
+ mp_int t;
+ unsigned long r;
+
+ /* Default to Non-square :) */
+ *ret = MP_NO;
+
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* digits used? (TSD) */
+ if (arg->used == 0) {
+ return MP_OKAY;
+ }
+
+ /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
+ if (rem_128[127 & DIGIT(arg,0)] == 1) {
+ return MP_OKAY;
+ }
+
+ /* Next check mod 105 (3*5*7) */
+ if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
+ return res;
+ }
+ if (rem_105[c] == 1) {
+ return MP_OKAY;
+ }
+
+
+ if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ r = mp_get_int(&t);
+ /* Check for other prime modules, note it's not an ERROR but we must
+ * free "t" so the easiest way is to goto ERR. We know that res
+ * is already equal to MP_OKAY from the mp_mod call
+ */
+ if ( (1L<<(r%11)) & 0x5C4L ) goto ERR;
+ if ( (1L<<(r%13)) & 0x9E4L ) goto ERR;
+ if ( (1L<<(r%17)) & 0x5CE8L ) goto ERR;
+ if ( (1L<<(r%19)) & 0x4F50CL ) goto ERR;
+ if ( (1L<<(r%23)) & 0x7ACCA0L ) goto ERR;
+ if ( (1L<<(r%29)) & 0xC2EDD0CL ) goto ERR;
+ if ( (1L<<(r%31)) & 0x6DE2B848L ) goto ERR;
+
+ /* Final check - is sqr(sqrt(arg)) == arg ? */
+ if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
+ERR:mp_clear(&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_is_square.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_is_square.c */
+
+/* Start: bn_mp_jacobi.c */
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes the jacobi c = (a | n) (or Legendre if n is prime)
+ * HAC pp. 73 Algorithm 2.149
+ */
+int mp_jacobi (mp_int * a, mp_int * p, int *c)
+{
+ mp_int a1, p1;
+ int k, s, r, res;
+ mp_digit residue;
+
+ /* if p <= 0 return MP_VAL */
+ if (mp_cmp_d(p, 0) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* step 1. if a == 0, return 0 */
+ if (mp_iszero (a) == 1) {
+ *c = 0;
+ return MP_OKAY;
+ }
+
+ /* step 2. if a == 1, return 1 */
+ if (mp_cmp_d (a, 1) == MP_EQ) {
+ *c = 1;
+ return MP_OKAY;
+ }
+
+ /* default */
+ s = 0;
+
+ /* step 3. write a = a1 * 2**k */
+ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&p1)) != MP_OKAY) {
+ goto LBL_A1;
+ }
+
+ /* divide out larger power of two */
+ k = mp_cnt_lsb(&a1);
+ if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+
+ /* step 4. if e is even set s=1 */
+ if ((k & 1) == 0) {
+ s = 1;
+ } else {
+ /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
+ residue = p->dp[0] & 7;
+
+ if (residue == 1 || residue == 7) {
+ s = 1;
+ } else if (residue == 3 || residue == 5) {
+ s = -1;
+ }
+ }
+
+ /* step 5. if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
+ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
+ s = -s;
+ }
+
+ /* if a1 == 1 we're done */
+ if (mp_cmp_d (&a1, 1) == MP_EQ) {
+ *c = s;
+ } else {
+ /* n1 = n mod a1 */
+ if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
+ goto LBL_P1;
+ }
+ *c = s * r;
+ }
+
+ /* done */
+ res = MP_OKAY;
+LBL_P1:mp_clear (&p1);
+LBL_A1:mp_clear (&a1);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_jacobi.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_jacobi.c */
+
+/* Start: bn_mp_karatsuba_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* c = |a| * |b| using Karatsuba Multiplication using
+ * three half size multiplications
+ *
+ * Let B represent the radix [e.g. 2**DIGIT_BIT] and
+ * let n represent half of the number of digits in
+ * the min(a,b)
+ *
+ * a = a1 * B**n + a0
+ * b = b1 * B**n + b0
+ *
+ * Then, a * b =>
+ a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
+ *
+ * Note that a1b1 and a0b0 are used twice and only need to be
+ * computed once. So in total three half size (half # of
+ * digit) multiplications are performed, a0b0, a1b1 and
+ * (a1+b1)(a0+b0)
+ *
+ * Note that a multiplication of half the digits requires
+ * 1/4th the number of single precision multiplications so in
+ * total after one call 25% of the single precision multiplications
+ * are saved. Note also that the call to mp_mul can end up back
+ * in this function if the a0, a1, b0, or b1 are above the threshold.
+ * This is known as divide-and-conquer and leads to the famous
+ * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
+ * the standard O(N**2) that the baseline/comba methods use.
+ * Generally though the overhead of this method doesn't pay off
+ * until a certain size (N ~ 80) is reached.
+ */
+int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
+ int B, err;
+
+ /* default the return code to an error */
+ err = MP_MEM;
+
+ /* min # of digits */
+ B = MIN (a->used, b->used);
+
+ /* now divide in two */
+ B = B >> 1;
+
+ /* init copy all the temps */
+ if (mp_init_size (&x0, B) != MP_OKAY)
+ goto ERR;
+ if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+ goto X0;
+ if (mp_init_size (&y0, B) != MP_OKAY)
+ goto X1;
+ if (mp_init_size (&y1, b->used - B) != MP_OKAY)
+ goto Y0;
+
+ /* init temps */
+ if (mp_init_size (&t1, B * 2) != MP_OKAY)
+ goto Y1;
+ if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
+ goto T1;
+ if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
+ goto X0Y0;
+
+ /* now shift the digits */
+ x0.used = y0.used = B;
+ x1.used = a->used - B;
+ y1.used = b->used - B;
+
+ {
+ register int x;
+ register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
+
+ /* we copy the digits directly instead of using higher level functions
+ * since we also need to shift the digits
+ */
+ tmpa = a->dp;
+ tmpb = b->dp;
+
+ tmpx = x0.dp;
+ tmpy = y0.dp;
+ for (x = 0; x < B; x++) {
+ *tmpx++ = *tmpa++;
+ *tmpy++ = *tmpb++;
+ }
+
+ tmpx = x1.dp;
+ for (x = B; x < a->used; x++) {
+ *tmpx++ = *tmpa++;
+ }
+
+ tmpy = y1.dp;
+ for (x = B; x < b->used; x++) {
+ *tmpy++ = *tmpb++;
+ }
+ }
+
+ /* only need to clamp the lower words since by definition the
+ * upper words x1/y1 must have a known number of digits
+ */
+ mp_clamp (&x0);
+ mp_clamp (&y0);
+
+ /* now calc the products x0y0 and x1y1 */
+ /* after this x0 is no longer required, free temp [x0==t2]! */
+ if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
+ goto X1Y1; /* x0y0 = x0*y0 */
+ if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
+ goto X1Y1; /* x1y1 = x1*y1 */
+
+ /* now calc x1+x0 and y1+y0 */
+ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = x1 - x0 */
+ if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
+ goto X1Y1; /* t2 = y1 - y0 */
+ if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */
+
+ /* add x0y0 */
+ if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
+ goto X1Y1; /* t2 = x0y0 + x1y1 */
+ if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
+
+ /* shift by B */
+ if (mp_lshd (&t1, B) != MP_OKAY)
+ goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+ if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
+ goto X1Y1; /* x1y1 = x1y1 << 2*B */
+
+ if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
+ goto X1Y1; /* t1 = x0y0 + t1 */
+ if (mp_add (&t1, &x1y1, c) != MP_OKAY)
+ goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
+
+ /* Algorithm succeeded set the return code to MP_OKAY */
+ err = MP_OKAY;
+
+X1Y1:mp_clear (&x1y1);
+X0Y0:mp_clear (&x0y0);
+T1:mp_clear (&t1);
+Y1:mp_clear (&y1);
+Y0:mp_clear (&y0);
+X1:mp_clear (&x1);
+X0:mp_clear (&x0);
+ERR:
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_mul.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_karatsuba_mul.c */
+
+/* Start: bn_mp_karatsuba_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Karatsuba squaring, computes b = a*a using three
+ * half size squarings
+ *
+ * See comments of karatsuba_mul for details. It
+ * is essentially the same algorithm but merely
+ * tuned to perform recursive squarings.
+ */
+int mp_karatsuba_sqr (mp_int * a, mp_int * b)
+{
+ mp_int x0, x1, t1, t2, x0x0, x1x1;
+ int B, err;
+
+ err = MP_MEM;
+
+ /* min # of digits */
+ B = a->used;
+
+ /* now divide in two */
+ B = B >> 1;
+
+ /* init copy all the temps */
+ if (mp_init_size (&x0, B) != MP_OKAY)
+ goto ERR;
+ if (mp_init_size (&x1, a->used - B) != MP_OKAY)
+ goto X0;
+
+ /* init temps */
+ if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
+ goto X1;
+ if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
+ goto T1;
+ if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
+ goto T2;
+ if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
+ goto X0X0;
+
+ {
+ register int x;
+ register mp_digit *dst, *src;
+
+ src = a->dp;
+
+ /* now shift the digits */
+ dst = x0.dp;
+ for (x = 0; x < B; x++) {
+ *dst++ = *src++;
+ }
+
+ dst = x1.dp;
+ for (x = B; x < a->used; x++) {
+ *dst++ = *src++;
+ }
+ }
+
+ x0.used = B;
+ x1.used = a->used - B;
+
+ mp_clamp (&x0);
+
+ /* now calc the products x0*x0 and x1*x1 */
+ if (mp_sqr (&x0, &x0x0) != MP_OKAY)
+ goto X1X1; /* x0x0 = x0*x0 */
+ if (mp_sqr (&x1, &x1x1) != MP_OKAY)
+ goto X1X1; /* x1x1 = x1*x1 */
+
+ /* now calc (x1+x0)**2 */
+ if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = x1 - x0 */
+ if (mp_sqr (&t1, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */
+
+ /* add x0y0 */
+ if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
+ goto X1X1; /* t2 = x0x0 + x1x1 */
+ if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
+
+ /* shift by B */
+ if (mp_lshd (&t1, B) != MP_OKAY)
+ goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
+ if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
+ goto X1X1; /* x1x1 = x1x1 << 2*B */
+
+ if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
+ goto X1X1; /* t1 = x0x0 + t1 */
+ if (mp_add (&t1, &x1x1, b) != MP_OKAY)
+ goto X1X1; /* t1 = x0x0 + t1 + x1x1 */
+
+ err = MP_OKAY;
+
+X1X1:mp_clear (&x1x1);
+X0X0:mp_clear (&x0x0);
+T2:mp_clear (&t2);
+T1:mp_clear (&t1);
+X1:mp_clear (&x1);
+X0:mp_clear (&x0);
+ERR:
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_karatsuba_sqr.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_karatsuba_sqr.c */
+
+/* Start: bn_mp_lcm.c */
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes least common multiple as |a*b|/(a, b) */
+int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res;
+ mp_int t1, t2;
+
+
+ if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* t1 = get the GCD of the two inputs */
+ if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
+ goto LBL_T;
+ }
+
+ /* divide the smallest by the GCD */
+ if (mp_cmp_mag(a, b) == MP_LT) {
+ /* store quotient in t2 such that t2 * b is the LCM */
+ if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(b, &t2, c);
+ } else {
+ /* store quotient in t2 such that t2 * a is the LCM */
+ if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
+ goto LBL_T;
+ }
+ res = mp_mul(a, &t2, c);
+ }
+
+ /* fix the sign to positive */
+ c->sign = MP_ZPOS;
+
+LBL_T:
+ mp_clear_multi (&t1, &t2, NULL);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_lcm.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_lcm.c */
+
+/* Start: bn_mp_lshd.c */
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift left a certain amount of digits */
+int mp_lshd (mp_int * a, int b)
+{
+ int x, res;
+
+ /* if its less than zero return */
+ if (b <= 0) {
+ return MP_OKAY;
+ }
+
+ /* grow to fit the new digits */
+ if (a->alloc < a->used + b) {
+ if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ {
+ register mp_digit *top, *bottom;
+
+ /* increment the used by the shift amount then copy upwards */
+ a->used += b;
+
+ /* top */
+ top = a->dp + a->used - 1;
+
+ /* base */
+ bottom = a->dp + a->used - 1 - b;
+
+ /* much like mp_rshd this is implemented using a sliding window
+ * except the window goes the otherway around. Copying from
+ * the bottom to the top. see bn_mp_rshd.c for more info.
+ */
+ for (x = a->used - 1; x >= b; x--) {
+ *top-- = *bottom--;
+ }
+
+ /* zero the lower digits */
+ top = a->dp;
+ for (x = 0; x < b; x++) {
+ *top++ = 0;
+ }
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_lshd.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_lshd.c */
+
+/* Start: bn_mp_mod.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* c = a mod b, 0 <= c < b */
+int
+mp_mod (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int t;
+ int res;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+
+ if (t.sign != b->sign) {
+ res = mp_add (b, &t, c);
+ } else {
+ res = MP_OKAY;
+ mp_exch (&t, c);
+ }
+
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mod.c */
+
+/* Start: bn_mp_mod_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* calc a value mod 2**b */
+int
+mp_mod_2d (mp_int * a, int b, mp_int * c)
+{
+ int x, res;
+
+ /* if b is <= 0 then zero the int */
+ if (b <= 0) {
+ mp_zero (c);
+ return MP_OKAY;
+ }
+
+ /* if the modulus is larger than the value than return */
+ if (b >= (int) (a->used * DIGIT_BIT)) {
+ res = mp_copy (a, c);
+ return res;
+ }
+
+ /* copy */
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+
+ /* zero digits above the last digit of the modulus */
+ for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
+ c->dp[x] = 0;
+ }
+ /* clear the digit that is not completely outside/inside the modulus */
+ c->dp[b / DIGIT_BIT] &=
+ (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mod_2d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mod_2d.c */
+
+/* Start: bn_mp_mod_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+int
+mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
+{
+ return mp_div_d(a, b, NULL, c);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mod_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mod_d.c */
+
+/* Start: bn_mp_montgomery_calc_normalization.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/*
+ * shifts with subtractions when the result is greater than b.
+ *
+ * The method is slightly modified to shift B unconditionally upto just under
+ * the leading bit of b. This saves alot of multiple precision shifting.
+ */
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+{
+ int x, bits, res;
+
+ /* how many bits of last digit does b use */
+ bits = mp_count_bits (b) % DIGIT_BIT;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
+ }
+
+
+ /* now compute C = A * B mod b */
+ for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
+ if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
+ return res;
+ }
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
+ return res;
+ }
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_montgomery_calc_normalization.c */
+
+/* Start: bn_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction */
+int
+mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+ int ix, res, digs;
+ mp_digit mu;
+
+ /* can the fast reduction [comba] method be used?
+ *
+ * Note that unlike in mul you're safely allowed *less*
+ * than the available columns [255 per default] since carries
+ * are fixed up in the inner loop.
+ */
+ digs = n->used * 2 + 1;
+ if ((digs < MP_WARRAY) &&
+ n->used <
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_mp_montgomery_reduce (x, n, rho);
+ }
+
+ /* grow the input as required */
+ if (x->alloc < digs) {
+ if ((res = mp_grow (x, digs)) != MP_OKAY) {
+ return res;
+ }
+ }
+ x->used = digs;
+
+ for (ix = 0; ix < n->used; ix++) {
+ /* mu = ai * rho mod b
+ *
+ * The value of rho must be precalculated via
+ * montgomery_setup() such that
+ * it equals -1/n0 mod b this allows the
+ * following inner loop to reduce the
+ * input one digit at a time
+ */
+ mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
+
+ /* a = a + mu * m * b**i */
+ {
+ register int iy;
+ register mp_digit *tmpn, *tmpx, u;
+ register mp_word r;
+
+ /* alias for digits of the modulus */
+ tmpn = n->dp;
+
+ /* alias for the digits of x [the input] */
+ tmpx = x->dp + ix;
+
+ /* set the carry to zero */
+ u = 0;
+
+ /* Multiply and add in place */
+ for (iy = 0; iy < n->used; iy++) {
+ /* compute product and sum */
+ r = ((mp_word)mu) * ((mp_word)*tmpn++) +
+ ((mp_word) u) + ((mp_word) * tmpx);
+
+ /* get carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+
+ /* fix digit */
+ *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
+ }
+ /* At this point the ix'th digit of x should be zero */
+
+
+ /* propagate carries upwards as required*/
+ while (u) {
+ *tmpx += u;
+ u = *tmpx >> DIGIT_BIT;
+ *tmpx++ &= MP_MASK;
+ }
+ }
+ }
+
+ /* at this point the n.used'th least
+ * significant digits of x are all zero
+ * which means we can shift x to the
+ * right by n.used digits and the
+ * residue is unchanged.
+ */
+
+ /* x = x/b**n.used */
+ mp_clamp(x);
+ mp_rshd (x, n->used);
+
+ /* if x >= n then x = x - n */
+ if (mp_cmp_mag (x, n) != MP_LT) {
+ return s_mp_sub (x, n, x);
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_montgomery_reduce.c */
+
+/* Start: bn_mp_montgomery_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* setups the montgomery reduction stuff */
+int
+mp_montgomery_setup (mp_int * n, mp_digit * rho)
+{
+ mp_digit x, b;
+
+/* fast inversion mod 2**k
+ *
+ * Based on the fact that
+ *
+ * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n)
+ * => 2*X*A - X*X*A*A = 1
+ * => 2*(1) - (1) = 1
+ */
+ b = n->dp[0];
+
+ if ((b & 1) == 0) {
+ return MP_VAL;
+ }
+
+ x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
+ x *= 2 - b * x; /* here x*a==1 mod 2**8 */
+#if !defined(MP_8BIT)
+ x *= 2 - b * x; /* here x*a==1 mod 2**16 */
+#endif
+#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
+ x *= 2 - b * x; /* here x*a==1 mod 2**32 */
+#endif
+#ifdef MP_64BIT
+ x *= 2 - b * x; /* here x*a==1 mod 2**64 */
+#endif
+
+ /* rho = -1/m mod b */
+ *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_montgomery_setup.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/12/04 21:34:03 $ */
+
+/* End: bn_mp_montgomery_setup.c */
+
+/* Start: bn_mp_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* high level multiplication (handles sign) */
+int mp_mul (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, neg;
+ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+
+ /* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
+ if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
+ res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
+ /* use Karatsuba? */
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ res = mp_karatsuba_mul (a, b, c);
+ } else
+#endif
+ {
+ /* can we use the fast multiplier?
+ *
+ * The fast multiplier can be used if the output will
+ * have less than MP_WARRAY digits and the number of
+ * digits won't affect carry propagation
+ */
+ int digs = a->used + b->used + 1;
+
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
+ if ((digs < MP_WARRAY) &&
+ MIN(a->used, b->used) <=
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ res = fast_s_mp_mul_digs (a, b, c, digs);
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
+
+ }
+ c->sign = (c->used > 0) ? neg : MP_ZPOS;
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mul.c */
+
+/* Start: bn_mp_mul_2.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = a*2 */
+int mp_mul_2(mp_int * a, mp_int * b)
+{
+ int x, res, oldused;
+
+ /* grow to accomodate result */
+ if (b->alloc < a->used + 1) {
+ if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ oldused = b->used;
+ b->used = a->used;
+
+ {
+ register mp_digit r, rr, *tmpa, *tmpb;
+
+ /* alias for source */
+ tmpa = a->dp;
+
+ /* alias for dest */
+ tmpb = b->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < a->used; x++) {
+
+ /* get what will be the *next* carry bit from the
+ * MSB of the current digit
+ */
+ rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
+
+ /* now shift up this digit, add in the carry [from the previous] */
+ *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
+
+ /* copy the carry that would be from the source
+ * digit into the next iteration
+ */
+ r = rr;
+ }
+
+ /* new leading digit? */
+ if (r != 0) {
+ /* add a MSB which is always 1 at this point */
+ *tmpb = 1;
+ ++(b->used);
+ }
+
+ /* now zero any excess digits on the destination
+ * that we didn't write to
+ */
+ tmpb = b->dp + b->used;
+ for (x = b->used; x < oldused; x++) {
+ *tmpb++ = 0;
+ }
+ }
+ b->sign = a->sign;
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mul_2.c */
+
+/* Start: bn_mp_mul_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift left by a certain bit count */
+int mp_mul_2d (mp_int * a, int b, mp_int * c)
+{
+ mp_digit d;
+ int res;
+
+ /* copy */
+ if (a != c) {
+ if ((res = mp_copy (a, c)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
+ if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift by as many digits in the bit count */
+ if (b >= (int)DIGIT_BIT) {
+ if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* shift any bit count < DIGIT_BIT */
+ d = (mp_digit) (b % DIGIT_BIT);
+ if (d != 0) {
+ register mp_digit *tmpc, shift, mask, r, rr;
+ register int x;
+
+ /* bitmask for carries */
+ mask = (((mp_digit)1) << d) - 1;
+
+ /* shift for msbs */
+ shift = DIGIT_BIT - d;
+
+ /* alias */
+ tmpc = c->dp;
+
+ /* carry */
+ r = 0;
+ for (x = 0; x < c->used; x++) {
+ /* get the higher bits of the current word */
+ rr = (*tmpc >> shift) & mask;
+
+ /* shift the current word and OR in the carry */
+ *tmpc = ((*tmpc << d) | r) & MP_MASK;
+ ++tmpc;
+
+ /* set the carry to the carry bits of the current word */
+ r = rr;
+ }
+
+ /* set final carry */
+ if (r != 0) {
+ c->dp[(c->used)++] = r;
+ }
+ }
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul_2d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mul_2d.c */
+
+/* Start: bn_mp_mul_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiply by a digit */
+int
+mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_digit u, *tmpa, *tmpc;
+ mp_word r;
+ int ix, res, olduse;
+
+ /* make sure c is big enough to hold a*b */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* get the original destinations used count */
+ olduse = c->used;
+
+ /* set the sign */
+ c->sign = a->sign;
+
+ /* alias for a->dp [source] */
+ tmpa = a->dp;
+
+ /* alias for c->dp [dest] */
+ tmpc = c->dp;
+
+ /* zero carry */
+ u = 0;
+
+ /* compute columns */
+ for (ix = 0; ix < a->used; ix++) {
+ /* compute product and carry sum for this term */
+ r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
+
+ /* mask off higher bits to get a single digit */
+ *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* send carry into next iteration */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+
+ /* store final carry [if any] and increment ix offset */
+ *tmpc++ = u;
+ ++ix;
+
+ /* now zero digits above the top */
+ while (ix++ < olduse) {
+ *tmpc++ = 0;
+ }
+
+ /* set used count */
+ c->used = a->used + 1;
+ mp_clamp(c);
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mul_d.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mul_d.c */
+
+/* Start: bn_mp_mulmod.c */
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* d = a * b (mod c) */
+int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_mulmod.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_mulmod.c */
+
+/* Start: bn_mp_n_root.c */
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* find the n'th root of an integer
+ *
+ * Result found such that (c)**b <= a and (c+1)**b > a
+ *
+ * This algorithm uses Newton's approximation
+ * x[i+1] = x[i] - f(x[i])/f'(x[i])
+ * which will find the root in log(N) time where
+ * each step involves a fair bit. This is not meant to
+ * find huge roots [square and cube, etc].
+ */
+int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_int t1, t2, t3;
+ int res, neg;
+
+ /* input must be positive if b is even */
+ if ((b & 1) == 0 && a->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ if ((res = mp_init (&t1)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&t2)) != MP_OKAY) {
+ goto LBL_T1;
+ }
+
+ if ((res = mp_init (&t3)) != MP_OKAY) {
+ goto LBL_T2;
+ }
+
+ /* if a is negative fudge the sign but keep track */
+ neg = a->sign;
+ a->sign = MP_ZPOS;
+
+ /* t2 = 2 */
+ mp_set (&t2, 2);
+
+ do {
+ /* t1 = t2 */
+ if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+
+ /* t3 = t1**(b-1) */
+ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* numerator */
+ /* t2 = t1**b */
+ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t2 = t1**b - a */
+ if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* denominator */
+ /* t3 = t1**(b-1) * b */
+ if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ /* t3 = (t1**b - a)/(b * t1**(b-1)) */
+ if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+ } while (mp_cmp (&t1, &t2) != MP_EQ);
+
+ /* result can be off by a few so check */
+ for (;;) {
+ if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+
+ if (mp_cmp (&t2, a) == MP_GT) {
+ if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
+ goto LBL_T3;
+ }
+ } else {
+ break;
+ }
+ }
+
+ /* reset the sign of a first */
+ a->sign = neg;
+
+ /* set the result */
+ mp_exch (&t1, c);
+
+ /* set the sign of the result */
+ c->sign = neg;
+
+ res = MP_OKAY;
+
+LBL_T3:mp_clear (&t3);
+LBL_T2:mp_clear (&t2);
+LBL_T1:mp_clear (&t1);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_n_root.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_n_root.c */
+
+/* Start: bn_mp_neg.c */
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* b = -a */
+int mp_neg (mp_int * a, mp_int * b)
+{
+ int res;
+ if (a != b) {
+ if ((res = mp_copy (a, b)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ if (mp_iszero(b) != MP_YES) {
+ b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ } else {
+ b->sign = MP_ZPOS;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_neg.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_neg.c */
+
+/* Start: bn_mp_or.c */
+#include <tommath.h>
+#ifdef BN_MP_OR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* OR two ints together */
+int mp_or (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] |= x->dp[ix];
+ }
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_or.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_or.c */
+
+/* Start: bn_mp_prime_fermat.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* performs one Fermat test.
+ *
+ * If "a" were prime then b**a == b (mod a) since the order of
+ * the multiplicative sub-group would be phi(a) = a-1. That means
+ * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
+ *
+ * Sets result to 1 if the congruence holds, or zero otherwise.
+ */
+int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
+{
+ mp_int t;
+ int err;
+
+ /* default to composite */
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* init t */
+ if ((err = mp_init (&t)) != MP_OKAY) {
+ return err;
+ }
+
+ /* compute t = b**a mod a */
+ if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
+ goto LBL_T;
+ }
+
+ /* is it equal to b? */
+ if (mp_cmp (&t, b) == MP_EQ) {
+ *result = MP_YES;
+ }
+
+ err = MP_OKAY;
+LBL_T:mp_clear (&t);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_fermat.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_prime_fermat.c */
+
+/* Start: bn_mp_prime_is_divisible.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if an integers is divisible by one
+ * of the first PRIME_SIZE primes or not
+ *
+ * sets result to 0 if not, 1 if yes
+ */
+int mp_prime_is_divisible (mp_int * a, int *result)
+{
+ int err, ix;
+ mp_digit res;
+
+ /* default to not */
+ *result = MP_NO;
+
+ for (ix = 0; ix < PRIME_SIZE; ix++) {
+ /* what is a mod LBL_prime_tab[ix] */
+ if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
+ return err;
+ }
+
+ /* is the residue zero? */
+ if (res == 0) {
+ *result = MP_YES;
+ return MP_OKAY;
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_divisible.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_prime_is_divisible.c */
+
+/* Start: bn_mp_prime_is_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* performs a variable number of rounds of Miller-Rabin
+ *
+ * Probability of error after t rounds is no more than
+
+ *
+ * Sets result to 1 if probably prime, 0 otherwise
+ */
+int mp_prime_is_prime (mp_int * a, int t, int *result)
+{
+ mp_int b;
+ int ix, err, res;
+
+ /* default to no */
+ *result = MP_NO;
+
+ /* valid value of t? */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* is the input equal to one of the primes in the table? */
+ for (ix = 0; ix < PRIME_SIZE; ix++) {
+ if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
+ *result = 1;
+ return MP_OKAY;
+ }
+ }
+
+ /* first perform trial division */
+ if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
+ return err;
+ }
+
+ /* return if it was trivially divisible */
+ if (res == MP_YES) {
+ return MP_OKAY;
+ }
+
+ /* now perform the miller-rabin rounds */
+ if ((err = mp_init (&b)) != MP_OKAY) {
+ return err;
+ }
+
+ for (ix = 0; ix < t; ix++) {
+ /* set the prime */
+ mp_set (&b, ltm_prime_tab[ix]);
+
+ if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
+ goto LBL_B;
+ }
+
+ if (res == MP_NO) {
+ goto LBL_B;
+ }
+ }
+
+ /* passed the test */
+ *result = MP_YES;
+LBL_B:mp_clear (&b);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_is_prime.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_prime_is_prime.c */
+
+/* Start: bn_mp_prime_miller_rabin.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Miller-Rabin test of "a" to the base of "b" as described in
+ * HAC pp. 139 Algorithm 4.24
+ *
+ * Sets result to 0 if definitely composite or 1 if probably prime.
+ * Randomly the chance of error is no more than 1/4 and often
+ * very much lower.
+ */
+int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
+{
+ mp_int n1, y, r;
+ int s, j, err;
+
+ /* default */
+ *result = MP_NO;
+
+ /* ensure b > 1 */
+ if (mp_cmp_d(b, 1) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* get n1 = a - 1 */
+ if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
+ goto LBL_N1;
+ }
+
+ /* set 2**s * r = n1 */
+ if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
+ goto LBL_N1;
+ }
+
+ /* count the number of least significant bits
+ * which are zero
+ */
+ s = mp_cnt_lsb(&r);
+
+ /* now divide n - 1 by 2**s */
+ if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
+ goto LBL_R;
+ }
+
+ /* compute y = b**r mod a */
+ if ((err = mp_init (&y)) != MP_OKAY) {
+ goto LBL_R;
+ }
+ if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if y != 1 and y != n1 do */
+ if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
+ j = 1;
+ /* while j <= s-1 and y != n1 */
+ while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
+ if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
+ goto LBL_Y;
+ }
+
+ /* if y == 1 then composite */
+ if (mp_cmp_d (&y, 1) == MP_EQ) {
+ goto LBL_Y;
+ }
+
+ ++j;
+ }
+
+ /* if y != n1 then composite */
+ if (mp_cmp (&y, &n1) != MP_EQ) {
+ goto LBL_Y;
+ }
+ }
+
+ /* probably prime now */
+ *result = MP_YES;
+LBL_Y:mp_clear (&y);
+LBL_R:mp_clear (&r);
+LBL_N1:mp_clear (&n1);
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_miller_rabin.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_prime_miller_rabin.c */
+
+/* Start: bn_mp_prime_next_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* finds the next prime after the number "a" using "t" trials
+ * of Miller-Rabin.
+ *
+ * bbs_style = 1 means the prime must be congruent to 3 mod 4
+ */
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
+{
+ int err, res, x, y;
+ mp_digit res_tab[PRIME_SIZE], step, kstep;
+ mp_int b;
+
+ /* ensure t is valid */
+ if (t <= 0 || t > PRIME_SIZE) {
+ return MP_VAL;
+ }
+
+ /* force positive */
+ a->sign = MP_ZPOS;
+
+ /* simple algo if a is less than the largest prime in the table */
+ if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
+ /* find which prime it is bigger than */
+ for (x = PRIME_SIZE - 2; x >= 0; x--) {
+ if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
+ if (bbs_style == 1) {
+ /* ok we found a prime smaller or
+ * equal [so the next is larger]
+ *
+ * however, the prime must be
+ * congruent to 3 mod 4
+ */
+ if ((ltm_prime_tab[x + 1] & 3) != 3) {
+ /* scan upwards for a prime congruent to 3 mod 4 */
+ for (y = x + 1; y < PRIME_SIZE; y++) {
+ if ((ltm_prime_tab[y] & 3) == 3) {
+ mp_set(a, ltm_prime_tab[y]);
+ return MP_OKAY;
+ }
+ }
+ }
+ } else {
+ mp_set(a, ltm_prime_tab[x + 1]);
+ return MP_OKAY;
+ }
+ }
+ }
+ /* at this point a maybe 1 */
+ if (mp_cmp_d(a, 1) == MP_EQ) {
+ mp_set(a, 2);
+ return MP_OKAY;
+ }
+ /* fall through to the sieve */
+ }
+
+ /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
+ if (bbs_style == 1) {
+ kstep = 4;
+ } else {
+ kstep = 2;
+ }
+
+ /* at this point we will use a combination of a sieve and Miller-Rabin */
+
+ if (bbs_style == 1) {
+ /* if a mod 4 != 3 subtract the correct value to make it so */
+ if ((a->dp[0] & 3) != 3) {
+ if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
+ }
+ } else {
+ if (mp_iseven(a) == 1) {
+ /* force odd */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
+ return err;
+ }
+ }
+ }
+
+ /* generate the restable */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
+ return err;
+ }
+ }
+
+ /* init temp used for Miller-Rabin Testing */
+ if ((err = mp_init(&b)) != MP_OKAY) {
+ return err;
+ }
+
+ for (;;) {
+ /* skip to the next non-trivially divisible candidate */
+ step = 0;
+ do {
+ /* y == 1 if any residue was zero [e.g. cannot be prime] */
+ y = 0;
+
+ /* increase step to next candidate */
+ step += kstep;
+
+ /* compute the new residue without using division */
+ for (x = 1; x < PRIME_SIZE; x++) {
+ /* add the step to each residue */
+ res_tab[x] += kstep;
+
+ /* subtract the modulus [instead of using division] */
+ if (res_tab[x] >= ltm_prime_tab[x]) {
+ res_tab[x] -= ltm_prime_tab[x];
+ }
+
+ /* set flag if zero */
+ if (res_tab[x] == 0) {
+ y = 1;
+ }
+ }
+ } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
+
+ /* add the step */
+ if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+
+ /* if didn't pass sieve and step == MAX then skip test */
+ if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
+ continue;
+ }
+
+ /* is this prime? */
+ for (x = 0; x < t; x++) {
+ mp_set(&b, ltm_prime_tab[t]);
+ if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+ goto LBL_ERR;
+ }
+ if (res == MP_NO) {
+ break;
+ }
+ }
+
+ if (res == MP_YES) {
+ break;
+ }
+ }
+
+ err = MP_OKAY;
+LBL_ERR:
+ mp_clear(&b);
+ return err;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_next_prime.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_prime_next_prime.c */
+
+/* Start: bn_mp_prime_rabin_miller_trials.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+
+static const struct {
+ int k, t;
+} sizes[] = {
+{ 128, 28 },
+{ 256, 16 },
+{ 384, 10 },
+{ 512, 7 },
+{ 640, 6 },
+{ 768, 5 },
+{ 896, 4 },
+{ 1024, 4 }
+};
+
+/* returns # of RM trials required for a given bit size */
+int mp_prime_rabin_miller_trials(int size)
+{
+ int x;
+
+ for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
+ if (sizes[x].k == size) {
+ return sizes[x].t;
+ } else if (sizes[x].k > size) {
+ return (x == 0) ? sizes[0].t : sizes[x - 1].t;
+ }
+ }
+ return sizes[x-1].t + 1;
+}
+
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_rabin_miller_trials.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_prime_rabin_miller_trials.c */
+
+/* Start: bn_mp_prime_random_ex.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* makes a truly random prime of a given size (bits),
+ *
+ * Flags are as follows:
+ *
+ * LTM_PRIME_BBS - make prime congruent to 3 mod 4
+ * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
+ * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
+ * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
+ *
+ * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
+ * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
+ * so it can be NULL
+ *
+ */
+
+/* This is possibly the mother of all prime generation functions, muahahahahaha! */
+int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
+{
+ unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
+ int res, err, bsize, maskOR_msb_offset;
+
+ /* sanity check the input */
+ if (size <= 1 || t <= 0) {
+ return MP_VAL;
+ }
+
+ /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
+ if (flags & LTM_PRIME_SAFE) {
+ flags |= LTM_PRIME_BBS;
+ }
+
+ /* calc the byte size */
+ bsize = (size>>3) + ((size&7)?1:0);
+
+ /* we need a buffer of bsize bytes */
+ tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
+ if (tmp == NULL) {
+ return MP_MEM;
+ }
+
+ /* calc the maskAND value for the MSbyte*/
+ maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));
+
+ /* calc the maskOR_msb */
+ maskOR_msb = 0;
+ maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
+ if (flags & LTM_PRIME_2MSB_ON) {
+ maskOR_msb |= 0x80 >> ((9 - size) & 7);
+ }
+
+ /* get the maskOR_lsb */
+ maskOR_lsb = 1;
+ if (flags & LTM_PRIME_BBS) {
+ maskOR_lsb |= 3;
+ }
+
+ do {
+ /* read the bytes */
+ if (cb(tmp, bsize, dat) != bsize) {
+ err = MP_VAL;
+ goto error;
+ }
+
+ /* work over the MSbyte */
+ tmp[0] &= maskAND;
+ tmp[0] |= 1 << ((size - 1) & 7);
+
+ /* mix in the maskORs */
+ tmp[maskOR_msb_offset] |= maskOR_msb;
+ tmp[bsize-1] |= maskOR_lsb;
+
+ /* read it in */
+ if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* see if (a-1)/2 is prime */
+ if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_div_2(a, a)) != MP_OKAY) { goto error; }
+
+ /* is it prime? */
+ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ }
+ } while (res == MP_NO);
+
+ if (flags & LTM_PRIME_SAFE) {
+ /* restore a to the original value */
+ if ((err = mp_mul_2(a, a)) != MP_OKAY) { goto error; }
+ if ((err = mp_add_d(a, 1, a)) != MP_OKAY) { goto error; }
+ }
+
+ err = MP_OKAY;
+error:
+ XFREE(tmp);
+ return err;
+}
+
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_prime_random_ex.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_prime_random_ex.c */
+
+/* Start: bn_mp_radix_size.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* returns size of ASCII reprensentation */
+int mp_radix_size (mp_int * a, int radix, int *size)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+
+ *size = 0;
+
+ /* special case for binary */
+ if (radix == 2) {
+ *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
+ return MP_OKAY;
+ }
+
+ /* make sure the radix is in range */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ if (mp_iszero(a) == MP_YES) {
+ *size = 2;
+ return MP_OKAY;
+ }
+
+ /* digs is the digit count */
+ digs = 0;
+
+ /* if it's negative add one for the sign */
+ if (a->sign == MP_NEG) {
+ ++digs;
+ }
+
+ /* init a copy of the input */
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* force temp to positive */
+ t.sign = MP_ZPOS;
+
+ /* fetch out all of the digits */
+ while (mp_iszero (&t) == MP_NO) {
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ ++digs;
+ }
+ mp_clear (&t);
+
+ /* return digs + 1, the 1 is for the NULL byte that would be required. */
+ *size = digs + 1;
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_radix_size.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_radix_size.c */
+
+/* Start: bn_mp_radix_smap.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* chars used in radix conversions */
+const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_radix_smap.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_radix_smap.c */
+
+/* Start: bn_mp_rand.c */
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* makes a pseudo-random int of a given size */
+int
+mp_rand (mp_int * a, int digits)
+{
+ int res;
+ mp_digit d;
+
+ mp_zero (a);
+ if (digits <= 0) {
+ return MP_OKAY;
+ }
+
+ /* first place a random non-zero digit */
+ do {
+ d = ((mp_digit) abs (rand ())) & MP_MASK;
+ } while (d == 0);
+
+ if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
+ return res;
+ }
+
+ while (--digits > 0) {
+ if ((res = mp_lshd (a, 1)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_rand.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_rand.c */
+
+/* Start: bn_mp_read_radix.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* read a string [ASCII] in a given radix */
+int mp_read_radix (mp_int * a, const char *str, int radix)
+{
+ int y, res, neg;
+ char ch;
+
+ /* zero the digit bignum */
+ mp_zero(a);
+
+ /* make sure the radix is ok */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* if the leading digit is a
+ * minus set the sign to negative.
+ */
+ if (*str == '-') {
+ ++str;
+ neg = MP_NEG;
+ } else {
+ neg = MP_ZPOS;
+ }
+
+ /* set the integer to the default of zero */
+ mp_zero (a);
+
+ /* process each digit of the string */
+ while (*str) {
+ /* if the radix < 36 the conversion is case insensitive
+ * this allows numbers like 1AB and 1ab to represent the same value
+ * [e.g. in hex]
+ */
+ ch = (char) ((radix < 36) ? toupper (*str) : *str);
+ for (y = 0; y < 64; y++) {
+ if (ch == mp_s_rmap[y]) {
+ break;
+ }
+ }
+
+ /* if the char was found in the map
+ * and is less than the given radix add it
+ * to the number, otherwise exit the loop.
+ */
+ if (y < radix) {
+ if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
+ return res;
+ }
+ if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ break;
+ }
+ ++str;
+ }
+
+ /* set the sign only if a != 0 */
+ if (mp_iszero(a) != 1) {
+ a->sign = neg;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_read_radix.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_read_radix.c */
+
+/* Start: bn_mp_read_signed_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* read signed bin, big endian, first byte is 0==positive or 1==negative */
+int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
+{
+ int res;
+
+ /* read magnitude */
+ if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* first byte is 0 for positive, non-zero for negative */
+ if (b[0] == 0) {
+ a->sign = MP_ZPOS;
+ } else {
+ a->sign = MP_NEG;
+ }
+
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_read_signed_bin.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_read_signed_bin.c */
+
+/* Start: bn_mp_read_unsigned_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reads a unsigned char array, assumes the msb is stored first [big endian] */
+int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
+{
+ int res;
+
+ /* make sure there are at least two digits */
+ if (a->alloc < 2) {
+ if ((res = mp_grow(a, 2)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* zero the int */
+ mp_zero (a);
+
+ /* read the bytes in */
+ while (c-- > 0) {
+ if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
+ return res;
+ }
+
+#ifndef MP_8BIT
+ a->dp[0] |= *b++;
+ a->used += 1;
+#else
+ a->dp[0] = (*b & MP_MASK);
+ a->dp[1] |= ((*b++ >> 7U) & 1);
+ a->used += 2;
+#endif
+ }
+ mp_clamp (a);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_read_unsigned_bin.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_read_unsigned_bin.c */
+
+/* Start: bn_mp_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduces x mod m, assumes 0 < x < m**2, mu is
+ * precomputed via mp_reduce_setup.
+ * From HAC pp.604 Algorithm 14.42
+ */
+int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
+{
+ mp_int q;
+ int res, um = m->used;
+
+ /* q = x */
+ if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
+ return res;
+ }
+
+ /* q1 = x / b**(k-1) */
+ mp_rshd (&q, um - 1);
+
+ /* according to HAC this optimization is ok */
+ if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
+ if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ } else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
+ if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
+ }
+
+ /* q3 = q2 / b**(k+1) */
+ mp_rshd (&q, um + 1);
+
+ /* x = x mod b**(k+1), quick (no division) */
+ if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* q = q * m mod b**(k+1), quick (no division) */
+ if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* x = x - q */
+ if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+
+ /* If x < 0, add b**(k+1) to it */
+ if (mp_cmp_d (x, 0) == MP_LT) {
+ mp_set (&q, 1);
+ if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
+ goto CLEANUP;
+ if ((res = mp_add (x, &q, x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ /* Back off if it's too big */
+ while (mp_cmp (x, m) != MP_LT) {
+ if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+ }
+
+CLEANUP:
+ mp_clear (&q);
+
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce.c */
+
+/* Start: bn_mp_reduce_2k.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d */
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (d != 1) {
+ /* q = q * d */
+ if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce_2k.c */
+
+/* Start: bn_mp_reduce_2k_l.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reduces a modulo n where n is of the form 2**p - d
+ This differs from reduce_2k since "d" can be larger
+ than a single digit.
+*/
+int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
+{
+ mp_int q;
+ int p, res;
+
+ if ((res = mp_init(&q)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(n);
+top:
+ /* q = a/2**p, a = a mod 2**p */
+ if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* q = q * d */
+ if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* a = a + q */
+ if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if (mp_cmp_mag(a, n) != MP_LT) {
+ s_mp_sub(a, n, a);
+ goto top;
+ }
+
+ERR:
+ mp_clear(&q);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_l.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce_2k_l.c */
+
+/* Start: bn_mp_reduce_2k_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
+{
+ int res, p;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ p = mp_count_bits(a);
+ if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ *d = tmp.dp[0];
+ mp_clear(&tmp);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce_2k_setup.c */
+
+/* Start: bn_mp_reduce_2k_setup_l.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines the setup value */
+int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
+{
+ int res;
+ mp_int tmp;
+
+ if ((res = mp_init(&tmp)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear(&tmp);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce_2k_setup_l.c */
+
+/* Start: bn_mp_reduce_is_2k.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if mp_reduce_2k can be used */
+int mp_reduce_is_2k(mp_int *a)
+{
+ int ix, iy, iw;
+ mp_digit iz;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ iy = mp_count_bits(a);
+ iz = 1;
+ iw = 1;
+
+ /* Test every bit from the second digit up, must be 1 */
+ for (ix = DIGIT_BIT; ix < iy; ix++) {
+ if ((a->dp[iw] & iz) == 0) {
+ return MP_NO;
+ }
+ iz <<= 1;
+ if (iz > (mp_digit)MP_MASK) {
+ ++iw;
+ iz = 1;
+ }
+ }
+ }
+ return MP_YES;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce_is_2k.c */
+
+/* Start: bn_mp_reduce_is_2k_l.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_L_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* determines if reduce_2k_l can be used */
+int mp_reduce_is_2k_l(mp_int *a)
+{
+ int ix, iy;
+
+ if (a->used == 0) {
+ return MP_NO;
+ } else if (a->used == 1) {
+ return MP_YES;
+ } else if (a->used > 1) {
+ /* if more than half of the digits are -1 we're sold */
+ for (iy = ix = 0; ix < a->used; ix++) {
+ if (a->dp[ix] == MP_MASK) {
+ ++iy;
+ }
+ }
+ return (iy >= (a->used/2)) ? MP_YES : MP_NO;
+
+ }
+ return MP_NO;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_is_2k_l.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce_is_2k_l.c */
+
+/* Start: bn_mp_reduce_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* pre-calculate the value required for Barrett reduction
+ * For a given modulus "b" it calulates the value required in "a"
+ */
+int mp_reduce_setup (mp_int * a, mp_int * b)
+{
+ int res;
+
+ if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
+ return res;
+ }
+ return mp_div (a, b, a, NULL);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_reduce_setup.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_reduce_setup.c */
+
+/* Start: bn_mp_rshd.c */
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shift right a certain amount of digits */
+void mp_rshd (mp_int * a, int b)
+{
+ int x;
+
+ /* if b <= 0 then ignore it */
+ if (b <= 0) {
+ return;
+ }
+
+ /* if b > used then simply zero it and return */
+ if (a->used <= b) {
+ mp_zero (a);
+ return;
+ }
+
+ {
+ register mp_digit *bottom, *top;
+
+ /* shift the digits down */
+
+ /* bottom */
+ bottom = a->dp;
+
+ /* top [offset into digits] */
+ top = a->dp + b;
+
+ /* this is implemented as a sliding window where
+ * the window is b-digits long and digits from
+ * the top of the window are copied to the bottom
+ *
+ * e.g.
+
+ b-2 | b-1 | b0 | b1 | b2 | ... | bb | ---->
+ /\ | ---->
+ \-------------------/ ---->
+ */
+ for (x = 0; x < (a->used - b); x++) {
+ *bottom++ = *top++;
+ }
+
+ /* zero the top digits */
+ for (; x < a->used; x++) {
+ *bottom++ = 0;
+ }
+ }
+
+ /* remove excess digits */
+ a->used -= b;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_rshd.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_rshd.c */
+
+/* Start: bn_mp_set.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* set to a digit */
+void mp_set (mp_int * a, mp_digit b)
+{
+ mp_zero (a);
+ a->dp[0] = b & MP_MASK;
+ a->used = (a->dp[0] != 0) ? 1 : 0;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_set.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_set.c */
+
+/* Start: bn_mp_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* set a 32-bit const */
+int mp_set_int (mp_int * a, unsigned long b)
+{
+ int x, res;
+
+ mp_zero (a);
+
+ /* set four bits at a time */
+ for (x = 0; x < 8; x++) {
+ /* shift the number up four bits */
+ if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* OR in the top four bits of the source */
+ a->dp[0] |= (b >> 28) & 15;
+
+ /* shift the source up to the next four bits */
+ b <<= 4;
+
+ /* ensure that digits are not clamped off */
+ a->used += 1;
+ }
+ mp_clamp (a);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_set_int.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_set_int.c */
+
+/* Start: bn_mp_shrink.c */
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* shrink a bignum */
+int mp_shrink (mp_int * a)
+{
+ mp_digit *tmp;
+ if (a->alloc != a->used && a->used > 0) {
+ if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * a->used)) == NULL) {
+ return MP_MEM;
+ }
+ a->dp = tmp;
+ a->alloc = a->used;
+ }
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_shrink.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_shrink.c */
+
+/* Start: bn_mp_signed_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* get the size for an signed equivalent */
+int mp_signed_bin_size (mp_int * a)
+{
+ return 1 + mp_unsigned_bin_size (a);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_signed_bin_size.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_signed_bin_size.c */
+
+/* Start: bn_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* computes b = a*a */
+int
+mp_sqr (mp_int * a, mp_int * b)
+{
+ int res;
+
+#ifdef BN_MP_TOOM_SQR_C
+ /* use Toom-Cook? */
+ if (a->used >= TOOM_SQR_CUTOFF) {
+ res = mp_toom_sqr(a, b);
+ /* Karatsuba? */
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ res = mp_karatsuba_sqr (a, b);
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
+ /* can we use the fast comba multiplier? */
+ if ((a->used * 2 + 1) < MP_WARRAY &&
+ a->used <
+ (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
+ res = fast_s_mp_sqr (a, b);
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
+ res = s_mp_sqr (a, b);
+#else
+ res = MP_VAL;
+#endif
+ }
+ b->sign = MP_ZPOS;
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_sqr.c */
+
+/* Start: bn_mp_sqrmod.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* c = a * a (mod b) */
+int
+mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_sqr (a, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, b, c);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sqrmod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_sqrmod.c */
+
+/* Start: bn_mp_sqrt.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* this function is less generic than mp_n_root, simpler and faster */
+int mp_sqrt(mp_int *arg, mp_int *ret)
+{
+ int res;
+ mp_int t1,t2;
+
+ /* must be positive */
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* easy out */
+ if (mp_iszero(arg) == MP_YES) {
+ mp_zero(ret);
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init(&t2)) != MP_OKAY) {
+ goto E2;
+ }
+
+ /* First approx. (not very bad for large arg) */
+ mp_rshd (&t1,t1.used/2);
+
+ /* t1 > 0 */
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* And now t1 > sqrt(arg) */
+ do {
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* t1 >= sqrt(arg) >= t2 at this point */
+ } while (mp_cmp_mag(&t1,&t2) == MP_GT);
+
+ mp_exch(&t1,ret);
+
+E1: mp_clear(&t2);
+E2: mp_clear(&t1);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sqrt.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_sqrt.c */
+
+/* Start: bn_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* high level subtraction (handles signs) */
+int
+mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int sa, sb, res;
+
+ sa = a->sign;
+ sb = b->sign;
+
+ if (sa != sb) {
+ /* subtract a negative from a positive, OR */
+ /* subtract a positive from a negative. */
+ /* In either case, ADD their magnitudes, */
+ /* and use the sign of the first number. */
+ c->sign = sa;
+ res = s_mp_add (a, b, c);
+ } else {
+ /* subtract a positive from a positive, OR */
+ /* subtract a negative from a negative. */
+ /* First, take the difference between their */
+ /* magnitudes, then... */
+ if (mp_cmp_mag (a, b) != MP_LT) {
+ /* Copy the sign from the first */
+ c->sign = sa;
+ /* The first has a larger or equal magnitude */
+ res = s_mp_sub (a, b, c);
+ } else {
+ /* The result has the *opposite* sign from */
+ /* the first number. */
+ c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
+ /* The second has a larger magnitude */
+ res = s_mp_sub (b, a, c);
+ }
+ }
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sub.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_sub.c */
+
+/* Start: bn_mp_sub_d.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* single digit subtraction */
+int
+mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
+{
+ mp_digit *tmpa, *tmpc, mu;
+ int res, ix, oldused;
+
+ /* grow c as required */
+ if (c->alloc < a->used + 1) {
+ if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* if a is negative just do an unsigned
+ * addition [with fudged signs]
+ */
+ if (a->sign == MP_NEG) {
+ a->sign = MP_ZPOS;
+ res = mp_add_d(a, b, c);
+ a->sign = c->sign = MP_NEG;
+
+ /* clamp */
+ mp_clamp(c);
+
+ return res;
+ }
+
+ /* setup regs */
+ oldused = c->used;
+ tmpa = a->dp;
+ tmpc = c->dp;
+
+ /* if a <= b simply fix the single digit */
+ if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
+ if (a->used == 1) {
+ *tmpc++ = b - *tmpa;
+ } else {
+ *tmpc++ = b;
+ }
+ ix = 1;
+
+ /* negative/1digit */
+ c->sign = MP_NEG;
+ c->used = 1;
+ } else {
+ /* positive/size */
+ c->sign = MP_ZPOS;
+ c->used = a->used;
+
+ /* subtract first digit */
+ *tmpc = *tmpa++ - b;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+
+ /* handle rest of the digits */
+ for (ix = 1; ix < a->used; ix++) {
+ *tmpc = *tmpa++ - mu;
+ mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+ *tmpc++ &= MP_MASK;
+ }
+ }
+
+ /* zero excess digits */
+ while (ix++ < oldused) {
+ *tmpc++ = 0;
+ }
+ mp_clamp(c);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_sub_d.c,v $ */
+/* $Revision: 1.5 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_sub_d.c */
+
+/* Start: bn_mp_submod.c */
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* d = a - b (mod c) */
+int
+mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ int res;
+ mp_int t;
+
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+ return res;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_submod.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_submod.c */
+
+/* Start: bn_mp_to_signed_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin (mp_int * a, unsigned char *b)
+{
+ int res;
+
+ if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
+ return res;
+ }
+ b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_to_signed_bin.c */
+
+/* Start: bn_mp_to_signed_bin_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in signed [big endian] format */
+int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+ if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_signed_bin_size(a);
+ return mp_to_signed_bin(a, b);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_signed_bin_n.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_to_signed_bin_n.c */
+
+/* Start: bn_mp_to_unsigned_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
+{
+ int x, res;
+ mp_int t;
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ x = 0;
+ while (mp_iszero (&t) == 0) {
+#ifndef MP_8BIT
+ b[x++] = (unsigned char) (t.dp[0] & 255);
+#else
+ b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
+#endif
+ if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ }
+ bn_reverse (b, x);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_to_unsigned_bin.c */
+
+/* Start: bn_mp_to_unsigned_bin_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* store in unsigned [big endian] format */
+int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
+{
+ if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
+ return MP_VAL;
+ }
+ *outlen = mp_unsigned_bin_size(a);
+ return mp_to_unsigned_bin(a, b);
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_to_unsigned_bin_n.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_to_unsigned_bin_n.c */
+
+/* Start: bn_mp_toom_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower
+ * asymptotic running time of O(N**1.464). This algorithm is
+ * only particularly useful on VERY large inputs
+ * (we're talking 1000s of digits here...).
+*/
+int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
+ int res, B;
+
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* B */
+ B = MIN(a->used, b->used) / 3;
+
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* b = b2 * B**2 + b1 * B + b0 */
+ if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(b, &b1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b1, B);
+ mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+
+ if ((res = mp_copy(b, &b2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&b2, B*2);
+
+ /* w0 = a0*b0 */
+ if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * b2 */
+ if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+
+
+ /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* now solve the matrix
+
+ 0 0 0 0 1
+ 1 2 4 8 16
+ 1 1 1 1 1
+ 16 8 4 2 1
+ 1 0 0 0 0
+
+ using 12 subtractions, 4 shifts,
+ 2 small divisions and 1 small multiplication
+ */
+
+ /* r1 - r4 */
+ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r0 */
+ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/2 */
+ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/2 */
+ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r2 - r0 - r4 */
+ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - 8r0 */
+ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - 8r4 */
+ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* 3r2 - r1 - r3 */
+ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/3 */
+ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/3 */
+ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* at this point shift W[n] by B*n */
+ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
+ &a0, &a1, &a2, &b0, &b1,
+ &b2, &tmp1, &tmp2, NULL);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_toom_mul.c */
+
+/* Start: bn_mp_toom_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* squaring using Toom-Cook 3-way algorithm */
+int
+mp_toom_sqr(mp_int *a, mp_int *b)
+{
+ mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
+ int res, B;
+
+ /* init temps */
+ if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* B */
+ B = a->used / 3;
+
+ /* a = a2 * B**2 + a1 * B + a0 */
+ if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a1, B);
+ mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+
+ if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+ goto ERR;
+ }
+ mp_rshd(&a2, B*2);
+
+ /* w0 = a0*a0 */
+ if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w4 = a2 * a2 */
+ if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w1 = (a2 + 2(a1 + 2a0))**2 */
+ if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* w3 = (a0 + 2(a1 + 2a2))**2 */
+ if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+
+
+ /* w2 = (a2 + a1 + a0)**2 */
+ if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* now solve the matrix
+
+ 0 0 0 0 1
+ 1 2 4 8 16
+ 1 1 1 1 1
+ 16 8 4 2 1
+ 1 0 0 0 0
+
+ using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
+ */
+
+ /* r1 - r4 */
+ if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r0 */
+ if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/2 */
+ if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/2 */
+ if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r2 - r0 - r4 */
+ if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - 8r0 */
+ if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - 8r4 */
+ if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* 3r2 - r1 - r3 */
+ if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1 - r2 */
+ if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3 - r2 */
+ if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r1/3 */
+ if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+ /* r3/3 */
+ if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ /* at this point shift W[n] by B*n */
+ if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+ goto ERR;
+ }
+ if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
+ goto ERR;
+ }
+
+ERR:
+ mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
+ return res;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toom_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_toom_sqr.c */
+
+/* Start: bn_mp_toradix.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* stores a bignum as a ASCII string in a given radix (2..64) */
+int mp_toradix (mp_int * a, char *str, int radix)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+ char *_s = str;
+
+ /* check range of the radix */
+ if (radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* quick out if its zero */
+ if (mp_iszero(a) == 1) {
+ *str++ = '0';
+ *str = '\0';
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* if it is negative output a - */
+ if (t.sign == MP_NEG) {
+ ++_s;
+ *str++ = '-';
+ t.sign = MP_ZPOS;
+ }
+
+ digs = 0;
+ while (mp_iszero (&t) == 0) {
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ *str++ = mp_s_rmap[d];
+ ++digs;
+ }
+
+ /* reverse the digits of the string. In this case _s points
+ * to the first digit [exluding the sign] of the number]
+ */
+ bn_reverse ((unsigned char *)_s, digs);
+
+ /* append a NULL so the string is properly terminated */
+ *str = '\0';
+
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toradix.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_toradix.c */
+
+/* Start: bn_mp_toradix_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_N_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* stores a bignum as a ASCII string in a given radix (2..64)
+ *
+ * Stores upto maxlen-1 chars and always a NULL byte
+ */
+int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
+{
+ int res, digs;
+ mp_int t;
+ mp_digit d;
+ char *_s = str;
+
+ /* check range of the maxlen, radix */
+ if (maxlen < 2 || radix < 2 || radix > 64) {
+ return MP_VAL;
+ }
+
+ /* quick out if its zero */
+ if (mp_iszero(a) == MP_YES) {
+ *str++ = '0';
+ *str = '\0';
+ return MP_OKAY;
+ }
+
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+
+ /* if it is negative output a - */
+ if (t.sign == MP_NEG) {
+ /* we have to reverse our digits later... but not the - sign!! */
+ ++_s;
+
+ /* store the flag and mark the number as positive */
+ *str++ = '-';
+ t.sign = MP_ZPOS;
+
+ /* subtract a char */
+ --maxlen;
+ }
+
+ digs = 0;
+ while (mp_iszero (&t) == 0) {
+ if (--maxlen < 1) {
+ /* no more room */
+ break;
+ }
+ if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ *str++ = mp_s_rmap[d];
+ ++digs;
+ }
+
+ /* reverse the digits of the string. In this case _s points
+ * to the first digit [exluding the sign] of the number
+ */
+ bn_reverse ((unsigned char *)_s, digs);
+
+ /* append a NULL so the string is properly terminated */
+ *str = '\0';
+
+ mp_clear (&t);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_toradix_n.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_toradix_n.c */
+
+/* Start: bn_mp_unsigned_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* get the size for an unsigned equivalent */
+int mp_unsigned_bin_size (mp_int * a)
+{
+ int size = mp_count_bits (a);
+ return (size / 8 + ((size & 7) != 0 ? 1 : 0));
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_unsigned_bin_size.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_unsigned_bin_size.c */
+
+/* Start: bn_mp_xor.c */
+#include <tommath.h>
+#ifdef BN_MP_XOR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* XOR two ints together */
+int
+mp_xor (mp_int * a, mp_int * b, mp_int * c)
+{
+ int res, ix, px;
+ mp_int t, *x;
+
+ if (a->used > b->used) {
+ if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+ return res;
+ }
+ px = b->used;
+ x = b;
+ } else {
+ if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+ return res;
+ }
+ px = a->used;
+ x = a;
+ }
+
+ for (ix = 0; ix < px; ix++) {
+ t.dp[ix] ^= x->dp[ix];
+ }
+ mp_clamp (&t);
+ mp_exch (c, &t);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_xor.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_xor.c */
+
+/* Start: bn_mp_zero.c */
+#include <tommath.h>
+#ifdef BN_MP_ZERO_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* set to zero */
+void mp_zero (mp_int * a)
+{
+ int n;
+ mp_digit *tmp;
+
+ a->sign = MP_ZPOS;
+ a->used = 0;
+
+ tmp = a->dp;
+ for (n = 0; n < a->alloc; n++) {
+ *tmp++ = 0;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_mp_zero.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_mp_zero.c */
+
+/* Start: bn_prime_tab.c */
+#include <tommath.h>
+#ifdef BN_PRIME_TAB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+const mp_digit ltm_prime_tab[] = {
+ 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
+ 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
+ 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
+ 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
+#ifndef MP_8BIT
+ 0x0083,
+ 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
+ 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
+ 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
+ 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
+
+ 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
+ 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
+ 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
+ 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
+ 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
+ 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
+ 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
+ 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
+
+ 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
+ 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
+ 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
+ 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
+ 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
+ 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
+ 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
+ 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
+
+ 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
+ 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
+ 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
+ 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
+ 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
+ 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
+ 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
+ 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
+#endif
+};
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_prime_tab.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_prime_tab.c */
+
+/* Start: bn_reverse.c */
+#include <tommath.h>
+#ifdef BN_REVERSE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* reverse an array, used for radix code */
+void
+bn_reverse (unsigned char *s, int len)
+{
+ int ix, iy;
+ unsigned char t;
+
+ ix = 0;
+ iy = len - 1;
+ while (ix < iy) {
+ t = s[ix];
+ s[ix] = s[iy];
+ s[iy] = t;
+ ++ix;
+ --iy;
+ }
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_reverse.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_reverse.c */
+
+/* Start: bn_s_mp_add.c */
+#include <tommath.h>
+#ifdef BN_S_MP_ADD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* low level addition, based on HAC pp.594, Algorithm 14.7 */
+int
+s_mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int *x;
+ int olduse, res, min, max;
+
+ /* find sizes, we let |a| <= |b| which means we have to sort
+ * them. "x" will point to the input with the most digits
+ */
+ if (a->used > b->used) {
+ min = b->used;
+ max = a->used;
+ x = a;
+ } else {
+ min = a->used;
+ max = b->used;
+ x = b;
+ }
+
+ /* init result */
+ if (c->alloc < max + 1) {
+ if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
+ return res;
+ }
+ }
+
+ /* get old used digit count and set new one */
+ olduse = c->used;
+ c->used = max + 1;
+
+ {
+ register mp_digit u, *tmpa, *tmpb, *tmpc;
+ register int i;
+
+ /* alias for digit pointers */
+
+ /* first input */
+ tmpa = a->dp;
+
+ /* second input */
+ tmpb = b->dp;
+
+ /* destination */
+ tmpc = c->dp;
+
+ /* zero the carry */
+ u = 0;
+ for (i = 0; i < min; i++) {
+ /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
+ *tmpc = *tmpa++ + *tmpb++ + u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)DIGIT_BIT);
+
+ /* take away carry bit from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* now copy higher words if any, that is in A+B
+ * if A or B has more digits add those in
+ */
+ if (min != max) {
+ for (; i < max; i++) {
+ /* T[i] = X[i] + U */
+ *tmpc = x->dp[i] + u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)DIGIT_BIT);
+
+ /* take away carry bit from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+ }
+
+ /* add carry */
+ *tmpc++ = u;
+
+ /* clear digits above oldused */
+ for (i = c->used; i < olduse; i++) {
+ *tmpc++ = 0;
+ }
+ }
+
+ mp_clamp (c);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_add.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_s_mp_add.c */
+
+/* Start: bn_s_mp_exptmod.c */
+#include <tommath.h>
+#ifdef BN_S_MP_EXPTMOD_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+#ifdef MP_LOW_MEM
+ #define TAB_SIZE 32
+#else
+ #define TAB_SIZE 256
+#endif
+
+int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+ mp_int M[TAB_SIZE], res, mu;
+ mp_digit buf;
+ int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+ int (*redux)(mp_int*,mp_int*,mp_int*);
+
+ /* find window size */
+ x = mp_count_bits (X);
+ if (x <= 7) {
+ winsize = 2;
+ } else if (x <= 36) {
+ winsize = 3;
+ } else if (x <= 140) {
+ winsize = 4;
+ } else if (x <= 450) {
+ winsize = 5;
+ } else if (x <= 1303) {
+ winsize = 6;
+ } else if (x <= 3529) {
+ winsize = 7;
+ } else {
+ winsize = 8;
+ }
+
+#ifdef MP_LOW_MEM
+ if (winsize > 5) {
+ winsize = 5;
+ }
+#endif
+
+ /* init M array */
+ /* init first cell */
+ if ((err = mp_init(&M[1])) != MP_OKAY) {
+ return err;
+ }
+
+ /* now init the second half of the array */
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ if ((err = mp_init(&M[x])) != MP_OKAY) {
+ for (y = 1<<(winsize-1); y < x; y++) {
+ mp_clear (&M[y]);
+ }
+ mp_clear(&M[1]);
+ return err;
+ }
+ }
+
+ /* create mu, used for Barrett reduction */
+ if ((err = mp_init (&mu)) != MP_OKAY) {
+ goto LBL_M;
+ }
+
+ if (redmode == 0) {
+ if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce;
+ } else {
+ if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ redux = mp_reduce_2k_l;
+ }
+
+ /* create M table
+ *
+ * The M table contains powers of the base,
+ * e.g. M[x] = G**x mod P
+ *
+ * The first half of the table is not
+ * computed though accept for M[0] and M[1]
+ */
+ if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* compute the value at M[1<<(winsize-1)] by squaring
+ * M[1] (winsize-1) times
+ */
+ if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ for (x = 0; x < (winsize - 1); x++) {
+ /* square it */
+ if ((err = mp_sqr (&M[1 << (winsize - 1)],
+ &M[1 << (winsize - 1)])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+
+ /* reduce modulo P */
+ if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
+ * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
+ */
+ for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+ if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ }
+
+ /* setup result */
+ if ((err = mp_init (&res)) != MP_OKAY) {
+ goto LBL_MU;
+ }
+ mp_set (&res, 1);
+
+ /* set initial mode and bit cnt */
+ mode = 0;
+ bitcnt = 1;
+ buf = 0;
+ digidx = X->used - 1;
+ bitcpy = 0;
+ bitbuf = 0;
+
+ for (;;) {
+ /* grab next digit as required */
+ if (--bitcnt == 0) {
+ /* if digidx == -1 we are out of digits */
+ if (digidx == -1) {
+ break;
+ }
+ /* read next digit and reset the bitcnt */
+ buf = X->dp[digidx--];
+ bitcnt = (int) DIGIT_BIT;
+ }
+
+ /* grab the next msb from the exponent */
+ y = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
+ buf <<= (mp_digit)1;
+
+ /* if the bit is zero and mode == 0 then we ignore it
+ * These represent the leading zero bits before the first 1 bit
+ * in the exponent. Technically this opt is not required but it
+ * does lower the # of trivial squaring/reductions used
+ */
+ if (mode == 0 && y == 0) {
+ continue;
+ }
+
+ /* if the bit is zero and mode == 1 then we square */
+ if (mode == 1 && y == 0) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ continue;
+ }
+
+ /* else we add it to the window */
+ bitbuf |= (y << (winsize - ++bitcpy));
+ mode = 2;
+
+ if (bitcpy == winsize) {
+ /* ok window is filled so square as required and multiply */
+ /* square first */
+ for (x = 0; x < winsize; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ /* empty window and reset */
+ bitcpy = 0;
+ bitbuf = 0;
+ mode = 1;
+ }
+ }
+
+ /* if bits remain then square/multiply */
+ if (mode == 2 && bitcpy > 0) {
+ /* square then multiply if the bit is set */
+ for (x = 0; x < bitcpy; x++) {
+ if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+
+ bitbuf <<= 1;
+ if ((bitbuf & (1 << winsize)) != 0) {
+ /* then multiply */
+ if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ if ((err = redux (&res, P, &mu)) != MP_OKAY) {
+ goto LBL_RES;
+ }
+ }
+ }
+ }
+
+ mp_exch (&res, Y);
+ err = MP_OKAY;
+LBL_RES:mp_clear (&res);
+LBL_MU:mp_clear (&mu);
+LBL_M:
+ mp_clear(&M[1]);
+ for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+ mp_clear (&M[x]);
+ }
+ return err;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_exptmod.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_s_mp_exptmod.c */
+
+/* Start: bn_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiplies |a| * |b| and only computes upto digs digits of result
+ * HAC pp. 595, Algorithm 14.12 Modified so you can control how
+ * many digits of output are created.
+ */
+int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ mp_int t;
+ int res, pa, pb, ix, iy;
+ mp_digit u;
+ mp_word r;
+ mp_digit tmpx, *tmpt, *tmpy;
+
+ /* can we use the fast multiplier? */
+ if (((digs) < MP_WARRAY) &&
+ MIN (a->used, b->used) <
+ (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_s_mp_mul_digs (a, b, c, digs);
+ }
+
+ if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
+ return res;
+ }
+ t.used = digs;
+
+ /* compute the digits of the product directly */
+ pa = a->used;
+ for (ix = 0; ix < pa; ix++) {
+ /* set the carry to zero */
+ u = 0;
+
+ /* limit ourselves to making digs digits of output */
+ pb = MIN (b->used, digs - ix);
+
+ /* setup some aliases */
+ /* copy of the digit from a used within the nested loop */
+ tmpx = a->dp[ix];
+
+ /* an alias for the destination shifted ix places */
+ tmpt = t.dp + ix;
+
+ /* an alias for the digits of b */
+ tmpy = b->dp;
+
+ /* compute the columns of the output and propagate the carry */
+ for (iy = 0; iy < pb; iy++) {
+ /* compute the column as a mp_word */
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
+
+ /* the new column is the lower part of the result */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get the carry word from the result */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+ /* set carry if it is placed below digs */
+ if (ix + iy < digs) {
+ *tmpt = u;
+ }
+ }
+
+ mp_clamp (&t);
+ mp_exch (&t, c);
+
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_digs.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_s_mp_mul_digs.c */
+
+/* Start: bn_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* multiplies |a| * |b| and does not compute the lower digs digits
+ * [meant to get the higher part of the product]
+ */
+int
+s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+ mp_int t;
+ int res, pa, pb, ix, iy;
+ mp_digit u;
+ mp_word r;
+ mp_digit tmpx, *tmpt, *tmpy;
+
+ /* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ if (((a->used + b->used + 1) < MP_WARRAY)
+ && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+ return fast_s_mp_mul_high_digs (a, b, c, digs);
+ }
+#endif
+
+ if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
+ return res;
+ }
+ t.used = a->used + b->used + 1;
+
+ pa = a->used;
+ pb = b->used;
+ for (ix = 0; ix < pa; ix++) {
+ /* clear the carry */
+ u = 0;
+
+ /* left hand side of A[ix] * B[iy] */
+ tmpx = a->dp[ix];
+
+ /* alias to the address of where the digits will be stored */
+ tmpt = &(t.dp[digs]);
+
+ /* alias for where to read the right hand side from */
+ tmpy = b->dp + (digs - ix);
+
+ for (iy = digs - ix; iy < pb; iy++) {
+ /* calculate the double precision result */
+ r = ((mp_word)*tmpt) +
+ ((mp_word)tmpx) * ((mp_word)*tmpy++) +
+ ((mp_word) u);
+
+ /* get the lower part */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* carry the carry */
+ u = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+ }
+ *tmpt = u;
+ }
+ mp_clamp (&t);
+ mp_exch (&t, c);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_mul_high_digs.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_s_mp_mul_high_digs.c */
+
+/* Start: bn_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SQR_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
+int s_mp_sqr (mp_int * a, mp_int * b)
+{
+ mp_int t;
+ int res, ix, iy, pa;
+ mp_word r;
+ mp_digit u, tmpx, *tmpt;
+
+ pa = a->used;
+ if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
+ return res;
+ }
+
+ /* default used is maximum possible size */
+ t.used = 2*pa + 1;
+
+ for (ix = 0; ix < pa; ix++) {
+ /* first calculate the digit at 2*ix */
+ /* calculate double precision result */
+ r = ((mp_word) t.dp[2*ix]) +
+ ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
+
+ /* store lower part in result */
+ t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get the carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+
+ /* left hand side of A[ix] * A[iy] */
+ tmpx = a->dp[ix];
+
+ /* alias for where to store the results */
+ tmpt = t.dp + (2*ix + 1);
+
+ for (iy = ix + 1; iy < pa; iy++) {
+ /* first calculate the product */
+ r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
+
+ /* now calculate the double precision result, note we use
+ * addition instead of *2 since it's easier to optimize
+ */
+ r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
+
+ /* store lower part */
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+ /* get carry */
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ }
+ /* propagate upwards */
+ while (u != ((mp_digit) 0)) {
+ r = ((mp_word) *tmpt) + ((mp_word) u);
+ *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ }
+ }
+
+ mp_clamp (&t);
+ mp_exch (&t, b);
+ mp_clear (&t);
+ return MP_OKAY;
+}
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_sqr.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_s_mp_sqr.c */
+
+/* Start: bn_s_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SUB_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
+int
+s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
+{
+ int olduse, res, min, max;
+
+ /* find sizes */
+ min = b->used;
+ max = a->used;
+
+ /* init result */
+ if (c->alloc < max) {
+ if ((res = mp_grow (c, max)) != MP_OKAY) {
+ return res;
+ }
+ }
+ olduse = c->used;
+ c->used = max;
+
+ {
+ register mp_digit u, *tmpa, *tmpb, *tmpc;
+ register int i;
+
+ /* alias for digit pointers */
+ tmpa = a->dp;
+ tmpb = b->dp;
+ tmpc = c->dp;
+
+ /* set carry to zero */
+ u = 0;
+ for (i = 0; i < min; i++) {
+ /* T[i] = A[i] - B[i] - U */
+ *tmpc = *tmpa++ - *tmpb++ - u;
+
+ /* U = carry bit of T[i]
+ * Note this saves performing an AND operation since
+ * if a carry does occur it will propagate all the way to the
+ * MSB. As a result a single shift is enough to get the carry
+ */
+ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+
+ /* Clear carry from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* now copy higher words if any, e.g. if A has more digits than B */
+ for (; i < max; i++) {
+ /* T[i] = A[i] - U */
+ *tmpc = *tmpa++ - u;
+
+ /* U = carry bit of T[i] */
+ u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+
+ /* Clear carry from T[i] */
+ *tmpc++ &= MP_MASK;
+ }
+
+ /* clear digits above used (since we may not have grown result above) */
+ for (i = c->used; i < olduse; i++) {
+ *tmpc++ = 0;
+ }
+ }
+
+ mp_clamp (c);
+ return MP_OKAY;
+}
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bn_s_mp_sub.c,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bn_s_mp_sub.c */
+
+/* Start: bncore.c */
+#include <tommath.h>
+#ifdef BNCORE_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+/* Known optimal configurations
+
+ CPU /Compiler /MUL CUTOFF/SQR CUTOFF
+-------------------------------------------------------------
+ Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
+ AMD Athlon64 /GCC v3.4.4 / 80/ 120/LTM 0.35
+
+*/
+
+int KARATSUBA_MUL_CUTOFF = 80, /* Min. number of digits before Karatsuba multiplication is used. */
+ KARATSUBA_SQR_CUTOFF = 120, /* Min. number of digits before Karatsuba squaring is used. */
+
+ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
+ TOOM_SQR_CUTOFF = 400;
+#endif
+
+/* $Source: /cvs/libtom/libtommath/bncore.c,v $ */
+/* $Revision: 1.4 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
+
+/* End: bncore.c */
+
+
+/* EOF */
diff --git a/libtommath/pretty.build b/libtommath/pretty.build
new file mode 100644
index 0000000..a708b8a
--- /dev/null
+++ b/libtommath/pretty.build
@@ -0,0 +1,66 @@
+#!/bin/perl -w
+#
+# Cute little builder for perl
+# Total waste of development time...
+#
+# This will build all the object files and then the archive .a file
+# requires GCC, GNU make and a sense of humour.
+#
+# Tom St Denis
+use strict;
+
+my $count = 0;
+my $starttime = time;
+my $rate = 0;
+print "Scanning for source files...\n";
+foreach my $filename (glob "*.c") {
+ ++$count;
+}
+print "Source files to build: $count\nBuilding...\n";
+my $i = 0;
+my $lines = 0;
+my $filesbuilt = 0;
+foreach my $filename (glob "*.c") {
+ printf("Building %3.2f%%, ", (++$i/$count)*100.0);
+ if ($i % 4 == 0) { print "/, "; }
+ if ($i % 4 == 1) { print "-, "; }
+ if ($i % 4 == 2) { print "\\, "; }
+ if ($i % 4 == 3) { print "|, "; }
+ if ($rate > 0) {
+ my $tleft = ($count - $i) / $rate;
+ my $tsec = $tleft%60;
+ my $tmin = ($tleft/60)%60;
+ my $thour = ($tleft/3600)%60;
+ printf("%2d:%02d:%02d left, ", $thour, $tmin, $tsec);
+ }
+ my $cnt = ($i/$count)*30.0;
+ my $x = 0;
+ print "[";
+ for (; $x < $cnt; $x++) { print "#"; }
+ for (; $x < 30; $x++) { print " "; }
+ print "]\r";
+ my $tmp = $filename;
+ $tmp =~ s/\.c/".o"/ge;
+ if (open(SRC, "<$tmp")) {
+ close SRC;
+ } else {
+ !system("make $tmp > /dev/null 2>/dev/null") or die "\nERROR: Failed to make $tmp!!!\n";
+ open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
+ ++$lines while (<SRC>);
+ close SRC or die "Error closing $filename after reading: $!";
+ ++$filesbuilt;
+ }
+
+ # update timer
+ if (time != $starttime) {
+ my $delay = time - $starttime;
+ $rate = $i/$delay;
+ }
+}
+
+# finish building the library
+printf("\nFinished building source (%d seconds, %3.2f files per second).\n", time - $starttime, $rate);
+print "Compiled approximately $filesbuilt files and $lines lines of code.\n";
+print "Doing final make (building archive...)\n";
+!system("make > /dev/null 2>/dev/null") or die "\nERROR: Failed to perform last make command!!!\n";
+print "done.\n";
\ No newline at end of file
diff --git a/libtommath/tombc/grammar.txt b/libtommath/tombc/grammar.txt
new file mode 100644
index 0000000..a780e75
--- /dev/null
+++ b/libtommath/tombc/grammar.txt
@@ -0,0 +1,35 @@
+program := program statement | statement | empty
+statement := { statement } |
+ identifier = numexpression; |
+ identifier[numexpression] = numexpression; |
+ function(expressionlist); |
+ for (identifer = numexpression; numexpression; identifier = numexpression) { statement } |
+ while (numexpression) { statement } |
+ if (numexpresion) { statement } elif |
+ break; |
+ continue;
+
+elif := else statement | empty
+function := abs | countbits | exptmod | jacobi | print | isprime | nextprime | issquare | readinteger | exit
+expressionlist := expressionlist, expression | expression
+
+// LR(1) !!!?
+expression := string | numexpression
+numexpression := cmpexpr && cmpexpr | cmpexpr \|\| cmpexpr | cmpexpr
+cmpexpr := boolexpr < boolexpr | boolexpr > boolexpr | boolexpr == boolexpr |
+ boolexpr <= boolexpr | boolexpr >= boolexpr | boolexpr
+boolexpr := shiftexpr & shiftexpr | shiftexpr ^ shiftexpr | shiftexpr \| shiftexpr | shiftexpr
+shiftexpr := addsubexpr << addsubexpr | addsubexpr >> addsubexpr | addsubexpr
+addsubexpr := mulexpr + mulexpr | mulexpr - mulexpr | mulexpr
+mulexpr := expr * expr | expr / expr | expr % expr | expr
+expr := -nexpr | nexpr
+nexpr := integer | identifier | ( numexpression ) | identifier[numexpression]
+
+identifier := identifer digits | identifier alpha | alpha
+alpha := a ... z | A ... Z
+integer := hexnumber | digits
+hexnumber := 0xhexdigits
+hexdigits := hexdigits hexdigit | hexdigit
+hexdigit := 0 ... 9 | a ... f | A ... F
+digits := digits digit | digit
+digit := 0 ... 9
diff --git a/libtommath/tommath.h b/libtommath/tommath.h
new file mode 100644
index 0000000..1ead3d0
--- /dev/null
+++ b/libtommath/tommath.h
@@ -0,0 +1,584 @@
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+#ifndef BN_H_
+#define BN_H_
+
+#include <stdio.h>
+#include <string.h>
+#include <stdlib.h>
+#include <ctype.h>
+#include <limits.h>
+
+#include "tommath_class.h"
+
+#ifndef MIN
+ #define MIN(x,y) ((x)<(y)?(x):(y))
+#endif
+
+#ifndef MAX
+ #define MAX(x,y) ((x)>(y)?(x):(y))
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+
+/* C++ compilers don't like assigning void * to mp_digit * */
+#define OPT_CAST(x) (x *)
+
+#else
+
+/* C on the other hand doesn't care */
+#define OPT_CAST(x)
+
+#endif
+
+
+/* detect 64-bit mode if possible */
+#if defined(__x86_64__)
+ #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
+ #define MP_64BIT
+ #endif
+#endif
+
+/* some default configurations.
+ *
+ * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
+ * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
+ *
+ * At the very least a mp_digit must be able to hold 7 bits
+ * [any size beyond that is ok provided it doesn't overflow the data type]
+ */
+#ifdef MP_8BIT
+ typedef unsigned char mp_digit;
+ typedef unsigned short mp_word;
+#elif defined(MP_16BIT)
+ typedef unsigned short mp_digit;
+ typedef unsigned long mp_word;
+#elif defined(MP_64BIT)
+ /* for GCC only on supported platforms */
+#ifndef CRYPT
+ typedef unsigned long long ulong64;
+ typedef signed long long long64;
+#endif
+
+ typedef unsigned long mp_digit;
+ typedef unsigned long mp_word __attribute__ ((mode(TI)));
+
+ #define DIGIT_BIT 60
+#else
+ /* this is the default case, 28-bit digits */
+
+ /* this is to make porting into LibTomCrypt easier :-) */
+#ifndef CRYPT
+ #if defined(_MSC_VER) || defined(__BORLANDC__)
+ typedef unsigned __int64 ulong64;
+ typedef signed __int64 long64;
+ #else
+ typedef unsigned long long ulong64;
+ typedef signed long long long64;
+ #endif
+#endif
+
+ typedef unsigned long mp_digit;
+ typedef ulong64 mp_word;
+
+#ifdef MP_31BIT
+ /* this is an extension that uses 31-bit digits */
+ #define DIGIT_BIT 31
+#else
+ /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
+ #define DIGIT_BIT 28
+ #define MP_28BIT
+#endif
+#endif
+
+/* define heap macros */
+#ifndef CRYPT
+ /* default to libc stuff */
+ #ifndef XMALLOC
+ #define XMALLOC malloc
+ #define XFREE free
+ #define XREALLOC realloc
+ #define XCALLOC calloc
+ #else
+ /* prototypes for our heap functions */
+ extern void *XMALLOC(size_t n);
+ extern void *XREALLOC(void *p, size_t n);
+ extern void *XCALLOC(size_t n, size_t s);
+ extern void XFREE(void *p);
+ #endif
+#endif
+
+
+/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
+#ifndef DIGIT_BIT
+ #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */
+#endif
+
+#define MP_DIGIT_BIT DIGIT_BIT
+#define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
+#define MP_DIGIT_MAX MP_MASK
+
+/* equalities */
+#define MP_LT -1 /* less than */
+#define MP_EQ 0 /* equal to */
+#define MP_GT 1 /* greater than */
+
+#define MP_ZPOS 0 /* positive integer */
+#define MP_NEG 1 /* negative */
+
+#define MP_OKAY 0 /* ok result */
+#define MP_MEM -2 /* out of mem */
+#define MP_VAL -3 /* invalid input */
+#define MP_RANGE MP_VAL
+
+#define MP_YES 1 /* yes response */
+#define MP_NO 0 /* no response */
+
+/* Primality generation flags */
+#define LTM_PRIME_BBS 0x0001 /* BBS style prime */
+#define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
+#define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
+
+typedef int mp_err;
+
+/* you'll have to tune these... */
+extern int KARATSUBA_MUL_CUTOFF,
+ KARATSUBA_SQR_CUTOFF,
+ TOOM_MUL_CUTOFF,
+ TOOM_SQR_CUTOFF;
+
+/* define this to use lower memory usage routines (exptmods mostly) */
+/* #define MP_LOW_MEM */
+
+/* default precision */
+#ifndef MP_PREC
+ #ifndef MP_LOW_MEM
+ #define MP_PREC 32 /* default digits of precision */
+ #else
+ #define MP_PREC 8 /* default digits of precision */
+ #endif
+#endif
+
+/* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
+#define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
+
+/* the infamous mp_int structure */
+typedef struct {
+ int used, alloc, sign;
+ mp_digit *dp;
+} mp_int;
+
+/* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
+typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
+
+
+#define USED(m) ((m)->used)
+#define DIGIT(m,k) ((m)->dp[(k)])
+#define SIGN(m) ((m)->sign)
+
+/* error code to char* string */
+char *mp_error_to_string(int code);
+
+/* ---> init and deinit bignum functions <--- */
+/* init a bignum */
+int mp_init(mp_int *a);
+
+/* free a bignum */
+void mp_clear(mp_int *a);
+
+/* init a null terminated series of arguments */
+int mp_init_multi(mp_int *mp, ...);
+
+/* clear a null terminated series of arguments */
+void mp_clear_multi(mp_int *mp, ...);
+
+/* exchange two ints */
+void mp_exch(mp_int *a, mp_int *b);
+
+/* shrink ram required for a bignum */
+int mp_shrink(mp_int *a);
+
+/* grow an int to a given size */
+int mp_grow(mp_int *a, int size);
+
+/* init to a given number of digits */
+int mp_init_size(mp_int *a, int size);
+
+/* ---> Basic Manipulations <--- */
+#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
+#define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
+#define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
+
+/* set to zero */
+void mp_zero(mp_int *a);
+
+/* set to a digit */
+void mp_set(mp_int *a, mp_digit b);
+
+/* set a 32-bit const */
+int mp_set_int(mp_int *a, unsigned long b);
+
+/* get a 32-bit value */
+unsigned long mp_get_int(mp_int * a);
+
+/* initialize and set a digit */
+int mp_init_set (mp_int * a, mp_digit b);
+
+/* initialize and set 32-bit value */
+int mp_init_set_int (mp_int * a, unsigned long b);
+
+/* copy, b = a */
+int mp_copy(mp_int *a, mp_int *b);
+
+/* inits and copies, a = b */
+int mp_init_copy(mp_int *a, mp_int *b);
+
+/* trim unused digits */
+void mp_clamp(mp_int *a);
+
+/* ---> digit manipulation <--- */
+
+/* right shift by "b" digits */
+void mp_rshd(mp_int *a, int b);
+
+/* left shift by "b" digits */
+int mp_lshd(mp_int *a, int b);
+
+/* c = a / 2**b */
+int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
+
+/* b = a/2 */
+int mp_div_2(mp_int *a, mp_int *b);
+
+/* c = a * 2**b */
+int mp_mul_2d(mp_int *a, int b, mp_int *c);
+
+/* b = a*2 */
+int mp_mul_2(mp_int *a, mp_int *b);
+
+/* c = a mod 2**d */
+int mp_mod_2d(mp_int *a, int b, mp_int *c);
+
+/* computes a = 2**b */
+int mp_2expt(mp_int *a, int b);
+
+/* Counts the number of lsbs which are zero before the first zero bit */
+int mp_cnt_lsb(mp_int *a);
+
+/* I Love Earth! */
+
+/* makes a pseudo-random int of a given size */
+int mp_rand(mp_int *a, int digits);
+
+/* ---> binary operations <--- */
+/* c = a XOR b */
+int mp_xor(mp_int *a, mp_int *b, mp_int *c);
+
+/* c = a OR b */
+int mp_or(mp_int *a, mp_int *b, mp_int *c);
+
+/* c = a AND b */
+int mp_and(mp_int *a, mp_int *b, mp_int *c);
+
+/* ---> Basic arithmetic <--- */
+
+/* b = -a */
+int mp_neg(mp_int *a, mp_int *b);
+
+/* b = |a| */
+int mp_abs(mp_int *a, mp_int *b);
+
+/* compare a to b */
+int mp_cmp(mp_int *a, mp_int *b);
+
+/* compare |a| to |b| */
+int mp_cmp_mag(mp_int *a, mp_int *b);
+
+/* c = a + b */
+int mp_add(mp_int *a, mp_int *b, mp_int *c);
+
+/* c = a - b */
+int mp_sub(mp_int *a, mp_int *b, mp_int *c);
+
+/* c = a * b */
+int mp_mul(mp_int *a, mp_int *b, mp_int *c);
+
+/* b = a*a */
+int mp_sqr(mp_int *a, mp_int *b);
+
+/* a/b => cb + d == a */
+int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
+
+/* c = a mod b, 0 <= c < b */
+int mp_mod(mp_int *a, mp_int *b, mp_int *c);
+
+/* ---> single digit functions <--- */
+
+/* compare against a single digit */
+int mp_cmp_d(mp_int *a, mp_digit b);
+
+/* c = a + b */
+int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
+
+/* c = a - b */
+int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
+
+/* c = a * b */
+int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
+
+/* a/b => cb + d == a */
+int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
+
+/* a/3 => 3c + d == a */
+int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
+
+/* c = a**b */
+int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
+
+/* c = a mod b, 0 <= c < b */
+int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
+
+/* ---> number theory <--- */
+
+/* d = a + b (mod c) */
+int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
+
+/* d = a - b (mod c) */
+int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
+
+/* d = a * b (mod c) */
+int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
+
+/* c = a * a (mod b) */
+int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
+
+/* c = 1/a (mod b) */
+int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
+
+/* c = (a, b) */
+int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
+
+/* produces value such that U1*a + U2*b = U3 */
+int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
+
+/* c = [a, b] or (a*b)/(a, b) */
+int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
+
+/* finds one of the b'th root of a, such that |c|**b <= |a|
+ *
+ * returns error if a < 0 and b is even
+ */
+int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
+
+/* special sqrt algo */
+int mp_sqrt(mp_int *arg, mp_int *ret);
+
+/* is number a square? */
+int mp_is_square(mp_int *arg, int *ret);
+
+/* computes the jacobi c = (a | n) (or Legendre if b is prime) */
+int mp_jacobi(mp_int *a, mp_int *n, int *c);
+
+/* used to setup the Barrett reduction for a given modulus b */
+int mp_reduce_setup(mp_int *a, mp_int *b);
+
+/* Barrett Reduction, computes a (mod b) with a precomputed value c
+ *
+ * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
+ * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
+ */
+int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
+
+/* setups the montgomery reduction */
+int mp_montgomery_setup(mp_int *a, mp_digit *mp);
+
+/* computes a = B**n mod b without division or multiplication useful for
+ * normalizing numbers in a Montgomery system.
+ */
+int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
+
+/* computes x/R == x (mod N) via Montgomery Reduction */
+int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
+
+/* returns 1 if a is a valid DR modulus */
+int mp_dr_is_modulus(mp_int *a);
+
+/* sets the value of "d" required for mp_dr_reduce */
+void mp_dr_setup(mp_int *a, mp_digit *d);
+
+/* reduces a modulo b using the Diminished Radix method */
+int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
+
+/* returns true if a can be reduced with mp_reduce_2k */
+int mp_reduce_is_2k(mp_int *a);
+
+/* determines k value for 2k reduction */
+int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
+
+/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
+int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
+
+/* returns true if a can be reduced with mp_reduce_2k_l */
+int mp_reduce_is_2k_l(mp_int *a);
+
+/* determines k value for 2k reduction */
+int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
+
+/* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
+int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
+
+/* d = a**b (mod c) */
+int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
+
+/* ---> Primes <--- */
+
+/* number of primes */
+#ifdef MP_8BIT
+ #define PRIME_SIZE 31
+#else
+ #define PRIME_SIZE 256
+#endif
+
+/* table of first PRIME_SIZE primes */
+extern const mp_digit ltm_prime_tab[];
+
+/* result=1 if a is divisible by one of the first PRIME_SIZE primes */
+int mp_prime_is_divisible(mp_int *a, int *result);
+
+/* performs one Fermat test of "a" using base "b".
+ * Sets result to 0 if composite or 1 if probable prime
+ */
+int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
+
+/* performs one Miller-Rabin test of "a" using base "b".
+ * Sets result to 0 if composite or 1 if probable prime
+ */
+int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
+
+/* This gives [for a given bit size] the number of trials required
+ * such that Miller-Rabin gives a prob of failure lower than 2^-96
+ */
+int mp_prime_rabin_miller_trials(int size);
+
+/* performs t rounds of Miller-Rabin on "a" using the first
+ * t prime bases. Also performs an initial sieve of trial
+ * division. Determines if "a" is prime with probability
+ * of error no more than (1/4)**t.
+ *
+ * Sets result to 1 if probably prime, 0 otherwise
+ */
+int mp_prime_is_prime(mp_int *a, int t, int *result);
+
+/* finds the next prime after the number "a" using "t" trials
+ * of Miller-Rabin.
+ *
+ * bbs_style = 1 means the prime must be congruent to 3 mod 4
+ */
+int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
+
+/* makes a truly random prime of a given size (bytes),
+ * call with bbs = 1 if you want it to be congruent to 3 mod 4
+ *
+ * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
+ * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
+ * so it can be NULL
+ *
+ * The prime generated will be larger than 2^(8*size).
+ */
+#define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
+
+/* makes a truly random prime of a given size (bits),
+ *
+ * Flags are as follows:
+ *
+ * LTM_PRIME_BBS - make prime congruent to 3 mod 4
+ * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
+ * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
+ * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
+ *
+ * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
+ * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
+ * so it can be NULL
+ *
+ */
+int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
+
+/* ---> radix conversion <--- */
+int mp_count_bits(mp_int *a);
+
+int mp_unsigned_bin_size(mp_int *a);
+int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
+int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
+int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
+
+int mp_signed_bin_size(mp_int *a);
+int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
+int mp_to_signed_bin(mp_int *a, unsigned char *b);
+int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
+
+int mp_read_radix(mp_int *a, const char *str, int radix);
+int mp_toradix(mp_int *a, char *str, int radix);
+int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
+int mp_radix_size(mp_int *a, int radix, int *size);
+
+int mp_fread(mp_int *a, int radix, FILE *stream);
+int mp_fwrite(mp_int *a, int radix, FILE *stream);
+
+#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
+#define mp_raw_size(mp) mp_signed_bin_size(mp)
+#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
+#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
+#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
+#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
+
+#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
+#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
+#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
+#define mp_tohex(M, S) mp_toradix((M), (S), 16)
+
+/* lowlevel functions, do not call! */
+int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
+int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
+#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
+int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int fast_s_mp_sqr(mp_int *a, mp_int *b);
+int s_mp_sqr(mp_int *a, mp_int *b);
+int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
+int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
+int mp_karatsuba_sqr(mp_int *a, mp_int *b);
+int mp_toom_sqr(mp_int *a, mp_int *b);
+int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
+int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
+int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
+int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
+void bn_reverse(unsigned char *s, int len);
+
+extern const char *mp_s_rmap;
+
+#ifdef __cplusplus
+ }
+#endif
+
+#endif
+
+
+/* $Source: /cvs/libtom/libtommath/tommath.h,v $ */
+/* $Revision: 1.8 $ */
+/* $Date: 2006/03/31 14:18:44 $ */
diff --git a/libtommath/tommath.out b/libtommath/tommath.out
new file mode 100644
index 0000000..9f62617
--- /dev/null
+++ b/libtommath/tommath.out
@@ -0,0 +1,139 @@
+\BOOKMARK [0][-]{chapter.1}{Introduction}{}
+\BOOKMARK [1][-]{section.1.1}{Multiple Precision Arithmetic}{chapter.1}
+\BOOKMARK [2][-]{subsection.1.1.1}{What is Multiple Precision Arithmetic?}{section.1.1}
+\BOOKMARK [2][-]{subsection.1.1.2}{The Need for Multiple Precision Arithmetic}{section.1.1}
+\BOOKMARK [2][-]{subsection.1.1.3}{Benefits of Multiple Precision Arithmetic}{section.1.1}
+\BOOKMARK [1][-]{section.1.2}{Purpose of This Text}{chapter.1}
+\BOOKMARK [1][-]{section.1.3}{Discussion and Notation}{chapter.1}
+\BOOKMARK [2][-]{subsection.1.3.1}{Notation}{section.1.3}
+\BOOKMARK [2][-]{subsection.1.3.2}{Precision Notation}{section.1.3}
+\BOOKMARK [2][-]{subsection.1.3.3}{Algorithm Inputs and Outputs}{section.1.3}
+\BOOKMARK [2][-]{subsection.1.3.4}{Mathematical Expressions}{section.1.3}
+\BOOKMARK [2][-]{subsection.1.3.5}{Work Effort}{section.1.3}
+\BOOKMARK [1][-]{section.1.4}{Exercises}{chapter.1}
+\BOOKMARK [1][-]{section.1.5}{Introduction to LibTomMath}{chapter.1}
+\BOOKMARK [2][-]{subsection.1.5.1}{What is LibTomMath?}{section.1.5}
+\BOOKMARK [2][-]{subsection.1.5.2}{Goals of LibTomMath}{section.1.5}
+\BOOKMARK [1][-]{section.1.6}{Choice of LibTomMath}{chapter.1}
+\BOOKMARK [2][-]{subsection.1.6.1}{Code Base}{section.1.6}
+\BOOKMARK [2][-]{subsection.1.6.2}{API Simplicity}{section.1.6}
+\BOOKMARK [2][-]{subsection.1.6.3}{Optimizations}{section.1.6}
+\BOOKMARK [2][-]{subsection.1.6.4}{Portability and Stability}{section.1.6}
+\BOOKMARK [2][-]{subsection.1.6.5}{Choice}{section.1.6}
+\BOOKMARK [0][-]{chapter.2}{Getting Started}{}
+\BOOKMARK [1][-]{section.2.1}{Library Basics}{chapter.2}
+\BOOKMARK [1][-]{section.2.2}{What is a Multiple Precision Integer?}{chapter.2}
+\BOOKMARK [2][-]{subsection.2.2.1}{The mp\137int Structure}{section.2.2}
+\BOOKMARK [1][-]{section.2.3}{Argument Passing}{chapter.2}
+\BOOKMARK [1][-]{section.2.4}{Return Values}{chapter.2}
+\BOOKMARK [1][-]{section.2.5}{Initialization and Clearing}{chapter.2}
+\BOOKMARK [2][-]{subsection.2.5.1}{Initializing an mp\137int}{section.2.5}
+\BOOKMARK [2][-]{subsection.2.5.2}{Clearing an mp\137int}{section.2.5}
+\BOOKMARK [1][-]{section.2.6}{Maintenance Algorithms}{chapter.2}
+\BOOKMARK [2][-]{subsection.2.6.1}{Augmenting an mp\137int's Precision}{section.2.6}
+\BOOKMARK [2][-]{subsection.2.6.2}{Initializing Variable Precision mp\137ints}{section.2.6}
+\BOOKMARK [2][-]{subsection.2.6.3}{Multiple Integer Initializations and Clearings}{section.2.6}
+\BOOKMARK [2][-]{subsection.2.6.4}{Clamping Excess Digits}{section.2.6}
+\BOOKMARK [0][-]{chapter.3}{Basic Operations}{}
+\BOOKMARK [1][-]{section.3.1}{Introduction}{chapter.3}
+\BOOKMARK [1][-]{section.3.2}{Assigning Values to mp\137int Structures}{chapter.3}
+\BOOKMARK [2][-]{subsection.3.2.1}{Copying an mp\137int}{section.3.2}
+\BOOKMARK [2][-]{subsection.3.2.2}{Creating a Clone}{section.3.2}
+\BOOKMARK [1][-]{section.3.3}{Zeroing an Integer}{chapter.3}
+\BOOKMARK [1][-]{section.3.4}{Sign Manipulation}{chapter.3}
+\BOOKMARK [2][-]{subsection.3.4.1}{Absolute Value}{section.3.4}
+\BOOKMARK [2][-]{subsection.3.4.2}{Integer Negation}{section.3.4}
+\BOOKMARK [1][-]{section.3.5}{Small Constants}{chapter.3}
+\BOOKMARK [2][-]{subsection.3.5.1}{Setting Small Constants}{section.3.5}
+\BOOKMARK [2][-]{subsection.3.5.2}{Setting Large Constants}{section.3.5}
+\BOOKMARK [1][-]{section.3.6}{Comparisons}{chapter.3}
+\BOOKMARK [2][-]{subsection.3.6.1}{Unsigned Comparisions}{section.3.6}
+\BOOKMARK [2][-]{subsection.3.6.2}{Signed Comparisons}{section.3.6}
+\BOOKMARK [0][-]{chapter.4}{Basic Arithmetic}{}
+\BOOKMARK [1][-]{section.4.1}{Introduction}{chapter.4}
+\BOOKMARK [1][-]{section.4.2}{Addition and Subtraction}{chapter.4}
+\BOOKMARK [2][-]{subsection.4.2.1}{Low Level Addition}{section.4.2}
+\BOOKMARK [2][-]{subsection.4.2.2}{Low Level Subtraction}{section.4.2}
+\BOOKMARK [2][-]{subsection.4.2.3}{High Level Addition}{section.4.2}
+\BOOKMARK [2][-]{subsection.4.2.4}{High Level Subtraction}{section.4.2}
+\BOOKMARK [1][-]{section.4.3}{Bit and Digit Shifting}{chapter.4}
+\BOOKMARK [2][-]{subsection.4.3.1}{Multiplication by Two}{section.4.3}
+\BOOKMARK [2][-]{subsection.4.3.2}{Division by Two}{section.4.3}
+\BOOKMARK [1][-]{section.4.4}{Polynomial Basis Operations}{chapter.4}
+\BOOKMARK [2][-]{subsection.4.4.1}{Multiplication by x}{section.4.4}
+\BOOKMARK [2][-]{subsection.4.4.2}{Division by x}{section.4.4}
+\BOOKMARK [1][-]{section.4.5}{Powers of Two}{chapter.4}
+\BOOKMARK [2][-]{subsection.4.5.1}{Multiplication by Power of Two}{section.4.5}
+\BOOKMARK [2][-]{subsection.4.5.2}{Division by Power of Two}{section.4.5}
+\BOOKMARK [2][-]{subsection.4.5.3}{Remainder of Division by Power of Two}{section.4.5}
+\BOOKMARK [0][-]{chapter.5}{Multiplication and Squaring}{}
+\BOOKMARK [1][-]{section.5.1}{The Multipliers}{chapter.5}
+\BOOKMARK [1][-]{section.5.2}{Multiplication}{chapter.5}
+\BOOKMARK [2][-]{subsection.5.2.1}{The Baseline Multiplication}{section.5.2}
+\BOOKMARK [2][-]{subsection.5.2.2}{Faster Multiplication by the ``Comba'' Method}{section.5.2}
+\BOOKMARK [2][-]{subsection.5.2.3}{Polynomial Basis Multiplication}{section.5.2}
+\BOOKMARK [2][-]{subsection.5.2.4}{Karatsuba Multiplication}{section.5.2}
+\BOOKMARK [2][-]{subsection.5.2.5}{Toom-Cook 3-Way Multiplication}{section.5.2}
+\BOOKMARK [2][-]{subsection.5.2.6}{Signed Multiplication}{section.5.2}
+\BOOKMARK [1][-]{section.5.3}{Squaring}{chapter.5}
+\BOOKMARK [2][-]{subsection.5.3.1}{The Baseline Squaring Algorithm}{section.5.3}
+\BOOKMARK [2][-]{subsection.5.3.2}{Faster Squaring by the ``Comba'' Method}{section.5.3}
+\BOOKMARK [2][-]{subsection.5.3.3}{Polynomial Basis Squaring}{section.5.3}
+\BOOKMARK [2][-]{subsection.5.3.4}{Karatsuba Squaring}{section.5.3}
+\BOOKMARK [2][-]{subsection.5.3.5}{Toom-Cook Squaring}{section.5.3}
+\BOOKMARK [2][-]{subsection.5.3.6}{High Level Squaring}{section.5.3}
+\BOOKMARK [0][-]{chapter.6}{Modular Reduction}{}
+\BOOKMARK [1][-]{section.6.1}{Basics of Modular Reduction}{chapter.6}
+\BOOKMARK [1][-]{section.6.2}{The Barrett Reduction}{chapter.6}
+\BOOKMARK [2][-]{subsection.6.2.1}{Fixed Point Arithmetic}{section.6.2}
+\BOOKMARK [2][-]{subsection.6.2.2}{Choosing a Radix Point}{section.6.2}
+\BOOKMARK [2][-]{subsection.6.2.3}{Trimming the Quotient}{section.6.2}
+\BOOKMARK [2][-]{subsection.6.2.4}{Trimming the Residue}{section.6.2}
+\BOOKMARK [2][-]{subsection.6.2.5}{The Barrett Algorithm}{section.6.2}
+\BOOKMARK [2][-]{subsection.6.2.6}{The Barrett Setup Algorithm}{section.6.2}
+\BOOKMARK [1][-]{section.6.3}{The Montgomery Reduction}{chapter.6}
+\BOOKMARK [2][-]{subsection.6.3.1}{Digit Based Montgomery Reduction}{section.6.3}
+\BOOKMARK [2][-]{subsection.6.3.2}{Baseline Montgomery Reduction}{section.6.3}
+\BOOKMARK [2][-]{subsection.6.3.3}{Faster ``Comba'' Montgomery Reduction}{section.6.3}
+\BOOKMARK [2][-]{subsection.6.3.4}{Montgomery Setup}{section.6.3}
+\BOOKMARK [1][-]{section.6.4}{The Diminished Radix Algorithm}{chapter.6}
+\BOOKMARK [2][-]{subsection.6.4.1}{Choice of Moduli}{section.6.4}
+\BOOKMARK [2][-]{subsection.6.4.2}{Choice of k}{section.6.4}
+\BOOKMARK [2][-]{subsection.6.4.3}{Restricted Diminished Radix Reduction}{section.6.4}
+\BOOKMARK [2][-]{subsection.6.4.4}{Unrestricted Diminished Radix Reduction}{section.6.4}
+\BOOKMARK [1][-]{section.6.5}{Algorithm Comparison}{chapter.6}
+\BOOKMARK [0][-]{chapter.7}{Exponentiation}{}
+\BOOKMARK [1][-]{section.7.1}{Exponentiation Basics}{chapter.7}
+\BOOKMARK [2][-]{subsection.7.1.1}{Single Digit Exponentiation}{section.7.1}
+\BOOKMARK [1][-]{section.7.2}{k-ary Exponentiation}{chapter.7}
+\BOOKMARK [2][-]{subsection.7.2.1}{Optimal Values of k}{section.7.2}
+\BOOKMARK [2][-]{subsection.7.2.2}{Sliding-Window Exponentiation}{section.7.2}
+\BOOKMARK [1][-]{section.7.3}{Modular Exponentiation}{chapter.7}
+\BOOKMARK [2][-]{subsection.7.3.1}{Barrett Modular Exponentiation}{section.7.3}
+\BOOKMARK [1][-]{section.7.4}{Quick Power of Two}{chapter.7}
+\BOOKMARK [0][-]{chapter.8}{Higher Level Algorithms}{}
+\BOOKMARK [1][-]{section.8.1}{Integer Division with Remainder}{chapter.8}
+\BOOKMARK [2][-]{subsection.8.1.1}{Quotient Estimation}{section.8.1}
+\BOOKMARK [2][-]{subsection.8.1.2}{Normalized Integers}{section.8.1}
+\BOOKMARK [2][-]{subsection.8.1.3}{Radix- Division with Remainder}{section.8.1}
+\BOOKMARK [1][-]{section.8.2}{Single Digit Helpers}{chapter.8}
+\BOOKMARK [2][-]{subsection.8.2.1}{Single Digit Addition and Subtraction}{section.8.2}
+\BOOKMARK [2][-]{subsection.8.2.2}{Single Digit Multiplication}{section.8.2}
+\BOOKMARK [2][-]{subsection.8.2.3}{Single Digit Division}{section.8.2}
+\BOOKMARK [2][-]{subsection.8.2.4}{Single Digit Root Extraction}{section.8.2}
+\BOOKMARK [1][-]{section.8.3}{Random Number Generation}{chapter.8}
+\BOOKMARK [1][-]{section.8.4}{Formatted Representations}{chapter.8}
+\BOOKMARK [2][-]{subsection.8.4.1}{Reading Radix-n Input}{section.8.4}
+\BOOKMARK [2][-]{subsection.8.4.2}{Generating Radix-n Output}{section.8.4}
+\BOOKMARK [0][-]{chapter.9}{Number Theoretic Algorithms}{}
+\BOOKMARK [1][-]{section.9.1}{Greatest Common Divisor}{chapter.9}
+\BOOKMARK [2][-]{subsection.9.1.1}{Complete Greatest Common Divisor}{section.9.1}
+\BOOKMARK [1][-]{section.9.2}{Least Common Multiple}{chapter.9}
+\BOOKMARK [1][-]{section.9.3}{Jacobi Symbol Computation}{chapter.9}
+\BOOKMARK [2][-]{subsection.9.3.1}{Jacobi Symbol}{section.9.3}
+\BOOKMARK [1][-]{section.9.4}{Modular Inverse}{chapter.9}
+\BOOKMARK [2][-]{subsection.9.4.1}{General Case}{section.9.4}
+\BOOKMARK [1][-]{section.9.5}{Primality Tests}{chapter.9}
+\BOOKMARK [2][-]{subsection.9.5.1}{Trial Division}{section.9.5}
+\BOOKMARK [2][-]{subsection.9.5.2}{The Fermat Test}{section.9.5}
+\BOOKMARK [2][-]{subsection.9.5.3}{The Miller-Rabin Test}{section.9.5}
diff --git a/libtommath/tommath_class.h b/libtommath/tommath_class.h
new file mode 100644
index 0000000..a4e275a
--- /dev/null
+++ b/libtommath/tommath_class.h
@@ -0,0 +1,1005 @@
+#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))
+#if defined(LTM2)
+#define LTM3
+#endif
+#if defined(LTM1)
+#define LTM2
+#endif
+#define LTM1
+
+#if defined(LTM_ALL)
+#define BN_ERROR_C
+#define BN_FAST_MP_INVMOD_C
+#define BN_FAST_MP_MONTGOMERY_REDUCE_C
+#define BN_FAST_S_MP_MUL_DIGS_C
+#define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+#define BN_FAST_S_MP_SQR_C
+#define BN_MP_2EXPT_C
+#define BN_MP_ABS_C
+#define BN_MP_ADD_C
+#define BN_MP_ADD_D_C
+#define BN_MP_ADDMOD_C
+#define BN_MP_AND_C
+#define BN_MP_CLAMP_C
+#define BN_MP_CLEAR_C
+#define BN_MP_CLEAR_MULTI_C
+#define BN_MP_CMP_C
+#define BN_MP_CMP_D_C
+#define BN_MP_CMP_MAG_C
+#define BN_MP_CNT_LSB_C
+#define BN_MP_COPY_C
+#define BN_MP_COUNT_BITS_C
+#define BN_MP_DIV_C
+#define BN_MP_DIV_2_C
+#define BN_MP_DIV_2D_C
+#define BN_MP_DIV_3_C
+#define BN_MP_DIV_D_C
+#define BN_MP_DR_IS_MODULUS_C
+#define BN_MP_DR_REDUCE_C
+#define BN_MP_DR_SETUP_C
+#define BN_MP_EXCH_C
+#define BN_MP_EXPT_D_C
+#define BN_MP_EXPTMOD_C
+#define BN_MP_EXPTMOD_FAST_C
+#define BN_MP_EXTEUCLID_C
+#define BN_MP_FREAD_C
+#define BN_MP_FWRITE_C
+#define BN_MP_GCD_C
+#define BN_MP_GET_INT_C
+#define BN_MP_GROW_C
+#define BN_MP_INIT_C
+#define BN_MP_INIT_COPY_C
+#define BN_MP_INIT_MULTI_C
+#define BN_MP_INIT_SET_C
+#define BN_MP_INIT_SET_INT_C
+#define BN_MP_INIT_SIZE_C
+#define BN_MP_INVMOD_C
+#define BN_MP_INVMOD_SLOW_C
+#define BN_MP_IS_SQUARE_C
+#define BN_MP_JACOBI_C
+#define BN_MP_KARATSUBA_MUL_C
+#define BN_MP_KARATSUBA_SQR_C
+#define BN_MP_LCM_C
+#define BN_MP_LSHD_C
+#define BN_MP_MOD_C
+#define BN_MP_MOD_2D_C
+#define BN_MP_MOD_D_C
+#define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+#define BN_MP_MONTGOMERY_REDUCE_C
+#define BN_MP_MONTGOMERY_SETUP_C
+#define BN_MP_MUL_C
+#define BN_MP_MUL_2_C
+#define BN_MP_MUL_2D_C
+#define BN_MP_MUL_D_C
+#define BN_MP_MULMOD_C
+#define BN_MP_N_ROOT_C
+#define BN_MP_NEG_C
+#define BN_MP_OR_C
+#define BN_MP_PRIME_FERMAT_C
+#define BN_MP_PRIME_IS_DIVISIBLE_C
+#define BN_MP_PRIME_IS_PRIME_C
+#define BN_MP_PRIME_MILLER_RABIN_C
+#define BN_MP_PRIME_NEXT_PRIME_C
+#define BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+#define BN_MP_PRIME_RANDOM_EX_C
+#define BN_MP_RADIX_SIZE_C
+#define BN_MP_RADIX_SMAP_C
+#define BN_MP_RAND_C
+#define BN_MP_READ_RADIX_C
+#define BN_MP_READ_SIGNED_BIN_C
+#define BN_MP_READ_UNSIGNED_BIN_C
+#define BN_MP_REDUCE_C
+#define BN_MP_REDUCE_2K_C
+#define BN_MP_REDUCE_2K_L_C
+#define BN_MP_REDUCE_2K_SETUP_C
+#define BN_MP_REDUCE_2K_SETUP_L_C
+#define BN_MP_REDUCE_IS_2K_C
+#define BN_MP_REDUCE_IS_2K_L_C
+#define BN_MP_REDUCE_SETUP_C
+#define BN_MP_RSHD_C
+#define BN_MP_SET_C
+#define BN_MP_SET_INT_C
+#define BN_MP_SHRINK_C
+#define BN_MP_SIGNED_BIN_SIZE_C
+#define BN_MP_SQR_C
+#define BN_MP_SQRMOD_C
+#define BN_MP_SQRT_C
+#define BN_MP_SUB_C
+#define BN_MP_SUB_D_C
+#define BN_MP_SUBMOD_C
+#define BN_MP_TO_SIGNED_BIN_C
+#define BN_MP_TO_SIGNED_BIN_N_C
+#define BN_MP_TO_UNSIGNED_BIN_C
+#define BN_MP_TO_UNSIGNED_BIN_N_C
+#define BN_MP_TOOM_MUL_C
+#define BN_MP_TOOM_SQR_C
+#define BN_MP_TORADIX_C
+#define BN_MP_TORADIX_N_C
+#define BN_MP_UNSIGNED_BIN_SIZE_C
+#define BN_MP_XOR_C
+#define BN_MP_ZERO_C
+#define BN_PRIME_TAB_C
+#define BN_REVERSE_C
+#define BN_S_MP_ADD_C
+#define BN_S_MP_EXPTMOD_C
+#define BN_S_MP_MUL_DIGS_C
+#define BN_S_MP_MUL_HIGH_DIGS_C
+#define BN_S_MP_SQR_C
+#define BN_S_MP_SUB_C
+#define BNCORE_C
+#endif
+
+#if defined(BN_ERROR_C)
+ #define BN_MP_ERROR_TO_STRING_C
+#endif
+
+#if defined(BN_FAST_MP_INVMOD_C)
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_COPY_C
+ #define BN_MP_MOD_C
+ #define BN_MP_SET_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_ADD_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_FAST_MP_MONTGOMERY_REDUCE_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_FAST_S_MP_MUL_DIGS_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_FAST_S_MP_SQR_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_2EXPT_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_ABS_C)
+ #define BN_MP_COPY_C
+#endif
+
+#if defined(BN_MP_ADD_C)
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_ADD_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_ADDMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_AND_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_CLAMP_C)
+#endif
+
+#if defined(BN_MP_CLEAR_C)
+#endif
+
+#if defined(BN_MP_CLEAR_MULTI_C)
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_CMP_C)
+ #define BN_MP_CMP_MAG_C
+#endif
+
+#if defined(BN_MP_CMP_D_C)
+#endif
+
+#if defined(BN_MP_CMP_MAG_C)
+#endif
+
+#if defined(BN_MP_CNT_LSB_C)
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_COPY_C)
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_COUNT_BITS_C)
+#endif
+
+#if defined(BN_MP_DIV_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_SET_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_ABS_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SUB_C
+ #define BN_MP_ADD_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_INIT_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DIV_2_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_DIV_2D_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_DIV_3_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DIV_D_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_COPY_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DR_IS_MODULUS_C)
+#endif
+
+#if defined(BN_MP_DR_REDUCE_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_DR_SETUP_C)
+#endif
+
+#if defined(BN_MP_EXCH_C)
+#endif
+
+#if defined(BN_MP_EXPT_D_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_SET_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MUL_C
+#endif
+
+#if defined(BN_MP_EXPTMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_INVMOD_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_ABS_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_REDUCE_IS_2K_L_C
+ #define BN_S_MP_EXPTMOD_C
+ #define BN_MP_DR_IS_MODULUS_C
+ #define BN_MP_REDUCE_IS_2K_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_EXPTMOD_FAST_C
+#endif
+
+#if defined(BN_MP_EXPTMOD_FAST_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MONTGOMERY_SETUP_C
+ #define BN_FAST_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_DR_SETUP_C
+ #define BN_MP_DR_REDUCE_C
+ #define BN_MP_REDUCE_2K_SETUP_C
+ #define BN_MP_REDUCE_2K_C
+ #define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+ #define BN_MP_MULMOD_C
+ #define BN_MP_SET_C
+ #define BN_MP_MOD_C
+ #define BN_MP_COPY_C
+ #define BN_MP_SQR_C
+ #define BN_MP_MUL_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_EXTEUCLID_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_SET_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SUB_C
+ #define BN_MP_NEG_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_FREAD_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_S_RMAP_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_CMP_D_C
+#endif
+
+#if defined(BN_MP_FWRITE_C)
+ #define BN_MP_RADIX_SIZE_C
+ #define BN_MP_TORADIX_C
+#endif
+
+#if defined(BN_MP_GCD_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ABS_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_GET_INT_C)
+#endif
+
+#if defined(BN_MP_GROW_C)
+#endif
+
+#if defined(BN_MP_INIT_C)
+#endif
+
+#if defined(BN_MP_INIT_COPY_C)
+ #define BN_MP_COPY_C
+#endif
+
+#if defined(BN_MP_INIT_MULTI_C)
+ #define BN_MP_ERR_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_INIT_SET_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+#endif
+
+#if defined(BN_MP_INIT_SET_INT_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_INT_C
+#endif
+
+#if defined(BN_MP_INIT_SIZE_C)
+ #define BN_MP_INIT_C
+#endif
+
+#if defined(BN_MP_INVMOD_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ISODD_C
+ #define BN_FAST_MP_INVMOD_C
+ #define BN_MP_INVMOD_SLOW_C
+#endif
+
+#if defined(BN_MP_INVMOD_SLOW_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_MOD_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_SET_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_IS_SQUARE_C)
+ #define BN_MP_MOD_D_C
+ #define BN_MP_INIT_SET_INT_C
+ #define BN_MP_MOD_C
+ #define BN_MP_GET_INT_C
+ #define BN_MP_SQRT_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_JACOBI_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_MOD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_KARATSUBA_MUL_C)
+ #define BN_MP_MUL_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_SUB_C
+ #define BN_MP_ADD_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_KARATSUBA_SQR_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_SQR_C
+ #define BN_MP_SUB_C
+ #define BN_S_MP_ADD_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_LCM_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_GCD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_DIV_C
+ #define BN_MP_MUL_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_LSHD_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_RSHD_C
+#endif
+
+#if defined(BN_MP_MOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_DIV_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_ADD_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_MOD_2D_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_COPY_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MOD_D_C)
+ #define BN_MP_DIV_D_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_CALC_NORMALIZATION_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_2EXPT_C
+ #define BN_MP_SET_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_REDUCE_C)
+ #define BN_FAST_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_SETUP_C)
+#endif
+
+#if defined(BN_MP_MUL_C)
+ #define BN_MP_TOOM_MUL_C
+ #define BN_MP_KARATSUBA_MUL_C
+ #define BN_FAST_S_MP_MUL_DIGS_C
+ #define BN_S_MP_MUL_C
+ #define BN_S_MP_MUL_DIGS_C
+#endif
+
+#if defined(BN_MP_MUL_2_C)
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_MUL_2D_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_GROW_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MUL_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MULMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_MUL_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_N_ROOT_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+ #define BN_MP_COPY_C
+ #define BN_MP_EXPT_D_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SUB_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_NEG_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_OR_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_FERMAT_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_INIT_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_CMP_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_IS_DIVISIBLE_C)
+ #define BN_MP_MOD_D_C
+#endif
+
+#if defined(BN_MP_PRIME_IS_PRIME_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_PRIME_IS_DIVISIBLE_C
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+ #define BN_MP_PRIME_MILLER_RABIN_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_MILLER_RABIN_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SQRMOD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_NEXT_PRIME_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_SET_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_MOD_D_C
+ #define BN_MP_INIT_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_PRIME_MILLER_RABIN_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_RABIN_MILLER_TRIALS_C)
+#endif
+
+#if defined(BN_MP_PRIME_RANDOM_EX_C)
+ #define BN_MP_READ_UNSIGNED_BIN_C
+ #define BN_MP_PRIME_IS_PRIME_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_D_C
+#endif
+
+#if defined(BN_MP_RADIX_SIZE_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_RADIX_SMAP_C)
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_RAND_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_LSHD_C
+#endif
+
+#if defined(BN_MP_READ_RADIX_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_S_RMAP_C
+ #define BN_MP_RADIX_SMAP_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_READ_SIGNED_BIN_C)
+ #define BN_MP_READ_UNSIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_READ_UNSIGNED_BIN_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_REDUCE_C)
+ #define BN_MP_REDUCE_SETUP_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_C
+ #define BN_S_MP_MUL_HIGH_DIGS_C
+ #define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #define BN_MP_MOD_2D_C
+ #define BN_S_MP_MUL_DIGS_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_SET_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CMP_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_L_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_MUL_C
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_SETUP_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_2EXPT_C
+ #define BN_MP_CLEAR_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_SETUP_L_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_2EXPT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_IS_2K_C)
+ #define BN_MP_REDUCE_2K_C
+ #define BN_MP_COUNT_BITS_C
+#endif
+
+#if defined(BN_MP_REDUCE_IS_2K_L_C)
+#endif
+
+#if defined(BN_MP_REDUCE_SETUP_C)
+ #define BN_MP_2EXPT_C
+ #define BN_MP_DIV_C
+#endif
+
+#if defined(BN_MP_RSHD_C)
+ #define BN_MP_ZERO_C
+#endif
+
+#if defined(BN_MP_SET_C)
+ #define BN_MP_ZERO_C
+#endif
+
+#if defined(BN_MP_SET_INT_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_SHRINK_C)
+#endif
+
+#if defined(BN_MP_SIGNED_BIN_SIZE_C)
+ #define BN_MP_UNSIGNED_BIN_SIZE_C
+#endif
+
+#if defined(BN_MP_SQR_C)
+ #define BN_MP_TOOM_SQR_C
+ #define BN_MP_KARATSUBA_SQR_C
+ #define BN_FAST_S_MP_SQR_C
+ #define BN_S_MP_SQR_C
+#endif
+
+#if defined(BN_MP_SQRMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_SQRT_C)
+ #define BN_MP_N_ROOT_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_DIV_C
+ #define BN_MP_ADD_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_SUB_C)
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_SUB_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_SUBMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_TO_SIGNED_BIN_C)
+ #define BN_MP_TO_UNSIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_TO_SIGNED_BIN_N_C)
+ #define BN_MP_SIGNED_BIN_SIZE_C
+ #define BN_MP_TO_SIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_TO_UNSIGNED_BIN_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_TO_UNSIGNED_BIN_N_C)
+ #define BN_MP_UNSIGNED_BIN_SIZE_C
+ #define BN_MP_TO_UNSIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_TOOM_MUL_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_TOOM_SQR_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_SQR_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_TORADIX_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_TORADIX_N_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_UNSIGNED_BIN_SIZE_C)
+ #define BN_MP_COUNT_BITS_C
+#endif
+
+#if defined(BN_MP_XOR_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_ZERO_C)
+#endif
+
+#if defined(BN_PRIME_TAB_C)
+#endif
+
+#if defined(BN_REVERSE_C)
+#endif
+
+#if defined(BN_S_MP_ADD_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_S_MP_EXPTMOD_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_REDUCE_SETUP_C
+ #define BN_MP_REDUCE_C
+ #define BN_MP_REDUCE_2K_SETUP_L_C
+ #define BN_MP_REDUCE_2K_L_C
+ #define BN_MP_MOD_C
+ #define BN_MP_COPY_C
+ #define BN_MP_SQR_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SET_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_S_MP_MUL_DIGS_C)
+ #define BN_FAST_S_MP_MUL_DIGS_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_MUL_HIGH_DIGS_C)
+ #define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_SQR_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_SUB_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BNCORE_C)
+#endif
+
+#ifdef LTM3
+#define LTM_LAST
+#endif
+#include "tommath_superclass.h"
+#include "tommath_class.h"
+#else
+#define LTM_LAST
+#endif
+
+/* Dropbear doesn't need these. */
+#undef BN_MP_KARATSUBA_MUL_C
+#undef BN_MP_KARATSUBA_SQR_C
+#undef BN_MP_TOOM_MUL_C
+#undef BN_MP_TOOM_SQR_C
+
+/* $Source: /cvs/libtom/libtommath/tommath_class.h,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2005/07/28 11:59:32 $ */
diff --git a/libtommath/tommath_superclass.h b/libtommath/tommath_superclass.h
new file mode 100644
index 0000000..2fdebe6
--- /dev/null
+++ b/libtommath/tommath_superclass.h
@@ -0,0 +1,76 @@
+/* super class file for PK algos */
+
+/* default ... include all MPI */
+#define LTM_ALL
+
+/* RSA only (does not support DH/DSA/ECC) */
+/* #define SC_RSA_1 */
+
+/* For reference.... On an Athlon64 optimizing for speed...
+
+ LTM's mpi.o with all functions [striped] is 142KiB in size.
+
+*/
+
+/* Works for RSA only, mpi.o is 68KiB */
+#ifdef SC_RSA_1
+ #define BN_MP_SHRINK_C
+ #define BN_MP_LCM_C
+ #define BN_MP_PRIME_RANDOM_EX_C
+ #define BN_MP_INVMOD_C
+ #define BN_MP_GCD_C
+ #define BN_MP_MOD_C
+ #define BN_MP_MULMOD_C
+ #define BN_MP_ADDMOD_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_SET_INT_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_UNSIGNED_BIN_SIZE_C
+ #define BN_MP_TO_UNSIGNED_BIN_C
+ #define BN_MP_MOD_D_C
+ #define BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+ #define BN_REVERSE_C
+ #define BN_PRIME_TAB_C
+
+ /* other modifiers */
+ #define BN_MP_DIV_SMALL /* Slower division, not critical */
+
+ /* here we are on the last pass so we turn things off. The functions classes are still there
+ * but we remove them specifically from the build. This also invokes tweaks in functions
+ * like removing support for even moduli, etc...
+ */
+#ifdef LTM_LAST
+ #undef BN_MP_TOOM_MUL_C
+ #undef BN_MP_TOOM_SQR_C
+ #undef BN_MP_KARATSUBA_MUL_C
+ #undef BN_MP_KARATSUBA_SQR_C
+ #undef BN_MP_REDUCE_C
+ #undef BN_MP_REDUCE_SETUP_C
+ #undef BN_MP_DR_IS_MODULUS_C
+ #undef BN_MP_DR_SETUP_C
+ #undef BN_MP_DR_REDUCE_C
+ #undef BN_MP_REDUCE_IS_2K_C
+ #undef BN_MP_REDUCE_2K_SETUP_C
+ #undef BN_MP_REDUCE_2K_C
+ #undef BN_S_MP_EXPTMOD_C
+ #undef BN_MP_DIV_3_C
+ #undef BN_S_MP_MUL_HIGH_DIGS_C
+ #undef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #undef BN_FAST_MP_INVMOD_C
+
+ /* To safely undefine these you have to make sure your RSA key won't exceed the Comba threshold
+ * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines]
+ * which means roughly speaking you can handle upto 2536-bit RSA keys with these defined without
+ * trouble.
+ */
+ #undef BN_S_MP_MUL_DIGS_C
+ #undef BN_S_MP_SQR_C
+ #undef BN_MP_MONTGOMERY_REDUCE_C
+#endif
+
+#endif
+
+/* $Source: /cvs/libtom/libtommath/tommath_superclass.h,v $ */
+/* $Revision: 1.3 $ */
+/* $Date: 2005/05/14 13:29:17 $ */
