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added libtommath-0.20

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Tom St Denis 2003-06-08 20:09:10 +00:00 committed by Steffen Jaeckel
parent ef490f30f6
commit 0fe7a2d4ff
18 changed files with 10 additions and 12990 deletions
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bn.pdf
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bn.tex
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@ -1,7 +1,7 @@
\documentclass[]{article} \documentclass[]{article}
\begin{document} \begin{document}
\title{LibTomMath v0.19 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org } \title{LibTomMath v0.20 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
\author{Tom St Denis \\ tomstdenis@iahu.ca} \author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle \maketitle
\newpage \newpage

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bn_mp_exptmod_fast.c
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@ -80,7 +80,6 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
if (((P->used * 2 + 1) < MP_WARRAY) && if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce; redux = fast_mp_montgomery_reduce;
} else { } else {
/* use slower baselien method */ /* use slower baselien method */
redux = mp_montgomery_reduce; redux = mp_montgomery_reduce;

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changes.txt
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@ -1,3 +1,7 @@
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 June 6th, 2003
v0.19 -- Fixed a bug in mp_montgomery_reduce() which was introduced when I tweaked mp_rshd() in the previous release. 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. Essentially the digits were not trimmed before the compare which cause a subtraction to occur all the time.

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etc/2kprime.1
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256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823 259-bits (k = 17745) = 926336713898529563388567880069503262826159877325124512315660672063305037101743
512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979

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etc/2kprime.c
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@ -7,7 +7,7 @@ int sizes[] = {256, 512, 768, 1024, 1536, 2048, 3072, 4096};
int main(void) int main(void)
{ {
char buf[2000]; char buf[2000];
int x, y, t; int x, y;
mp_int q, p; mp_int q, p;
FILE *out; FILE *out;
clock_t t1; clock_t t1;

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makefile
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@ -1,6 +1,6 @@
CFLAGS += -I./ -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops CFLAGS += -I./ -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops
VERSION=0.19 VERSION=0.20
default: libtommath.a default: libtommath.a
@ -103,5 +103,6 @@ clean:
zipup: clean manual poster zipup: clean manual poster
perl gen.pl ; mv mpi.c pre_gen/ ; \ perl gen.pl ; mv mpi.c pre_gen/ ; \
cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \ cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \
cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; tar -c libtommath-$(VERSION)/* > ltm-$(VERSION).tar ; \ cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; cp tdcal.pdf ./libtommath-$(VERSION)/ ; cd ./libtommath-$(VERSION) ; rm -f tommath.src tommath.tex tommath.out ; cd pics ; rm -f * ; cd .. ; cd .. ; ls ; \
tar -c libtommath-$(VERSION)/* > ltm-$(VERSION).tar ; \
bzip2 -9vv ltm-$(VERSION).tar ; zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* bzip2 -9vv ltm-$(VERSION).tar ; zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/*

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pics/makefile
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# makes the images... yeah
default: pses
sliding_window.ps: sliding_window.tif
tiff2ps -c -e sliding_window.tif > sliding_window.ps
expt_state.ps: expt_state.tif
tiff2ps -c -e expt_state.tif > expt_state.ps
sliding_window.pdf: sliding_window.ps
epstopdf sliding_window.ps
expt_state.pdf: expt_state.ps
epstopdf expt_state.ps
pses: sliding_window.ps expt_state.ps
pdfes: sliding_window.pdf expt_state.pdf
clean:
rm -rf *.ps *.pdf .xvpics

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pre_gen/mpi.c
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@ -2155,7 +2155,6 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
if (((P->used * 2 + 1) < MP_WARRAY) && if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce; redux = fast_mp_montgomery_reduce;
} else { } else {
/* use slower baselien method */ /* use slower baselien method */
redux = mp_montgomery_reduce; redux = mp_montgomery_reduce;

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tommath.out
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@ -1,143 +0,0 @@
\BOOKMARK [0][-]{chapter.1}{Introduction}{}
\BOOKMARK [1][-]{section.1.1}{Multiple Precision Arithmetic}{chapter.1}
\BOOKMARK [2][-]{subsection.1.1.1}{The Need for Multiple Precision Arithmetic}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.2}{Multiple Precision Arithmetic}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.3}{Benefits of Multiple Precision Arithmetic}{section.1.1}
\BOOKMARK [2][-]{subsection.1.1.4}{Basis of Operations}{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}{Work Effort}{section.1.3}
\BOOKMARK [1][-]{section.1.4}{Exercises}{chapter.1}
\BOOKMARK [0][-]{chapter.2}{Introduction to LibTomMath}{}
\BOOKMARK [1][-]{section.2.1}{What is LibTomMath?}{chapter.2}
\BOOKMARK [1][-]{section.2.2}{Goals of LibTomMath}{chapter.2}
\BOOKMARK [1][-]{section.2.3}{Choice of LibTomMath}{chapter.2}
\BOOKMARK [2][-]{subsection.2.3.1}{Code Base}{section.2.3}
\BOOKMARK [2][-]{subsection.2.3.2}{API Simplicity}{section.2.3}
\BOOKMARK [2][-]{subsection.2.3.3}{Optimizations}{section.2.3}
\BOOKMARK [2][-]{subsection.2.3.4}{Portability and Stability}{section.2.3}
\BOOKMARK [2][-]{subsection.2.3.5}{Choice}{section.2.3}
\BOOKMARK [0][-]{chapter.3}{Getting Started}{}
\BOOKMARK [1][-]{section.3.1}{Library Basics}{chapter.3}
\BOOKMARK [1][-]{section.3.2}{What is a Multiple Precision Integer?}{chapter.3}
\BOOKMARK [2][-]{subsection.3.2.1}{The mp\137int structure}{section.3.2}
\BOOKMARK [1][-]{section.3.3}{Argument Passing}{chapter.3}
\BOOKMARK [1][-]{section.3.4}{Return Values}{chapter.3}
\BOOKMARK [1][-]{section.3.5}{Initialization and Clearing}{chapter.3}
\BOOKMARK [2][-]{subsection.3.5.1}{Initializing an mp\137int}{section.3.5}
\BOOKMARK [2][-]{subsection.3.5.2}{Clearing an mp\137int}{section.3.5}
\BOOKMARK [1][-]{section.3.6}{Other Initialization Routines}{chapter.3}
\BOOKMARK [2][-]{subsection.3.6.1}{Initializing Variable Sized mp\137int Structures}{section.3.6}
\BOOKMARK [2][-]{subsection.3.6.2}{Creating a Clone}{section.3.6}
\BOOKMARK [2][-]{subsection.3.6.3}{Multiple Integer Initializations And Clearings}{section.3.6}
\BOOKMARK [1][-]{section.3.7}{Maintenance}{chapter.3}
\BOOKMARK [2][-]{subsection.3.7.1}{Augmenting Integer Precision}{section.3.7}
\BOOKMARK [2][-]{subsection.3.7.2}{Clamping Excess Digits}{section.3.7}
\BOOKMARK [0][-]{chapter.4}{Basic Operations}{}
\BOOKMARK [1][-]{section.4.1}{Copying an Integer}{chapter.4}
\BOOKMARK [1][-]{section.4.2}{Zeroing an Integer}{chapter.4}
\BOOKMARK [1][-]{section.4.3}{Sign Manipulation}{chapter.4}
\BOOKMARK [2][-]{subsection.4.3.1}{Absolute Value}{section.4.3}
\BOOKMARK [2][-]{subsection.4.3.2}{Integer Negation}{section.4.3}
\BOOKMARK [1][-]{section.4.4}{Small Constants}{chapter.4}
\BOOKMARK [2][-]{subsection.4.4.1}{Setting Small Constants}{section.4.4}
\BOOKMARK [2][-]{subsection.4.4.2}{Setting Large Constants}{section.4.4}
\BOOKMARK [1][-]{section.4.5}{Comparisons}{chapter.4}
\BOOKMARK [2][-]{subsection.4.5.1}{Unsigned Comparisions}{section.4.5}
\BOOKMARK [2][-]{subsection.4.5.2}{Signed Comparisons}{section.4.5}
\BOOKMARK [0][-]{chapter.5}{Basic Arithmetic}{}
\BOOKMARK [1][-]{section.5.1}{Building Blocks}{chapter.5}
\BOOKMARK [1][-]{section.5.2}{Addition and Subtraction}{chapter.5}
\BOOKMARK [2][-]{subsection.5.2.1}{Low Level Addition}{section.5.2}
\BOOKMARK [2][-]{subsection.5.2.2}{Low Level Subtraction}{section.5.2}
\BOOKMARK [2][-]{subsection.5.2.3}{High Level Addition}{section.5.2}
\BOOKMARK [2][-]{subsection.5.2.4}{High Level Subtraction}{section.5.2}
\BOOKMARK [1][-]{section.5.3}{Bit and Digit Shifting}{chapter.5}
\BOOKMARK [2][-]{subsection.5.3.1}{Multiplication by Two}{section.5.3}
\BOOKMARK [2][-]{subsection.5.3.2}{Division by Two}{section.5.3}
\BOOKMARK [1][-]{section.5.4}{Polynomial Basis Operations}{chapter.5}
\BOOKMARK [2][-]{subsection.5.4.1}{Multiplication by x}{section.5.4}
\BOOKMARK [2][-]{subsection.5.4.2}{Division by x}{section.5.4}
\BOOKMARK [1][-]{section.5.5}{Powers of Two}{chapter.5}
\BOOKMARK [2][-]{subsection.5.5.1}{Multiplication by Power of Two}{section.5.5}
\BOOKMARK [2][-]{subsection.5.5.2}{Division by Power of Two}{section.5.5}
\BOOKMARK [2][-]{subsection.5.5.3}{Remainder of Division by Power of Two}{section.5.5}
\BOOKMARK [0][-]{chapter.6}{Multiplication and Squaring}{}
\BOOKMARK [1][-]{section.6.1}{The Multipliers}{chapter.6}
\BOOKMARK [1][-]{section.6.2}{Multiplication}{chapter.6}
\BOOKMARK [2][-]{subsection.6.2.1}{The Baseline Multiplication}{section.6.2}
\BOOKMARK [2][-]{subsection.6.2.2}{Faster Multiplication by the ``Comba'' Method}{section.6.2}
\BOOKMARK [2][-]{subsection.6.2.3}{Polynomial Basis Multiplication}{section.6.2}
\BOOKMARK [2][-]{subsection.6.2.4}{Karatsuba Multiplication}{section.6.2}
\BOOKMARK [2][-]{subsection.6.2.5}{Toom-Cook 3-Way Multiplication}{section.6.2}
\BOOKMARK [2][-]{subsection.6.2.6}{Signed Multiplication}{section.6.2}
\BOOKMARK [1][-]{section.6.3}{Squaring}{chapter.6}
\BOOKMARK [2][-]{subsection.6.3.1}{The Baseline Squaring Algorithm}{section.6.3}
\BOOKMARK [2][-]{subsection.6.3.2}{Faster Squaring by the ``Comba'' Method}{section.6.3}
\BOOKMARK [2][-]{subsection.6.3.3}{Polynomial Basis Squaring}{section.6.3}
\BOOKMARK [2][-]{subsection.6.3.4}{Karatsuba Squaring}{section.6.3}
\BOOKMARK [2][-]{subsection.6.3.5}{Toom-Cook Squaring}{section.6.3}
\BOOKMARK [2][-]{subsection.6.3.6}{High Level Squaring}{section.6.3}
\BOOKMARK [0][-]{chapter.7}{Modular Reduction}{}
\BOOKMARK [1][-]{section.7.1}{Basics of Modular Reduction}{chapter.7}
\BOOKMARK [1][-]{section.7.2}{The Barrett Reduction}{chapter.7}
\BOOKMARK [2][-]{subsection.7.2.1}{Fixed Point Arithmetic}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.2}{Choosing a Radix Point}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.3}{Trimming the Quotient}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.4}{Trimming the Residue}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.5}{The Barrett Algorithm}{section.7.2}
\BOOKMARK [2][-]{subsection.7.2.6}{The Barrett Setup Algorithm}{section.7.2}
\BOOKMARK [1][-]{section.7.3}{The Montgomery Reduction}{chapter.7}
\BOOKMARK [2][-]{subsection.7.3.1}{Digit Based Montgomery Reduction}{section.7.3}
\BOOKMARK [2][-]{subsection.7.3.2}{Baseline Montgomery Reduction}{section.7.3}
\BOOKMARK [2][-]{subsection.7.3.3}{Faster ``Comba'' Montgomery Reduction}{section.7.3}
\BOOKMARK [2][-]{subsection.7.3.4}{Montgomery Setup}{section.7.3}
\BOOKMARK [1][-]{section.7.4}{The Diminished Radix Algorithm}{chapter.7}
\BOOKMARK [2][-]{subsection.7.4.1}{Choice of Moduli}{section.7.4}
\BOOKMARK [2][-]{subsection.7.4.2}{Choice of k}{section.7.4}
\BOOKMARK [2][-]{subsection.7.4.3}{Restricted Diminished Radix Reduction}{section.7.4}
\BOOKMARK [2][-]{subsection.7.4.4}{Unrestricted Diminished Radix Reduction}{section.7.4}
\BOOKMARK [1][-]{section.7.5}{Algorithm Comparison}{chapter.7}
\BOOKMARK [0][-]{chapter.8}{Exponentiation}{}
\BOOKMARK [1][-]{section.8.1}{Exponentiation Basics}{chapter.8}
\BOOKMARK [2][-]{subsection.8.1.1}{Single Digit Exponentiation}{section.8.1}
\BOOKMARK [1][-]{section.8.2}{k-ary Exponentiation}{chapter.8}
\BOOKMARK [2][-]{subsection.8.2.1}{Optimal Values of k}{section.8.2}
\BOOKMARK [2][-]{subsection.8.2.2}{Sliding-Window Exponentiation}{section.8.2}
\BOOKMARK [1][-]{section.8.3}{Modular Exponentiation}{chapter.8}
\BOOKMARK [2][-]{subsection.8.3.1}{Barrett Modular Exponentiation}{section.8.3}
\BOOKMARK [1][-]{section.8.4}{Quick Power of Two}{chapter.8}
\BOOKMARK [0][-]{chapter.9}{Higher Level Algorithms}{}
\BOOKMARK [1][-]{section.9.1}{Integer Division with Remainder}{chapter.9}
\BOOKMARK [1][-]{section.9.2}{Single Digit Helpers}{chapter.9}
\BOOKMARK [2][-]{subsection.9.2.1}{Single Digit Addition}{section.9.2}
\BOOKMARK [2][-]{subsection.9.2.2}{Single Digit Subtraction}{section.9.2}
\BOOKMARK [2][-]{subsection.9.2.3}{Single Digit Multiplication}{section.9.2}
\BOOKMARK [2][-]{subsection.9.2.4}{Single Digit Division}{section.9.2}
\BOOKMARK [2][-]{subsection.9.2.5}{Single Digit Modulo}{section.9.2}
\BOOKMARK [2][-]{subsection.9.2.6}{Single Digit Root Extraction}{section.9.2}
\BOOKMARK [1][-]{section.9.3}{Random Number Generation}{chapter.9}
\BOOKMARK [1][-]{section.9.4}{Formatted Output}{chapter.9}
\BOOKMARK [2][-]{subsection.9.4.1}{Getting The Output Size}{section.9.4}
\BOOKMARK [2][-]{subsection.9.4.2}{Generating Radix-n Output}{section.9.4}
\BOOKMARK [2][-]{subsection.9.4.3}{Reading Radix-n Input}{section.9.4}
\BOOKMARK [1][-]{section.9.5}{Unformatted Output}{chapter.9}
\BOOKMARK [2][-]{subsection.9.5.1}{Getting The Output Size}{section.9.5}
\BOOKMARK [2][-]{subsection.9.5.2}{Generating Output}{section.9.5}
\BOOKMARK [2][-]{subsection.9.5.3}{Reading Input}{section.9.5}
\BOOKMARK [0][-]{chapter.10}{Number Theoretic Algorithms}{}
\BOOKMARK [1][-]{section.10.1}{Greatest Common Divisor}{chapter.10}
\BOOKMARK [1][-]{section.10.2}{Least Common Multiple}{chapter.10}
\BOOKMARK [1][-]{section.10.3}{Jacobi Symbol Computation}{chapter.10}
\BOOKMARK [1][-]{section.10.4}{Modular Inverse}{chapter.10}
\BOOKMARK [2][-]{subsection.10.4.1}{General Case}{section.10.4}
\BOOKMARK [2][-]{subsection.10.4.2}{Odd Moduli}{section.10.4}
\BOOKMARK [1][-]{section.10.5}{Primality Tests}{chapter.10}
\BOOKMARK [2][-]{subsection.10.5.1}{Trial Division}{section.10.5}
\BOOKMARK [2][-]{subsection.10.5.2}{The Fermat Test}{section.10.5}
\BOOKMARK [2][-]{subsection.10.5.3}{The Miller-Rabin Test}{section.10.5}
\BOOKMARK [2][-]{subsection.10.5.4}{Primality Test in a Bottle}{section.10.5}
\BOOKMARK [2][-]{subsection.10.5.5}{The Next Prime}{section.10.5}
\BOOKMARK [1][-]{section.10.6}{Root Extraction}{chapter.10}
\BOOKMARK [0][-]{appendix*.16}{Appendix}{}

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