TeaSpeak/tommath
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

added libtommath-0.20

Browse Source
This commit is contained in:
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
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

BIN
bn.pdf
View File

Binary file not shown.

2
bn.tex
View File

@ -1,7 +1,7 @@
\documentclass[]{article}
\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}
\maketitle
\newpage

1
bn_mp_exptmod_fast.c
View File

@ -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) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
} else {
/* use slower baselien method */
redux = mp_montgomery_reduce;

4
changes.txt
View File

@ -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
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.

3
etc/2kprime.1
View File

@ -1,2 +1 @@
256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823
512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979
259-bits (k = 17745) = 926336713898529563388567880069503262826159877325124512315660672063305037101743

2
etc/2kprime.c
View File

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

5
makefile
View File

@ -1,6 +1,6 @@
CFLAGS += -I./ -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops
VERSION=0.19
VERSION=0.20
default: libtommath.a
@ -103,5 +103,6 @@ clean:
zipup: clean manual poster
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)/* > 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)/*

BIN
pics/expt_state.sxd
View File

Binary file not shown.

BIN
pics/expt_state.tif
View File

Binary file not shown.

23
pics/makefile
View File

@ -1,23 +0,0 @@
# 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

BIN
pics/sliding_window.TIF
View File

Binary file not shown.

BIN
pics/sliding_window.sxd
View File

Binary file not shown.

BIN
poster.pdf
View File

Binary file not shown.

1
pre_gen/mpi.c
View File

@ -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) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
} else {
/* use slower baselien method */
redux = mp_montgomery_reduce;

BIN
tdcal.pdf Normal file
View File

Binary file not shown.

143
tommath.out
View File

@ -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}{}

4675
tommath.src
View File

File diff suppressed because it is too large Load Diff

8141
tommath.tex
View File

File diff suppressed because it is too large Load Diff