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Merge branch 'release/1.1.0'

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This commit is contained in:
Steffen Jaeckel 2019-01-28 20:32:32 +01:00
commit 08549ad6bc
206 changed files with 21575 additions and 25816 deletions
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1
.gitattributes vendored
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@ -1,4 +1,5 @@
/.gitattributes export-ignore
/.gitignore export-ignore
/.travis.yml export-ignore
/** export-subst

29
.gitignore vendored
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@ -6,16 +6,18 @@
*.gcno
*.gcov
*.lib
Debug/
Release/
[Dd]ebug/
[Rr]elease/
/MSVC_*
.libs/
.coveralls.yml
coverage*/
coverage.info
pre_gen/*
# suppress output of build process and *nix/windows test executables
ltmtest
ltmtest.exe
timing
timing.exe
test
test.exe
mtest
@ -31,6 +33,25 @@ mtest.exe
# ignore user specific settings
*.user
*.suo
*.userosscache
*.sln.docstates
*.userprefs
# cache/options directory
.vs/
# Backup & report files from converting an old project file to a newer Visual Studio version
_UpgradeReport_Files/
Backup*/
UpgradeLog*.XML
UpgradeLog*.htm
# Visual Studio 6 build log + workspace options file
*.plg
*.opt
# visual studio profiler
*.psess
*.vsp
*.vspx
*.sap
# ignore stuff generated by "make manual" and "make poster"
*.aux

31
.travis.yml
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@ -1,18 +1,35 @@
language: c
compiler:
- gcc
script:
- make travis_mtest
- head -n 5 test.log
- tail -n 2 test.log
- ./testme.sh --with-cc=gcc --with-low-mp
install:
- sudo apt-get update -qq
- sudo apt-get install gcc-multilib
matrix:
fast_finish: true
branches:
only:
- master
- develop
- /^release\/.*$/
compiler:
- gcc
- clang
script:
- ./testme.sh --with-cc=$CC ${BUILDOPTIONS}
env:
- |
BUILDOPTIONS="--test-vs-mtest=333333"
- |
BUILDOPTIONS="--test-vs-mtest=333333 --mtest-real-rand"
- |
BUILDOPTIONS="--with-low-mp"
- |
BUILDOPTIONS="--with-m64 --with-m32 --with-mx32"
after_failure:
- cat test_*.log
- cat gcc_errors_*.log
notifications:
irc: "chat.freenode.net#libtom-notifications"

45
LICENSE
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@ -1,29 +1,26 @@
LibTomMath is licensed under DUAL licensing terms.
The LibTom license
Choose and use the license of your needs.
This is free and unencumbered software released into the public domain.
[LICENSE #1]
Anyone is free to copy, modify, publish, use, compile, sell, or
distribute this software, either in source code form or as a compiled
binary, for any purpose, commercial or non-commercial, and by any
means.
LibTomMath is public domain. As should all quality software be.
In jurisdictions that recognize copyright laws, the author or authors
of this software dedicate any and all copyright interest in the
software to the public domain. We make this dedication for the benefit
of the public at large and to the detriment of our heirs and
successors. We intend this dedication to be an overt act of
relinquishment in perpetuity of all present and future rights to this
software under copyright law.
Tom St Denis
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
[/LICENSE #1]
[LICENSE #2]
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
Version 2, December 2004
Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>
Everyone is permitted to copy and distribute verbatim or modified
copies of this license document, and changing it is allowed as long
as the name is changed.
DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. You just DO WHAT THE FUCK YOU WANT TO.
[/LICENSE #2]
For more information, please refer to <http://unlicense.org/>

16
README.md
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@ -1,8 +1,16 @@
[![Build Status - master](https://travis-ci.org/libtom/libtommath.png?branch=master)](https://travis-ci.org/libtom/libtommath)
# libtommath
[![Build Status - develop](https://travis-ci.org/libtom/libtommath.png?branch=develop)](https://travis-ci.org/libtom/libtommath)
This is the git repository for [LibTomMath](http://www.libtom.net/LibTomMath/), a free open source portable number theoretic multiple-precision integer (MPI) library written entirely in C.
This is the git repository for [LibTomMath](http://www.libtom.org/), a free open source portable number theoretic multiple-precision integer (MPI) library written entirely in C.
## Build Status
master: [![Build Status](https://api.travis-ci.org/libtom/libtommath.png?branch=master)](https://travis-ci.org/libtom/libtommath)
develop: [![Build Status](https://api.travis-ci.org/libtom/libtommath.png?branch=develop)](https://travis-ci.org/libtom/libtommath)
API/ABI changes: [check here](https://abi-laboratory.pro/tracker/timeline/libtommath/)
## Summary
The `develop` branch contains the in-development version. Stable releases are tagged.
@ -10,6 +18,8 @@ Documentation is built from the LaTeX file `bn.tex`. There is also limited docum
The project can be build by using `make`. Along with the usual `make`, `make clean` and `make install`, there are several other build targets, see the makefile for details. There are also makefiles for certain specific platforms.
## Testing
Tests are located in `demo/` and can be built in two flavors.
* `make test` creates a test binary that is intended to be run against `mtest`. `mtest` can be built with `make mtest` and test execution is done like `./mtest/mtest | ./test`. `mtest` is creating test vectors using an alternative MPI library and `test` is consuming these vectors to verify correct behavior of ltm
* `make test_standalone` creates a stand-alone test binary that executes several test routines.

27
astylerc Normal file
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@ -0,0 +1,27 @@
# Artistic Style, see http://astyle.sourceforge.net/
# full documentation, see: http://astyle.sourceforge.net/astyle.html
#
# usage:
# astyle --options=astylerc *.[ch]
## Bracket Style Options
style=kr
## Tab Options
indent=spaces=3
## Bracket Modify Options
## Indentation Options
min-conditional-indent=0
## Padding Options
pad-header
unpad-paren
align-pointer=name
## Formatting Options
break-after-logical
max-code-length=120
convert-tabs
mode=c

27
bn_error.c
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@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,31 +9,28 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
static const struct {
int code;
const char *msg;
int code;
const char *msg;
} msgs[] = {
{ MP_OKAY, "Successful" },
{ MP_MEM, "Out of heap" },
{ MP_VAL, "Value out of range" }
{ MP_OKAY, "Successful" },
{ MP_MEM, "Out of heap" },
{ MP_VAL, "Value out of range" }
};
/* return a char * string for a given code */
const char *mp_error_to_string(int code)
{
int x;
size_t 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;
}
for (x = 0; x < (sizeof(msgs) / sizeof(msgs[0])); x++) {
if (msgs[x].code == code) {
return msgs[x].msg;
}
}
/* generic reply for invalid code */

236
bn_fast_mp_invmod.c
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@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,137 +9,149 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
/* 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
* 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)
int fast_mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int x, y, u, v, B, D;
int res, neg;
mp_int x, y, u, v, B, D;
int res, neg;
/* 2. [modified] b must be odd */
if (mp_iseven (b) == MP_YES) {
return MP_VAL;
}
/* 2. [modified] b must be odd */
if (mp_iseven(b) == MP_YES) {
return MP_VAL;
}
/* init all our temps */
if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
return res;
}
/* 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;
}
/* 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;
}
/* 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);
/* if one of x,y is zero return an error! */
if ((mp_iszero(&x) == MP_YES) || (mp_iszero(&y) == MP_YES)) {
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(&D, 1uL);
top:
/* 4. while u is even do */
while (mp_iseven (&u) == MP_YES) {
/* 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) == MP_YES) {
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
/* 4. while u is even do */
while (mp_iseven(&u) == MP_YES) {
/* 4.1 u = u/2 */
if ((res = mp_div_2(&u, &u)) != 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) == MP_YES) {
/* 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) == MP_YES) {
/* D = (D-x)/2 */
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
goto LBL_ERR;
/* 4.2 if B is odd then */
if (mp_isodd(&B) == MP_YES) {
if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) {
goto LBL_ERR;
}
}
}
/* D = D/2 */
if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
/* 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) == MP_YES) {
/* 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) == MP_YES) {
/* 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) == MP_NO) {
goto top;
}
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d(&v, 1uL) != MP_EQ) {
res = MP_VAL;
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;
}
/* 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;
}
}
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;
}
/* too big */
while (mp_cmp_mag(&D, b) != MP_LT) {
if ((res = mp_sub(&D, b, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
goto LBL_ERR;
}
}
mp_exch(&D, c);
c->sign = neg;
res = MP_OKAY;
/* if not zero goto step 4 */
if (mp_iszero (&u) == MP_NO) {
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;
LBL_ERR:
mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL);
return res;
}
#endif

257
bn_fast_mp_montgomery_reduce.c
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@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* computes xR**-1 == x (mod N) via Montgomery Reduction
@ -23,147 +20,151 @@
*
* 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 fast_mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
{
int ix, res, olduse;
mp_word W[MP_WARRAY];
int ix, res, olduse;
mp_word W[MP_WARRAY];
/* get old used count */
olduse = x->used;
if (x->used > (int)MP_WARRAY) {
return MP_VAL;
}
/* grow a as required */
if (x->alloc < (n->used + 1)) {
if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
return res;
}
}
/* get old used count */
olduse = x->used;
/* first we have to get the digits of the input into
* an array of double precision words W[...]
*/
{
mp_word *_W;
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)
*/
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
*/
{
int iy;
mp_digit *tmpn;
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++);
/* grow a as required */
if (x->alloc < (n->used + 1)) {
if ((res = mp_grow(x, n->used + 1)) != MP_OKAY) {
return res;
}
}
}
/* now fix carry for next digit, W[ix+1] */
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
/* first we have to get the digits of the input into
* an array of double precision words W[...]
*/
{
mp_word *_W;
mp_digit *tmpx;
/* now we have to propagate the carries and
* shift the words downward [all those least
* significant digits we zeroed].
*/
{
mp_digit *tmpx;
mp_word *_W, *_W1;
/* alias for the W[] array */
_W = W;
/* nox fix rest of carries */
/* alias for the digits of x*/
tmpx = x->dp;
/* alias for current word */
_W1 = W + ix;
/* copy the digits of a into W[0..a->used-1] */
for (ix = 0; ix < x->used; ix++) {
*_W++ = *tmpx++;
}
/* alias for next word, where the carry goes */
_W = W + ++ix;
/* zero the high words of W[a->used..m->used*2] */
for (; ix < ((n->used * 2) + 1); ix++) {
*_W++ = 0;
}
}
for (; ix <= ((n->used * 2) + 1); ix++) {
*_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
}
/* 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)
*/
mp_digit mu;
mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
/* 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
*/
/* 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
*/
{
int iy;
mp_digit *tmpn;
mp_word *_W;
/* alias for destination word */
tmpx = x->dp;
/* alias for the digits of the modulus */
tmpn = n->dp;
/* alias for shifted double precision result */
_W = W + n->used;
/* Alias for the columns set by an offset of ix */
_W = W + ix;
for (ix = 0; ix < (n->used + 1); ix++) {
*tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
}
/* inner loop */
for (iy = 0; iy < n->used; iy++) {
*_W++ += (mp_word)mu * (mp_word)*tmpn++;
}
}
/* 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;
}
}
/* now fix carry for next digit, W[ix+1] */
W[ix + 1] += W[ix] >> (mp_word)DIGIT_BIT;
}
/* set the max used and clamp */
x->used = n->used + 1;
mp_clamp (x);
/* now we have to propagate the carries and
* shift the words downward [all those least
* significant digits we zeroed].
*/
{
mp_digit *tmpx;
mp_word *_W, *_W1;
/* 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;
/* 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++ = *_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

93
bn_fast_s_mp_mul_digs.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,47 +9,44 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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
* 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
* 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 fast_s_mp_mul_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
int olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY];
mp_word _W;
int olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY];
mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
if ((res = mp_grow (c, digs)) != MP_OKAY) {
return res;
}
}
/* 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);
/* number of output digits to produce */
pa = MIN(digs, a->used + b->used);
/* clear the carry */
_W = 0;
for (ix = 0; ix < pa; ix++) {
/* clear the carry */
_W = 0;
for (ix = 0; ix < pa; ix++) {
int tx, ty;
int iy;
mp_digit *tmpx, *tmpy;
@ -62,43 +59,43 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
tmpx = a->dp + tx;
tmpy = b->dp + ty;
/* this is the number of times the loop will iterrate, essentially
/* 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--);
_W += (mp_word)*tmpx++ * (mp_word)*tmpy--;
}
/* store term */
W[ix] = ((mp_digit)_W) & MP_MASK;
W[ix] = (mp_digit)_W & MP_MASK;
/* make next carry */
_W = _W >> ((mp_word)DIGIT_BIT);
}
_W = _W >> (mp_word)DIGIT_BIT;
}
/* setup dest */
olduse = c->used;
c->used = pa;
/* setup dest */
olduse = c->used;
c->used = pa;
{
mp_digit *tmpc;
tmpc = c->dp;
for (ix = 0; ix < (pa + 1); ix++) {
/* now extract the previous digit [below the carry] */
*tmpc++ = W[ix];
}
{
mp_digit *tmpc;
tmpc = c->dp;
for (ix = 0; 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;
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp(c);
return MP_OKAY;
}
#endif

83
bn_fast_s_mp_mul_high_digs.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* this is a modified version of fast_s_mul_digs that only produces
@ -24,24 +21,24 @@
*
* 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 fast_s_mp_mul_high_digs(const mp_int *a, const mp_int *b, mp_int *c, int digs)
{
int olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY];
mp_word _W;
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;
}
}
/* 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++) {
/* 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;
@ -53,43 +50,43 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
tmpx = a->dp + tx;
tmpy = b->dp + ty;
/* this is the number of times the loop will iterrate, essentially its
/* 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--);
_W += (mp_word)*tmpx++ * (mp_word)*tmpy--;
}
/* store term */
W[ix] = ((mp_digit)_W) & MP_MASK;
W[ix] = (mp_digit)_W & MP_MASK;
/* make next carry */
_W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
olduse = c->used;
c->used = pa;
_W = _W >> (mp_word)DIGIT_BIT;
}
{
mp_digit *tmpc;
/* setup dest */
olduse = c->used;
c->used = pa;
tmpc = c->dp + digs;
for (ix = digs; ix < pa; ix++) {
/* now extract the previous digit [below the carry] */
*tmpc++ = W[ix];
}
{
mp_digit *tmpc;
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
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

87
bn_fast_s_mp_sqr.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,39 +9,36 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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.
* 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
* (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 fast_s_mp_sqr(const mp_int *a, mp_int *b)
{
int olduse, res, pa, ix, iz;
mp_digit W[MP_WARRAY], *tmpx;
mp_word W1;
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;
}
}
/* 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++) {
/* number of output digits to produce */
W1 = 0;
for (ix = 0; ix < pa; ix++) {
int tx, ty, iy;
mp_word _W;
mp_digit *tmpy;
@ -62,7 +59,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
*/
iy = MIN(a->used-tx, ty+1);
/* now for squaring tx can never equal ty
/* 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
*/
@ -70,42 +67,42 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
/* execute loop */
for (iz = 0; iz < iy; iz++) {
_W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
_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]);
if (((unsigned)ix & 1u) == 0u) {
_W += (mp_word)a->dp[ix>>1] * (mp_word)a->dp[ix>>1];
}
/* store it */
W[ix] = (mp_digit)(_W & MP_MASK);
W[ix] = _W & MP_MASK;
/* make next carry */
W1 = _W >> ((mp_word)DIGIT_BIT);
}
W1 = _W >> (mp_word)DIGIT_BIT;
}
/* setup dest */
olduse = b->used;
b->used = a->used+a->used;
/* 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;
}
{
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;
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
mp_clamp(b);
return MP_OKAY;
}
#endif

36
bn_mp_2expt.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,37 +9,33 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* computes a = 2**b
/* 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 mp_2expt(mp_int *a, int b)
{
int res;
int res;
/* zero a as per default */
mp_zero (a);
/* 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;
}
/* 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;
/* 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);
/* put the single bit in its place */
a->dp[b / DIGIT_BIT] = (mp_digit)1 << (mp_digit)(b % DIGIT_BIT);
return MP_OKAY;
return MP_OKAY;
}
#endif

32
bn_mp_abs.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,32 +9,28 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* b = |a|
/* b = |a|
*
* Simple function copies the input and fixes the sign to positive
*/
int
mp_abs (mp_int * a, mp_int * b)
int mp_abs(const mp_int *a, mp_int *b)
{
int res;
int res;
/* copy a to b */
if (a != b) {
if ((res = mp_copy (a, b)) != MP_OKAY) {
return 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;
/* force the sign of b to positive */
b->sign = MP_ZPOS;
return MP_OKAY;
return MP_OKAY;
}
#endif

55
bn_mp_add.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,41 +9,38 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
int mp_add(const mp_int *a, const mp_int *b, mp_int *c)
{
int sa, sb, res;
int sa, sb, res;
/* get sign of both inputs */
sa = a->sign;
sb = b->sign;
/* 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 {
/* 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_sub (a, b, c);
}
}
return res;
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

145
bn_mp_add_d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,100 +9,97 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* single digit addition */
int
mp_add_d (mp_int * a, mp_digit b, mp_int * c)
int mp_add_d(const mp_int *a, mp_digit b, mp_int *c)
{
int res, ix, oldused;
mp_digit *tmpa, *tmpc, mu;
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;
}
}
/* 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;
/* if a is negative and |a| >= b, call c = |a| - b */
if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) {
mp_int a_ = *a;
/* temporarily fix sign of a */
a_.sign = MP_ZPOS;
/* c = |a| - b */
res = mp_sub_d(a, b, c);
/* c = |a| - b */
res = mp_sub_d(&a_, b, c);
/* fix sign */
a->sign = c->sign = MP_NEG;
/* fix sign */
c->sign = MP_NEG;
/* clamp */
mp_clamp(c);
/* clamp */
mp_clamp(c);
return res;
}
return res;
}
/* old number of used digits in c */
oldused = c->used;
/* old number of used digits in c */
oldused = c->used;
/* source alias */
tmpa = a->dp;
/* source alias */
tmpa = a->dp;
/* destination alias */
tmpc = c->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;
/* 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;
/* 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;
/* 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;
}
/* 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;
}
/* setup count so the clearing of oldused
* can fall through correctly
*/
ix = 1;
}
/* sign always positive */
c->sign = MP_ZPOS;
/* sign always positive */
c->sign = MP_ZPOS;
/* now zero to oldused */
while (ix++ < oldused) {
*tmpc++ = 0;
}
mp_clamp(c);
/* now zero to oldused */
while (ix++ < oldused) {
*tmpc++ = 0;
}
mp_clamp(c);
return MP_OKAY;
return MP_OKAY;
}
#endif

34
bn_mp_addmod.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,30 +9,26 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* d = a + b (mod c) */
int
mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
int res;
mp_int t;
int res;
mp_int t;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}
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;
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

63
bn_mp_and.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,46 +9,43 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* AND two ints together */
int
mp_and (mp_int * a, mp_int * b, mp_int * c)
int mp_and(const mp_int *a, const mp_int *b, mp_int *c)
{
int res, ix, px;
mp_int t, *x;
int res, ix, px;
mp_int t;
const mp_int *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;
}
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];
}
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;
}
/* 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;
mp_clamp(&t);
mp_exch(c, &t);
mp_clear(&t);
return MP_OKAY;
}
#endif

32
bn_mp_clamp.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,33 +9,29 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* trim unused digits
/* 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)
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);
}
/* decrease used while the most significant digit is
* zero.
*/
while ((a->used > 0) && (a->dp[a->used - 1] == 0u)) {
--(a->used);
}
/* reset the sign flag if used == 0 */
if (a->used == 0) {
a->sign = MP_ZPOS;
}
/* reset the sign flag if used == 0 */
if (a->used == 0) {
a->sign = MP_ZPOS;
}
}
#endif

38
bn_mp_clear.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,33 +9,29 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* clear one (frees) */
void
mp_clear (mp_int * a)
void mp_clear(mp_int *a)
{
int i;
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;
}
/* 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);
/* free ram */
XFREE(a->dp);
/* reset members to make debugging easier */
a->dp = NULL;
a->alloc = a->used = 0;
a->sign = MP_ZPOS;
}
/* reset members to make debugging easier */
a->dp = NULL;
a->alloc = a->used = 0;
a->sign = MP_ZPOS;
}
}
#endif

26
bn_mp_clear_multi.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,23 +9,21 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
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);
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

42
bn_mp_cmp.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,32 +9,28 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* compare two ints (signed)*/
int
mp_cmp (mp_int * a, mp_int * b)
int mp_cmp(const mp_int *a, const 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);
}
/* 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

41
bn_mp_cmp_d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,33 +9,30 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* compare a digit */
int mp_cmp_d(mp_int * a, mp_digit b)
int mp_cmp_d(const mp_int *a, mp_digit b)
{
/* compare based on sign */
if (a->sign == MP_NEG) {
return MP_LT;
}
/* compare based on sign */
if (a->sign == MP_NEG) {
return MP_LT;
}
/* compare based on magnitude */
if (a->used > 1) {
return MP_GT;
}
/* 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;
}
/* 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

59
bn_mp_cmp_mag.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,44 +9,41 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (mp_int * a, mp_int * b)
int mp_cmp_mag(const mp_int *a, const mp_int *b)
{
int n;
mp_digit *tmpa, *tmpb;
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) {
/* compare based on # of non-zero digits */
if (a->used > b->used) {
return MP_GT;
}
}
if (*tmpa < *tmpb) {
if (a->used < b->used) {
return MP_LT;
}
}
return MP_EQ;
}
/* 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

19
bn_mp_cnt_lsb.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,18 +9,15 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
static const int lnz[16] = {
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 mp_cnt_lsb(const mp_int *a)
{
int x;
mp_digit q, qq;
@ -31,17 +28,17 @@ int mp_cnt_lsb(mp_int *a)
}
/* scan lower digits until non-zero */
for (x = 0; (x < a->used) && (a->dp[x] == 0); x++) {}
for (x = 0; (x < a->used) && (a->dp[x] == 0u); x++) {}
q = a->dp[x];
x *= DIGIT_BIT;
/* now scan this digit until a 1 is found */
if ((q & 1) == 0) {
if ((q & 1u) == 0u) {
do {
qq = q & 15;
qq = q & 15u;
x += lnz[qq];
q >>= 4;
} while (qq == 0);
} while (qq == 0u);
}
return x;
}

25
bn_mp_complement.c Normal file
View File

@ -0,0 +1,25 @@
#include "tommath_private.h"
#ifdef BN_MP_COMPLEMENT_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.
*
* SPDX-License-Identifier: Unlicense
*/
/* b = ~a */
int mp_complement(const mp_int *a, mp_int *b)
{
int res = mp_neg(a, b);
return (res == MP_OKAY) ? mp_sub_d(b, 1uL, b) : res;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

74
bn_mp_copy.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,57 +9,53 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* copy, b = a */
int
mp_copy (mp_int * a, mp_int * b)
int mp_copy(const mp_int *a, mp_int *b)
{
int res, n;
int res, n;
/* if dst == src do nothing */
if (a == b) {
return MP_OKAY;
}
/* 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;
}
}
/* 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 */
{
mp_digit *tmpa, *tmpb;
/* zero b and copy the parameters over */
{
mp_digit *tmpa, *tmpb;
/* pointer aliases */
/* pointer aliases */
/* source */
tmpa = a->dp;
/* source */
tmpa = a->dp;
/* destination */
tmpb = b->dp;
/* destination */
tmpb = b->dp;
/* copy all the digits */
for (n = 0; n < a->used; n++) {
*tmpb++ = *tmpa++;
}
/* copy all the digits */
for (n = 0; n < a->used; n++) {
*tmpb++ = *tmpa++;
}
/* clear high digits */
for (; n < b->used; n++) {
*tmpb++ = 0;
}
}
/* 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;
/* copy used count and sign */
b->used = a->used;
b->sign = a->sign;
return MP_OKAY;
}
#endif

42
bn_mp_count_bits.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,34 +9,30 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* returns the number of bits in an int */
int
mp_count_bits (mp_int * a)
int mp_count_bits(const mp_int *a)
{
int r;
mp_digit q;
int r;
mp_digit q;
/* shortcut */
if (a->used == 0) {
return 0;
}
/* 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;
/* 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

460
bn_mp_div.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,77 +9,74 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
#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)
int mp_div(const mp_int *a, const 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) == MP_YES) {
return MP_VAL;
}
/* is divisor zero ? */
if (mp_iszero(b) == MP_YES) {
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 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;
}
/* 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)) {
mp_set(&tq, 1uL);
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;
}
}
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;
}
/* 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;
@ -100,190 +97,195 @@ LBL_ERR:
* 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)
int mp_div(const mp_int *a, const mp_int *b, mp_int *c, mp_int *d)
{
mp_int q, x, y, t1, t2;
int res, n, t, i, norm, neg;
mp_int q, x, y, t1, t2;
int res, n, t, i, norm, neg;
/* is divisor zero ? */
if (mp_iszero (b) == MP_YES) {
return MP_VAL;
}
/* is divisor zero ? */
if (mp_iszero(b) == MP_YES) {
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;
/* 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;
}
q.dp[(i - t) - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
}
if (c != NULL) {
mp_zero(c);
}
return res;
}
/* while (q{i-t-1} * (yt * b + y{t-1})) >
xi * b**2 + xi-1 * b + xi-2
if ((res = mp_init_size(&q, a->used + 2)) != MP_OKAY) {
return res;
}
q.used = a->used + 2;
do q{i-t-1} -= 1;
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 < (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 << (mp_digit)DIGIT_BIT) - (mp_digit)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] + 1uL) & (mp_digit)MP_MASK;
do {
q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1uL) & (mp_digit)MP_MASK;
/* find left hand */
mp_zero(&t1);
t1.dp[0] = ((t - 1) < 0) ? 0u : 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) ? 0u : x.dp[i - 2];
t2.dp[1] = ((i - 1) < 0) ? 0u : 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]
*/
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;
/* 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);
}
/* 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);
res = MP_OKAY;
/* 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;
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

77
bn_mp_div_2.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,57 +9,54 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
int mp_div_2(const mp_int *a, mp_int *b)
{
int x, res, oldused;
int x, res, oldused;
/* copy */
if (b->alloc < a->used) {
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
return res;
}
}
/* copy */
if (b->alloc < a->used) {
if ((res = mp_grow(b, a->used)) != MP_OKAY) {
return res;
}
}
oldused = b->used;
b->used = a->used;
{
mp_digit r, rr, *tmpa, *tmpb;
oldused = b->used;
b->used = a->used;
{
mp_digit r, rr, *tmpa, *tmpb;
/* source alias */
tmpa = a->dp + b->used - 1;
/* source alias */
tmpa = a->dp + b->used - 1;
/* dest alias */
tmpb = b->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;
/* carry */
r = 0;
for (x = b->used - 1; x >= 0; x--) {
/* get the carry for the next iteration */
rr = *tmpa & 1u;
/* shift the current digit, add in carry and store */
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
/* shift the current digit, add in carry and store */
*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
/* forward carry to next iteration */
r = rr;
}
/* 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;
/* 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

109
bn_mp_div_2d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,75 +9,72 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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)
int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d)
{
mp_digit D, r, rr;
int x, res;
mp_digit D, r, rr;
int x, res;
/* 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;
}
/* copy */
if ((res = mp_copy (a, c)) != MP_OKAY) {
return res;
}
/* 'a' should not be used after here - it might be the same as d */
/* get the remainder */
if (d != NULL) {
if ((res = mp_mod_2d (a, b, d)) != MP_OKAY) {
/* 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;
}
}
}
/* shift by as many digits in the bit count */
if (b >= (int)DIGIT_BIT) {
mp_rshd (c, b / DIGIT_BIT);
}
/* copy */
if ((res = mp_copy(a, c)) != MP_OKAY) {
return res;
}
/* 'a' should not be used after here - it might be the same as d */
/* shift any bit count < DIGIT_BIT */
D = (mp_digit) (b % DIGIT_BIT);
if (D != 0) {
mp_digit *tmpc, mask, shift;
/* get the remainder */
if (d != NULL) {
if ((res = mp_mod_2d(a, b, d)) != MP_OKAY) {
return res;
}
}
/* mask */
mask = (((mp_digit)1) << D) - 1;
/* shift by as many digits in the bit count */
if (b >= DIGIT_BIT) {
mp_rshd(c, b / DIGIT_BIT);
}
/* shift for lsb */
shift = DIGIT_BIT - D;
/* shift any bit count < DIGIT_BIT */
D = (mp_digit)(b % DIGIT_BIT);
if (D != 0u) {
mp_digit *tmpc, mask, shift;
/* alias */
tmpc = c->dp + (c->used - 1);
/* mask */
mask = ((mp_digit)1 << D) - 1uL;
/* 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 for lsb */
shift = (mp_digit)DIGIT_BIT - D;
/* shift the current word and mix in the carry bits from the previous word */
*tmpc = (*tmpc >> D) | (r << shift);
--tmpc;
/* alias */
tmpc = c->dp + (c->used - 1);
/* set the carry to the carry bits of the current word found above */
r = rr;
}
}
mp_clamp (c);
return MP_OKAY;
/* 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);
return MP_OKAY;
}
#endif

94
bn_mp_div_3.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,67 +9,63 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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)
int mp_div_3(const 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);
mp_int q;
mp_word w, t;
mp_digit b;
int res, ix;
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]);
/* b = 2**DIGIT_BIT / 3 */
b = ((mp_word)1 << (mp_word)DIGIT_BIT) / (mp_word)3;
if (w >= 3) {
/* multiply w by [1/3] */
t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
return res;
}
/* now subtract 3 * [w/3] from w, to get the remainder */
w -= t+t+t;
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];
/* fixup the remainder as required since
* the optimization is not exact.
*/
while (w >= 3) {
t += 1;
w -= 3;
}
if (w >= 3u) {
/* 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 >= 3u) {
t += 1u;
w -= 3u;
}
} else {
t = 0;
t = 0;
}
q.dp[ix] = (mp_digit)t;
}
}
/* [optional] store the remainder */
if (d != NULL) {
*d = (mp_digit)w;
}
/* [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;
/* [optional] store the quotient */
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
}
mp_clear(&q);
return res;
}
#endif

135
bn_mp_div_d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
static int s_is_power_of_two(mp_digit b, int *p)
@ -20,12 +17,12 @@ static int s_is_power_of_two(mp_digit b, int *p)
int x;
/* fast return if no power of two */
if ((b == 0) || ((b & (b-1)) != 0)) {
if ((b == 0u) || ((b & (b-1u)) != 0u)) {
return 0;
}
for (x = 0; x < DIGIT_BIT; x++) {
if (b == (((mp_digit)1)<<x)) {
if (b == ((mp_digit)1<<(mp_digit)x)) {
*p = x;
return 1;
}
@ -34,78 +31,78 @@ static int s_is_power_of_two(mp_digit b, int *p)
}
/* single digit division (based on routine from MPI) */
int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
int mp_div_d(const mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
{
mp_int q;
mp_word w;
mp_digit t;
int res, ix;
mp_int q;
mp_word w;
mp_digit t;
int res, ix;
/* cannot divide by zero */
if (b == 0) {
return MP_VAL;
}
/* cannot divide by zero */
if (b == 0u) {
return MP_VAL;
}
/* quick outs */
if ((b == 1) || (mp_iszero(a) == MP_YES)) {
if (d != NULL) {
*d = 0;
}
if (c != NULL) {
return mp_copy(a, c);
}
return MP_OKAY;
}
/* quick outs */
if ((b == 1u) || (mp_iszero(a) == MP_YES)) {
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;
}
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
*d = a->dp[0] & (((mp_digit)1<<(mp_digit)ix) - 1uL);
}
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);
}
/* three? */
if (b == 3u) {
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);
/* 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;
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;
q.dp[ix] = t;
}
if (d != NULL) {
*d = (mp_digit)w;
}
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);
}
mp_clear(&q);
return res;
}
#endif

15
bn_mp_dr_is_modulus.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,14 +9,11 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
int mp_dr_is_modulus(const mp_int *a)
{
int ix;
@ -29,9 +26,9 @@ int mp_dr_is_modulus(mp_int *a)
* 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;
}
if (a->dp[ix] != MP_MASK) {
return 0;
}
}
return 1;
}

94
bn_mp_dr_reduce.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
@ -29,65 +26,64 @@
*
* 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 mp_dr_reduce(mp_int *x, const mp_int *n, mp_digit k)
{
int err, i, m;
mp_word r;
mp_digit mu, *tmpx1, *tmpx2;
int err, i, m;
mp_word r;
mp_digit mu, *tmpx1, *tmpx2;
/* m = digits in modulus */
m = n->used;
/* 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;
}
}
/* 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 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;
/* 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;
/* alias for upper half of x, or x/B**m */
tmpx2 = x->dp + m;
/* set carry to zero */
mu = 0;
/* 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;
/* 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;
/* set final carry */
*tmpx1++ = mu;
/* zero words above m */
for (i = m + 1; i < x->used; i++) {
/* zero words above m */
for (i = m + 1; i < x->used; i++) {
*tmpx1++ = 0;
}
}
/* clamp, sub and return */
mp_clamp (x);
/* 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) {
if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
return err;
}
goto top;
}
return MP_OKAY;
/* 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) {
if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
return err;
}
goto top;
}
return MP_OKAY;
}
#endif

12
bn_mp_dr_setup.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,20 +9,16 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
void mp_dr_setup(const 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]));
*d = (mp_digit)(((mp_word)1 << (mp_word)DIGIT_BIT) - (mp_word)a->dp[0]);
}
#endif

20
bn_mp_exch.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,23 +9,19 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* swap the elements of two integers, for cases where you can't simply swap the
/* 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)
void mp_exch(mp_int *a, mp_int *b)
{
mp_int t;
mp_int t;
t = *a;
*a = *b;
*b = t;
t = *a;
*a = *b;
*b = t;
}
#endif

104
bn_mp_export.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_EXPORT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,76 +9,72 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* based on gmp's mpz_export.
* see http://gmplib.org/manual/Integer-Import-and-Export.html
*/
int mp_export(void* rop, size_t* countp, int order, size_t size,
int endian, size_t nails, mp_int* op) {
int result;
size_t odd_nails, nail_bytes, i, j, bits, count;
unsigned char odd_nail_mask;
int mp_export(void *rop, size_t *countp, int order, size_t size,
int endian, size_t nails, const mp_int *op)
{
int result;
size_t odd_nails, nail_bytes, i, j, bits, count;
unsigned char odd_nail_mask;
mp_int t;
mp_int t;
if ((result = mp_init_copy(&t, op)) != MP_OKAY) {
return result;
}
if ((result = mp_init_copy(&t, op)) != MP_OKAY) {
return result;
}
if (endian == 0) {
union {
unsigned int i;
char c[4];
} lint;
lint.i = 0x01020304;
endian = (lint.c[0] == 4) ? -1 : 1;
}
if (endian == 0) {
union {
unsigned int i;
char c[4];
} lint;
lint.i = 0x01020304;
odd_nails = (nails % 8);
odd_nail_mask = 0xff;
for (i = 0; i < odd_nails; ++i) {
odd_nail_mask ^= (1 << (7 - i));
}
nail_bytes = nails / 8;
endian = (lint.c[0] == '\x04') ? -1 : 1;
}
bits = mp_count_bits(&t);
count = (bits / ((size * 8) - nails)) + (((bits % ((size * 8) - nails)) != 0) ? 1 : 0);
odd_nails = (nails % 8u);
odd_nail_mask = 0xff;
for (i = 0; i < odd_nails; ++i) {
odd_nail_mask ^= (unsigned char)(1u << (7u - i));
}
nail_bytes = nails / 8u;
for (i = 0; i < count; ++i) {
for (j = 0; j < size; ++j) {
unsigned char* byte = (
(unsigned char*)rop +
(((order == -1) ? i : ((count - 1) - i)) * size) +
((endian == -1) ? j : ((size - 1) - j))
);
bits = (size_t)mp_count_bits(&t);
count = (bits / ((size * 8u) - nails)) + (((bits % ((size * 8u) - nails)) != 0u) ? 1u : 0u);
if (j >= (size - nail_bytes)) {
*byte = 0;
continue;
}
for (i = 0; i < count; ++i) {
for (j = 0; j < size; ++j) {
unsigned char *byte = (unsigned char *)rop +
(((order == -1) ? i : ((count - 1u) - i)) * size) +
((endian == -1) ? j : ((size - 1u) - j));
*byte = (unsigned char)((j == ((size - nail_bytes) - 1)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFF));
if (j >= (size - nail_bytes)) {
*byte = 0;
continue;
}
if ((result = mp_div_2d(&t, ((j == ((size - nail_bytes) - 1)) ? (8 - odd_nails) : 8), &t, NULL)) != MP_OKAY) {
mp_clear(&t);
return result;
}
}
}
*byte = (unsigned char)((j == ((size - nail_bytes) - 1u)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFFuL));
mp_clear(&t);
if ((result = mp_div_2d(&t, (j == ((size - nail_bytes) - 1u)) ? (int)(8u - odd_nails) : 8, &t, NULL)) != MP_OKAY) {
mp_clear(&t);
return result;
}
}
}
if (countp != NULL) {
*countp = count;
}
mp_clear(&t);
return MP_OKAY;
if (countp != NULL) {
*countp = count;
}
return MP_OKAY;
}
#endif

11
bn_mp_expt_d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,16 +9,13 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* wrapper function for mp_expt_d_ex() */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
int mp_expt_d(const mp_int *a, mp_digit b, mp_int *c)
{
return mp_expt_d_ex(a, b, c, 0);
return mp_expt_d_ex(a, b, c, 0);
}
#endif

106
bn_mp_expt_d_ex.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_EXPT_D_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,72 +9,68 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
int mp_expt_d_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
{
int res;
unsigned int x;
int res;
unsigned int x;
mp_int g;
mp_int g;
if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
return res;
}
if ((res = mp_init_copy(&g, a)) != MP_OKAY) {
return res;
}
/* set initial result */
mp_set (c, 1);
/* set initial result */
mp_set(c, 1uL);
if (fast != 0) {
while (b > 0) {
/* if the bit is set multiply */
if ((b & 1) != 0) {
if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
mp_clear (&g);
return res;
}
if (fast != 0) {
while (b > 0u) {
/* if the bit is set multiply */
if ((b & 1u) != 0u) {
if ((res = mp_mul(c, &g, c)) != MP_OKAY) {
mp_clear(&g);
return res;
}
}
/* square */
if (b > 1u) {
if ((res = mp_sqr(&g, &g)) != MP_OKAY) {
mp_clear(&g);
return res;
}
}
/* shift to next bit */
b >>= 1;
}
} else {
for (x = 0; x < (unsigned)DIGIT_BIT; x++) {
/* square */
if ((res = mp_sqr(c, c)) != MP_OKAY) {
mp_clear(&g);
return res;
}
/* square */
if (b > 1) {
if ((res = mp_sqr (&g, &g)) != MP_OKAY) {
mp_clear (&g);
return res;
}
/* if the bit is set multiply */
if ((b & ((mp_digit)1 << (DIGIT_BIT - 1))) != 0u) {
if ((res = mp_mul(c, &g, c)) != MP_OKAY) {
mp_clear(&g);
return res;
}
}
/* shift to next bit */
b <<= 1;
}
} /* if ... else */
/* shift to next bit */
b >>= 1;
}
}
else {
for (x = 0; x < 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;
}
} /* if ... else */
mp_clear (&g);
return MP_OKAY;
mp_clear(&g);
return MP_OKAY;
}
#endif

121
bn_mp_exptmod.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
@ -21,87 +18,87 @@
* 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 mp_exptmod(const mp_int *G, const mp_int *X, const mp_int *P, mp_int *Y)
{
int dr;
int dr;
/* modulus P must be positive */
if (P->sign == MP_NEG) {
return MP_VAL;
}
/* 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) {
/* 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;
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;
}
/* 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;
}
/* 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;
/* 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 */
/* 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);
}
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);
/* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
#else
/* default to no */
dr = 0;
/* 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;
}
/* 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 */
/* if the modulus is odd or dr != 0 use the montgomery method */
#ifdef BN_MP_EXPTMOD_FAST_C
if ((mp_isodd (P) == MP_YES) || (dr != 0)) {
return mp_exptmod_fast (G, X, P, Y, dr);
} else {
if ((mp_isodd(P) == MP_YES) || (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);
/* otherwise use the generic Barrett reduction technique */
return s_mp_exptmod(G, X, P, Y, 0);
#else
/* no exptmod for evens */
return MP_VAL;
/* no exptmod for evens */
return MP_VAL;
#endif
#ifdef BN_MP_EXPTMOD_FAST_C
}
}
#endif
}

478
bn_mp_exptmod_fast.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
@ -24,294 +21,295 @@
*/
#ifdef MP_LOW_MEM
#define TAB_SIZE 32
# define TAB_SIZE 32
#else
#define TAB_SIZE 256
# define TAB_SIZE 256
#endif
int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
int mp_exptmod_fast(const mp_int *G, const mp_int *X, const 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;
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);
/* 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 *x, const mp_int *n, mp_digit rho);
/* 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;
}
/* 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;
}
if (winsize > 5) {
winsize = 5;
}
#endif
/* init M array */
/* init first cell */
if ((err = mp_init_size(&M[1], P->alloc)) != 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_size(&M[x], P->alloc)) != MP_OKAY) {
for (y = 1<<(winsize-1); y < x; y++) {
mp_clear (&M[y]);
}
mp_clear(&M[1]);
/* init M array */
/* init first cell */
if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
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;
}
/* now init the second half of the array */
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
if ((err = mp_init_size(&M[x], P->alloc)) != 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;
err = MP_VAL;
goto LBL_M;
#endif
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
/* 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) &&
if ((((P->used * 2) + 1) < (int)MP_WARRAY) &&
(P->used < (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
redux = fast_mp_montgomery_reduce;
} else
redux = fast_mp_montgomery_reduce;
} else
#endif
{
{
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
#else
err = MP_VAL;
goto LBL_M;
err = MP_VAL;
goto LBL_M;
#endif
}
} else if (redmode == 1) {
}
} 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;
/* 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;
err = MP_VAL;
goto LBL_M;
#endif
} else {
} 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;
/* 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;
err = MP_VAL;
goto LBL_M;
#endif
}
}
/* setup result */
if ((err = mp_init_size (&res, P->alloc)) != MP_OKAY) {
goto LBL_M;
}
/* setup result */
if ((err = mp_init_size(&res, P->alloc)) != MP_OKAY) {
goto LBL_M;
}
/* create M table
*
/* create M table
*
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
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;
}
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) {
goto LBL_RES;
}
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
goto LBL_RES;
}
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod(G, &res, P, &M[1])) != MP_OKAY) {
goto LBL_RES;
}
#else
err = MP_VAL;
goto LBL_RES;
err = MP_VAL;
goto LBL_RES;
#endif
} else {
mp_set(&res, 1);
if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
goto LBL_RES;
}
}
} else {
mp_set(&res, 1uL);
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) {
/* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
if ((err = mp_copy(&M[1], &M[(size_t)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;
for (x = 0; x < (winsize - 1); x++) {
if ((err = mp_sqr(&M[(size_t)1 << (winsize - 1)], &M[(size_t)1 << (winsize - 1)])) != MP_OKAY) {
goto LBL_RES;
}
/* 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(&M[(size_t)1 << (winsize - 1)], P, mp)) != MP_OKAY) {
goto LBL_RES;
}
if ((err = redux (&res, 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;
}
continue;
}
if ((err = redux(&M[x], P, mp)) != MP_OKAY) {
goto LBL_RES;
}
}
/* else we add it to the window */
bitbuf |= (y << (winsize - ++bitcpy));
mode = 2;
/* set initial mode and bit cnt */
mode = 0;
bitcnt = 1;
buf = 0;
digidx = X->used - 1;
bitcpy = 0;
bitbuf = 0;
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;
}
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;
}
/* 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;
/* 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;
}
/* 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;
/* 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;
}
/* 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;
}
/* 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 (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;
}
}
/* 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;
}
/* swap res with Y */
mp_exch (&res, Y);
err = MP_OKAY;
LBL_RES:mp_clear (&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;
mp_clear(&M[1]);
for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
mp_clear(&M[x]);
}
return err;
}
#endif

107
bn_mp_exteuclid.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,18 +9,15 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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)
int mp_exteuclid(const mp_int *a, const 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;
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) {
@ -28,48 +25,90 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
}
/* initialize, (u1,u2,u3) = (1,0,a) */
mp_set(&u1, 1);
if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto LBL_ERR; }
mp_set(&u1, 1uL);
if ((err = mp_copy(a, &u3)) != MP_OKAY) {
goto LBL_ERR;
}
/* initialize, (v1,v2,v3) = (0,1,b) */
mp_set(&v2, 1);
if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto LBL_ERR; }
mp_set(&v2, 1uL);
if ((err = mp_copy(b, &v3)) != MP_OKAY) {
goto LBL_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 LBL_ERR; }
/* q = u3/v3 */
if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) {
goto LBL_ERR;
}
/* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto LBL_ERR; }
/* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) {
goto LBL_ERR;
}
/* (u1,u2,u3) = (v1,v2,v3) */
if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto LBL_ERR; }
/* (u1,u2,u3) = (v1,v2,v3) */
if ((err = mp_copy(&v1, &u1)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_copy(&v2, &u2)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_copy(&v3, &u3)) != MP_OKAY) {
goto LBL_ERR;
}
/* (v1,v2,v3) = (t1,t2,t3) */
if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto LBL_ERR; }
/* (v1,v2,v3) = (t1,t2,t3) */
if ((err = mp_copy(&t1, &v1)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_copy(&t2, &v2)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_copy(&t3, &v3)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* make sure U3 >= 0 */
if (u3.sign == MP_NEG) {
if ((err = mp_neg(&u1, &u1)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_neg(&u2, &u2)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_neg(&u3, &u3)) != MP_OKAY) { goto LBL_ERR; }
if ((err = mp_neg(&u1, &u1)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_neg(&u2, &u2)) != MP_OKAY) {
goto LBL_ERR;
}
if ((err = mp_neg(&u3, &u3)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* copy result out */
if (U1 != NULL) { mp_exch(U1, &u1); }
if (U2 != NULL) { mp_exch(U2, &u2); }
if (U3 != NULL) { mp_exch(U3, &u3); }
if (U1 != NULL) {
mp_exch(U1, &u1);
}
if (U2 != NULL) {
mp_exch(U2, &u2);
}
if (U3 != NULL) {
mp_exch(U3, &u3);
}
err = MP_OKAY;
LBL_ERR:

43
bn_mp_fread.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
#ifndef LTM_NO_FILE
@ -20,44 +17,46 @@
int mp_fread(mp_int *a, int radix, FILE *stream)
{
int err, ch, neg, y;
unsigned pos;
/* clear a */
mp_zero(a);
/* if first digit is - then set negative */
ch = fgetc(stream);
if (ch == '-') {
if (ch == (int)'-') {
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) {
pos = (unsigned)(ch - (int)'(');
if (mp_s_rmap_reverse_sz < pos) {
break;
}
y = (int)mp_s_rmap_reverse[pos];
if ((y == 0xff) || (y >= radix)) {
break;
}
/* shift up and add */
if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
if ((err = mp_mul_d(a, (mp_digit)radix, a)) != MP_OKAY) {
return err;
}
if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
if ((err = mp_add_d(a, (mp_digit)y, a)) != MP_OKAY) {
return err;
}
ch = fgetc(stream);
}
if (mp_cmp_d(a, 0) != MP_EQ) {
if (mp_cmp_d(a, 0uL) != MP_EQ) {
a->sign = neg;
}
return MP_OKAY;
}
#endif

31
bn_mp_fwrite.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,40 +9,37 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
#ifndef LTM_NO_FILE
int mp_fwrite(mp_int *a, int radix, FILE *stream)
int mp_fwrite(const 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);
buf = OPT_CAST(char) XMALLOC((size_t)len);
if (buf == NULL) {
return MP_MEM;
}
if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
XFREE (buf);
XFREE(buf);
return err;
}
for (x = 0; x < len; x++) {
if (fputc(buf[x], stream) == EOF) {
XFREE (buf);
return MP_VAL;
}
if (fputc((int)buf[x], stream) == EOF) {
XFREE(buf);
return MP_VAL;
}
}
XFREE (buf);
XFREE(buf);
return MP_OKAY;
}
#endif

147
bn_mp_gcd.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,94 +9,93 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
int mp_gcd(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int u, v;
int k, u_lsb, v_lsb, res;
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);
}
/* 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;
}
/* 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;
}
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;
/* 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);
/* 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 (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;
}
}
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;
}
}
/* 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;
}
}
if (v_lsb != k) {
if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
goto LBL_V;
}
}
while (mp_iszero(&v) == MP_NO) {
/* 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;
}
}
while (mp_iszero(&v) == MP_NO) {
/* 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);
}
/* 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;
/* 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

54
bn_mp_get_bit.c Normal file
View File

@ -0,0 +1,54 @@
#include "tommath_private.h"
#ifdef BN_MP_GET_BIT_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.
*
* SPDX-License-Identifier: Unlicense
*/
/* Checks the bit at position b and returns MP_YES
if the bit is 1, MP_NO if it is 0 and MP_VAL
in case of error */
int mp_get_bit(const mp_int *a, int b)
{
int limb;
mp_digit bit, isset;
if (b < 0) {
return MP_VAL;
}
limb = b / DIGIT_BIT;
/*
* Zero is a special value with the member "used" set to zero.
* Needs to be tested before the check for the upper boundary
* otherwise (limb >= a->used) would be true for a = 0
*/
if (mp_iszero(a) != MP_NO) {
return MP_NO;
}
if (limb >= a->used) {
return MP_VAL;
}
bit = (mp_digit)(1) << (b % DIGIT_BIT);
isset = a->dp[limb] & bit;
return (isset != 0u) ? MP_YES : MP_NO;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

31
bn_mp_get_double.c Normal file
View File

@ -0,0 +1,31 @@
#include "tommath_private.h"
#ifdef BN_MP_GET_DOUBLE_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.
*
* SPDX-License-Identifier: Unlicense
*/
double mp_get_double(const mp_int *a)
{
int i;
double d = 0.0, fac = 1.0;
for (i = 0; i < DIGIT_BIT; ++i) {
fac *= 2.0;
}
for (i = USED(a); i --> 0;) {
d = (d * fac) + (double)DIGIT(a, i);
}
return (mp_isneg(a) != MP_NO) ? -d : d;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

37
bn_mp_get_int.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,34 +9,31 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
unsigned long mp_get_int(const mp_int *a)
{
int i;
mp_min_u32 res;
int i;
mp_min_u32 res;
if (a->used == 0) {
return 0;
}
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 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);
/* get most significant digit of result */
res = DIGIT(a, i);
while (--i >= 0) {
res = (res << DIGIT_BIT) | 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;
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
return res & 0xFFFFFFFFUL;
}
#endif

39
bn_mp_get_long.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_GET_LONG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,33 +9,34 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* get the lower unsigned long of an mp_int, platform dependent */
unsigned long mp_get_long(mp_int * a)
unsigned long mp_get_long(const mp_int *a)
{
int i;
unsigned long res;
int i;
unsigned long res;
if (a->used == 0) {
return 0;
}
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 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);
/* get most significant digit of result */
res = DIGIT(a, i);
#if (ULONG_MAX != 0xffffffffuL) || (DIGIT_BIT < 32)
while (--i >= 0) {
res = (res << DIGIT_BIT) | DIGIT(a,i);
}
while (--i >= 0) {
res = (res << DIGIT_BIT) | DIGIT(a, i);
}
#endif
return res;
return res;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

39
bn_mp_get_long_long.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_GET_LONG_LONG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,33 +9,34 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* get the lower unsigned long long of an mp_int, platform dependent */
unsigned long long mp_get_long_long (mp_int * a)
unsigned long long mp_get_long_long(const mp_int *a)
{
int i;
unsigned long long res;
int i;
unsigned long long res;
if (a->used == 0) {
return 0;
}
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 long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
/* get number of digits of the lsb we have to read */
i = MIN(a->used, ((((int)sizeof(unsigned long long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
/* get most significant digit of result */
res = DIGIT(a,i);
/* get most significant digit of result */
res = DIGIT(a, i);
#if DIGIT_BIT < 64
while (--i >= 0) {
res = (res << DIGIT_BIT) | DIGIT(a,i);
}
while (--i >= 0) {
res = (res << DIGIT_BIT) | DIGIT(a, i);
}
#endif
return res;
return res;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

63
bn_mp_grow.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,46 +9,43 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* grow as required */
int mp_grow (mp_int * a, int size)
int mp_grow(mp_int *a, int size)
{
int i;
mp_digit *tmp;
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);
/* 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;
}
/* 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_t)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;
/* 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;
/* zero excess digits */
i = a->alloc;
a->alloc = size;
for (; i < a->alloc; i++) {
a->dp[i] = 0;
}
}
return MP_OKAY;
}
#endif

81
bn_mp_import.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_IMPORT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,61 +9,56 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* based on gmp's mpz_import.
* see http://gmplib.org/manual/Integer-Import-and-Export.html
*/
int mp_import(mp_int* rop, size_t count, int order, size_t size,
int endian, size_t nails, const void* op) {
int result;
size_t odd_nails, nail_bytes, i, j;
unsigned char odd_nail_mask;
int mp_import(mp_int *rop, size_t count, int order, size_t size,
int endian, size_t nails, const void *op)
{
int result;
size_t odd_nails, nail_bytes, i, j;
unsigned char odd_nail_mask;
mp_zero(rop);
mp_zero(rop);
if (endian == 0) {
union {
unsigned int i;
char c[4];
} lint;
lint.i = 0x01020304;
endian = (lint.c[0] == 4) ? -1 : 1;
}
if (endian == 0) {
union {
unsigned int i;
char c[4];
} lint;
lint.i = 0x01020304;
odd_nails = (nails % 8);
odd_nail_mask = 0xff;
for (i = 0; i < odd_nails; ++i) {
odd_nail_mask ^= (1 << (7 - i));
}
nail_bytes = nails / 8;
endian = (lint.c[0] == '\x04') ? -1 : 1;
}
for (i = 0; i < count; ++i) {
for (j = 0; j < (size - nail_bytes); ++j) {
unsigned char byte = *(
(unsigned char*)op +
(((order == 1) ? i : ((count - 1) - i)) * size) +
((endian == 1) ? (j + nail_bytes) : (((size - 1) - j) - nail_bytes))
);
odd_nails = (nails % 8u);
odd_nail_mask = 0xff;
for (i = 0; i < odd_nails; ++i) {
odd_nail_mask ^= (unsigned char)(1u << (7u - i));
}
nail_bytes = nails / 8u;
if (
(result = mp_mul_2d(rop, ((j == 0) ? (8 - odd_nails) : 8), rop)) != MP_OKAY) {
return result;
}
for (i = 0; i < count; ++i) {
for (j = 0; j < (size - nail_bytes); ++j) {
unsigned char byte = *((unsigned char *)op +
(((order == 1) ? i : ((count - 1u) - i)) * size) +
((endian == 1) ? (j + nail_bytes) : (((size - 1u) - j) - nail_bytes)));
rop->dp[0] |= (j == 0) ? (byte & odd_nail_mask) : byte;
rop->used += 1;
}
}
if ((result = mp_mul_2d(rop, (j == 0u) ? (int)(8u - odd_nails) : 8, rop)) != MP_OKAY) {
return result;
}
mp_clamp(rop);
rop->dp[0] |= (j == 0u) ? (mp_digit)(byte & odd_nail_mask) : (mp_digit)byte;
rop->used += 1;
}
}
return MP_OKAY;
mp_clamp(rop);
return MP_OKAY;
}
#endif

39
bn_mp_init.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,35 +9,32 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* init a new mp_int */
int mp_init (mp_int * a)
int mp_init(mp_int *a)
{
int i;
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;
}
/* allocate memory required and clear it */
a->dp = OPT_CAST(mp_digit) XMALLOC(sizeof(mp_digit) * (size_t)MP_PREC);
if (a->dp == NULL) {
return MP_MEM;
}
/* set the digits to zero */
for (i = 0; i < MP_PREC; i++) {
/* 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;
/* 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;
return MP_OKAY;
}
#endif

25
bn_mp_init_copy.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,26 +9,23 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
int mp_init_copy(mp_int *a, const mp_int *b)
{
int res;
int res;
if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
return res;
}
if ((res = mp_init_size(a, b->used)) != MP_OKAY) {
return res;
}
if((res = mp_copy (b, a)) != MP_OKAY) {
mp_clear(a);
}
if ((res = mp_copy(b, a)) != MP_OKAY) {
mp_clear(a);
}
return res;
return res;
}
#endif

66
bn_mp_init_multi.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,44 +9,42 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
#include <stdarg.h>
int mp_init_multi(mp_int *mp, ...)
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;
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;
/* now start cleaning up */
cur_arg = mp;
va_start(clean_args, mp);
while (n-- != 0) {
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. */
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;
/* now start cleaning up */
cur_arg = mp;
va_start(clean_args, mp);
while (n-- != 0) {
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

21
bn_mp_init_set.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,21 +9,18 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
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;
int err;
if ((err = mp_init(a)) != MP_OKAY) {
return err;
}
mp_set(a, b);
return err;
}
#endif

19
bn_mp_init_set_int.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,20 +9,17 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
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);
int err;
if ((err = mp_init(a)) != MP_OKAY) {
return err;
}
return mp_set_int(a, b);
}
#endif

43
bn_mp_init_size.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,37 +9,34 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
int mp_init_size(mp_int *a, int size)
{
int x;
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;
}
/* pad size so there are always extra digits */
size += (MP_PREC * 2) - (size % MP_PREC);
/* set the members */
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
/* alloc mem */
a->dp = OPT_CAST(mp_digit) XMALLOC(sizeof(mp_digit) * (size_t)size);
if (a->dp == NULL) {
return MP_MEM;
}
/* zero the digits */
for (x = 0; x < size; x++) {
/* 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;
return MP_OKAY;
}
#endif

29
bn_mp_invmod.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,31 +9,28 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
int mp_invmod(const mp_int *a, const mp_int *b, mp_int *c)
{
/* b cannot be negative */
if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
return MP_VAL;
}
/* b cannot be negative and has to be >1 */
if ((b->sign == MP_NEG) || (mp_cmp_d(b, 1uL) != MP_GT)) {
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) == MP_YES) && (mp_cmp_d(b, 1) != MP_EQ)) {
return fast_mp_invmod (a, b, c);
}
/* if the modulus is odd we can use a faster routine instead */
if ((mp_isodd(b) == MP_YES)) {
return fast_mp_invmod(a, b, c);
}
#endif
#ifdef BN_MP_INVMOD_SLOW_C
return mp_invmod_slow(a, b, c);
return mp_invmod_slow(a, b, c);
#else
return MP_VAL;
return MP_VAL;
#endif
}
#endif

260
bn_mp_invmod_slow.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_INVMOD_SLOW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,164 +9,162 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* hac 14.61, pp608 */
int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
int mp_invmod_slow(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int x, y, u, v, A, B, C, D;
int res;
mp_int x, y, u, v, A, B, C, D;
int res;
/* b cannot be negative */
if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
return MP_VAL;
}
/* b cannot be negative */
if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
return MP_VAL;
}
/* init temps */
if ((res = mp_init_multi(&x, &y, &u, &v,
&A, &B, &C, &D, NULL)) != MP_OKAY) {
return res;
}
/* 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) {
/* 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;
}
}
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) == MP_YES) && (mp_iseven (&y) == MP_YES)) {
res = MP_VAL;
goto LBL_ERR;
}
/* 2. [modified] if x,y are both even then return an error! */
if ((mp_iseven(&x) == MP_YES) && (mp_iseven(&y) == MP_YES)) {
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);
/* 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, 1uL);
mp_set(&D, 1uL);
top:
/* 4. while u is even do */
while (mp_iseven (&u) == MP_YES) {
/* 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) == MP_YES) || (mp_isodd (&B) == MP_YES)) {
/* A = (A+y)/2, B = (B-x)/2 */
if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
/* 4. while u is even do */
while (mp_iseven(&u) == MP_YES) {
/* 4.1 u = u/2 */
if ((res = mp_div_2(&u, &u)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
/* 4.2 if A or B is odd then */
if ((mp_isodd(&A) == MP_YES) || (mp_isodd(&B) == MP_YES)) {
/* 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;
}
}
/* 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) == MP_YES) {
/* 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) == MP_YES) || (mp_isodd (&D) == MP_YES)) {
/* C = (C+y)/2, D = (D-x)/2 */
if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
if ((res = mp_div_2(&B, &B)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
}
/* 5. while v is even do */
while (mp_iseven(&v) == MP_YES) {
/* 5.1 v = v/2 */
if ((res = mp_div_2(&v, &v)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* C = C/2, D = D/2 */
if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
/* 5.2 if C or D is odd then */
if ((mp_isodd(&C) == MP_YES) || (mp_isodd(&D) == MP_YES)) {
/* 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) == MP_NO)
goto top;
/* now a = C, b = D, gcd == g*v */
/* if v != 1 then there is no inverse */
if (mp_cmp_d(&v, 1uL) != MP_EQ) {
res = MP_VAL;
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) == MP_NO)
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 its too low */
while (mp_cmp_d(&C, 0uL) == MP_LT) {
if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
goto LBL_ERR;
}
}
/* too big */
while (mp_cmp_mag(&C, b) != MP_LT) {
}
/* 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;
}
/* 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

144
bn_mp_is_square.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,98 +9,96 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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
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
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 mp_is_square(const mp_int *arg, int *ret)
{
int res;
mp_digit c;
mp_int t;
unsigned long r;
int res;
mp_digit c;
mp_int t;
unsigned long r;
/* Default to Non-square :) */
*ret = MP_NO;
/* Default to Non-square :) */
*ret = MP_NO;
if (arg->sign == MP_NEG) {
return MP_VAL;
}
if (arg->sign == MP_NEG) {
return MP_VAL;
}
/* digits used? (TSD) */
if (arg->used == 0) {
return MP_OKAY;
}
/* 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;
}
/* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
if (rem_128[127u & DIGIT(arg, 0)] == (char)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;
}
/* Next check mod 105 (3*5*7) */
if ((res = mp_mod_d(arg, 105uL, &c)) != MP_OKAY) {
return res;
}
if (rem_105[c] == (char)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) != 0L) goto ERR;
if (((1L<<(r%13)) & 0x9E4L) != 0L) goto ERR;
if (((1L<<(r%17)) & 0x5CE8L) != 0L) goto ERR;
if (((1L<<(r%19)) & 0x4F50CL) != 0L) goto ERR;
if (((1L<<(r%23)) & 0x7ACCA0L) != 0L) goto ERR;
if (((1L<<(r%29)) & 0xC2EDD0CL) != 0L) goto ERR;
if (((1L<<(r%31)) & 0x6DE2B848L) != 0L) goto ERR;
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 LBL_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 LBL_ERR. We know that res
* is already equal to MP_OKAY from the mp_mod call
*/
if (((1uL<<(r%11uL)) & 0x5C4uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%13uL)) & 0x9E4uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%17uL)) & 0x5CE8uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%19uL)) & 0x4F50CuL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%23uL)) & 0x7ACCA0uL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%29uL)) & 0xC2EDD0CuL) != 0uL) goto LBL_ERR;
if (((1uL<<(r%31uL)) & 0x6DE2B848uL) != 0uL) goto LBL_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;
}
/* Final check - is sqr(sqrt(arg)) == arg ? */
if ((res = mp_sqrt(arg, &t)) != MP_OKAY) {
goto LBL_ERR;
}
if ((res = mp_sqr(&t, &t)) != MP_OKAY) {
goto LBL_ERR;
}
*ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
ERR:mp_clear(&t);
return res;
*ret = (mp_cmp_mag(&t, arg) == MP_EQ) ? MP_YES : MP_NO;
LBL_ERR:
mp_clear(&t);
return res;
}
#endif

107
bn_mp_jacobi.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,106 +9,25 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
* HAC is wrong here, as the special case of (0 | 1) is not
* handled correctly.
* Kept for legacy reasons, please use mp_kronecker() instead
*/
int mp_jacobi (mp_int * a, mp_int * n, int *c)
int mp_jacobi(const mp_int *a, const mp_int *n, int *c)
{
mp_int a1, p1;
int k, s, r, res;
mp_digit residue;
/* if a < 0 return MP_VAL */
if (mp_isneg(a) == MP_YES) {
return MP_VAL;
}
/* if a < 0 return MP_VAL */
if (mp_isneg(a) == MP_YES) {
return MP_VAL;
}
/* if n <= 0 return MP_VAL */
if (mp_cmp_d(n, 0uL) != MP_GT) {
return MP_VAL;
}
/* if n <= 0 return MP_VAL */
if (mp_cmp_d(n, 0) != MP_GT) {
return MP_VAL;
}
/* step 1. handle case of a == 0 */
if (mp_iszero (a) == MP_YES) {
/* special case of a == 0 and n == 1 */
if (mp_cmp_d (n, 1) == MP_EQ) {
*c = 1;
} else {
*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 = n->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 ( ((n->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 (n, &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;
return mp_kronecker(a, n, c);
}
#endif

234
bn_mp_karatsuba_mul.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,156 +9,160 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* c = |a| * |b| using Karatsuba Multiplication using
/* 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
* 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 =>
* 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
* 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
* 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)
int mp_karatsuba_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
int B, err;
mp_int x0, x1, y0, y1, t1, x0y0, x1y1;
int B, err;
/* default the return code to an error */
err = MP_MEM;
/* default the return code to an error */
err = MP_MEM;
/* min # of digits */
B = MIN (a->used, b->used);
/* min # of digits */
B = MIN(a->used, b->used);
/* now divide in two */
B = B >> 1;
/* 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 copy all the temps */
if (mp_init_size(&x0, B) != MP_OKAY)
goto LBL_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;
/* 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;
/* now shift the digits */
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;
{
int x;
mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
{
int x;
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;
/* 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 = 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++;
}
tmpx = x1.dp;
for (x = B; x < a->used; x++) {
*tmpx++ = *tmpa++;
}
tmpy = y1.dp;
for (x = B; x < b->used; x++) {
*tmpy++ = *tmpb++;
}
}
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);
/* 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 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) */
/* 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) */
/* 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 */
/* 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 */
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;
/* 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;
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);
LBL_ERR:
return err;
}
#endif

163
bn_mp_karatsuba_sqr.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,110 +9,113 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* Karatsuba squaring, computes b = a*a using three
/* 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
* 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)
int mp_karatsuba_sqr(const mp_int *a, mp_int *b)
{
mp_int x0, x1, t1, t2, x0x0, x1x1;
int B, err;
mp_int x0, x1, t1, t2, x0x0, x1x1;
int B, err;
err = MP_MEM;
err = MP_MEM;
/* min # of digits */
B = a->used;
/* min # of digits */
B = a->used;
/* now divide in two */
B = B >> 1;
/* 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 copy all the temps */
if (mp_init_size(&x0, B) != MP_OKAY)
goto LBL_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;
/* 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;
{
int x;
mp_digit *dst, *src;
{
int x;
mp_digit *dst, *src;
src = a->dp;
src = a->dp;
/* now shift the digits */
dst = x0.dp;
for (x = 0; x < B; x++) {
*dst++ = *src++;
}
/* 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++;
}
}
dst = x1.dp;
for (x = B; x < a->used; x++) {
*dst++ = *src++;
}
}
x0.used = B;
x1.used = a->used - B;
x0.used = B;
x1.used = a->used - B;
mp_clamp (&x0);
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 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) */
/* 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) */
/* 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 */
/* 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 */
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;
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;
X1X1:
mp_clear(&x1x1);
X0X0:
mp_clear(&x0x0);
T2:
mp_clear(&t2);
T1:
mp_clear(&t1);
X1:
mp_clear(&x1);
X0:
mp_clear(&x0);
LBL_ERR:
return err;
}
#endif

144
bn_mp_kronecker.c Normal file
View File

@ -0,0 +1,144 @@
#include "tommath_private.h"
#ifdef BN_MP_KRONECKER_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.
*
* SPDX-License-Identifier: Unlicense
*/
/*
Kronecker symbol (a|p)
Straightforward implementation of algorithm 1.4.10 in
Henri Cohen: "A Course in Computational Algebraic Number Theory"
@book{cohen2013course,
title={A course in computational algebraic number theory},
author={Cohen, Henri},
volume={138},
year={2013},
publisher={Springer Science \& Business Media}
}
*/
int mp_kronecker(const mp_int *a, const mp_int *p, int *c)
{
mp_int a1, p1, r;
int e = MP_OKAY;
int v, k;
static const int table[8] = {0, 1, 0, -1, 0, -1, 0, 1};
if (mp_iszero(p) != MP_NO) {
if ((a->used == 1) && (a->dp[0] == 1u)) {
*c = 1;
return e;
} else {
*c = 0;
return e;
}
}
if ((mp_iseven(a) != MP_NO) && (mp_iseven(p) != MP_NO)) {
*c = 0;
return e;
}
if ((e = mp_init_copy(&a1, a)) != MP_OKAY) {
return e;
}
if ((e = mp_init_copy(&p1, p)) != MP_OKAY) {
goto LBL_KRON_0;
}
v = mp_cnt_lsb(&p1);
if ((e = mp_div_2d(&p1, v, &p1, NULL)) != MP_OKAY) {
goto LBL_KRON_1;
}
if ((v & 0x1) == 0) {
k = 1;
} else {
k = table[a->dp[0] & 7u];
}
if (p1.sign == MP_NEG) {
p1.sign = MP_ZPOS;
if (a1.sign == MP_NEG) {
k = -k;
}
}
if ((e = mp_init(&r)) != MP_OKAY) {
goto LBL_KRON_1;
}
for (;;) {
if (mp_iszero(&a1) != MP_NO) {
if (mp_cmp_d(&p1, 1uL) == MP_EQ) {
*c = k;
goto LBL_KRON;
} else {
*c = 0;
goto LBL_KRON;
}
}
v = mp_cnt_lsb(&a1);
if ((e = mp_div_2d(&a1, v, &a1, NULL)) != MP_OKAY) {
goto LBL_KRON;
}
if ((v & 0x1) == 1) {
k = k * table[p1.dp[0] & 7u];
}
if (a1.sign == MP_NEG) {
/*
* Compute k = (-1)^((a1)*(p1-1)/4) * k
* a1.dp[0] + 1 cannot overflow because the MSB
* of the type mp_digit is not set by definition
*/
if (((a1.dp[0] + 1u) & p1.dp[0] & 2u) != 0u) {
k = -k;
}
} else {
/* compute k = (-1)^((a1-1)*(p1-1)/4) * k */
if ((a1.dp[0] & p1.dp[0] & 2u) != 0u) {
k = -k;
}
}
if ((e = mp_copy(&a1, &r)) != MP_OKAY) {
goto LBL_KRON;
}
r.sign = MP_ZPOS;
if ((e = mp_mod(&p1, &r, &a1)) != MP_OKAY) {
goto LBL_KRON;
}
if ((e = mp_copy(&r, &p1)) != MP_OKAY) {
goto LBL_KRON;
}
}
LBL_KRON:
mp_clear(&r);
LBL_KRON_1:
mp_clear(&p1);
LBL_KRON_0:
mp_clear(&a1);
return e;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

63
bn_mp_lcm.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,49 +9,46 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
int mp_lcm(const mp_int *a, const mp_int *b, mp_int *c)
{
int res;
mp_int t1, t2;
int res;
mp_int t1, t2;
if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
return res;
}
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;
}
/* 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);
}
/* 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;
/* fix the sign to positive */
c->sign = MP_ZPOS;
LBL_T:
mp_clear_multi (&t1, &t2, NULL);
return res;
mp_clear_multi(&t1, &t2, NULL);
return res;
}
#endif

79
bn_mp_lshd.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,56 +9,57 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
int mp_lshd(mp_int *a, int b)
{
int x, res;
int x, res;
/* if its less than zero return */
if (b <= 0) {
return MP_OKAY;
}
/* if its less than zero return */
if (b <= 0) {
return MP_OKAY;
}
/* no need to shift 0 around */
if (mp_iszero(a) == MP_YES) {
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;
}
}
/* grow to fit the new digits */
if (a->alloc < (a->used + b)) {
if ((res = mp_grow(a, a->used + b)) != MP_OKAY) {
return res;
}
}
{
mp_digit *top, *bottom;
{
mp_digit *top, *bottom;
/* increment the used by the shift amount then copy upwards */
a->used += b;
/* increment the used by the shift amount then copy upwards */
a->used += b;
/* top */
top = a->dp + a->used - 1;
/* top */
top = a->dp + a->used - 1;
/* base */
bottom = (a->dp + a->used - 1) - b;
/* 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--;
}
/* 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;
/* zero the lower digits */
top = a->dp;
for (x = 0; x < b; x++) {
*top++ = 0;
}
}
return MP_OKAY;
}
#endif

44
bn_mp_mod.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,37 +9,33 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
int
mp_mod (mp_int * a, mp_int * b, mp_int * c)
int mp_mod(const mp_int *a, const mp_int *b, mp_int *c)
{
mp_int t;
int res;
mp_int t;
int res;
if ((res = mp_init_size (&t, b->used)) != MP_OKAY) {
return res;
}
if ((res = mp_init_size(&t, b->used)) != MP_OKAY) {
return res;
}
if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
mp_clear (&t);
return res;
}
if ((res = mp_div(a, b, NULL, &t)) != MP_OKAY) {
mp_clear(&t);
return res;
}
if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
res = MP_OKAY;
mp_exch (&t, c);
} else {
res = mp_add (b, &t, c);
}
if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
res = MP_OKAY;
mp_exch(&t, c);
} else {
res = mp_add(b, &t, c);
}
mp_clear (&t);
return res;
mp_clear(&t);
return res;
}
#endif

58
bn_mp_mod_2d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,44 +9,40 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* calc a value mod 2**b */
int
mp_mod_2d (mp_int * a, int b, mp_int * c)
int mp_mod_2d(const mp_int *a, int b, mp_int *c)
{
int x, res;
int x, res;
/* if b is <= 0 then zero the int */
if (b <= 0) {
mp_zero (c);
return MP_OKAY;
}
/* 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;
}
/* if the modulus is larger than the value than return */
if (b >= (a->used * DIGIT_BIT)) {
res = mp_copy(a, c);
return res;
}
/* copy */
if ((res = mp_copy (a, c)) != MP_OKAY) {
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;
/* 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)1 << (mp_digit)(b % DIGIT_BIT)) - (mp_digit)1;
mp_clamp(c);
return MP_OKAY;
}
#endif

12
bn_mp_mod_d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,16 +9,12 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
int mp_mod_d(const mp_int *a, mp_digit b, mp_digit *c)
{
return mp_div_d(a, b, NULL, c);
return mp_div_d(a, b, NULL, c);
}
#endif

57
bn_mp_montgomery_calc_normalization.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/*
@ -21,36 +18,36 @@
* 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 mp_montgomery_calc_normalization(mp_int *a, const mp_int *b)
{
int x, bits, res;
int x, bits, res;
/* how many bits of last digit does b use */
bits = mp_count_bits (b) % DIGIT_BIT;
/* 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;
if (b->used > 1) {
if ((res = mp_2expt(a, ((b->used - 1) * DIGIT_BIT) + bits - 1)) != MP_OKAY) {
return res;
}
}
}
} else {
mp_set(a, 1uL);
bits = 1;
}
return MP_OKAY;
/* 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

173
bn_mp_montgomery_reduce.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,107 +9,104 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
int mp_montgomery_reduce(mp_int *x, const mp_int *n, mp_digit rho)
{
int ix, res, digs;
mp_digit mu;
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);
}
/* 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 < (int)MP_WARRAY) &&
(x->used <= (int)MP_WARRAY) &&
(n->used <
(int)(1u << (((size_t)CHAR_BIT * sizeof(mp_word)) - (2u * (size_t)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 */
{
int iy;
mp_digit *tmpn, *tmpx, u;
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));
/* grow the input as required */
if (x->alloc < digs) {
if ((res = mp_grow(x, digs)) != MP_OKAY) {
return res;
}
/* At this point the ix'th digit of x should be zero */
}
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 */
{
int iy;
mp_digit *tmpn, *tmpx, u;
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 != 0) {
*tmpx += u;
u = *tmpx >> DIGIT_BIT;
*tmpx++ &= MP_MASK;
/* propagate carries upwards as required*/
while (u != 0u) {
*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.
*/
/* 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);
/* 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);
}
/* 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;
return MP_OKAY;
}
#endif

52
bn_mp_montgomery_setup.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,48 +9,44 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* setups the montgomery reduction stuff */
int
mp_montgomery_setup (mp_int * n, mp_digit * rho)
int mp_montgomery_setup(const mp_int *n, mp_digit *rho)
{
mp_digit x, b;
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];
/* 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;
}
if ((b & 1u) == 0u) {
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 */
x = (((b + 2u) & 4u) << 1) + b; /* here x*a==1 mod 2**4 */
x *= 2u - (b * x); /* here x*a==1 mod 2**8 */
#if !defined(MP_8BIT)
x *= 2 - (b * x); /* here x*a==1 mod 2**16 */
x *= 2u - (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 */
x *= 2u - (b * x); /* here x*a==1 mod 2**32 */
#endif
#ifdef MP_64BIT
x *= 2 - (b * x); /* here x*a==1 mod 2**64 */
x *= 2u - (b * x); /* here x*a==1 mod 2**64 */
#endif
/* rho = -1/m mod b */
*rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
/* rho = -1/m mod b */
*rho = (mp_digit)(((mp_word)1 << (mp_word)DIGIT_BIT) - x) & MP_MASK;
return MP_OKAY;
return MP_OKAY;
}
#endif

69
bn_mp_mul.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,56 +9,53 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
int mp_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
int res, neg;
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
int res, neg;
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
/* use Toom-Cook? */
/* 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
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
/* 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;
{
/* 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
if ((digs < (int)MP_WARRAY) &&
(MIN(a->used, b->used) <=
(int)(1u << (((size_t)CHAR_BIT * sizeof(mp_word)) - (2u * (size_t)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 */
res = s_mp_mul(a, b, c); /* uses s_mp_mul_digs */
#else
res = MP_VAL;
res = MP_VAL;
#endif
}
}
c->sign = (c->used > 0) ? neg : MP_ZPOS;
return res;
}
}
c->sign = (c->used > 0) ? neg : MP_ZPOS;
return res;
}
#endif

109
bn_mp_mul_2.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,71 +9,68 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
int mp_mul_2(const mp_int *a, mp_int *b)
{
int x, res, oldused;
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;
}
}
/* 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;
oldused = b->used;
b->used = a->used;
{
mp_digit r, rr, *tmpa, *tmpb;
{
mp_digit r, rr, *tmpa, *tmpb;
/* alias for source */
tmpa = a->dp;
/* alias for dest */
tmpb = b->dp;
/* alias for source */
tmpa = a->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
/* 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++ << 1uL) | r) & MP_MASK;
/* copy the carry that would be from the source
* digit into the next iteration
*/
r = rr;
}
/* new leading digit? */
if (r != 0u) {
/* 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
*/
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;
tmpb = b->dp + b->used;
for (x = b->used; x < oldused; x++) {
*tmpb++ = 0;
}
}
b->sign = a->sign;
return MP_OKAY;
}
#endif

107
bn_mp_mul_2d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,74 +9,71 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* shift left by a certain bit count */
int mp_mul_2d (mp_int * a, int b, mp_int * c)
int mp_mul_2d(const mp_int *a, int b, mp_int *c)
{
mp_digit d;
int res;
mp_digit d;
int res;
/* copy */
if (a != c) {
if ((res = mp_copy (a, c)) != MP_OKAY) {
return 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;
}
}
if (c->alloc < (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 by as many digits in the bit count */
if (b >= 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) {
mp_digit *tmpc, shift, mask, r, rr;
int x;
/* shift any bit count < DIGIT_BIT */
d = (mp_digit)(b % DIGIT_BIT);
if (d != 0u) {
mp_digit *tmpc, shift, mask, r, rr;
int x;
/* bitmask for carries */
mask = (((mp_digit)1) << d) - 1;
/* bitmask for carries */
mask = ((mp_digit)1 << d) - (mp_digit)1;
/* shift for msbs */
shift = DIGIT_BIT - d;
/* shift for msbs */
shift = (mp_digit)DIGIT_BIT - d;
/* alias */
tmpc = c->dp;
/* 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;
/* 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;
/* 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;
/* set the carry to the carry bits of the current word */
r = rr;
}
/* set final carry */
if (r != 0u) {
c->dp[(c->used)++] = r;
}
}
mp_clamp(c);
return MP_OKAY;
}
#endif

88
bn_mp_mul_d.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,68 +9,64 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* multiply by a digit */
int
mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
int mp_mul_d(const mp_int *a, mp_digit b, mp_int *c)
{
mp_digit u, *tmpa, *tmpc;
mp_word r;
int ix, res, olduse;
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;
}
}
/* 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;
/* get the original destinations used count */
olduse = c->used;
/* set the sign */
c->sign = a->sign;
/* set the sign */
c->sign = a->sign;
/* alias for a->dp [source] */
tmpa = a->dp;
/* alias for a->dp [source] */
tmpa = a->dp;
/* alias for c->dp [dest] */
tmpc = c->dp;
/* alias for c->dp [dest] */
tmpc = c->dp;
/* zero carry */
u = 0;
/* 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);
/* 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));
/* 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));
}
/* 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;
/* store final carry [if any] and increment ix offset */
*tmpc++ = u;
++ix;
/* now zero digits above the top */
while (ix++ < olduse) {
*tmpc++ = 0;
}
/* now zero digits above the top */
while (ix++ < olduse) {
*tmpc++ = 0;
}
/* set used count */
c->used = a->used + 1;
mp_clamp(c);
/* set used count */
c->used = a->used + 1;
mp_clamp(c);
return MP_OKAY;
return MP_OKAY;
}
#endif

33
bn_mp_mulmod.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,29 +9,26 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* d = a * b (mod c) */
int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d)
{
int res;
mp_int t;
int res;
mp_int t;
if ((res = mp_init_size (&t, c->used)) != MP_OKAY) {
return res;
}
if ((res = mp_init_size(&t, c->used)) != 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;
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

11
bn_mp_n_root.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,18 +9,15 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* wrapper function for mp_n_root_ex()
* computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
*/
int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
int mp_n_root(const mp_int *a, mp_digit b, mp_int *c)
{
return mp_n_root_ex(a, b, c, 0);
return mp_n_root_ex(a, b, c, 0);
}
#endif

175
bn_mp_n_root_ex.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_N_ROOT_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* find the n'th root of an integer
@ -25,105 +22,105 @@
* each step involves a fair bit. This is not meant to
* find huge roots [square and cube, etc].
*/
int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
int mp_n_root_ex(const mp_int *a, mp_digit b, mp_int *c, int fast)
{
mp_int t1, t2, t3;
int res, neg;
mp_int t1, t2, t3, a_;
int res;
/* input must be positive if b is even */
if (((b & 1) == 0) && (a->sign == MP_NEG)) {
return MP_VAL;
}
/* input must be positive if b is even */
if (((b & 1u) == 0u) && (a->sign == MP_NEG)) {
return MP_VAL;
}
if ((res = mp_init (&t1)) != MP_OKAY) {
return res;
}
if ((res = mp_init(&t1)) != MP_OKAY) {
return res;
}
if ((res = mp_init (&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init(&t2)) != MP_OKAY) {
goto LBL_T1;
}
if ((res = mp_init (&t3)) != MP_OKAY) {
goto LBL_T2;
}
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;
/* if a is negative fudge the sign but keep track */
a_ = *a;
a_.sign = MP_ZPOS;
/* t2 = 2 */
mp_set (&t2, 2);
/* t2 = 2 */
mp_set(&t2, 2uL);
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_ex (&t1, b - 1, &t3, fast)) != 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_ex (&t1, b, &t2, fast)) != MP_OKAY) {
goto LBL_T3;
}
if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
do {
/* t1 = t2 */
if ((res = mp_copy(&t2, &t1)) != MP_OKAY) {
goto LBL_T3;
}
} else {
break;
}
}
/* reset the sign of a first */
a->sign = neg;
/* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
/* set the result */
mp_exch (&t1, c);
/* t3 = t1**(b-1) */
if ((res = mp_expt_d_ex(&t1, b - 1u, &t3, fast)) != MP_OKAY) {
goto LBL_T3;
}
/* set the sign of the result */
c->sign = neg;
/* numerator */
/* t2 = t1**b */
if ((res = mp_mul(&t3, &t1, &t2)) != MP_OKAY) {
goto LBL_T3;
}
res = MP_OKAY;
/* t2 = t1**b - a */
if ((res = mp_sub(&t2, &a_, &t2)) != MP_OKAY) {
goto LBL_T3;
}
LBL_T3:mp_clear (&t3);
LBL_T2:mp_clear (&t2);
LBL_T1:mp_clear (&t1);
return res;
/* 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_ex(&t1, b, &t2, fast)) != MP_OKAY) {
goto LBL_T3;
}
if (mp_cmp(&t2, &a_) == MP_GT) {
if ((res = mp_sub_d(&t1, 1uL, &t1)) != MP_OKAY) {
goto LBL_T3;
}
} else {
break;
}
}
/* set the result */
mp_exch(&t1, c);
/* set the sign of the result */
c->sign = a->sign;
res = MP_OKAY;
LBL_T3:
mp_clear(&t3);
LBL_T2:
mp_clear(&t2);
LBL_T1:
mp_clear(&t1);
return res;
}
#endif

33
bn_mp_neg.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,29 +9,26 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* b = -a */
int mp_neg (mp_int * a, mp_int * b)
int mp_neg(const mp_int *a, mp_int *b)
{
int res;
if (a != b) {
if ((res = mp_copy (a, b)) != MP_OKAY) {
return res;
}
}
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;
}
if (mp_iszero(b) != MP_YES) {
b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
} else {
b->sign = MP_ZPOS;
}
return MP_OKAY;
return MP_OKAY;
}
#endif

54
bn_mp_or.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,39 +9,37 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
int mp_or(const mp_int *a, const mp_int *b, mp_int *c)
{
int res, ix, px;
mp_int t, *x;
int res, ix, px;
mp_int t;
const mp_int *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;
}
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;
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

58
bn_mp_prime_fermat.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,51 +9,49 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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)
int mp_prime_fermat(const mp_int *a, const mp_int *b, int *result)
{
mp_int t;
int err;
mp_int t;
int err;
/* default to composite */
*result = MP_NO;
/* default to composite */
*result = MP_NO;
/* ensure b > 1 */
if (mp_cmp_d(b, 1) != MP_GT) {
return MP_VAL;
}
/* ensure b > 1 */
if (mp_cmp_d(b, 1uL) != MP_GT) {
return MP_VAL;
}
/* init t */
if ((err = mp_init (&t)) != MP_OKAY) {
return err;
}
/* 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;
}
/* 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;
}
/* 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;
err = MP_OKAY;
LBL_T:
mp_clear(&t);
return err;
}
#endif

198
bn_mp_prime_frobenius_underwood.c Normal file
View File

@ -0,0 +1,198 @@
#include "tommath_private.h"
#ifdef BN_MP_PRIME_FROBENIUS_UNDERWOOD_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.
*
* SPDX-License-Identifier: Unlicense
*/
/*
* See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
*/
#ifndef LTM_USE_FIPS_ONLY
#ifdef MP_8BIT
/*
* floor of positive solution of
* (2^16)-1 = (a+4)*(2*a+5)
* TODO: Both values are smaller than N^(1/4), would have to use a bigint
* for a instead but any a biger than about 120 are already so rare that
* it is possible to ignore them and still get enough pseudoprimes.
* But it is still a restriction of the set of available pseudoprimes
* which makes this implementation less secure if used stand-alone.
*/
#define LTM_FROBENIUS_UNDERWOOD_A 177
#else
#define LTM_FROBENIUS_UNDERWOOD_A 32764
#endif
int mp_prime_frobenius_underwood(const mp_int *N, int *result)
{
mp_int T1z, T2z, Np1z, sz, tz;
int a, ap2, length, i, j, isset;
int e;
*result = MP_NO;
if ((e = mp_init_multi(&T1z, &T2z, &Np1z, &sz, &tz, NULL)) != MP_OKAY) {
return e;
}
for (a = 0; a < LTM_FROBENIUS_UNDERWOOD_A; a++) {
/* TODO: That's ugly! No, really, it is! */
if ((a==2) || (a==4) || (a==7) || (a==8) || (a==10) ||
(a==14) || (a==18) || (a==23) || (a==26) || (a==28)) {
continue;
}
/* (32764^2 - 4) < 2^31, no bigint for >MP_8BIT needed) */
if ((e = mp_set_long(&T1z, (unsigned long)a)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_sqr(&T1z, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_sub_d(&T1z, 4uL, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_kronecker(&T1z, N, &j)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if (j == -1) {
break;
}
if (j == 0) {
/* composite */
goto LBL_FU_ERR;
}
}
/* Tell it a composite and set return value accordingly */
if (a >= LTM_FROBENIUS_UNDERWOOD_A) {
e = MP_ITER;
goto LBL_FU_ERR;
}
/* Composite if N and (a+4)*(2*a+5) are not coprime */
if ((e = mp_set_long(&T1z, (unsigned long)((a+4)*((2*a)+5)))) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_gcd(N, &T1z, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if (!((T1z.used == 1) && (T1z.dp[0] == 1u))) {
goto LBL_FU_ERR;
}
ap2 = a + 2;
if ((e = mp_add_d(N, 1uL, &Np1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
mp_set(&sz, 1uL);
mp_set(&tz, 2uL);
length = mp_count_bits(&Np1z);
for (i = length - 2; i >= 0; i--) {
/*
* temp = (sz*(a*sz+2*tz))%N;
* tz = ((tz-sz)*(tz+sz))%N;
* sz = temp;
*/
if ((e = mp_mul_2(&tz, &T2z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
/* a = 0 at about 50% of the cases (non-square and odd input) */
if (a != 0) {
if ((e = mp_mul_d(&sz, (mp_digit)a, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_add(&T1z, &T2z, &T2z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
}
if ((e = mp_mul(&T2z, &sz, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_sub(&tz, &sz, &T2z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_add(&sz, &tz, &sz)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_mul(&sz, &T2z, &tz)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_mod(&tz, N, &tz)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_mod(&T1z, N, &sz)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((isset = mp_get_bit(&Np1z, i)) == MP_VAL) {
e = isset;
goto LBL_FU_ERR;
}
if (isset == MP_YES) {
/*
* temp = (a+2) * sz + tz
* tz = 2 * tz - sz
* sz = temp
*/
if (a == 0) {
if ((e = mp_mul_2(&sz, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
} else {
if ((e = mp_mul_d(&sz, (mp_digit)ap2, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
}
if ((e = mp_add(&T1z, &tz, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_mul_2(&tz, &T2z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_sub(&T2z, &sz, &tz)) != MP_OKAY) {
goto LBL_FU_ERR;
}
mp_exch(&sz, &T1z);
}
}
if ((e = mp_set_long(&T1z, (unsigned long)((2 * a) + 5))) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((e = mp_mod(&T1z, N, &T1z)) != MP_OKAY) {
goto LBL_FU_ERR;
}
if ((mp_iszero(&sz) != MP_NO) && (mp_cmp(&tz, &T1z) == MP_EQ)) {
*result = MP_YES;
goto LBL_FU_ERR;
}
LBL_FU_ERR:
mp_clear_multi(&tz, &sz, &Np1z, &T2z, &T1z, NULL);
return e;
}
#endif
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

43
bn_mp_prime_is_divisible.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,39 +9,36 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* determines if an integers is divisible by one
/* 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 mp_prime_is_divisible(const mp_int *a, int *result)
{
int err, ix;
mp_digit res;
int err, ix;
mp_digit res;
/* default to not */
*result = MP_NO;
/* 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;
}
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;
}
}
/* is the residue zero? */
if (res == 0u) {
*result = MP_YES;
return MP_OKAY;
}
}
return MP_OKAY;
return MP_OKAY;
}
#endif

387
bn_mp_prime_is_prime.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,73 +9,360 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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)
/* portable integer log of two with small footprint */
static unsigned int s_floor_ilog2(int value)
{
mp_int b;
int ix, err, res;
unsigned int r = 0;
while ((value >>= 1) != 0) {
r++;
}
return r;
}
/* default to no */
*result = MP_NO;
/* valid value of t? */
if ((t <= 0) || (t > PRIME_SIZE)) {
return MP_VAL;
}
int mp_prime_is_prime(const mp_int *a, int t, int *result)
{
mp_int b;
int ix, err, res, p_max = 0, size_a, len;
unsigned int fips_rand, mask;
/* 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) {
/* default to no */
*result = MP_NO;
/* valid value of t? */
if (t > PRIME_SIZE) {
return MP_VAL;
}
/* Some shortcuts */
/* N > 3 */
if (a->used == 1) {
if ((a->dp[0] == 0u) || (a->dp[0] == 1u)) {
*result = 0;
return MP_OKAY;
}
if (a->dp[0] == 2u) {
*result = 1;
return MP_OKAY;
}
}
}
/* first perform trial division */
if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
return err;
}
/* N must be odd */
if (mp_iseven(a) == MP_YES) {
return MP_OKAY;
}
/* N is not a perfect square: floor(sqrt(N))^2 != N */
if ((err = mp_is_square(a, &res)) != MP_OKAY) {
return err;
}
if (res != 0) {
return MP_OKAY;
}
/* return if it was trivially divisible */
if (res == MP_YES) {
return MP_OKAY;
}
/* 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 = MP_YES;
return MP_OKAY;
}
}
#ifdef MP_8BIT
/* The search in the loop above was exhaustive in this case */
if ((a->used == 1) && (PRIME_SIZE >= 31)) {
return MP_OKAY;
}
#endif
/* now perform the miller-rabin rounds */
if ((err = mp_init (&b)) != MP_OKAY) {
return err;
}
/* first perform trial division */
if ((err = mp_prime_is_divisible(a, &res)) != MP_OKAY) {
return err;
}
for (ix = 0; ix < t; ix++) {
/* set the prime */
mp_set (&b, ltm_prime_tab[ix]);
/* return if it was trivially divisible */
if (res == MP_YES) {
return MP_OKAY;
}
if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
/*
Run the Miller-Rabin test with base 2 for the BPSW test.
*/
if ((err = mp_init_set(&b, 2uL)) != MP_OKAY) {
return err;
}
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
}
if (res == MP_NO) {
goto LBL_B;
}
}
}
/*
Rumours have it that Mathematica does a second M-R test with base 3.
Other rumours have it that their strong L-S test is slightly different.
It does not hurt, though, beside a bit of extra runtime.
*/
b.dp[0]++;
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;
/*
* Both, the Frobenius-Underwood test and the the Lucas-Selfridge test are quite
* slow so if speed is an issue, define LTM_USE_FIPS_ONLY to use M-R tests with
* bases 2, 3 and t random bases.
*/
#ifndef LTM_USE_FIPS_ONLY
if (t >= 0) {
/*
* Use a Frobenius-Underwood test instead of the Lucas-Selfridge test for
* MP_8BIT (It is unknown if the Lucas-Selfridge test works with 16-bit
* integers but the necesssary analysis is on the todo-list).
*/
#if defined (MP_8BIT) || defined (LTM_USE_FROBENIUS_TEST)
err = mp_prime_frobenius_underwood(a, &res);
if ((err != MP_OKAY) && (err != MP_ITER)) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
#else
if ((err = mp_prime_strong_lucas_selfridge(a, &res)) != MP_OKAY) {
goto LBL_B;
}
if (res == MP_NO) {
goto LBL_B;
}
#endif
}
#endif
/* run at least one Miller-Rabin test with a random base */
if (t == 0) {
t = 1;
}
/*
abs(t) extra rounds of M-R to extend the range of primes it can find if t < 0.
Only recommended if the input range is known to be < 3317044064679887385961981
It uses the bases for a deterministic M-R test if input < 3317044064679887385961981
The caller has to check the size.
Not for cryptographic use because with known bases strong M-R pseudoprimes can
be constructed. Use at least one M-R test with a random base (t >= 1).
The 1119 bit large number
80383745745363949125707961434194210813883768828755814583748891752229742737653\
33652186502336163960045457915042023603208766569966760987284043965408232928738\
79185086916685732826776177102938969773947016708230428687109997439976544144845\
34115587245063340927902227529622941498423068816854043264575340183297861112989\
60644845216191652872597534901
has been constructed by F. Arnault (F. Arnault, "Rabin-Miller primality test:
composite numbers which pass it.", Mathematics of Computation, 1995, 64. Jg.,
Nr. 209, S. 355-361), is a semiprime with the two factors
40095821663949960541830645208454685300518816604113250877450620473800321707011\
96242716223191597219733582163165085358166969145233813917169287527980445796800\
452592031836601
20047910831974980270915322604227342650259408302056625438725310236900160853505\
98121358111595798609866791081582542679083484572616906958584643763990222898400\
226296015918301
and it is a strong pseudoprime to all forty-six prime M-R bases up to 200
It does not fail the strong Bailley-PSP test as implemented here, it is just
given as an example, if not the reason to use the BPSW-test instead of M-R-tests
with a sequence of primes 2...n.
*/
if (t < 0) {
t = -t;
/*
Sorenson, Jonathan; Webster, Jonathan (2015).
"Strong Pseudoprimes to Twelve Prime Bases".
*/
/* 0x437ae92817f9fc85b7e5 = 318665857834031151167461 */
if ((err = mp_read_radix(&b, "437ae92817f9fc85b7e5", 16)) != MP_OKAY) {
goto LBL_B;
}
if (mp_cmp(a, &b) == MP_LT) {
p_max = 12;
} else {
/* 0x2be6951adc5b22410a5fd = 3317044064679887385961981 */
if ((err = mp_read_radix(&b, "2be6951adc5b22410a5fd", 16)) != MP_OKAY) {
goto LBL_B;
}
if (mp_cmp(a, &b) == MP_LT) {
p_max = 13;
} else {
err = MP_VAL;
goto LBL_B;
}
}
/* for compatibility with the current API (well, compatible within a sign's width) */
if (p_max < t) {
p_max = t;
}
if (p_max > PRIME_SIZE) {
err = MP_VAL;
goto LBL_B;
}
/* we did bases 2 and 3 already, skip them */
for (ix = 2; ix < p_max; ix++) {
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;
}
}
}
/*
Do "t" M-R tests with random bases between 3 and "a".
See Fips 186.4 p. 126ff
*/
else if (t > 0) {
/*
* The mp_digit's have a defined bit-size but the size of the
* array a.dp is a simple 'int' and this library can not assume full
* compliance to the current C-standard (ISO/IEC 9899:2011) because
* it gets used for small embeded processors, too. Some of those MCUs
* have compilers that one cannot call standard compliant by any means.
* Hence the ugly type-fiddling in the following code.
*/
size_a = mp_count_bits(a);
mask = (1u << s_floor_ilog2(size_a)) - 1u;
/*
Assuming the General Rieman hypothesis (never thought to write that in a
comment) the upper bound can be lowered to 2*(log a)^2.
E. Bach, "Explicit bounds for primality testing and related problems,"
Math. Comp. 55 (1990), 355-380.
size_a = (size_a/10) * 7;
len = 2 * (size_a * size_a);
E.g.: a number of size 2^2048 would be reduced to the upper limit
floor(2048/10)*7 = 1428
2 * 1428^2 = 4078368
(would have been ~4030331.9962 with floats and natural log instead)
That number is smaller than 2^28, the default bit-size of mp_digit.
*/
/*
How many tests, you might ask? Dana Jacobsen of Math::Prime::Util fame
does exactly 1. In words: one. Look at the end of _GMP_is_prime() in
Math-Prime-Util-GMP-0.50/primality.c if you do not believe it.
The function mp_rand() goes to some length to use a cryptographically
good PRNG. That also means that the chance to always get the same base
in the loop is non-zero, although very low.
If the BPSW test and/or the addtional Frobenious test have been
performed instead of just the Miller-Rabin test with the bases 2 and 3,
a single extra test should suffice, so such a very unlikely event
will not do much harm.
To preemptivly answer the dangling question: no, a witness does not
need to be prime.
*/
for (ix = 0; ix < t; ix++) {
/* mp_rand() guarantees the first digit to be non-zero */
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
goto LBL_B;
}
/*
* Reduce digit before casting because mp_digit might be bigger than
* an unsigned int and "mask" on the other side is most probably not.
*/
fips_rand = (unsigned int)(b.dp[0] & (mp_digit) mask);
#ifdef MP_8BIT
/*
* One 8-bit digit is too small, so concatenate two if the size of
* unsigned int allows for it.
*/
if (((sizeof(unsigned int) * CHAR_BIT)/2) >= (sizeof(mp_digit) * CHAR_BIT)) {
if ((err = mp_rand(&b, 1)) != MP_OKAY) {
goto LBL_B;
}
fips_rand <<= sizeof(mp_digit) * CHAR_BIT;
fips_rand |= (unsigned int) b.dp[0];
fips_rand &= mask;
}
#endif
if (fips_rand > (unsigned int)(INT_MAX - DIGIT_BIT)) {
len = INT_MAX / DIGIT_BIT;
} else {
len = (((int)fips_rand + DIGIT_BIT) / DIGIT_BIT);
}
/* Unlikely. */
if (len < 0) {
ix--;
continue;
}
/*
* As mentioned above, one 8-bit digit is too small and
* although it can only happen in the unlikely case that
* an "unsigned int" is smaller than 16 bit a simple test
* is cheap and the correction even cheaper.
*/
#ifdef MP_8BIT
/* All "a" < 2^8 have been caught before */
if (len == 1) {
len++;
}
#endif
if ((err = mp_rand(&b, len)) != MP_OKAY) {
goto LBL_B;
}
/*
* That number might got too big and the witness has to be
* smaller than or equal to "a"
*/
len = mp_count_bits(&b);
if (len > size_a) {
len = len - size_a;
if ((err = mp_div_2d(&b, len, &b, NULL)) != MP_OKAY) {
goto LBL_B;
}
}
/* Although the chance for b <= 3 is miniscule, try again. */
if (mp_cmp_d(&b, 3uL) != MP_GT) {
ix--;
continue;
}
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
/* ref: $Format:%D$ */

140
bn_mp_prime_miller_rabin.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,92 +9,92 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* Miller-Rabin test of "a" to the base of "b" as described in
/* 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
* 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)
int mp_prime_miller_rabin(const mp_int *a, const mp_int *b, int *result)
{
mp_int n1, y, r;
int s, j, err;
mp_int n1, y, r;
int s, j, err;
/* default */
*result = MP_NO;
/* default */
*result = MP_NO;
/* ensure b > 1 */
if (mp_cmp_d(b, 1) != MP_GT) {
return MP_VAL;
}
/* ensure b > 1 */
if (mp_cmp_d(b, 1uL) != 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;
}
/* get n1 = a - 1 */
if ((err = mp_init_copy(&n1, a)) != MP_OKAY) {
return err;
}
if ((err = mp_sub_d(&n1, 1uL, &n1)) != MP_OKAY) {
goto LBL_N1;
}
/* set 2**s * r = n1 */
if ((err = mp_init_copy (&r, &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);
/* 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;
}
/* 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) {
/* 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;
}
}
}
/* probably prime now */
*result = MP_YES;
LBL_Y:mp_clear (&y);
LBL_R:mp_clear (&r);
LBL_N1:mp_clear (&n1);
return err;
/* if y != 1 and y != n1 do */
if ((mp_cmp_d(&y, 1uL) != 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, 1uL) == 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

104
bn_mp_prime_next_prime.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,10 +9,7 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* finds the next prime after the number "a" using "t" trials
@ -26,11 +23,6 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
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;
@ -38,32 +30,32 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
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;
}
}
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] & 3u) != 3u) {
/* scan upwards for a prime congruent to 3 mod 4 */
for (y = x + 1; y < PRIME_SIZE; y++) {
if ((ltm_prime_tab[y] & 3u) == 3u) {
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);
if (mp_cmp_d(a, 1uL) == MP_EQ) {
mp_set(a, 2uL);
return MP_OKAY;
}
/* fall through to the sieve */
@ -80,13 +72,15 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
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; };
if ((a->dp[0] & 3u) != 3u) {
if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) {
return err;
};
}
} else {
if (mp_iseven(a) == MP_YES) {
/* force odd */
if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) {
return err;
}
}
@ -116,20 +110,20 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
/* compute the new residue without using division */
for (x = 1; x < PRIME_SIZE; x++) {
/* add the step to each residue */
res_tab[x] += kstep;
/* 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];
}
/* 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;
}
/* set flag if zero */
if (res_tab[x] == 0u) {
y = 1;
}
}
} while ((y == 1) && (step < ((((mp_digit)1) << DIGIT_BIT) - kstep)));
} while ((y == 1) && (step < (((mp_digit)1 << DIGIT_BIT) - kstep)));
/* add the step */
if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
@ -137,21 +131,13 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
}
/* if didn't pass sieve and step == MAX then skip test */
if ((y == 1) && (step >= ((((mp_digit)1) << DIGIT_BIT) - kstep))) {
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[x]);
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_ERR;
}
if (res == MP_NO) {
break;
}
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
goto LBL_ERR;
}
if (res == MP_YES) {
break;
}

42
bn_mp_prime_rabin_miller_trials.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,37 +9,41 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
static const struct {
int k, t;
} sizes[] = {
{ 128, 28 },
{ 256, 16 },
{ 384, 10 },
{ 512, 7 },
{ 640, 6 },
{ 768, 5 },
{ 896, 4 },
{ 1024, 4 }
{ 80, -1 }, /* Use deterministic algorithm for size <= 80 bits */
{ 81, 39 },
{ 96, 37 },
{ 128, 32 },
{ 160, 27 },
{ 192, 21 },
{ 256, 16 },
{ 384, 10 },
{ 512, 7 },
{ 640, 6 },
{ 768, 5 },
{ 896, 4 },
{ 1024, 4 },
{ 2048, 2 },
{ 4096, 1 },
};
/* returns # of RM trials required for a given bit size */
/* returns # of RM trials required for a given bit size and max. error of 2^(-96)*/
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;
}
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;
}

47
bn_mp_prime_random_ex.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_PRIME_RANDOM_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,16 +9,13 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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_ON - make the 2nd highest bit one
@ -49,7 +46,7 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
bsize = (size>>3) + ((size&7)?1:0);
/* we need a buffer of bsize bytes */
tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
tmp = OPT_CAST(unsigned char) XMALLOC((size_t)bsize);
if (tmp == NULL) {
return MP_MEM;
}
@ -62,7 +59,7 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
if ((flags & LTM_PRIME_2MSB_ON) != 0) {
maskOR_msb |= 0x80 >> ((9 - size) & 7);
}
}
/* get the maskOR_lsb */
maskOR_lsb = 1;
@ -76,7 +73,7 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
err = MP_VAL;
goto error;
}
/* work over the MSbyte */
tmp[0] &= maskAND;
tmp[0] |= 1 << ((size - 1) & 7);
@ -86,28 +83,42 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
tmp[bsize-1] |= maskOR_lsb;
/* read it in */
if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY) { goto error; }
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) {
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
goto error;
}
if (res == MP_NO) {
continue;
}
if ((flags & LTM_PRIME_SAFE) != 0) {
/* 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; }
if ((err = mp_sub_d(a, 1uL, 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; }
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
goto error;
}
}
} while (res == MP_NO);
if ((flags & LTM_PRIME_SAFE) != 0) {
/* 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; }
if ((err = mp_mul_2(a, a)) != MP_OKAY) {
goto error;
}
if ((err = mp_add_d(a, 1uL, a)) != MP_OKAY) {
goto error;
}
}
err = MP_OKAY;

411
bn_mp_prime_strong_lucas_selfridge.c Normal file
View File

@ -0,0 +1,411 @@
#include "tommath_private.h"
#ifdef BN_MP_PRIME_STRONG_LUCAS_SELFRIDGE_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.
*
* SPDX-License-Identifier: Unlicense
*/
/*
* See file bn_mp_prime_is_prime.c or the documentation in doc/bn.tex for the details
*/
#ifndef LTM_USE_FIPS_ONLY
/*
* 8-bit is just too small. You can try the Frobenius test
* but that frobenius test can fail, too, for the same reason.
*/
#ifndef MP_8BIT
/*
* multiply bigint a with int d and put the result in c
* Like mp_mul_d() but with a signed long as the small input
*/
static int s_mp_mul_si(const mp_int *a, long d, mp_int *c)
{
mp_int t;
int err, neg = 0;
if ((err = mp_init(&t)) != MP_OKAY) {
return err;
}
if (d < 0) {
neg = 1;
d = -d;
}
/*
* mp_digit might be smaller than a long, which excludes
* the use of mp_mul_d() here.
*/
if ((err = mp_set_long(&t, (unsigned long) d)) != MP_OKAY) {
goto LBL_MPMULSI_ERR;
}
if ((err = mp_mul(a, &t, c)) != MP_OKAY) {
goto LBL_MPMULSI_ERR;
}
if (neg == 1) {
c->sign = (a->sign == MP_NEG) ? MP_ZPOS: MP_NEG;
}
LBL_MPMULSI_ERR:
mp_clear(&t);
return err;
}
/*
Strong Lucas-Selfridge test.
returns MP_YES if it is a strong L-S prime, MP_NO if it is composite
Code ported from Thomas Ray Nicely's implementation of the BPSW test
at http://www.trnicely.net/misc/bpsw.html
Freeware copyright (C) 2016 Thomas R. Nicely <http://www.trnicely.net>.
Released into the public domain by the author, who disclaims any legal
liability arising from its use
The multi-line comments are made by Thomas R. Nicely and are copied verbatim.
Additional comments marked "CZ" (without the quotes) are by the code-portist.
(If that name sounds familiar, he is the guy who found the fdiv bug in the
Pentium (P5x, I think) Intel processor)
*/
int mp_prime_strong_lucas_selfridge(const mp_int *a, int *result)
{
/* CZ TODO: choose better variable names! */
mp_int Dz, gcd, Np1, Uz, Vz, U2mz, V2mz, Qmz, Q2mz, Qkdz, T1z, T2z, T3z, T4z, Q2kdz;
/* CZ TODO: Some of them need the full 32 bit, hence the (temporary) exclusion of MP_8BIT */
int32_t D, Ds, J, sign, P, Q, r, s, u, Nbits;
int e;
int isset, oddness;
*result = MP_NO;
/*
Find the first element D in the sequence {5, -7, 9, -11, 13, ...}
such that Jacobi(D,N) = -1 (Selfridge's algorithm). Theory
indicates that, if N is not a perfect square, D will "nearly
always" be "small." Just in case, an overflow trap for D is
included.
*/
if ((e = mp_init_multi(&Dz, &gcd, &Np1, &Uz, &Vz, &U2mz, &V2mz, &Qmz, &Q2mz, &Qkdz, &T1z, &T2z, &T3z, &T4z, &Q2kdz,
NULL)) != MP_OKAY) {
return e;
}
D = 5;
sign = 1;
for (;;) {
Ds = sign * D;
sign = -sign;
if ((e = mp_set_long(&Dz, (unsigned long)D)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_gcd(a, &Dz, &gcd)) != MP_OKAY) {
goto LBL_LS_ERR;
}
/* if 1 < GCD < N then N is composite with factor "D", and
Jacobi(D,N) is technically undefined (but often returned
as zero). */
if ((mp_cmp_d(&gcd, 1uL) == MP_GT) && (mp_cmp(&gcd, a) == MP_LT)) {
goto LBL_LS_ERR;
}
if (Ds < 0) {
Dz.sign = MP_NEG;
}
if ((e = mp_kronecker(&Dz, a, &J)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if (J == -1) {
break;
}
D += 2;
if (D > (INT_MAX - 2)) {
e = MP_VAL;
goto LBL_LS_ERR;
}
}
P = 1; /* Selfridge's choice */
Q = (1 - Ds) / 4; /* Required so D = P*P - 4*Q */
/* NOTE: The conditions (a) N does not divide Q, and
(b) D is square-free or not a perfect square, are included by
some authors; e.g., "Prime numbers and computer methods for
factorization," Hans Riesel (2nd ed., 1994, Birkhauser, Boston),
p. 130. For this particular application of Lucas sequences,
these conditions were found to be immaterial. */
/* Now calculate N - Jacobi(D,N) = N + 1 (even), and calculate the
odd positive integer d and positive integer s for which
N + 1 = 2^s*d (similar to the step for N - 1 in Miller's test).
The strong Lucas-Selfridge test then returns N as a strong
Lucas probable prime (slprp) if any of the following
conditions is met: U_d=0, V_d=0, V_2d=0, V_4d=0, V_8d=0,
V_16d=0, ..., etc., ending with V_{2^(s-1)*d}=V_{(N+1)/2}=0
(all equalities mod N). Thus d is the highest index of U that
must be computed (since V_2m is independent of U), compared
to U_{N+1} for the standard Lucas-Selfridge test; and no
index of V beyond (N+1)/2 is required, just as in the
standard Lucas-Selfridge test. However, the quantity Q^d must
be computed for use (if necessary) in the latter stages of
the test. The result is that the strong Lucas-Selfridge test
has a running time only slightly greater (order of 10 %) than
that of the standard Lucas-Selfridge test, while producing
only (roughly) 30 % as many pseudoprimes (and every strong
Lucas pseudoprime is also a standard Lucas pseudoprime). Thus
the evidence indicates that the strong Lucas-Selfridge test is
more effective than the standard Lucas-Selfridge test, and a
Baillie-PSW test based on the strong Lucas-Selfridge test
should be more reliable. */
if ((e = mp_add_d(a, 1uL, &Np1)) != MP_OKAY) {
goto LBL_LS_ERR;
}
s = mp_cnt_lsb(&Np1);
/* CZ
* This should round towards zero because
* Thomas R. Nicely used GMP's mpz_tdiv_q_2exp()
* and mp_div_2d() is equivalent. Additionally:
* dividing an even number by two does not produce
* any leftovers.
*/
if ((e = mp_div_2d(&Np1, s, &Dz, NULL)) != MP_OKAY) {
goto LBL_LS_ERR;
}
/* We must now compute U_d and V_d. Since d is odd, the accumulated
values U and V are initialized to U_1 and V_1 (if the target
index were even, U and V would be initialized instead to U_0=0
and V_0=2). The values of U_2m and V_2m are also initialized to
U_1 and V_1; the FOR loop calculates in succession U_2 and V_2,
U_4 and V_4, U_8 and V_8, etc. If the corresponding bits
(1, 2, 3, ...) of t are on (the zero bit having been accounted
for in the initialization of U and V), these values are then
combined with the previous totals for U and V, using the
composition formulas for addition of indices. */
mp_set(&Uz, 1uL); /* U=U_1 */
mp_set(&Vz, (mp_digit)P); /* V=V_1 */
mp_set(&U2mz, 1uL); /* U_1 */
mp_set(&V2mz, (mp_digit)P); /* V_1 */
if (Q < 0) {
Q = -Q;
if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
/* Initializes calculation of Q^d */
if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
goto LBL_LS_ERR;
}
Qmz.sign = MP_NEG;
Q2mz.sign = MP_NEG;
Qkdz.sign = MP_NEG;
Q = -Q;
} else {
if ((e = mp_set_long(&Qmz, (unsigned long)Q)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
/* Initializes calculation of Q^d */
if ((e = mp_set_long(&Qkdz, (unsigned long)Q)) != MP_OKAY) {
goto LBL_LS_ERR;
}
}
Nbits = mp_count_bits(&Dz);
for (u = 1; u < Nbits; u++) { /* zero bit off, already accounted for */
/* Formulas for doubling of indices (carried out mod N). Note that
* the indices denoted as "2m" are actually powers of 2, specifically
* 2^(ul-1) beginning each loop and 2^ul ending each loop.
*
* U_2m = U_m*V_m
* V_2m = V_m*V_m - 2*Q^m
*/
if ((e = mp_mul(&U2mz, &V2mz, &U2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mod(&U2mz, a, &U2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_sqr(&V2mz, &V2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_sub(&V2mz, &Q2mz, &V2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mod(&V2mz, a, &V2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
/* Must calculate powers of Q for use in V_2m, also for Q^d later */
if ((e = mp_sqr(&Qmz, &Qmz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
/* prevents overflow */ /* CZ still necessary without a fixed prealloc'd mem.? */
if ((e = mp_mod(&Qmz, a, &Qmz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mul_2(&Qmz, &Q2mz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((isset = mp_get_bit(&Dz, u)) == MP_VAL) {
e = isset;
goto LBL_LS_ERR;
}
if (isset == MP_YES) {
/* Formulas for addition of indices (carried out mod N);
*
* U_(m+n) = (U_m*V_n + U_n*V_m)/2
* V_(m+n) = (V_m*V_n + D*U_m*U_n)/2
*
* Be careful with division by 2 (mod N)!
*/
if ((e = mp_mul(&U2mz, &Vz, &T1z)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mul(&Uz, &V2mz, &T2z)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mul(&V2mz, &Vz, &T3z)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mul(&U2mz, &Uz, &T4z)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = s_mp_mul_si(&T4z, (long)Ds, &T4z)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_add(&T1z, &T2z, &Uz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if (mp_isodd(&Uz) != MP_NO) {
if ((e = mp_add(&Uz, a, &Uz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
}
/* CZ
* This should round towards negative infinity because
* Thomas R. Nicely used GMP's mpz_fdiv_q_2exp().
* But mp_div_2() does not do so, it is truncating instead.
*/
oddness = mp_isodd(&Uz);
if ((e = mp_div_2(&Uz, &Uz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((Uz.sign == MP_NEG) && (oddness != MP_NO)) {
if ((e = mp_sub_d(&Uz, 1uL, &Uz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
}
if ((e = mp_add(&T3z, &T4z, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if (mp_isodd(&Vz) != MP_NO) {
if ((e = mp_add(&Vz, a, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
}
oddness = mp_isodd(&Vz);
if ((e = mp_div_2(&Vz, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((Vz.sign == MP_NEG) && (oddness != MP_NO)) {
if ((e = mp_sub_d(&Vz, 1uL, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
}
if ((e = mp_mod(&Uz, a, &Uz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
/* Calculating Q^d for later use */
if ((e = mp_mul(&Qkdz, &Qmz, &Qkdz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
}
}
/* If U_d or V_d is congruent to 0 mod N, then N is a prime or a
strong Lucas pseudoprime. */
if ((mp_iszero(&Uz) != MP_NO) || (mp_iszero(&Vz) != MP_NO)) {
*result = MP_YES;
goto LBL_LS_ERR;
}
/* NOTE: Ribenboim ("The new book of prime number records," 3rd ed.,
1995/6) omits the condition V0 on p.142, but includes it on
p. 130. The condition is NECESSARY; otherwise the test will
return false negatives---e.g., the primes 29 and 2000029 will be
returned as composite. */
/* Otherwise, we must compute V_2d, V_4d, V_8d, ..., V_{2^(s-1)*d}
by repeated use of the formula V_2m = V_m*V_m - 2*Q^m. If any of
these are congruent to 0 mod N, then N is a prime or a strong
Lucas pseudoprime. */
/* Initialize 2*Q^(d*2^r) for V_2m */
if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
for (r = 1; r < s; r++) {
if ((e = mp_sqr(&Vz, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_sub(&Vz, &Q2kdz, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mod(&Vz, a, &Vz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if (mp_iszero(&Vz) != MP_NO) {
*result = MP_YES;
goto LBL_LS_ERR;
}
/* Calculate Q^{d*2^r} for next r (final iteration irrelevant). */
if (r < (s - 1)) {
if ((e = mp_sqr(&Qkdz, &Qkdz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mod(&Qkdz, a, &Qkdz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
if ((e = mp_mul_2(&Qkdz, &Q2kdz)) != MP_OKAY) {
goto LBL_LS_ERR;
}
}
}
LBL_LS_ERR:
mp_clear_multi(&Q2kdz, &T4z, &T3z, &T2z, &T1z, &Qkdz, &Q2mz, &Qmz, &V2mz, &U2mz, &Vz, &Uz, &Np1, &gcd, &Dz, NULL);
return e;
}
#endif
#endif
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */

93
bn_mp_radix_size.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,66 +9,63 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
int mp_radix_size(const mp_int *a, int radix, int *size)
{
int res, digs;
mp_int t;
mp_digit d;
int res, digs;
mp_int t;
mp_digit d;
*size = 0;
*size = 0;
/* make sure the radix is in range */
if ((radix < 2) || (radix > 64)) {
return MP_VAL;
}
/* 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;
}
if (mp_iszero(a) == MP_YES) {
*size = 2;
return MP_OKAY;
}
/* special case for binary */
if (radix == 2) {
*size = mp_count_bits (a) + ((a->sign == MP_NEG) ? 1 : 0) + 1;
return MP_OKAY;
}
/* special case for binary */
if (radix == 2) {
*size = mp_count_bits(a) + ((a->sign == MP_NEG) ? 1 : 0) + 1;
return MP_OKAY;
}
/* digs is the digit count */
digs = 0;
/* digs is the digit count */
digs = 0;
/* if it's negative add one for the sign */
if (a->sign == MP_NEG) {
++digs;
}
/* 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);
/* init a copy of the input */
if ((res = mp_init_copy(&t, a)) != MP_OKAY) {
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;
/* 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

23
bn_mp_radix_smap.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,14 +9,25 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
const char *const mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
const uint8_t mp_s_rmap_reverse[] = {
0xff, 0xff, 0xff, 0x3e, 0xff, 0xff, 0xff, 0x3f, /* ()*+,-./ */
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, /* 01234567 */
0x08, 0x09, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* 89:;<=>? */
0xff, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, /* @ABCDEFG */
0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, /* HIJKLMNO */
0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, /* PQRSTUVW */
0x21, 0x22, 0x23, 0xff, 0xff, 0xff, 0xff, 0xff, /* XYZ[\]^_ */
0xff, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, /* `abcdefg */
0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, /* hijklmno */
0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, /* pqrstuvw */
0x3b, 0x3c, 0x3d, 0xff, 0xff, 0xff, 0xff, 0xff, /* xyz{|}~. */
};
const size_t mp_s_rmap_reverse_sz = sizeof(mp_s_rmap_reverse);
#endif
/* ref: $Format:%D$ */

240
bn_mp_rand.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,69 +9,211 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
#if MP_GEN_RANDOM_MAX == 0xffffffff
#define MP_GEN_RANDOM_SHIFT 32
#elif MP_GEN_RANDOM_MAX == 32767
/* SHRT_MAX */
#define MP_GEN_RANDOM_SHIFT 15
#elif MP_GEN_RANDOM_MAX == 2147483647
/* INT_MAX */
#define MP_GEN_RANDOM_SHIFT 31
#elif !defined(MP_GEN_RANDOM_SHIFT)
#error Thou shalt define their own valid MP_GEN_RANDOM_SHIFT
/* First the OS-specific special cases
* - *BSD
* - Windows
*/
#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
#define MP_ARC4RANDOM
#define MP_GEN_RANDOM_MAX 0xffffffffu
#define MP_GEN_RANDOM_SHIFT 32
static int s_read_arc4random(mp_digit *p)
{
mp_digit d = 0, msk = 0;
do {
d <<= MP_GEN_RANDOM_SHIFT;
d |= ((mp_digit) arc4random());
msk <<= MP_GEN_RANDOM_SHIFT;
msk |= (MP_MASK & MP_GEN_RANDOM_MAX);
} while ((MP_MASK & msk) != MP_MASK);
*p = d;
return MP_OKAY;
}
#endif
/* makes a pseudo-random int of a given size */
static mp_digit s_gen_random(void)
#if defined(_WIN32) || defined(_WIN32_WCE)
#define MP_WIN_CSP
#ifndef _WIN32_WINNT
#define _WIN32_WINNT 0x0400
#endif
#ifdef _WIN32_WCE
#define UNDER_CE
#define ARM
#endif
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include <wincrypt.h>
static HCRYPTPROV hProv = 0;
static void s_cleanup_win_csp(void)
{
mp_digit d = 0, msk = 0;
do {
d <<= MP_GEN_RANDOM_SHIFT;
d |= ((mp_digit) MP_GEN_RANDOM());
msk <<= MP_GEN_RANDOM_SHIFT;
msk |= (MP_MASK & MP_GEN_RANDOM_MAX);
} while ((MP_MASK & msk) != MP_MASK);
d &= MP_MASK;
return d;
CryptReleaseContext(hProv, 0);
hProv = 0;
}
int
mp_rand (mp_int * a, int digits)
static int s_read_win_csp(mp_digit *p)
{
int res;
mp_digit d;
int ret = -1;
if (hProv == 0) {
if (!CryptAcquireContext(&hProv, NULL, MS_DEF_PROV, PROV_RSA_FULL,
(CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET)) &&
!CryptAcquireContext(&hProv, NULL, MS_DEF_PROV, PROV_RSA_FULL,
CRYPT_VERIFYCONTEXT | CRYPT_MACHINE_KEYSET | CRYPT_NEWKEYSET)) {
hProv = 0;
return ret;
}
atexit(s_cleanup_win_csp);
}
if (CryptGenRandom(hProv, sizeof(*p), (void *)p) == TRUE) {
ret = MP_OKAY;
}
return ret;
}
#endif /* WIN32 */
mp_zero (a);
if (digits <= 0) {
return MP_OKAY;
}
#if !defined(MP_WIN_CSP) && defined(__linux__) && defined(__GLIBC_PREREQ)
#if __GLIBC_PREREQ(2, 25)
#define MP_GETRANDOM
#include <sys/random.h>
#include <errno.h>
/* first place a random non-zero digit */
do {
d = s_gen_random();
} while (d == 0);
static int s_read_getrandom(mp_digit *p)
{
int ret;
do {
ret = getrandom(p, sizeof(*p), 0);
} while ((ret == -1) && (errno == EINTR));
if (ret == sizeof(*p)) return MP_OKAY;
return -1;
}
#endif
#endif
if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
return res;
}
/* We assume all platforms besides windows provide "/dev/urandom".
* In case yours doesn't, define MP_NO_DEV_URANDOM at compile-time.
*/
#if !defined(MP_WIN_CSP) && !defined(MP_NO_DEV_URANDOM)
#ifndef MP_DEV_URANDOM
#define MP_DEV_URANDOM "/dev/urandom"
#endif
#include <fcntl.h>
#include <errno.h>
#include <unistd.h>
while (--digits > 0) {
if ((res = mp_lshd (a, 1)) != MP_OKAY) {
static int s_read_dev_urandom(mp_digit *p)
{
ssize_t r;
int fd;
do {
fd = open(MP_DEV_URANDOM, O_RDONLY);
} while ((fd == -1) && (errno == EINTR));
if (fd == -1) return -1;
do {
r = read(fd, p, sizeof(*p));
} while ((r == -1) && (errno == EINTR));
close(fd);
if (r != sizeof(*p)) return -1;
return MP_OKAY;
}
#endif
#if defined(MP_PRNG_ENABLE_LTM_RNG)
unsigned long (*ltm_rng)(unsigned char *out, unsigned long outlen, void (*callback)(void));
void (*ltm_rng_callback)(void);
static int s_read_ltm_rng(mp_digit *p)
{
unsigned long ret;
if (ltm_rng == NULL) return -1;
ret = ltm_rng((void *)p, sizeof(*p), ltm_rng_callback);
if (ret != sizeof(*p)) return -1;
return MP_OKAY;
}
#endif
static int s_rand_digit(mp_digit *p)
{
int ret = -1;
#if defined(MP_ARC4RANDOM)
ret = s_read_arc4random(p);
if (ret == MP_OKAY) return ret;
#endif
#if defined(MP_WIN_CSP)
ret = s_read_win_csp(p);
if (ret == MP_OKAY) return ret;
#else
#if defined(MP_GETRANDOM)
ret = s_read_getrandom(p);
if (ret == MP_OKAY) return ret;
#endif
#if defined(MP_DEV_URANDOM)
ret = s_read_dev_urandom(p);
if (ret == MP_OKAY) return ret;
#endif
#endif /* MP_WIN_CSP */
#if defined(MP_PRNG_ENABLE_LTM_RNG)
ret = s_read_ltm_rng(p);
if (ret == MP_OKAY) return ret;
#endif
return ret;
}
/* makes a pseudo-random int of a given size */
int mp_rand_digit(mp_digit *r)
{
int ret = s_rand_digit(r);
*r &= MP_MASK;
return ret;
}
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 {
if (mp_rand_digit(&d) != MP_OKAY) {
return MP_VAL;
}
} while (d == 0u);
if ((res = mp_add_d(a, d, a)) != MP_OKAY) {
return res;
}
}
if ((res = mp_add_d (a, s_gen_random(), a)) != MP_OKAY) {
return res;
}
}
while (--digits > 0) {
if ((res = mp_lshd(a, 1)) != MP_OKAY) {
return res;
}
return MP_OKAY;
if (mp_rand_digit(&d) != MP_OKAY) {
return MP_VAL;
}
if ((res = mp_add_d(a, d, a)) != MP_OKAY) {
return res;
}
}
return MP_OKAY;
}
#endif

111
bn_mp_read_radix.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,74 +9,77 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, const char *str, int radix)
int mp_read_radix(mp_int *a, const char *str, int radix)
{
int y, res, neg;
char ch;
int y, res, neg;
unsigned pos;
char ch;
/* zero the digit bignum */
mp_zero(a);
/* zero the digit bignum */
mp_zero(a);
/* make sure the radix is ok */
if ((radix < 2) || (radix > 64)) {
return MP_VAL;
}
/* 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;
}
/* 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 != '\0') {
/* 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 = (radix <= 36) ? (char)toupper((int)*str) : *str;
for (y = 0; y < 64; y++) {
if (ch == mp_s_rmap[y]) {
/* set the integer to the default of zero */
mp_zero(a);
/* process each digit of the string */
while (*str != '\0') {
/* 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 = (radix <= 36) ? (char)toupper((int)*str) : *str;
pos = (unsigned)(ch - '(');
if (mp_s_rmap_reverse_sz < pos) {
break;
}
}
y = (int)mp_s_rmap_reverse[pos];
/* 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) {
/* 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 == 0xff) || (y >= radix)) {
break;
}
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) {
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) != MP_YES) {
a->sign = neg;
}
return MP_OKAY;
++str;
}
/* if an illegal character was found, fail. */
if (!((*str == '\0') || (*str == '\r') || (*str == '\n'))) {
mp_zero(a);
return MP_VAL;
}
/* set the sign only if a != 0 */
if (mp_iszero(a) != MP_YES) {
a->sign = neg;
}
return MP_OKAY;
}
#endif

33
bn_mp_read_signed_bin.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,30 +9,27 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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 mp_read_signed_bin(mp_int *a, const unsigned char *b, int c)
{
int res;
int res;
/* read magnitude */
if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
return 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;
}
/* first byte is 0 for positive, non-zero for negative */
if (b[0] == (unsigned char)0) {
a->sign = MP_ZPOS;
} else {
a->sign = MP_NEG;
}
return MP_OKAY;
return MP_OKAY;
}
#endif

53
bn_mp_read_unsigned_bin.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,44 +9,41 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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 mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c)
{
int res;
int res;
/* make sure there are at least two digits */
if (a->alloc < 2) {
if ((res = mp_grow(a, 2)) != MP_OKAY) {
return 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);
/* 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;
}
/* 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;
a->dp[0] |= *b++;
a->used += 1;
#else
a->dp[0] = (*b & MP_MASK);
a->dp[1] |= ((*b++ >> 7U) & 1);
a->used += 2;
a->dp[0] = (*b & MP_MASK);
a->dp[1] |= ((*b++ >> 7) & 1u);
a->used += 2;
#endif
}
mp_clamp (a);
return MP_OKAY;
}
mp_clamp(a);
return MP_OKAY;
}
#endif

121
bn_mp_reduce.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,89 +9,86 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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)
int mp_reduce(mp_int *x, const mp_int *m, const mp_int *mu)
{
mp_int q;
int res, um = m->used;
mp_int q;
int res, um = m->used;
/* q = x */
if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
return res;
}
/* q = x */
if ((res = mp_init_copy(&q, x)) != MP_OKAY) {
return res;
}
/* q1 = x / b**(k-1) */
mp_rshd (&q, um - 1);
/* q1 = x / b**(k-1) */
mp_rshd(&q, um - 1);
/* according to HAC this optimization is ok */
if (((mp_digit) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
goto CLEANUP;
}
} else {
/* according to HAC this optimization is ok */
if ((mp_digit)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;
}
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;
}
if ((res = fast_s_mp_mul_high_digs(&q, mu, &q, um)) != MP_OKAY) {
goto CLEANUP;
}
#else
{
res = MP_VAL;
goto CLEANUP;
}
{
res = MP_VAL;
goto CLEANUP;
}
#endif
}
}
/* q3 = q2 / b**(k+1) */
mp_rshd (&q, um + 1);
/* 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)
/* x = x mod b**(k+1), quick (no division) */
if ((res = mp_mod_2d(x, DIGIT_BIT * (um + 1), x)) != 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) {
/* 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, 0uL) == MP_LT) {
mp_set(&q, 1uL);
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);
mp_clear(&q);
return res;
return res;
}
#endif

21
bn_mp_reduce_2k.c
View File

@ -1,4 +1,4 @@
#include <tommath_private.h>
#include "tommath_private.h"
#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
@ -9,14 +9,11 @@
* 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, tstdenis82@gmail.com, http://libtom.org
* SPDX-License-Identifier: Unlicense
*/
/* 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)
int mp_reduce_2k(mp_int *a, const mp_int *n, mp_digit d)
{
mp_int q;
int p, res;
@ -29,29 +26,29 @@ int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
top:
/* q = a/2**p, a = a mod 2**p */
if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
goto ERR;
goto LBL_ERR;
}
if (d != 1) {
if (d != 1u) {
/* q = q * d */
if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
goto ERR;
goto LBL_ERR;
}
}
/* a = a + q */
if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
goto ERR;
goto LBL_ERR;
}
if (mp_cmp_mag(a, n) != MP_LT) {
if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
goto ERR;
goto LBL_ERR;
}
goto top;
}
ERR:
LBL_ERR:
mp_clear(&q);
return res;
}

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