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added libtommath-0.25

This commit is contained in:
Tom St Denis 2003-08-05 01:24:44 +00:00 committed by Steffen Jaeckel
parent 03cc01b578
commit c1da6aa2de
121 changed files with 2906 additions and 2554 deletions
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4
LICENSE Normal file
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@ -0,0 +1,4 @@
LibTomMath is hereby released into the Public Domain.
-- Tom St Denis

BIN
bn.pdf
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2
bn.tex
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@ -1,7 +1,7 @@
\documentclass[]{article}
\begin{document}
\title{LibTomMath v0.24 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
\title{LibTomMath v0.25 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
\author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle
\newpage

41
bn_error.c Normal file
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@ -0,0 +1,41 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
static const struct {
int code;
char *msg;
} msgs[] = {
{ MP_OKAY, "Successful" },
{ MP_MEM, "Out of heap" },
{ MP_VAL, "Value out of range" }
};
/* return a char * string for a given code */
char *mp_error_to_string(int code)
{
int x;
/* scan the lookup table for the given message */
for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
if (msgs[x].code == code) {
return msgs[x].msg;
}
}
/* generic reply for invalid code */
return "Invalid error code";
}

21
bn_fast_mp_invmod.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -26,6 +26,14 @@ fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
mp_int x, y, u, v, B, D;
int res, neg;
/* 2. [modified] if a,b are both even then return an error!
*
* That is if gcd(a,b) = 2**k * q then obviously there is no inverse.
*/
if (mp_iseven (a) == 1 && mp_iseven (b) == 1) {
return MP_VAL;
}
/* init all our temps */
if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
return res;
@ -41,15 +49,6 @@ fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
goto __ERR;
}
/* 2. [modified] if x,y are both even then return an error!
*
* That is if gcd(x,y) = 2 * k then obviously there is no inverse.
*/
if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
res = MP_VAL;
goto __ERR;
}
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
if ((res = mp_copy (&x, &u)) != MP_OKAY) {
goto __ERR;

25
bn_fast_mp_montgomery_reduce.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -38,6 +38,9 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
}
/* first we have to get the digits of the input into
* an array of double precision words W[...]
*/
{
register mp_word *_W;
register mp_digit *tmpx;
@ -56,6 +59,9 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
}
/* now we proceed to zero successive digits
* from the least significant upwards
*/
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * m' mod b
*
@ -101,12 +107,20 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
/* now we have to propagate the carries and
* shift the words downward [all those least
* significant digits we zeroed].
*/
{
register mp_digit *tmpx;
register mp_word *_W, *_W1;
/* nox fix rest of carries */
/* alias for current word */
_W1 = W + ix;
/* alias for next word, where the carry goes */
_W = W + ++ix;
for (; ix <= n->used * 2 + 1; ix++) {
@ -119,7 +133,11 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
* 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++) {
@ -127,7 +145,8 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
/* zero oldused digits, if the input a was larger than
* m->used+1 we'll have to clear the digits */
* m->used+1 we'll have to clear the digits
*/
for (; ix < olduse; ix++) {
*tmpx++ = 0;
}

4
bn_fast_s_mp_mul_digs.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

6
bn_fast_s_mp_mul_high_digs.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -12,7 +12,7 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
#include <tommath.h>
/* this is a modified version of fast_s_mp_mul_digs that only produces
* output digits *above* digs. See the comments for fast_s_mp_mul_digs

27
bn_fast_s_mp_sqr.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -48,14 +48,14 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
/* zero temp buffer (columns)
* Note that there are two buffers. Since squaring requires
* a outter and inner product and the inner product requires
* a outer and inner product and the inner product requires
* computing a product and doubling it (a relatively expensive
* op to perform n**2 times if you don't have to) the inner and
* outer products are computed in different buffers. This way
* the inner product can be doubled using n doublings instead of
* n**2
*/
memset (W, 0, newused * sizeof (mp_word));
memset (W, 0, newused * sizeof (mp_word));
memset (W2, 0, newused * sizeof (mp_word));
/* This computes the inner product. To simplify the inner N**2 loop
@ -67,6 +67,7 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
* Note that every outer product is computed
* for a particular column only once which means that
* there is no need todo a double precision addition
* into the W2[] array.
*/
W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
@ -95,7 +96,12 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
olduse = b->used;
b->used = newused;
/* now compute digits */
/* now compute digits
*
* We have to double the inner product sums, add in the
* outer product sums, propagate carries and convert
* to single precision.
*/
{
register mp_digit *tmpb;
@ -109,16 +115,21 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
/* double/add next digit */
W[ix] += W[ix] + W2[ix];
/* propagate carry forwards [from the previous digit] */
W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
/* store the current digit now that the carry isn't
* needed
*/
*tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
/* set the last value. Note even if the carry is zero
* this is required since the next step will not zero
/* set the last value. Note even if the carry is zero
* this is required since the next step will not zero
* it if b originally had a value at b->dp[2*a.used]
*/
*tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
/* clear high digits */
/* clear high digits of b if there were any originally */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}

11
bn_mp_2expt.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -24,11 +24,18 @@ mp_2expt (mp_int * a, int b)
{
int res;
/* zero a as per default */
mp_zero (a);
/* grow a to accomodate the single bit */
if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
return res;
}
/* set the used count of where the bit will go */
a->used = b / DIGIT_BIT + 1;
/* put the single bit in its place */
a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
return MP_OKAY;

15
bn_mp_abs.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -22,9 +22,16 @@ int
mp_abs (mp_int * a, mp_int * b)
{
int res;
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;
return MP_OKAY;
}

4
bn_mp_add.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

10
bn_mp_add_d.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -82,7 +82,11 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
c->used = 1;
/* the result is a single digit */
*tmpc++ = b - a->dp[0];
if (a->used == 1) {
*tmpc++ = b - a->dp[0];
} else {
*tmpc++ = b;
}
/* setup count so the clearing of oldused
* can fall through correctly

4
bn_mp_addmod.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_and.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

9
bn_mp_clamp.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -24,9 +24,14 @@
void
mp_clamp (mp_int * a)
{
/* decrease used while the most significant digit is
* zero.
*/
while (a->used > 0 && a->dp[a->used - 1] == 0) {
--(a->used);
}
/* reset the sign flag if used == 0 */
if (a->used == 0) {
a->sign = MP_ZPOS;
}

8
bn_mp_clear.c
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@ -1,10 +1,10 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
@ -18,6 +18,7 @@
void
mp_clear (mp_int * a)
{
/* only do anything if a hasn't been freed previously */
if (a->dp != NULL) {
/* first zero the digits */
memset (a->dp, 0, sizeof (mp_digit) * a->used);
@ -28,5 +29,6 @@ mp_clear (mp_int * a)
/* reset members to make debugging easier */
a->dp = NULL;
a->alloc = a->used = 0;
a->sign = MP_ZPOS;
}
}

28
bn_mp_clear_multi.c Normal file
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@ -0,0 +1,28 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
{
mp_int* next_mp = mp;
va_list args;
va_start(args, mp);
while (next_mp != NULL) {
mp_clear(next_mp);
next_mp = va_arg(args, mp_int*);
}
va_end(args);
}

4
bn_mp_cmp.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

8
bn_mp_cmp_d.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -18,15 +18,17 @@
int
mp_cmp_d (mp_int * a, mp_digit b)
{
/* compare based on sign */
if (a->sign == MP_NEG) {
return MP_LT;
}
/* compare based on magnitude */
if (a->used > 1) {
return MP_GT;
}
/* compare the only digit of a to b */
if (a->dp[0] > b) {
return MP_GT;
} else if (a->dp[0] < b) {

4
bn_mp_cmp_mag.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

5
bn_mp_cnt_lsb.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -20,6 +20,7 @@ int mp_cnt_lsb(mp_int *a)
int x;
mp_digit q;
/* easy out */
if (mp_iszero(a) == 1) {
return 0;
}

16
bn_mp_copy.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -26,8 +26,10 @@ mp_copy (mp_int * a, mp_int * b)
}
/* grow dest */
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
return res;
if (b->alloc < a->used) {
if ((res = mp_grow (b, a->used)) != MP_OKAY) {
return res;
}
}
/* zero b and copy the parameters over */
@ -35,7 +37,11 @@ mp_copy (mp_int * a, mp_int * b)
register mp_digit *tmpa, *tmpb;
/* pointer aliases */
/* source */
tmpa = a->dp;
/* destination */
tmpb = b->dp;
/* copy all the digits */
@ -48,6 +54,8 @@ mp_copy (mp_int * a, mp_int * b)
*tmpb++ = 0;
}
}
/* copy used count and sign */
b->used = a->used;
b->sign = a->sign;
return MP_OKAY;

4
bn_mp_count_bits.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_div.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_div_2.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_div_2d.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

19
bn_mp_div_3.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -35,10 +35,17 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
w = 0;
for (ix = a->used - 1; ix >= 0; ix--) {
w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
if (w >= 3) {
/* multiply w by [1/3] */
t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
/* now subtract 3 * [w/3] from w, to get the remainder */
w -= (t << ((mp_word)1)) + t;
/* fixup the remainder as required since
* the optimization is not exact.
*/
while (w >= 3) {
t += 1;
w -= 3;
@ -48,11 +55,13 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
}
q.dp[ix] = (mp_digit)t;
}
/* [optional] store the remainder */
if (d != NULL) {
*d = (mp_digit)w;
}
/* [optional] store the quotient */
if (c != NULL) {
mp_clamp(&q);
mp_exch(&q, c);

4
bn_mp_div_d.c
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@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

71
bn_mp_dr_is_modulus.c
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@ -1,34 +1,37 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
int ix;
/* must be at least two digits */
if (a->used < 2) {
return 0;
}
for (ix = 1; ix < a->used; ix++) {
if (a->dp[ix] != MP_MASK) {
return 0;
}
}
return 1;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
{
int ix;
/* must be at least two digits */
if (a->used < 2) {
return 0;
}
/* must be of the form b**k - a [a <= b] so all
* but the first digit must be equal to -1 (mod b).
*/
for (ix = 1; ix < a->used; ix++) {
if (a->dp[ix] != MP_MASK) {
return 0;
}
}
return 1;
}

6
bn_mp_dr_reduce.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -57,7 +57,7 @@ top:
/* set carry to zero */
mu = 0;
/* compute (x mod B**m) + mp * [x/B**m] inline and inplace */
/* 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);

52
bn_mp_dr_setup.c
View File

@ -1,26 +1,26 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
/* the casts are required if DIGIT_BIT is one less than
* the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
*/
*d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
((mp_word)a->dp[0]));
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
{
/* the casts are required if DIGIT_BIT is one less than
* the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
*/
*d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
((mp_word)a->dp[0]));
}

6
bn_mp_exch.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -22,7 +22,7 @@ mp_exch (mp_int * a, mp_int * b)
{
mp_int t;
t = *a;
t = *a;
*a = *b;
*b = t;
}

4
bn_mp_expt_d.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

8
bn_mp_exptmod.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -60,7 +60,10 @@ mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
return err;
}
/* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
/* if not, is it a uDR modulus? */
if (dr == 0) {
dr = mp_reduce_is_2k(P) << 1;
}
@ -69,6 +72,7 @@ mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
if (mp_isodd (P) == 1 || dr != 0) {
return mp_exptmod_fast (G, X, P, Y, dr);
} else {
/* otherwise use the generic Barrett reduction technique */
return s_mp_exptmod (G, X, P, Y);
}
}

33
bn_mp_exptmod_fast.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -94,15 +94,15 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
} else {
/* use slower baselien method */
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
}
} else if (redmode == 1) {
/* setup DR reduction */
/* setup DR reduction for moduli of the form B**k - b */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
} else {
/* setup 2k reduction */
/* setup DR reduction for moduli of the form 2**k - b */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
goto __M;
}
@ -111,7 +111,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* setup result */
if ((err = mp_init (&res)) != MP_OKAY) {
goto __RES;
goto __M;
}
/* create M table
@ -173,15 +173,17 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
for (;;) {
/* grab next digit as required */
if (--bitcnt == 0) {
/* if digidx == -1 we are out of digits so break */
if (digidx == -1) {
break;
}
buf = X->dp[digidx--];
bitcnt = (int) DIGIT_BIT;
/* 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;
y = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
buf <<= (mp_digit)1;
/* if the bit is zero and mode == 0 then we ignore it
@ -206,7 +208,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* else we add it to the window */
bitbuf |= (y << (winsize - ++bitcpy));
mode = 2;
mode = 2;
if (bitcpy == winsize) {
/* ok window is filled so square as required and multiply */
@ -231,7 +233,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* empty window and reset */
bitcpy = 0;
bitbuf = 0;
mode = 1;
mode = 1;
}
}
@ -246,6 +248,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
goto __RES;
}
/* get next bit of the window */
bitbuf <<= 1;
if ((bitbuf & (1 << winsize)) != 0) {
/* then multiply */
@ -260,12 +263,18 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
}
if (redmode == 0) {
/* fixup result if Montgomery reduction is used */
/* 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 = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
/* swap res with Y */
mp_exch (&res, Y);
err = MP_OKAY;
__RES:mp_clear (&res);

122
bn_mp_fread.c
View File

@ -1,61 +1,61 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
int err, ch, neg, y;
/* clear a */
mp_zero(a);
/* if first digit is - then set negative */
ch = fgetc(stream);
if (ch == '-') {
neg = MP_NEG;
ch = fgetc(stream);
} else {
neg = MP_ZPOS;
}
for (;;) {
/* find y in the radix map */
for (y = 0; y < radix; y++) {
if (mp_s_rmap[y] == ch) {
break;
}
}
if (y == radix) {
break;
}
/* shift up and add */
if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
return err;
}
if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
return err;
}
ch = fgetc(stream);
}
if (mp_cmp_d(a, 0) != MP_EQ) {
a->sign = neg;
}
return MP_OKAY;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
{
int err, ch, neg, y;
/* clear a */
mp_zero(a);
/* if first digit is - then set negative */
ch = fgetc(stream);
if (ch == '-') {
neg = MP_NEG;
ch = fgetc(stream);
} else {
neg = MP_ZPOS;
}
for (;;) {
/* find y in the radix map */
for (y = 0; y < radix; y++) {
if (mp_s_rmap[y] == ch) {
break;
}
}
if (y == radix) {
break;
}
/* shift up and add */
if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
return err;
}
if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
return err;
}
ch = fgetc(stream);
}
if (mp_cmp_d(a, 0) != MP_EQ) {
a->sign = neg;
}
return MP_OKAY;
}

4
bn_mp_fwrite.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

37
bn_mp_gcd.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -23,16 +23,21 @@ mp_gcd (mp_int * a, mp_int * b, mp_int * c)
/* either zero than gcd is the largest */
if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
return mp_copy (b, c);
return mp_abs (b, c);
}
if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
return mp_copy (a, c);
return mp_abs (a, c);
}
if (mp_iszero (a) == 1 && mp_iszero (b) == 1) {
/* optimized. At this point if a == 0 then
* b must equal zero too
*/
if (mp_iszero (a) == 1) {
mp_zero(c);
return MP_OKAY;
}
/* get copies of a and b we can modify */
if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
return res;
}
@ -49,12 +54,15 @@ mp_gcd (mp_int * a, mp_int * b, mp_int * c)
v_lsb = mp_cnt_lsb(&v);
k = MIN(u_lsb, v_lsb);
if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
goto __V;
}
if (k > 0) {
/* divide the power of two out */
if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
goto __V;
}
if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
goto __V;
if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
goto __V;
}
}
/* divide any remaining factors of two out */
@ -69,10 +77,11 @@ mp_gcd (mp_int * a, mp_int * b, mp_int * c)
goto __V;
}
}
while (mp_iszero(&v) == 0) {
/* make sure v is the largest */
if (mp_cmp_mag(&u, &v) == MP_GT) {
/* swap u and v to make sure v is >= u */
mp_exch(&u, &v);
}
@ -86,10 +95,10 @@ mp_gcd (mp_int * a, mp_int * b, mp_int * c)
goto __V;
}
}
/* multiply by 2**k which we divided out at the beginning */
/* multiply by 2**k which we divided out at the beginning */
if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
goto __V;
goto __V;
}
c->sign = MP_ZPOS;
res = MP_OKAY;

6
bn_mp_grow.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -23,7 +23,7 @@ mp_grow (mp_int * a, int size)
/* 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 - 1));
size += (MP_PREC * 2) - (size % MP_PREC);
a->dp = OPT_CAST realloc (a->dp, sizeof (mp_digit) * size);
if (a->dp == NULL) {

8
bn_mp_init.c
View File

@ -1,10 +1,10 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
@ -18,7 +18,7 @@
int
mp_init (mp_int * a)
{
/* allocate ram required and clear it */
/* allocate memory required and clear it */
a->dp = OPT_CAST calloc (sizeof (mp_digit), MP_PREC);
if (a->dp == NULL) {
return MP_MEM;

4
bn_mp_init_copy.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

18
bn_mp_multi.c → bn_mp_init_multi.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -49,16 +49,4 @@ int mp_init_multi(mp_int *mp, ...)
}
va_end(args);
return res; /* Assumed ok, if error flagged above. */
}
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);
}
}

13
bn_mp_init_size.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -14,22 +14,21 @@
*/
#include <tommath.h>
/* init a mp_init and grow it to a given size */
/* init an mp_init for a given size */
int
mp_init_size (mp_int * a, int size)
{
/* pad size so there are always extra digits */
size += (MP_PREC * 2) - (size & (MP_PREC - 1));
size += (MP_PREC * 2) - (size % MP_PREC);
/* alloc mem */
a->dp = OPT_CAST calloc (sizeof (mp_digit), size);
if (a->dp == NULL) {
return MP_MEM;
}
a->used = 0;
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
a->sign = MP_ZPOS;
return MP_OKAY;
}

4
bn_mp_invmod.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

20
bn_mp_jacobi.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -24,6 +24,11 @@ mp_jacobi (mp_int * a, mp_int * p, int *c)
int k, s, r, res;
mp_digit residue;
/* if p <= 0 return MP_VAL */
if (mp_cmp_d(p, 0) != MP_GT) {
return MP_VAL;
}
/* step 1. if a == 0, return 0 */
if (mp_iszero (a) == 1) {
*c = 0;
@ -37,7 +42,7 @@ mp_jacobi (mp_int * a, mp_int * p, int *c)
}
/* default */
k = s = 0;
s = 0;
/* step 3. write a = a1 * 2**k */
if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
@ -48,11 +53,10 @@ mp_jacobi (mp_int * a, mp_int * p, int *c)
goto __A1;
}
while (mp_iseven (&a1) == 1) {
k = k + 1;
if ((res = mp_div_2 (&a1, &a1)) != MP_OKAY) {
goto __P1;
}
/* divide out larger power of two */
k = mp_cnt_lsb(&a1);
if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
goto __P1;
}
/* step 4. if e is even set s=1 */

4
bn_mp_karatsuba_mul.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_karatsuba_sqr.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_lcm.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_lshd.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_mod.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

5
bn_mp_mod_2d.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -20,7 +20,6 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
{
int x, res;
/* if b is <= 0 then zero the int */
if (b <= 0) {
mp_zero (c);

4
bn_mp_mod_d.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_montgomery_calc_normalization.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_montgomery_reduce.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_montgomery_setup.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

9
bn_mp_mul.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -20,13 +20,14 @@ mp_mul (mp_int * a, mp_int * b, mp_int * c)
{
int res, neg;
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
/* use Toom-Cook? */
if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
res = mp_toom_mul(a, b, c);
/* use Karatsuba? */
} else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
} else {
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will

6
bn_mp_mul_2.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -61,7 +61,7 @@ mp_mul_2 (mp_int * a, mp_int * b)
if (r != 0) {
/* add a MSB which is always 1 at this point */
*tmpb = 1;
++b->used;
++(b->used);
}
/* now zero any excess digits on the destination

6
bn_mp_mul_2d.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -72,7 +72,7 @@ mp_mul_2d (mp_int * a, int b, mp_int * c)
/* set final carry */
if (r != 0) {
c->dp[c->used++] = r;
c->dp[(c->used)++] = r;
}
}
mp_clamp (c);

4
bn_mp_mul_d.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_mulmod.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

6
bn_mp_n_root.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -48,7 +48,7 @@ mp_n_root (mp_int * a, mp_digit b, mp_int * c)
}
/* if a is negative fudge the sign but keep track */
neg = a->sign;
neg = a->sign;
a->sign = MP_ZPOS;
/* t2 = 2 */

4
bn_mp_neg.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_or.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

6
bn_mp_prime_fermat.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -28,7 +28,7 @@ mp_prime_fermat (mp_int * a, mp_int * b, int *result)
mp_int t;
int err;
/* default to fail */
/* default to composite */
*result = 0;
/* ensure b > 1 */

4
bn_mp_prime_is_divisible.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_prime_is_prime.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_prime_miller_rabin.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

12
bn_mp_prime_next_prime.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -31,9 +31,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
}
/* force positive */
if (a->sign == MP_NEG) {
a->sign = MP_ZPOS;
}
a->sign = MP_ZPOS;
/* simple algo if a is less than the largest prime in the table */
if (mp_cmp_d(a, __prime_tab[PRIME_SIZE-1]) == MP_LT) {
@ -137,8 +135,8 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
goto __ERR;
}
/* if step == MAX then skip test */
if (step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
/* if didn't pass sieve and step == MAX then skip test */
if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
continue;
}

108
bn_mp_radix_size.c
View File

@ -1,54 +1,54 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* returns size of ASCII reprensentation */
int
mp_radix_size (mp_int * a, int radix)
{
int res, digs;
mp_int t;
mp_digit d;
/* special case for binary */
if (radix == 2) {
return mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
}
if (radix < 2 || radix > 64) {
return 0;
}
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
return 0;
}
digs = 0;
if (t.sign == MP_NEG) {
++digs;
t.sign = MP_ZPOS;
}
while (mp_iszero (&t) == 0) {
if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
mp_clear (&t);
return 0;
}
++digs;
}
mp_clear (&t);
return digs + 1;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* returns size of ASCII reprensentation */
int
mp_radix_size (mp_int * a, int radix)
{
int res, digs;
mp_int t;
mp_digit d;
/* special case for binary */
if (radix == 2) {
return mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
}
if (radix < 2 || radix > 64) {
return 0;
}
if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
return 0;
}
digs = 0;
if (t.sign == MP_NEG) {
++digs;
t.sign = MP_ZPOS;
}
while (mp_iszero (&t) == 0) {
if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
mp_clear (&t);
return 0;
}
++digs;
}
mp_clear (&t);
return digs + 1;
}

36
bn_mp_radix_smap.c
View File

@ -1,18 +1,18 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";

4
bn_mp_rand.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

154
bn_mp_read_radix.c
View File

@ -1,77 +1,77 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* read a string [ASCII] in a given radix */
int
mp_read_radix (mp_int * a, char *str, int radix)
{
int y, res, neg;
char ch;
/* make sure the radix is ok */
if (radix < 2 || radix > 64) {
return MP_VAL;
}
/* if the leading digit is a
* minus set the sign to negative.
*/
if (*str == '-') {
++str;
neg = MP_NEG;
} else {
neg = MP_ZPOS;
}
/* set the integer to the default of zero */
mp_zero (a);
/* process each digit of the string */
while (*str) {
/* if the radix < 36 the conversion is case insensitive
* this allows numbers like 1AB and 1ab to represent the same value
* [e.g. in hex]
*/
ch = (char) ((radix < 36) ? toupper (*str) : *str);
for (y = 0; y < 64; y++) {
if (ch == mp_s_rmap[y]) {
break;
}
}
/* if the char was found in the map
* and is less than the given radix add it
* to the number, otherwise exit the loop.
*/
if (y < radix) {
if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
return res;
}
if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
return res;
}
} else {
break;
}
++str;
}
/* set the sign only if a != 0 */
if (mp_iszero(a) != 1) {
a->sign = neg;
}
return MP_OKAY;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* read a string [ASCII] in a given radix */
int
mp_read_radix (mp_int * a, char *str, int radix)
{
int y, res, neg;
char ch;
/* make sure the radix is ok */
if (radix < 2 || radix > 64) {
return MP_VAL;
}
/* if the leading digit is a
* minus set the sign to negative.
*/
if (*str == '-') {
++str;
neg = MP_NEG;
} else {
neg = MP_ZPOS;
}
/* set the integer to the default of zero */
mp_zero (a);
/* process each digit of the string */
while (*str) {
/* if the radix < 36 the conversion is case insensitive
* this allows numbers like 1AB and 1ab to represent the same value
* [e.g. in hex]
*/
ch = (char) ((radix < 36) ? toupper (*str) : *str);
for (y = 0; y < 64; y++) {
if (ch == mp_s_rmap[y]) {
break;
}
}
/* if the char was found in the map
* and is less than the given radix add it
* to the number, otherwise exit the loop.
*/
if (y < radix) {
if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
return res;
}
if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
return res;
}
} else {
break;
}
++str;
}
/* set the sign only if a != 0 */
if (mp_iszero(a) != 1) {
a->sign = neg;
}
return MP_OKAY;
}

4
bn_mp_read_signed_bin.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_read_unsigned_bin.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_reduce.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

112
bn_mp_reduce_2k.c
View File

@ -1,56 +1,56 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* reduces a modulo n where n is of the form 2**p - k */
int
mp_reduce_2k(mp_int *a, mp_int *n, mp_digit k)
{
mp_int q;
int p, res;
if ((res = mp_init(&q)) != MP_OKAY) {
return res;
}
p = mp_count_bits(n);
top:
/* q = a/2**p, a = a mod 2**p */
if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
goto ERR;
}
if (k != 1) {
/* q = q * k */
if ((res = mp_mul_d(&q, k, &q)) != MP_OKAY) {
goto ERR;
}
}
/* a = a + q */
if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
goto ERR;
}
if (mp_cmp_mag(a, n) != MP_LT) {
s_mp_sub(a, n, a);
goto top;
}
ERR:
mp_clear(&q);
return res;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* reduces a modulo n where n is of the form 2**p - k */
int
mp_reduce_2k(mp_int *a, mp_int *n, mp_digit k)
{
mp_int q;
int p, res;
if ((res = mp_init(&q)) != MP_OKAY) {
return res;
}
p = mp_count_bits(n);
top:
/* q = a/2**p, a = a mod 2**p */
if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
goto ERR;
}
if (k != 1) {
/* q = q * k */
if ((res = mp_mul_d(&q, k, &q)) != MP_OKAY) {
goto ERR;
}
}
/* a = a + q */
if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
goto ERR;
}
if (mp_cmp_mag(a, n) != MP_LT) {
s_mp_sub(a, n, a);
goto top;
}
ERR:
mp_clear(&q);
return res;
}

84
bn_mp_reduce_2k_setup.c
View File

@ -1,42 +1,42 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines the setup value */
int
mp_reduce_2k_setup(mp_int *a, mp_digit *d)
{
int res, p;
mp_int tmp;
if ((res = mp_init(&tmp)) != MP_OKAY) {
return res;
}
p = mp_count_bits(a);
if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
mp_clear(&tmp);
return res;
}
if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
mp_clear(&tmp);
return res;
}
*d = tmp.dp[0];
mp_clear(&tmp);
return MP_OKAY;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines the setup value */
int
mp_reduce_2k_setup(mp_int *a, mp_digit *d)
{
int res, p;
mp_int tmp;
if ((res = mp_init(&tmp)) != MP_OKAY) {
return res;
}
p = mp_count_bits(a);
if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
mp_clear(&tmp);
return res;
}
if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
mp_clear(&tmp);
return res;
}
*d = tmp.dp[0];
mp_clear(&tmp);
return MP_OKAY;
}

76
bn_mp_reduce_is_2k.c
View File

@ -1,38 +1,38 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines if mp_reduce_2k can be used */
int
mp_reduce_is_2k(mp_int *a)
{
int ix, iy;
if (a->used == 0) {
return 0;
} else if (a->used == 1) {
return 1;
} else if (a->used > 1) {
iy = mp_count_bits(a);
for (ix = DIGIT_BIT; ix < iy; ix++) {
if ((a->dp[ix/DIGIT_BIT] &
((mp_digit)1 << (mp_digit)(ix % DIGIT_BIT))) == 0) {
return 0;
}
}
}
return 1;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* determines if mp_reduce_2k can be used */
int
mp_reduce_is_2k(mp_int *a)
{
int ix, iy;
if (a->used == 0) {
return 0;
} else if (a->used == 1) {
return 1;
} else if (a->used > 1) {
iy = mp_count_bits(a);
for (ix = DIGIT_BIT; ix < iy; ix++) {
if ((a->dp[ix/DIGIT_BIT] &
((mp_digit)1 << (mp_digit)(ix % DIGIT_BIT))) == 0) {
return 0;
}
}
}
return 1;
}

58
bn_mp_reduce_setup.c
View File

@ -1,29 +1,29 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* pre-calculate the value required for Barrett reduction
* For a given modulus "b" it calulates the value required in "a"
*/
int
mp_reduce_setup (mp_int * a, mp_int * b)
{
int res;
if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
return res;
}
return mp_div (a, b, a, NULL);
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* pre-calculate the value required for Barrett reduction
* For a given modulus "b" it calulates the value required in "a"
*/
int
mp_reduce_setup (mp_int * a, mp_int * b)
{
int res;
if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
return res;
}
return mp_div (a, b, a, NULL);
}

4
bn_mp_rshd.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

6
bn_mp_set.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -20,5 +20,5 @@ mp_set (mp_int * a, mp_digit b)
{
mp_zero (a);
a->dp[0] = b & MP_MASK;
a->used = (a->dp[0] != 0) ? 1 : 0;
a->used = (a->dp[0] != 0) ? 1 : 0;
}

4
bn_mp_set_int.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_shrink.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_signed_bin_size.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

9
bn_mp_sqr.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -19,13 +19,14 @@ int
mp_sqr (mp_int * a, mp_int * b)
{
int res;
/* use Toom-Cook? */
if (a->used >= TOOM_SQR_CUTOFF) {
res = mp_toom_sqr(a, b);
/* Karatsuba? */
} else if (a->used >= KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
} else {
/* can we use the fast multiplier? */
/* can we use the fast comba multiplier? */
if ((a->used * 2 + 1) < MP_WARRAY &&
a->used <
(1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {

5
bn_mp_sqrmod.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -21,7 +21,6 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
int res;
mp_int t;
if ((res = mp_init (&t)) != MP_OKAY) {
return res;
}

4
bn_mp_sub.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

10
bn_mp_sub_d.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
@ -45,7 +45,11 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
/* if a <= b simply fix the single digit */
if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
*tmpc++ = b - *tmpa;
if (a->used == 1) {
*tmpc++ = b - *tmpa;
} else {
*tmpc++ = b;
}
ix = 1;
/* negative/1digit */

4
bn_mp_submod.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_to_signed_bin.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_to_unsigned_bin.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

546
bn_mp_toom_mul.c
View File

@ -1,273 +1,273 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* multiplication using the Toom-Cook 3-way algorithm */
int
mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
int res, B;
/* init temps */
if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
&a0, &a1, &a2, &b0, &b1,
&b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
return res;
}
/* B */
B = MIN(a->used, b->used) / 3;
/* a = a2 * B**2 + a1 * B + a0 */
if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_copy(a, &a1)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a1, B);
mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
if ((res = mp_copy(a, &a2)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a2, B*2);
/* b = b2 * B**2 + b1 * B + b0 */
if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_copy(b, &b1)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&b1, B);
mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
if ((res = mp_copy(b, &b2)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&b2, B*2);
/* w0 = a0*b0 */
if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
goto ERR;
}
/* w4 = a2 * b2 */
if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
goto ERR;
}
/* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
goto ERR;
}
/* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
goto ERR;
}
/* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
goto ERR;
}
/* now solve the matrix
0 0 0 0 1
1 2 4 8 16
1 1 1 1 1
16 8 4 2 1
1 0 0 0 0
using 12 subtractions, 4 shifts,
2 small divisions and 1 small multiplication
*/
/* r1 - r4 */
if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r0 */
if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/2 */
if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3/2 */
if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
goto ERR;
}
/* r2 - r0 - r4 */
if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1 - 8r0 */
if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - 8r4 */
if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
goto ERR;
}
/* 3r2 - r1 - r3 */
if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/3 */
if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
goto ERR;
}
/* r3/3 */
if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
goto ERR;
}
/* at this point shift W[n] by B*n */
if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
goto ERR;
}
ERR:
mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
&a0, &a1, &a2, &b0, &b1,
&b2, &tmp1, &tmp2, NULL);
return res;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* multiplication using the Toom-Cook 3-way algorithm */
int
mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
int res, B;
/* init temps */
if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
&a0, &a1, &a2, &b0, &b1,
&b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
return res;
}
/* B */
B = MIN(a->used, b->used) / 3;
/* a = a2 * B**2 + a1 * B + a0 */
if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_copy(a, &a1)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a1, B);
mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
if ((res = mp_copy(a, &a2)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a2, B*2);
/* b = b2 * B**2 + b1 * B + b0 */
if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_copy(b, &b1)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&b1, B);
mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
if ((res = mp_copy(b, &b2)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&b2, B*2);
/* w0 = a0*b0 */
if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
goto ERR;
}
/* w4 = a2 * b2 */
if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
goto ERR;
}
/* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
goto ERR;
}
/* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
goto ERR;
}
/* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
goto ERR;
}
/* now solve the matrix
0 0 0 0 1
1 2 4 8 16
1 1 1 1 1
16 8 4 2 1
1 0 0 0 0
using 12 subtractions, 4 shifts,
2 small divisions and 1 small multiplication
*/
/* r1 - r4 */
if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r0 */
if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/2 */
if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3/2 */
if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
goto ERR;
}
/* r2 - r0 - r4 */
if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1 - 8r0 */
if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - 8r4 */
if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
goto ERR;
}
/* 3r2 - r1 - r3 */
if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/3 */
if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
goto ERR;
}
/* r3/3 */
if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
goto ERR;
}
/* at this point shift W[n] by B*n */
if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
goto ERR;
}
ERR:
mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
&a0, &a1, &a2, &b0, &b1,
&b2, &tmp1, &tmp2, NULL);
return res;
}

440
bn_mp_toom_sqr.c
View File

@ -1,220 +1,220 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* squaring using Toom-Cook 3-way algorithm */
int
mp_toom_sqr(mp_int *a, mp_int *b)
{
mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
int res, B;
/* init temps */
if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
return res;
}
/* B */
B = a->used / 3;
/* a = a2 * B^2 + a1 * B + a0 */
if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_copy(a, &a1)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a1, B);
mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
if ((res = mp_copy(a, &a2)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a2, B*2);
/* w0 = a0*a0 */
if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
goto ERR;
}
/* w4 = a2 * a2 */
if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
goto ERR;
}
/* w1 = (a2 + 2(a1 + 2a0))**2 */
if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
goto ERR;
}
/* w3 = (a0 + 2(a1 + 2a2))**2 */
if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
goto ERR;
}
/* w2 = (a2 + a1 + a0)**2 */
if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
goto ERR;
}
/* now solve the matrix
0 0 0 0 1
1 2 4 8 16
1 1 1 1 1
16 8 4 2 1
1 0 0 0 0
using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
*/
/* r1 - r4 */
if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r0 */
if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/2 */
if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3/2 */
if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
goto ERR;
}
/* r2 - r0 - r4 */
if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1 - 8r0 */
if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - 8r4 */
if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
goto ERR;
}
/* 3r2 - r1 - r3 */
if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/3 */
if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
goto ERR;
}
/* r3/3 */
if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
goto ERR;
}
/* at this point shift W[n] by B*n */
if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
goto ERR;
}
ERR:
mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
return res;
}
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
#include <tommath.h>
/* squaring using Toom-Cook 3-way algorithm */
int
mp_toom_sqr(mp_int *a, mp_int *b)
{
mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
int res, B;
/* init temps */
if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
return res;
}
/* B */
B = a->used / 3;
/* a = a2 * B^2 + a1 * B + a0 */
if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_copy(a, &a1)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a1, B);
mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
if ((res = mp_copy(a, &a2)) != MP_OKAY) {
goto ERR;
}
mp_rshd(&a2, B*2);
/* w0 = a0*a0 */
if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
goto ERR;
}
/* w4 = a2 * a2 */
if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
goto ERR;
}
/* w1 = (a2 + 2(a1 + 2a0))**2 */
if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
goto ERR;
}
/* w3 = (a0 + 2(a1 + 2a2))**2 */
if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
goto ERR;
}
/* w2 = (a2 + a1 + a0)**2 */
if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
goto ERR;
}
/* now solve the matrix
0 0 0 0 1
1 2 4 8 16
1 1 1 1 1
16 8 4 2 1
1 0 0 0 0
using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
*/
/* r1 - r4 */
if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r0 */
if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/2 */
if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3/2 */
if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
goto ERR;
}
/* r2 - r0 - r4 */
if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1 - 8r0 */
if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - 8r4 */
if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
goto ERR;
}
/* 3r2 - r1 - r3 */
if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
goto ERR;
}
/* r1 - r2 */
if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
goto ERR;
}
/* r3 - r2 */
if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
goto ERR;
}
/* r1/3 */
if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
goto ERR;
}
/* r3/3 */
if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
goto ERR;
}
/* at this point shift W[n] by B*n */
if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
goto ERR;
}
if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
goto ERR;
}
ERR:
mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
return res;
}

4
bn_mp_toradix.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_unsigned_bin_size.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_xor.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_mp_zero.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_prime_tab.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

4
bn_reverse.c
View File

@ -1,9 +1,9 @@
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is library that provides for multiple-precision
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library is designed directly after the MPI library by
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*

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