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added libtommath-0.23

This commit is contained in:
Tom St Denis 2003-07-12 14:31:43 +00:00 committed by Steffen Jaeckel
parent 4c1d3f0838
commit eed6765fe9
36 changed files with 600 additions and 243 deletions
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bn.pdf
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2
bn.tex
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@ -1,7 +1,7 @@
\documentclass[]{article}
\begin{document}
\title{LibTomMath v0.22 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
\title{LibTomMath v0.23 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
\author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle
\newpage

5
bn_fast_mp_montgomery_reduce.c
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@ -64,7 +64,7 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
* that W[ix-1] have the carry cleared (see after the inner loop)
*/
register mp_digit mu;
mu = (((mp_digit) (W[ix] & MP_MASK)) * rho) & MP_MASK;
mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
/* a = a + mu * m * b**i
*
@ -93,7 +93,7 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* inner loop */
for (iy = 0; iy < n->used; iy++) {
*_W++ += ((mp_word) mu) * ((mp_word) * tmpn++);
*_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
}
}
@ -101,7 +101,6 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
{
register mp_digit *tmpx;
register mp_word *_W, *_W1;

13
bn_fast_s_mp_mul_digs.c
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@ -81,7 +81,7 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
pb = MIN (b->used, digs - ix);
for (iy = 0; iy < pb; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
*_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
}
}
@ -104,20 +104,27 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
* from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
* cost of the shifting. On very small numbers this is slower
* but on most cryptographic size numbers it is faster.
*
* In this particular implementation we feed the carries from
* behind which means when the loop terminates we still have one
* last digit to copy
*/
tmpc = c->dp;
for (ix = 1; ix < digs; ix++) {
/* forward the carry from the previous temp */
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
/* now extract the previous digit [below the carry] */
*tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
/* fetch the last digit */
*tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused */
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}

9
bn_fast_s_mp_mul_high_digs.c
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@ -71,7 +71,7 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
/* compute column products for digits above the minimum */
for (; iy < pb; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
*_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++);
}
}
}
@ -80,12 +80,15 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
oldused = c->used;
c->used = newused;
/* now convert the array W downto what we need */
/* now convert the array W downto what we need
*
* See comments in bn_fast_s_mp_mul_digs.c
*/
for (ix = digs + 1; ix < newused; ix++) {
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
c->dp[(pa + pb + 1) - 1] = (mp_digit) (W[(pa + pb + 1) - 1] & ((mp_word) MP_MASK));
c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
for (; ix < oldused; ix++) {
c->dp[ix] = 0;

4
bn_fast_s_mp_sqr.c
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@ -68,7 +68,7 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
* for a particular column only once which means that
* there is no need todo a double precision addition
*/
W2[ix + ix] = ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
{
register mp_digit tmpx, *tmpy;
@ -86,7 +86,7 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
/* inner products */
for (iy = ix + 1; iy < pa; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
*_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
}
}
}

3
bn_mp_clear.c
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@ -19,7 +19,6 @@ void
mp_clear (mp_int * a)
{
if (a->dp != NULL) {
/* first zero the digits */
memset (a->dp, 0, sizeof (mp_digit) * a->used);
@ -27,7 +26,7 @@ mp_clear (mp_int * a)
free (a->dp);
/* reset members to make debugging easier */
a->dp = NULL;
a->dp = NULL;
a->alloc = a->used = 0;
}
}

44
bn_mp_div_d.c
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@ -14,6 +14,19 @@
*/
#include <tommath.h>
static int s_is_power_of_two(mp_digit b, int *p)
{
int x;
for (x = 1; x < DIGIT_BIT; x++) {
if (b == (((mp_digit)1)<<x)) {
*p = x;
return 1;
}
}
return 0;
}
/* single digit division (based on routine from MPI) */
int
mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
@ -22,15 +35,40 @@ mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
mp_word w;
mp_digit t;
int res, ix;
/* cannot divide by zero */
if (b == 0) {
return MP_VAL;
}
/* quick outs */
if (b == 1 || mp_iszero(a) == 1) {
if (d != NULL) {
*d = 0;
}
if (c != NULL) {
return mp_copy(a, c);
}
return MP_OKAY;
}
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
*d = a->dp[0] & ((1<<ix) - 1);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
}
return MP_OKAY;
}
/* three? */
if (b == 3) {
return mp_div_3(a, c, d);
}
/* no easy answer [c'est la vie]. Just division */
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
return res;
}

1
bn_mp_exptmod_fast.c
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@ -82,7 +82,6 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
}
}
/* determine and setup reduction code */
if (redmode == 0) {
/* now setup montgomery */

4
bn_mp_montgomery_reduce.c
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@ -44,7 +44,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * m' mod b */
mu = (x->dp[ix] * rho) & MP_MASK;
mu = ((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK;
/* a = a + mu * m * b**i */
{
@ -61,7 +61,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
r = ((mp_word) mu) * ((mp_word) * tmpn++) +
r = ((mp_word)mu) * ((mp_word)*tmpn++) +
((mp_word) u) + ((mp_word) * tmpx);
u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
*tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));

2
bn_mp_mul_d.c
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@ -50,7 +50,7 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
u = 0;
for (ix = 0; ix < pa; ix++) {
/* compute product and carry sum for this term */
r = ((mp_word) u) + ((mp_word) * tmpa++) * ((mp_word) b);
r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
/* mask off higher bits to get a single digit */
*tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));

5
bn_mp_prime_fermat.c
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@ -31,6 +31,11 @@ mp_prime_fermat (mp_int * a, mp_int * b, int *result)
/* default to fail */
*result = 0;
/* ensure b > 1 */
if (mp_cmp_d(b, 1) != MP_GT) {
return MP_VAL;
}
/* init t */
if ((err = mp_init (&t)) != MP_OKAY) {
return err;

6
bn_mp_prime_is_prime.c
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@ -17,7 +17,7 @@
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
* (1/4)^t when 1 <= t <= 256
* (1/4)^t when 1 <= t <= PRIME_SIZE
*
* Sets result to 1 if probably prime, 0 otherwise
*/
@ -31,7 +31,7 @@ mp_prime_is_prime (mp_int * a, int t, int *result)
*result = 0;
/* valid value of t? */
if (t < 1 || t > PRIME_SIZE) {
if (t <= 0 || t > PRIME_SIZE) {
return MP_VAL;
}
@ -47,6 +47,8 @@ mp_prime_is_prime (mp_int * a, int t, int *result)
if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
return err;
}
/* return if it was trivially divisible */
if (res == 1) {
return MP_OKAY;
}

12
bn_mp_prime_miller_rabin.c
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@ -30,6 +30,11 @@ mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
/* default */
*result = 0;
/* ensure b > 1 */
if (mp_cmp_d(b, 1) != MP_GT) {
return MP_VAL;
}
/* get n1 = a - 1 */
if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
return err;
@ -42,8 +47,13 @@ mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
goto __N1;
}
/* count the number of least significant bits
* which are zero
*/
s = mp_cnt_lsb(&r);
/* now divide n - 1 by 2^s */
if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
goto __R;
}

144
bn_mp_prime_next_prime.c
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@ -16,39 +16,151 @@
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
*
* bbs_style = 1 means the prime must be congruent to 3 mod 4
*/
int mp_prime_next_prime(mp_int *a, int t)
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
int err, res;
int err, res, x, y;
mp_digit res_tab[PRIME_SIZE], step, kstep;
mp_int b;
if (mp_iseven(a) == 1) {
/* force odd */
if ((err = mp_add_d(a, 1, a)) != MP_OKAY) {
return err;
/* ensure t is valid */
if (t <= 0 || t > PRIME_SIZE) {
return MP_VAL;
}
/* force positive */
if (a->sign == MP_NEG) {
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) {
/* find which prime it is bigger than */
for (x = PRIME_SIZE - 2; x >= 0; x--) {
if (mp_cmp_d(a, __prime_tab[x]) != MP_LT) {
if (bbs_style == 1) {
/* ok we found a prime smaller or
* equal [so the next is larger]
*
* however, the prime must be
* congruent to 3 mod 4
*/
if ((__prime_tab[x + 1] & 3) != 3) {
/* scan upwards for a prime congruent to 3 mod 4 */
for (y = x + 1; y < PRIME_SIZE; y++) {
if ((__prime_tab[y] & 3) == 3) {
mp_set(a, __prime_tab[y]);
return MP_OKAY;
}
}
}
} else {
mp_set(a, __prime_tab[x + 1]);
return MP_OKAY;
}
}
}
/* at this point a maybe 1 */
if (mp_cmp_d(a, 1) == MP_EQ) {
mp_set(a, 2);
return MP_OKAY;
}
/* fall through to the sieve */
}
/* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
if (bbs_style == 1) {
kstep = 4;
} else {
kstep = 2;
}
/* at this point we will use a combination of a sieve and Miller-Rabin */
if (bbs_style == 1) {
/* if a mod 4 != 3 subtract the correct value to make it so */
if ((a->dp[0] & 3) != 3) {
if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
}
} else {
/* force to next odd number */
if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
if (mp_iseven(a) == 1) {
/* force odd */
if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
return err;
}
}
}
/* generate the restable */
for (x = 1; x < PRIME_SIZE; x++) {
if ((err = mp_mod_d(a, __prime_tab[x], res_tab + x)) != MP_OKAY) {
return err;
}
}
/* init temp used for Miller-Rabin Testing */
if ((err = mp_init(&b)) != MP_OKAY) {
return err;
}
for (;;) {
/* skip to the next non-trivially divisible candidate */
step = 0;
do {
/* y == 1 if any residue was zero [e.g. cannot be prime] */
y = 0;
/* increase step to next odd */
step += kstep;
/* compute the new residue without using division */
for (x = 1; x < PRIME_SIZE; x++) {
/* add the step to each residue */
res_tab[x] += kstep;
/* subtract the modulus [instead of using division] */
if (res_tab[x] >= __prime_tab[x]) {
res_tab[x] -= __prime_tab[x];
}
/* set flag if zero */
if (res_tab[x] == 0) {
y = 1;
}
}
} while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
/* add the step */
if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
goto __ERR;
}
/* if step == MAX then skip test */
if (step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
continue;
}
/* is this prime? */
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
return err;
for (x = 0; x < t; x++) {
mp_set(&b, __prime_tab[t]);
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto __ERR;
}
if (res == 0) {
break;
}
}
if (res == 1) {
break;
}
/* add two, next candidate */
if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
return err;
}
}
return MP_OKAY;
err = MP_OKAY;
__ERR:
mp_clear(&b);
return err;
}

6
bn_mp_read_unsigned_bin.c
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@ -25,14 +25,14 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
return res;
}
if (DIGIT_BIT != 7) {
#ifndef MP_8BIT
a->dp[0] |= *b++;
a->used += 1;
} else {
#else
a->dp[0] = (*b & MP_MASK);
a->dp[1] |= ((*b++ >> 7U) & 1);
a->used += 2;
}
#endif
}
mp_clamp (a);
return MP_OKAY;

6
bn_mp_to_unsigned_bin.c
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@ -27,11 +27,11 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
x = 0;
while (mp_iszero (&t) == 0) {
if (DIGIT_BIT != 7) {
#ifndef MP_8BIT
b[x++] = (unsigned char) (t.dp[0] & 255);
} else {
#else
b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
}
#endif
if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
mp_clear (&t);
return res;

2
bn_s_mp_mul_digs.c
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@ -62,7 +62,7 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
for (iy = 0; iy < pb; iy++) {
/* compute the column as a mp_word */
r = ((mp_word) *tmpt) +
((mp_word) tmpx) * ((mp_word) * tmpy++) +
((mp_word)tmpx) * ((mp_word)*tmpy++) +
((mp_word) u);
/* the new column is the lower part of the result */

2
bn_s_mp_mul_high_digs.c
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@ -55,7 +55,7 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
for (iy = digs - ix; iy < pb; iy++) {
/* calculate the double precision result */
r = ((mp_word) * tmpt) + ((mp_word) tmpx) * ((mp_word) * tmpy++) + ((mp_word) u);
r = ((mp_word) * tmpt) + ((mp_word)tmpx) * ((mp_word)*tmpy++) + ((mp_word) u);
/* get the lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

8
bn_s_mp_sqr.c
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@ -32,8 +32,8 @@ s_mp_sqr (mp_int * a, mp_int * b)
for (ix = 0; ix < pa; ix++) {
/* first calculate the digit at 2*ix */
/* calculate double precision result */
r = ((mp_word) t.dp[2*ix]) +
((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
r = ((mp_word) t.dp[2*ix]) +
((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
/* store lower part in result */
t.dp[2*ix] = (mp_digit) (r & ((mp_word) MP_MASK));
@ -49,12 +49,12 @@ s_mp_sqr (mp_int * a, mp_int * b)
for (iy = ix + 1; iy < pa; iy++) {
/* first calculate the product */
r = ((mp_word) tmpx) * ((mp_word) a->dp[iy]);
r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
/* now calculate the double precision result, note we use
* addition instead of *2 since it's easier to optimize
*/
r = ((mp_word) * tmpt) + r + r + ((mp_word) u);
r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
/* store lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

18
changes.txt
View File

@ -1,3 +1,21 @@
July 12th, 2003
v0.23 -- Optimized mp_prime_next_prime() to not use mp_mod [via is_divisible()] in each
iteration. Instead now a smaller table is kept of the residues which can be updated
without division.
-- Fixed a bug in next_prime() where an input of zero would be treated as odd and
have two added to it [to move to the next odd].
-- fixed a bug in prime_fermat() and prime_miller_rabin() which allowed the base
to be negative, zero or one. Normally the test is only valid if the base is
greater than one.
-- changed the next_prime() prototype to accept a new parameter "bbs_style" which
will find the next prime congruent to 3 mod 4. The default [bbs_style==0] will
make primes which are either congruent to 1 or 3 mod 4.
-- fixed mp_read_unsigned_bin() so that it doesn't include both code for
the case DIGIT_BIT < 8 and >= 8
-- optimized div_d() to easy out on division by 1 [or if a == 0] and use
logical shifts if the divisor is a power of two.
-- the default DIGIT_BIT type was not int for non-default builds. Fixed.
July 2nd, 2003
v0.22 -- Fixed up mp_invmod so the result is properly in range now [was always congruent to the inverse...]
-- Fixed up s_mp_exptmod and mp_exptmod_fast so the lower half of the pre-computed table isn't allocated

28
demo/demo.c
View File

@ -65,6 +65,31 @@ int main(void)
srand(time(NULL));
#if 0
for (;;) {
fgets(buf, sizeof(buf), stdin);
mp_read_radix(&a, buf, 10);
mp_prime_next_prime(&a, 5, 1);
mp_toradix(&a, buf, 10);
printf("%s, %lu\n", buf, a.dp[0] & 3);
}
#endif
#if 0
{
mp_word aa, bb;
for (;;) {
aa = abs(rand()) & MP_MASK;
bb = abs(rand()) & MP_MASK;
if (MULT(aa,bb) != (aa*bb)) {
printf("%llu * %llu == %llu or %llu?\n", aa, bb, (ulong64)MULT(aa,bb), (ulong64)(aa*bb));
return 0;
}
}
}
#endif
#if 0
/* test mp_cnt_lsb */
mp_set(&a, 1);
@ -122,7 +147,6 @@ int main(void)
/* test the DR reduction */
#if 0
for (cnt = 2; cnt < 32; cnt++) {
printf("%d digit modulus\n", cnt);
mp_grow(&a, cnt);
@ -175,8 +199,6 @@ int main(void)
fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
fclose(log);
return 0;
log = fopen("logs/sub.log", "w");
for (cnt = 8; cnt <= 128; cnt += 8) {

3
etc/2kprime.1
View File

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

24
etc/drprime.c
View File

@ -1,7 +1,7 @@
/* Makes safe primes of a DR nature */
#include <tommath.h>
const int sizes[] = { 8, 19, 28, 37, 55, 74, 110, 147 };
int sizes[] = { 256/DIGIT_BIT, 512/DIGIT_BIT, 768/DIGIT_BIT, 1024/DIGIT_BIT, 2048/DIGIT_BIT, 4096/DIGIT_BIT };
int main(void)
{
int res, x, y;
@ -14,6 +14,7 @@ int main(void)
out = fopen("drprimes.txt", "w");
for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) {
top:
printf("Seeking a %d-bit safe prime\n", sizes[x] * DIGIT_BIT);
mp_grow(&a, sizes[x]);
mp_zero(&a);
@ -22,21 +23,26 @@ int main(void)
}
/* make a DR modulus */
a.dp[0] = 1;
a.dp[0] = -1;
a.used = sizes[x];
/* now loop */
do {
fflush(stdout);
mp_prime_next_prime(&a, 3);
printf(".");
for (;;) {
a.dp[0] += 4;
if (a.dp[0] >= MP_MASK) break;
mp_prime_is_prime(&a, 1, &res);
if (res == 0) continue;
printf("."); fflush(stdout);
mp_sub_d(&a, 1, &b);
mp_div_2(&b, &b);
mp_prime_is_prime(&b, 3, &res);
} while (res == 0);
if (res == 0) continue;
mp_prime_is_prime(&a, 3, &res);
if (res == 1) break;
}
if (mp_dr_is_modulus(&a) != 1) {
printf("Error not DR modulus\n");
if (res != 1) {
printf("Error not DR modulus\n"); sizes[x] += 1; goto top;
} else {
mp_toradix(&a, buf, 10);
printf("\n\np == %s\n\n", buf);

2
etc/drprimes.1 → etc/drprimes.28
View File

@ -1,3 +1,5 @@
DR safe primes for 28-bit digits.
224-bit prime:
p == 26959946667150639794667015087019630673637144422540572481103341844143

17
etc/drprimes.txt
View File

@ -1,6 +1,15 @@
224-bit prime:
p == 26959946667150639794667015087019630673637144422540572481103341844143
300-bit prime:
p == 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183393387
532-bit prime:
p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747
510-bit prime:
p == 3351951982485649274893506249551461531869841455148098344430890360930441007518386744200468574541725856922507964546621512713438470702986642486608412251494847
765-bit prime:
p == 194064761537588616893622436057812819407110752139587076392381504753256369085797110791359801103580809743810966337141384150771447505514351798930535909380147642400556872002606238193783160703949805603157874899214558593861605856727005843
1740-bit prime:
p == 61971563797913992479098926650774597592238975917324828616370329001490282756182680310375299496755876376552390992409906202402580445340335946188208371182877207703039791403230793200138374588682414508868522097839706723444887189794752005280474068640895359332705297533442094790319040758184131464298255306336601284054032615054089107503261218395204931877449590906016855549287497608058070532126514935495184332288660623518513755499687752752528983258754107553298994358814410594621086881204713587661301862918471291451469190214535690028223
2145-bit prime:
p == 5120834017984591518147028606005386392991070803233539296225079797126347381640561714282620018633786528684625023495254338414266418034876748837569635527008462887513799703364491256252208677097644781218029521545625387720450034199300257983090290650191518075514440227307582827991892955933645635564359934476985058395497772801264225688705417270604479898255105628816161764712152286804906915652283101897505006786990112535065979412882966109410722156057838063961993103028819293481078313367826492291911499907219457764211473530756735049840415233164976184864760203928986194694093688479274544786530457604655777313274555786861719645260099496565700321073395329400403

16
logs/add.log
View File

@ -0,0 +1,16 @@
224 12444616
448 10412040
672 8825112
896 7519080
1120 6428432
1344 5794784
1568 5242952
1792 4737008
2016 4434104
2240 4132912
2464 3827752
2688 3589672
2912 3350176
3136 3180208
3360 3014160
3584 2847672

17
logs/sqr.log
View File

@ -1,17 +0,0 @@
896 415472
1344 223736
1792 141232
2240 97624
2688 71400
3136 54800
3584 16904
4032 13528
4480 10968
4928 9128
5376 7784
5824 6672
6272 5760
6720 5056
7168 4440
7616 3952
8064 3512

32
logs/sub.log
View File

@ -1,16 +1,16 @@
224 9728504
448 8573648
672 7488096
896 6714064
1120 5950472
1344 5457400
1568 5038896
1792 4683632
2016 4384656
2240 4105976
2464 3871608
2688 3650680
2912 3463552
3136 3290016
3360 3135272
3584 2993848
224 10876088
448 9103552
672 7823536
896 6724960
1120 5993496
1344 5278984
1568 4947736
1792 4478384
2016 4108840
2240 3838696
2464 3604128
2688 3402192
2912 3166568
3136 3090672
3360 2946720
3584 2781288

2
makefile
View File

@ -1,6 +1,6 @@
CFLAGS += -I./ -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops
VERSION=0.22
VERSION=0.23
default: libtommath.a

4
makefile.msvc
View File

@ -2,7 +2,7 @@
#
#Tom St Denis
CFLAGS = /I. /Ox /DWIN32 /W3 /WX
CFLAGS = /I. /Ox /DWIN32 /W3
default: library
@ -29,7 +29,5 @@ bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj
library: $(OBJECTS)
lib /out:tommath.lib $(OBJECTS)

BIN
poster.pdf
View File

Binary file not shown.

72
poster.tex
View File

@ -1,36 +1,36 @@
\documentclass[landscape,11pt]{article}
\usepackage{amsmath, amssymb}
\usepackage{hyperref}
\begin{document}
\hspace*{-3in}
\begin{tabular}{llllll}
$c = a + b$ & {\tt mp\_add(\&a, \&b, \&c)} & $b = 2a$ & {\tt mp\_mul\_2(\&a, \&b)} & \\
$c = a - b$ & {\tt mp\_sub(\&a, \&b, \&c)} & $b = a/2$ & {\tt mp\_div\_2(\&a, \&b)} & \\
$c = ab $ & {\tt mp\_mul(\&a, \&b, \&c)} & $c = 2^ba$ & {\tt mp\_mul\_2d(\&a, b, \&c)} \\
$b = a^2 $ & {\tt mp\_sqr(\&a, \&b)} & $c = a/2^b, d = a \mod 2^b$ & {\tt mp\_div\_2d(\&a, b, \&c, \&d)} \\
$c = \lfloor a/b \rfloor, d = a \mod b$ & {\tt mp\_div(\&a, \&b, \&c, \&d)} & $c = a \mod 2^b $ & {\tt mp\_mod\_2d(\&a, b, \&c)} \\
&& \\
$a = b $ & {\tt mp\_set\_int(\&a, b)} & $c = a \vee b$ & {\tt mp\_or(\&a, \&b, \&c)} \\
$b = a $ & {\tt mp\_copy(\&a, \&b)} & $c = a \wedge b$ & {\tt mp\_and(\&a, \&b, \&c)} \\
&& $c = a \oplus b$ & {\tt mp\_xor(\&a, \&b, \&c)} \\
& \\
$b = -a $ & {\tt mp\_neg(\&a, \&b)} & $d = a + b \mod c$ & {\tt mp\_addmod(\&a, \&b, \&c, \&d)} \\
$b = |a| $ & {\tt mp\_abs(\&a, \&b)} & $d = a - b \mod c$ & {\tt mp\_submod(\&a, \&b, \&c, \&d)} \\
&& $d = ab \mod c$ & {\tt mp\_mulmod(\&a, \&b, \&c, \&d)} \\
Compare $a$ and $b$ & {\tt mp\_cmp(\&a, \&b)} & $c = a^2 \mod b$ & {\tt mp\_sqrmod(\&a, \&b, \&c)} \\
Is Zero? & {\tt mp\_iszero(\&a)} & $c = a^{-1} \mod b$ & {\tt mp\_invmod(\&a, \&b, \&c)} \\
Is Even? & {\tt mp\_iseven(\&a)} & $d = a^b \mod c$ & {\tt mp\_exptmod(\&a, \&b, \&c, \&d)} \\
Is Odd ? & {\tt mp\_isodd(\&a)} \\
&\\
$\vert \vert a \vert \vert$ & {\tt mp\_unsigned\_bin\_size(\&a)} & $res$ = 1 if $a$ prime to $t$ rounds? & {\tt mp\_prime\_is\_prime(\&a, t, \&res)} \\
$buf \leftarrow a$ & {\tt mp\_to\_unsigned\_bin(\&a, buf)} & Next prime after $a$ to $t$ rounds. & {\tt mp\_prime\_next\_prime(\&a, t)} \\
$a \leftarrow buf[0..len-1]$ & {\tt mp\_read\_unsigned\_bin(\&a, buf, len)} \\
&\\
$b = \sqrt{a}$ & {\tt mp\_sqrt(\&a, \&b)} & $c = \mbox{gcd}(a, b)$ & {\tt mp\_gcd(\&a, \&b, \&c)} \\
$c = a^{1/b}$ & {\tt mp\_n\_root(\&a, b, \&c)} & $c = \mbox{lcm}(a, b)$ & {\tt mp\_lcm(\&a, \&b, \&c)} \\
&\\
Greater Than & MP\_GT & Equal To & MP\_EQ \\
Less Than & MP\_LT & Bits per digit & DIGIT\_BIT \\
\end{tabular}
\end{document}
\documentclass[landscape,11pt]{article}
\usepackage{amsmath, amssymb}
\usepackage{hyperref}
\begin{document}
\hspace*{-3in}
\begin{tabular}{llllll}
$c = a + b$ & {\tt mp\_add(\&a, \&b, \&c)} & $b = 2a$ & {\tt mp\_mul\_2(\&a, \&b)} & \\
$c = a - b$ & {\tt mp\_sub(\&a, \&b, \&c)} & $b = a/2$ & {\tt mp\_div\_2(\&a, \&b)} & \\
$c = ab $ & {\tt mp\_mul(\&a, \&b, \&c)} & $c = 2^ba$ & {\tt mp\_mul\_2d(\&a, b, \&c)} \\
$b = a^2 $ & {\tt mp\_sqr(\&a, \&b)} & $c = a/2^b, d = a \mod 2^b$ & {\tt mp\_div\_2d(\&a, b, \&c, \&d)} \\
$c = \lfloor a/b \rfloor, d = a \mod b$ & {\tt mp\_div(\&a, \&b, \&c, \&d)} & $c = a \mod 2^b $ & {\tt mp\_mod\_2d(\&a, b, \&c)} \\
&& \\
$a = b $ & {\tt mp\_set\_int(\&a, b)} & $c = a \vee b$ & {\tt mp\_or(\&a, \&b, \&c)} \\
$b = a $ & {\tt mp\_copy(\&a, \&b)} & $c = a \wedge b$ & {\tt mp\_and(\&a, \&b, \&c)} \\
&& $c = a \oplus b$ & {\tt mp\_xor(\&a, \&b, \&c)} \\
& \\
$b = -a $ & {\tt mp\_neg(\&a, \&b)} & $d = a + b \mod c$ & {\tt mp\_addmod(\&a, \&b, \&c, \&d)} \\
$b = |a| $ & {\tt mp\_abs(\&a, \&b)} & $d = a - b \mod c$ & {\tt mp\_submod(\&a, \&b, \&c, \&d)} \\
&& $d = ab \mod c$ & {\tt mp\_mulmod(\&a, \&b, \&c, \&d)} \\
Compare $a$ and $b$ & {\tt mp\_cmp(\&a, \&b)} & $c = a^2 \mod b$ & {\tt mp\_sqrmod(\&a, \&b, \&c)} \\
Is Zero? & {\tt mp\_iszero(\&a)} & $c = a^{-1} \mod b$ & {\tt mp\_invmod(\&a, \&b, \&c)} \\
Is Even? & {\tt mp\_iseven(\&a)} & $d = a^b \mod c$ & {\tt mp\_exptmod(\&a, \&b, \&c, \&d)} \\
Is Odd ? & {\tt mp\_isodd(\&a)} \\
&\\
$\vert \vert a \vert \vert$ & {\tt mp\_unsigned\_bin\_size(\&a)} & $res$ = 1 if $a$ prime to $t$ rounds? & {\tt mp\_prime\_is\_prime(\&a, t, \&res)} \\
$buf \leftarrow a$ & {\tt mp\_to\_unsigned\_bin(\&a, buf)} & Next prime after $a$ to $t$ rounds. & {\tt mp\_prime\_next\_prime(\&a, t, bbs\_style)} \\
$a \leftarrow buf[0..len-1]$ & {\tt mp\_read\_unsigned\_bin(\&a, buf, len)} \\
&\\
$b = \sqrt{a}$ & {\tt mp\_sqrt(\&a, \&b)} & $c = \mbox{gcd}(a, b)$ & {\tt mp\_gcd(\&a, \&b, \&c)} \\
$c = a^{1/b}$ & {\tt mp\_n\_root(\&a, b, \&c)} & $c = \mbox{lcm}(a, b)$ & {\tt mp\_lcm(\&a, \&b, \&c)} \\
&\\
Greater Than & MP\_GT & Equal To & MP\_EQ \\
Less Than & MP\_LT & Bits per digit & DIGIT\_BIT \\
\end{tabular}
\end{document}

276
pre_gen/mpi.c
View File

@ -216,7 +216,7 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
* that W[ix-1] have the carry cleared (see after the inner loop)
*/
register mp_digit mu;
mu = (((mp_digit) (W[ix] & MP_MASK)) * rho) & MP_MASK;
mu = ((W[ix] & MP_MASK) * rho) & MP_MASK;
/* a = a + mu * m * b**i
*
@ -245,7 +245,7 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* inner loop */
for (iy = 0; iy < n->used; iy++) {
*_W++ += ((mp_word) mu) * ((mp_word) * tmpn++);
*_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
}
}
@ -253,7 +253,6 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
}
{
register mp_digit *tmpx;
register mp_word *_W, *_W1;
@ -383,7 +382,7 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
pb = MIN (b->used, digs - ix);
for (iy = 0; iy < pb; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
*_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
}
}
@ -406,20 +405,27 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
* from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
* cost of the shifting. On very small numbers this is slower
* but on most cryptographic size numbers it is faster.
*
* In this particular implementation we feed the carries from
* behind which means when the loop terminates we still have one
* last digit to copy
*/
tmpc = c->dp;
for (ix = 1; ix < digs; ix++) {
/* forward the carry from the previous temp */
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
/* now extract the previous digit [below the carry] */
*tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
/* fetch the last digit */
*tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused */
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpc++ = 0;
}
}
mp_clamp (c);
return MP_OKAY;
}
@ -500,7 +506,7 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
/* compute column products for digits above the minimum */
for (; iy < pb; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
*_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++);
}
}
}
@ -509,12 +515,15 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
oldused = c->used;
c->used = newused;
/* now convert the array W downto what we need */
/* now convert the array W downto what we need
*
* See comments in bn_fast_s_mp_mul_digs.c
*/
for (ix = digs + 1; ix < newused; ix++) {
W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
}
c->dp[(pa + pb + 1) - 1] = (mp_digit) (W[(pa + pb + 1) - 1] & ((mp_word) MP_MASK));
c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
for (; ix < oldused; ix++) {
c->dp[ix] = 0;
@ -596,7 +605,7 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
* for a particular column only once which means that
* there is no need todo a double precision addition
*/
W2[ix + ix] = ((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
{
register mp_digit tmpx, *tmpy;
@ -614,7 +623,7 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
/* inner products */
for (iy = ix + 1; iy < pa; iy++) {
*_W++ += ((mp_word) tmpx) * ((mp_word) * tmpy++);
*_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
}
}
}
@ -972,7 +981,6 @@ void
mp_clear (mp_int * a)
{
if (a->dp != NULL) {
/* first zero the digits */
memset (a->dp, 0, sizeof (mp_digit) * a->used);
@ -980,7 +988,7 @@ mp_clear (mp_int * a)
free (a->dp);
/* reset members to make debugging easier */
a->dp = NULL;
a->dp = NULL;
a->alloc = a->used = 0;
}
}
@ -1724,6 +1732,19 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
*/
#include <tommath.h>
static int s_is_power_of_two(mp_digit b, int *p)
{
int x;
for (x = 1; x < DIGIT_BIT; x++) {
if (b == (((mp_digit)1)<<x)) {
*p = x;
return 1;
}
}
return 0;
}
/* single digit division (based on routine from MPI) */
int
mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
@ -1732,15 +1753,40 @@ mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
mp_word w;
mp_digit t;
int res, ix;
/* cannot divide by zero */
if (b == 0) {
return MP_VAL;
}
/* quick outs */
if (b == 1 || mp_iszero(a) == 1) {
if (d != NULL) {
*d = 0;
}
if (c != NULL) {
return mp_copy(a, c);
}
return MP_OKAY;
}
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
*d = a->dp[0] & ((1<<ix) - 1);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
}
return MP_OKAY;
}
/* three? */
if (b == 3) {
return mp_div_3(a, c, d);
}
/* no easy answer [c'est la vie]. Just division */
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
return res;
}
@ -2186,7 +2232,6 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
}
}
/* determine and setup reduction code */
if (redmode == 0) {
/* now setup montgomery */
@ -3666,7 +3711,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
for (ix = 0; ix < n->used; ix++) {
/* mu = ai * m' mod b */
mu = (x->dp[ix] * rho) & MP_MASK;
mu = ((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK;
/* a = a + mu * m * b**i */
{
@ -3683,7 +3728,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
r = ((mp_word) mu) * ((mp_word) * tmpn++) +
r = ((mp_word)mu) * ((mp_word)*tmpn++) +
((mp_word) u) + ((mp_word) * tmpx);
u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
*tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
@ -4039,7 +4084,7 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
u = 0;
for (ix = 0; ix < pa; ix++) {
/* compute product and carry sum for this term */
r = ((mp_word) u) + ((mp_word) * tmpa++) * ((mp_word) b);
r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
/* mask off higher bits to get a single digit */
*tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
@ -4415,6 +4460,11 @@ mp_prime_fermat (mp_int * a, mp_int * b, int *result)
/* default to fail */
*result = 0;
/* ensure b > 1 */
if (mp_cmp_d(b, 1) != MP_GT) {
return MP_VAL;
}
/* init t */
if ((err = mp_init (&t)) != MP_OKAY) {
return err;
@ -4506,7 +4556,7 @@ mp_prime_is_divisible (mp_int * a, int *result)
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
* (1/4)^t when 1 <= t <= 256
* (1/4)^t when 1 <= t <= PRIME_SIZE
*
* Sets result to 1 if probably prime, 0 otherwise
*/
@ -4520,7 +4570,7 @@ mp_prime_is_prime (mp_int * a, int t, int *result)
*result = 0;
/* valid value of t? */
if (t < 1 || t > PRIME_SIZE) {
if (t <= 0 || t > PRIME_SIZE) {
return MP_VAL;
}
@ -4536,6 +4586,8 @@ mp_prime_is_prime (mp_int * a, int t, int *result)
if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
return err;
}
/* return if it was trivially divisible */
if (res == 1) {
return MP_OKAY;
}
@ -4599,6 +4651,11 @@ mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
/* default */
*result = 0;
/* ensure b > 1 */
if (mp_cmp_d(b, 1) != MP_GT) {
return MP_VAL;
}
/* get n1 = a - 1 */
if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
return err;
@ -4611,8 +4668,13 @@ mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
goto __N1;
}
/* count the number of least significant bits
* which are zero
*/
s = mp_cnt_lsb(&r);
/* now divide n - 1 by 2^s */
if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
goto __R;
}
@ -4677,40 +4739,152 @@ __N1:mp_clear (&n1);
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
*
* bbs_style = 1 means the prime must be congruent to 3 mod 4
*/
int mp_prime_next_prime(mp_int *a, int t)
int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
{
int err, res;
int err, res, x, y;
mp_digit res_tab[PRIME_SIZE], step, kstep;
mp_int b;
if (mp_iseven(a) == 1) {
/* force odd */
if ((err = mp_add_d(a, 1, a)) != MP_OKAY) {
return err;
/* ensure t is valid */
if (t <= 0 || t > PRIME_SIZE) {
return MP_VAL;
}
/* force positive */
if (a->sign == MP_NEG) {
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) {
/* find which prime it is bigger than */
for (x = PRIME_SIZE - 2; x >= 0; x--) {
if (mp_cmp_d(a, __prime_tab[x]) != MP_LT) {
if (bbs_style == 1) {
/* ok we found a prime smaller or
* equal [so the next is larger]
*
* however, the prime must be
* congruent to 3 mod 4
*/
if ((__prime_tab[x + 1] & 3) != 3) {
/* scan upwards for a prime congruent to 3 mod 4 */
for (y = x + 1; y < PRIME_SIZE; y++) {
if ((__prime_tab[y] & 3) == 3) {
mp_set(a, __prime_tab[y]);
return MP_OKAY;
}
}
}
} else {
mp_set(a, __prime_tab[x + 1]);
return MP_OKAY;
}
}
}
/* at this point a maybe 1 */
if (mp_cmp_d(a, 1) == MP_EQ) {
mp_set(a, 2);
return MP_OKAY;
}
/* fall through to the sieve */
}
/* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
if (bbs_style == 1) {
kstep = 4;
} else {
kstep = 2;
}
/* at this point we will use a combination of a sieve and Miller-Rabin */
if (bbs_style == 1) {
/* if a mod 4 != 3 subtract the correct value to make it so */
if ((a->dp[0] & 3) != 3) {
if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
}
} else {
/* force to next odd number */
if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
if (mp_iseven(a) == 1) {
/* force odd */
if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
return err;
}
}
}
/* generate the restable */
for (x = 1; x < PRIME_SIZE; x++) {
if ((err = mp_mod_d(a, __prime_tab[x], res_tab + x)) != MP_OKAY) {
return err;
}
}
/* init temp used for Miller-Rabin Testing */
if ((err = mp_init(&b)) != MP_OKAY) {
return err;
}
for (;;) {
/* skip to the next non-trivially divisible candidate */
step = 0;
do {
/* y == 1 if any residue was zero [e.g. cannot be prime] */
y = 0;
/* increase step to next odd */
step += kstep;
/* compute the new residue without using division */
for (x = 1; x < PRIME_SIZE; x++) {
/* add the step to each residue */
res_tab[x] += kstep;
/* subtract the modulus [instead of using division] */
if (res_tab[x] >= __prime_tab[x]) {
res_tab[x] -= __prime_tab[x];
}
/* set flag if zero */
if (res_tab[x] == 0) {
y = 1;
}
}
} while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
/* add the step */
if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
goto __ERR;
}
/* if step == MAX then skip test */
if (step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
continue;
}
/* is this prime? */
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
return err;
for (x = 0; x < t; x++) {
mp_set(&b, __prime_tab[t]);
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto __ERR;
}
if (res == 0) {
break;
}
}
if (res == 1) {
break;
}
/* add two, next candidate */
if ((err = mp_add_d(a, 2, a)) != MP_OKAY) {
return err;
}
}
return MP_OKAY;
err = MP_OKAY;
__ERR:
mp_clear(&b);
return err;
}
@ -4990,14 +5164,14 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
return res;
}
if (DIGIT_BIT != 7) {
#ifndef MP_8BIT
a->dp[0] |= *b++;
a->used += 1;
} else {
#else
a->dp[0] = (*b & MP_MASK);
a->dp[1] |= ((*b++ >> 7U) & 1);
a->used += 2;
}
#endif
}
mp_clamp (a);
return MP_OKAY;
@ -5756,11 +5930,11 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
x = 0;
while (mp_iszero (&t) == 0) {
if (DIGIT_BIT != 7) {
#ifndef MP_8BIT
b[x++] = (unsigned char) (t.dp[0] & 255);
} else {
#else
b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
}
#endif
if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
mp_clear (&t);
return res;
@ -6954,7 +7128,7 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
for (iy = 0; iy < pb; iy++) {
/* compute the column as a mp_word */
r = ((mp_word) *tmpt) +
((mp_word) tmpx) * ((mp_word) * tmpy++) +
((mp_word)tmpx) * ((mp_word)*tmpy++) +
((mp_word) u);
/* the new column is the lower part of the result */
@ -7036,7 +7210,7 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
for (iy = digs - ix; iy < pb; iy++) {
/* calculate the double precision result */
r = ((mp_word) * tmpt) + ((mp_word) tmpx) * ((mp_word) * tmpy++) + ((mp_word) u);
r = ((mp_word) * tmpt) + ((mp_word)tmpx) * ((mp_word)*tmpy++) + ((mp_word) u);
/* get the lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
@ -7089,8 +7263,8 @@ s_mp_sqr (mp_int * a, mp_int * b)
for (ix = 0; ix < pa; ix++) {
/* first calculate the digit at 2*ix */
/* calculate double precision result */
r = ((mp_word) t.dp[2*ix]) +
((mp_word) a->dp[ix]) * ((mp_word) a->dp[ix]);
r = ((mp_word) t.dp[2*ix]) +
((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
/* store lower part in result */
t.dp[2*ix] = (mp_digit) (r & ((mp_word) MP_MASK));
@ -7106,12 +7280,12 @@ s_mp_sqr (mp_int * a, mp_int * b)
for (iy = ix + 1; iy < pa; iy++) {
/* first calculate the product */
r = ((mp_word) tmpx) * ((mp_word) a->dp[iy]);
r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
/* now calculate the double precision result, note we use
* addition instead of *2 since it's easier to optimize
*/
r = ((mp_word) * tmpt) + r + r + ((mp_word) u);
r = ((mp_word) *tmpt) + r + r + ((mp_word) u);
/* store lower part */
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));

46
test.c
View File

@ -1,46 +0,0 @@
#include <tommath.h>
int main(int argc, char ** argv) {
const unsigned int a = 65537;
char b[] =
"272621192922230283305477639564135351471136149273956463844361347729298759183125368038593484043149128512765280523210111782526587388894777249539002925324108547349408624093466297893486263619517809026841716115227596170065100354451708345238523975900663359145770823068375223714001310312030819080370340176730626251422070";
char radix[1000];
mp_int vala, valb, valc;
if (mp_init(&vala) != MP_OKAY) {
fprintf(stderr, "failed to init vala\n");
exit(1);
}
if (mp_init(&valb) != MP_OKAY) {
fprintf(stderr, "failed to init valb\n");
exit(1);
}
if (mp_init(&valc) != MP_OKAY) {
fprintf(stderr, "failed to init valc\n");
exit(1);
}
if (mp_set_int(&vala, 65537) != MP_OKAY) {
fprintf(stderr, "failed to set vala to 65537\n");
exit(1);
}
if (mp_read_radix(&valb, b, 10) != MP_OKAY) {
fprintf(stderr, "failed to set valb to %s\n", b);
exit(1);
}
if (mp_invmod(&vala, &valb, &valc) != MP_OKAY) {
fprintf(stderr, "mp_invmod failed\n");
exit(1);
}
if (mp_toradix(&valc, radix, 10) != MP_OKAY) {
fprintf(stderr, "failed to convert value to radix 10\n");
exit(1);
}
fprintf(stderr, "a = %d\nb = %s\nc = %s\n", a, b, radix);
return 0;
}

8
tommath.h
View File

@ -85,12 +85,13 @@ extern "C" {
#define DIGIT_BIT 31
#else
#define DIGIT_BIT 28
#define MP_28BIT
#endif
#endif
/* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
#ifndef DIGIT_BIT
#define DIGIT_BIT ((CHAR_BIT * sizeof(mp_digit) - 1)) /* bits per digit */
#define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */
#endif
@ -400,9 +401,10 @@ int mp_prime_is_prime(mp_int *a, int t, int *result);
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
*
* bbs_style = 1 means the prime must be congruent to 3 mod 4
*/
int mp_prime_next_prime(mp_int *a, int t);
int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
/* ---> radix conversion <--- */
int mp_count_bits(mp_int *a);