tomcrypt/prime.c
2010-06-16 12:37:53 +02:00

295 lines
8.3 KiB
C

#include "mycrypt.h"
#ifdef MPI
#define UPPER_LIMIT (sizeof(prime_tab) / sizeof(prime_tab[0]))
static const mp_digit prime_tab[] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083,
0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 };
/* figures out if a number is prime (MR test) */
#ifdef CLEAN_STACK
static int _is_prime(mp_int *N, int *result)
#else
int is_prime(mp_int *N, int *result)
#endif
{
long x, s, j;
int res;
mp_int n1, a, y, r;
mp_digit d;
_ARGCHK(N != NULL);
_ARGCHK(result != NULL);
/* default to answer of no */
*result = 0;
/* divisible by any of the first primes? */
for (x = 0; x < (long)UPPER_LIMIT; x++) {
/* is N equal to a small prime? */
if (mp_cmp_d(N, prime_tab[x]) == 0) {
*result = 1;
return CRYPT_OK;
}
/* is N mod prime_tab[x] == 0, then its divisible by it */
if (mp_mod_d(N, prime_tab[x], &d) != MP_OKAY) {
return CRYPT_MEM;
}
if (d == 0) {
return CRYPT_OK;
}
}
/* init variables */
if (mp_init_multi(&r, &n1, &a, &y, NULL) != MP_OKAY) {
return CRYPT_MEM;
}
/* n1 = N - 1 */
if (mp_sub_d(N, 1, &n1) != MP_OKAY) { goto error; }
/* r = N - 1 */
if (mp_copy(&n1, &r) != MP_OKAY) { goto error; }
/* find s such that N-1 = (2^s)r */
s = 0;
while (mp_iseven(&r) != 0) {
++s;
if (mp_div_2(&r, &r) != MP_OKAY) {
goto error;
}
}
for (x = 0; x < 8; x++) {
/* choose a */
mp_set(&a, prime_tab[x]);
/* compute y = a^r mod n */
if (mp_exptmod(&a, &r, N, &y) != MP_OKAY) { goto error; }
/* (y != 1) AND (y != N-1) */
if ((mp_cmp_d(&y, 1) != 0) && (mp_cmp(&y, &n1) != 0)) {
/* while j <= s-1 and y != n-1 */
for (j = 1; (j <= (s-1)) && (mp_cmp(&y, &n1) != 0); j++) {
/* y = y^2 mod N */
if (mp_sqrmod(&y, N, &y) != MP_OKAY) { goto error; }
/* if y == 1 return false */
if (mp_cmp_d(&y, 1) == 0) { goto ok; }
}
/* if y != n-1 return false */
if (mp_cmp(&y, &n1) != 0) { goto ok; }
}
}
*result = 1;
ok:
res = CRYPT_OK;
goto done;
error:
res = CRYPT_MEM;
done:
mp_clear_multi(&a, &y, &n1, &r, NULL);
return res;
}
#ifdef CLEAN_STACK
int is_prime(mp_int *N, int *result)
{
int x;
x = _is_prime(N, result);
burn_stack(sizeof(long) * 3 + sizeof(int) + sizeof(mp_int) * 4 + sizeof(mp_digit));
return x;
}
#endif
static int next_prime(mp_int *N, mp_digit step)
{
long x, s, j, total_dist;
int res;
mp_int n1, a, y, r;
mp_digit dist, residues[UPPER_LIMIT];
_ARGCHK(N != NULL);
/* first find the residues */
for (x = 0; x < (long)UPPER_LIMIT; x++) {
if (mp_mod_d(N, prime_tab[x], &residues[x]) != MP_OKAY) {
return CRYPT_MEM;
}
}
/* init variables */
if (mp_init_multi(&r, &n1, &a, &y, NULL) != MP_OKAY) {
return CRYPT_MEM;
}
total_dist = 0;
loop:
/* while one of the residues is zero keep looping */
dist = step;
for (x = 0; (dist < (MP_DIGIT_MAX-step-1)) && (x < (long)UPPER_LIMIT); x++) {
j = (long)residues[x] + (long)dist + total_dist;
if (j % (long)prime_tab[x] == 0) {
dist += step; x = -1;
}
}
/* recalc the total distance from where we started */
total_dist += dist;
/* add to N */
if (mp_add_d(N, dist, N) != MP_OKAY) { goto error; }
/* n1 = N - 1 */
if (mp_sub_d(N, 1, &n1) != MP_OKAY) { goto error; }
/* r = N - 1 */
if (mp_copy(&n1, &r) != MP_OKAY) { goto error; }
/* find s such that N-1 = (2^s)r */
s = 0;
while (mp_iseven(&r)) {
++s;
if (mp_div_2(&r, &r) != MP_OKAY) {
goto error;
}
}
for (x = 0; x < 8; x++) {
/* choose a */
mp_set(&a, prime_tab[x]);
/* compute y = a^r mod n */
if (mp_exptmod(&a, &r, N, &y) != MP_OKAY) { goto error; }
/* (y != 1) AND (y != N-1) */
if ((mp_cmp_d(&y, 1) != 0) && (mp_cmp(&y, &n1) != 0)) {
/* while j <= s-1 and y != n-1 */
for (j = 1; (j <= (s-1)) && (mp_cmp(&y, &n1) != 0); j++) {
/* y = y^2 mod N */
if (mp_sqrmod(&y, N, &y) != MP_OKAY) { goto error; }
/* if y == 1 return false */
if (mp_cmp_d(&y, 1) == 0) { goto loop; }
}
/* if y != n-1 return false */
if (mp_cmp(&y, &n1) != 0) { goto loop; }
}
}
res = CRYPT_OK;
goto done;
error:
res = CRYPT_MEM;
done:
mp_clear_multi(&a, &y, &n1, &r, NULL);
#ifdef CLEAN_STACK
zeromem(residues, sizeof(residues));
#endif
return res;
}
int rand_prime(mp_int *N, long len, prng_state *prng, int wprng)
{
unsigned char buf[260];
int err, step, ormask;
_ARGCHK(N != NULL);
/* pass a negative size if you want a prime congruent to 3 mod 4 */
if (len < 0) {
step = 4;
ormask = 3;
len = -len;
} else {
step = 2;
ormask = 1;
}
/* allow sizes between 2 and 256 bytes for a prime size */
if (len < 2 || len > 256) {
return CRYPT_INVALID_PRIME_SIZE;
}
/* valid PRNG? */
if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
return err;
}
/* read the prng */
if (prng_descriptor[wprng].read(buf+2, (unsigned long)len, prng) != (unsigned long)len) {
return CRYPT_ERROR_READPRNG;
}
/* set sign byte to zero */
buf[0] = (unsigned char)0;
/* Set the top byte to 0x01 which makes the number a len*8 bit number */
buf[1] = (unsigned char)0x01;
/* set the LSB to the desired settings
* (1 for any prime, 3 for primes congruent to 3 mod 4)
*/
buf[len+1] |= (unsigned char)ormask;
/* read the number in */
if (mp_read_raw(N, buf, 2+len) != MP_OKAY) {
return CRYPT_MEM;
}
/* add the step size to it while N is not prime */
if ((err = next_prime(N, step)) != CRYPT_OK) {
return err;
}
#ifdef CLEAN_STACK
zeromem(buf, sizeof(buf));
#endif
return CRYPT_OK;
}
#endif