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#include "tommath_private.h"
#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
* integer arithmetic as well as number theoretic functionality.
*
* The library was designed directly after the MPI library by
* Michael Fromberger but has been written from scratch with
* additional optimizations in place.
*
* The library is free for all purposes without any express
* guarantee it works.
*/
/* 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 bbs_style)
{
int err, res = MP_NO, x, y;
mp_digit res_tab[PRIME_SIZE], step, kstep;
mp_int b;
/* ensure t is valid */
if ((t <= 0) || (t > PRIME_SIZE)) {
return MP_VAL;
}
/* force positive */
a->sign = MP_ZPOS;
/* simple algo if a is less than the largest prime in the table */
if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
/* find which prime it is bigger than */
for (x = PRIME_SIZE - 2; x >= 0; x--) {
if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
if (bbs_style == 1) {
/* ok we found a prime smaller or
* equal [so the next is larger]
*
* however, the prime must be
* congruent to 3 mod 4
*/
if ((ltm_prime_tab[x + 1] & 3u) != 3u) {
/* scan upwards for a prime congruent to 3 mod 4 */
for (y = x + 1; y < PRIME_SIZE; y++) {
if ((ltm_prime_tab[y] & 3u) == 3u) {
mp_set(a, ltm_prime_tab[y]);
return MP_OKAY;
}
}
}
} else {
mp_set(a, ltm_prime_tab[x + 1]);
return MP_OKAY;
}
}
}
/* at this point a maybe 1 */
if (mp_cmp_d(a, 1uL) == MP_EQ) {
mp_set(a, 2uL);
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] & 3u) != 3u) {
if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) {
return err;
};
}
} else {
if (mp_iseven(a) == MP_YES) {
/* force odd */
if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) {
return err;
}
}
}
/* generate the restable */
for (x = 1; x < PRIME_SIZE; x++) {
if ((err = mp_mod_d(a, ltm_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 candidate */
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] >= ltm_prime_tab[x]) {
res_tab[x] -= ltm_prime_tab[x];
}
/* set flag if zero */
if (res_tab[x] == 0u) {
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 LBL_ERR;
}
/* if didn't pass sieve and step == MAX then skip test */
if ((y == 1) && (step >= (((mp_digit)1 << DIGIT_BIT) - kstep))) {
continue;
}
/* is this prime? */
for (x = 0; x < t; x++) {
mp_set(&b, ltm_prime_tab[x]);
if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
goto LBL_ERR;
}
if (res == MP_NO) {
break;
}
}
if (res == MP_YES) {
break;
}
}
err = MP_OKAY;
LBL_ERR:
mp_clear(&b);
return err;
}
#endif
/* ref: $Format:%D$ */
/* git commit: $Format:%H$ */
/* commit time: $Format:%ai$ */
|
