128 lines
3.4 KiB
C
128 lines
3.4 KiB
C
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#include "tommath_private.h"
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#ifdef MP_PRIME_NEXT_PRIME_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis */
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/* SPDX-License-Identifier: Unlicense */
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/* finds the next prime after the number "a" using "t" trials
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* of Miller-Rabin.
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*
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* bbs_style = true means the prime must be congruent to 3 mod 4
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*/
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mp_err mp_prime_next_prime(mp_int *a, int t, bool bbs_style)
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{
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int x;
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mp_err err;
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bool res = false;
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mp_digit res_tab[MP_PRIME_TAB_SIZE], kstep;
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mp_int b;
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/* force positive */
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a->sign = MP_ZPOS;
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/* simple algo if a is less than the largest prime in the table */
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if (mp_cmp_d(a, s_mp_prime_tab[MP_PRIME_TAB_SIZE-1]) == MP_LT) {
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/* find which prime it is bigger than "a" */
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for (x = 0; x < MP_PRIME_TAB_SIZE; x++) {
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mp_ord cmp = mp_cmp_d(a, s_mp_prime_tab[x]);
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if (cmp == MP_EQ) {
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continue;
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}
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if (cmp != MP_GT) {
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if ((bbs_style) && ((s_mp_prime_tab[x] & 3u) != 3u)) {
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/* try again until we get a prime congruent to 3 mod 4 */
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continue;
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} else {
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mp_set(a, s_mp_prime_tab[x]);
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return MP_OKAY;
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}
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}
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}
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/* fall through to the sieve */
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}
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/* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
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kstep = bbs_style ? 4 : 2;
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/* at this point we will use a combination of a sieve and Miller-Rabin */
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if (bbs_style) {
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/* if a mod 4 != 3 subtract the correct value to make it so */
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if ((a->dp[0] & 3u) != 3u) {
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if ((err = mp_sub_d(a, (a->dp[0] & 3u) + 1u, a)) != MP_OKAY) {
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return err;
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}
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}
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} else {
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if (mp_iseven(a)) {
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/* force odd */
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if ((err = mp_sub_d(a, 1uL, a)) != MP_OKAY) {
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return err;
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}
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}
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}
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/* generate the restable */
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for (x = 1; x < MP_PRIME_TAB_SIZE; x++) {
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if ((err = mp_mod_d(a, s_mp_prime_tab[x], res_tab + x)) != MP_OKAY) {
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return err;
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}
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}
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/* init temp used for Miller-Rabin Testing */
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if ((err = mp_init(&b)) != MP_OKAY) {
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return err;
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}
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for (;;) {
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mp_digit step = 0;
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bool y;
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/* skip to the next non-trivially divisible candidate */
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do {
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/* y == true if any residue was zero [e.g. cannot be prime] */
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y = false;
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/* increase step to next candidate */
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step += kstep;
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/* compute the new residue without using division */
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for (x = 1; x < MP_PRIME_TAB_SIZE; x++) {
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/* add the step to each residue */
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res_tab[x] += kstep;
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/* subtract the modulus [instead of using division] */
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if (res_tab[x] >= s_mp_prime_tab[x]) {
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res_tab[x] -= s_mp_prime_tab[x];
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}
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/* set flag if zero */
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if (res_tab[x] == 0u) {
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y = true;
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}
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}
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} while (y && (step < (((mp_digit)1 << MP_DIGIT_BIT) - kstep)));
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/* add the step */
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if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
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goto LBL_ERR;
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}
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/* if didn't pass sieve and step == MP_MAX then skip test */
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if (y && (step >= (((mp_digit)1 << MP_DIGIT_BIT) - kstep))) {
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continue;
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}
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if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) {
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goto LBL_ERR;
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}
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if (res) {
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break;
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}
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}
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LBL_ERR:
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mp_clear(&b);
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return err;
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}
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#endif
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