220 lines
6.5 KiB
C
220 lines
6.5 KiB
C
/*
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* Generates provable primes
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*
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* Tom St Denis, tomstdenis@gmail.com, http://tom.gmail.com
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*
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*/
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#include <stdlib.h>
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#include <time.h>
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#include "../tommath_private.h"
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static void mp_print(const char *s, const mp_int *a, int radix, FILE *stream)
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{
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mp_err err;
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fputs(s, stream);
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err = mp_fwrite(a, radix, stream);
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if (err != MP_OKAY) {
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fprintf(stderr,"mp_fwrite in mp_print failed. error = %s\n", mp_error_to_string(err));
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exit(EXIT_FAILURE);
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}
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fputc('\n',stream);
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}
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static mp_digit prime_digit(int bits)
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{
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mp_digit d = 0;
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mp_int a;
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mp_err err;
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if ((err = mp_init(&a)) != MP_OKAY) {
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return 0;
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}
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if ((err = mp_prime_rand(&a, 1, bits, false)) != MP_OKAY) goto LTM_ERR;
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d = a.dp[0];
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LTM_ERR:
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mp_clear(&a);
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return d;
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}
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/* makes a prime of at least k bits */
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static mp_err pprime(int k, int li, mp_int *p, mp_int *q)
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{
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mp_int a, b, c, n, x, y, z, v;
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mp_err err = MP_OKAY;
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int ii, bits;
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/* single digit ? */
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if (k < (int) MP_DIGIT_BIT) {
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mp_set(p, prime_digit(k));
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if (mp_iszero(p)) {
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return MP_VAL;
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}
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return MP_OKAY;
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}
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if ((err = mp_init_multi(&a, &b, &c, &n, &x, &y, &z, &v, NULL)) != MP_OKAY) {
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return err;
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}
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/* product of first 50 primes */
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if ((err = mp_read_radix(&v, "9NPvy2By/eZ0N6s68ky5K/8UTD0Q7fInhDK9BHnueH92HfzU4+U", 64)) != MP_OKAY) {
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goto LTM_ERR;
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}
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/* set the prime */
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mp_set(&a, prime_digit(MP_DIGIT_BIT));
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if (mp_iszero(&a)) {
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err = MP_VAL;
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goto LTM_ERR;
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}
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/* now loop making the single digit */
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while (mp_count_bits(&a) < k) {
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bits = k - mp_count_bits(&a);
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fprintf(stderr, "prime has %4d bits left\r", bits);
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fflush(stderr);
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top:
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if (bits < MP_DIGIT_BIT) {
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mp_set(&b, prime_digit(bits));
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} else {
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mp_set(&b, prime_digit(MP_DIGIT_BIT));
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}
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if (mp_iszero(&b)) {
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err = MP_VAL;
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goto LTM_ERR;
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}
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/* now compute z = a * b * 2 */
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/* z = a * b */
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if ((err = mp_mul(&a, &b, &z)) != MP_OKAY) goto LTM_ERR;
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/* c = a * b */
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if ((err = mp_copy(&z, &c)) != MP_OKAY) goto LTM_ERR;
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/* z = 2 * a * b */
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if ((err = mp_mul_2(&z, &z)) != MP_OKAY) goto LTM_ERR;
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/* n = z + 1 */
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if ((err = mp_add_d(&z, 1uL, &n)) != MP_OKAY) goto LTM_ERR;
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/* check (n, v) == 1; y = (n, v) */
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if ((err = mp_gcd(&n, &v, &y)) != MP_OKAY) goto LTM_ERR;
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if (mp_cmp_d(&y, 1uL) != MP_EQ) {
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goto top;
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}
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mp_set(&x, 2u);
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/* now try base x=bases[ii] */
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for (ii = 0; ii < li; ii++) {
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if ((err = mp_prime_next_prime(&x, -1, false)) != MP_OKAY) goto LTM_ERR;
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/* compute x^a mod n; y = x^a mod n */
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if ((err = mp_exptmod(&x, &a, &n, &y)) != MP_OKAY) goto LTM_ERR;
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/* if y == 1 loop */
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if (mp_cmp_d(&y, 1uL) == MP_EQ) {
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continue;
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}
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/* now x^2a mod n ; y = x^2a mod n*/
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if ((err = mp_sqrmod(&y, &n, &y)) != MP_OKAY) goto LTM_ERR;
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if (mp_cmp_d(&y, 1uL) == MP_EQ) {
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continue;
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}
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/* compute x^b mod n ; y = x^b mod n*/
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if ((err = mp_exptmod(&x, &b, &n, &y)) != MP_OKAY) goto LTM_ERR;
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/* if y == 1 loop */
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if (mp_cmp_d(&y, 1uL) == MP_EQ) {
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continue;
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}
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/* now x^2b mod n; y = x^2b mod n */
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if ((err = mp_sqrmod(&y, &n, &y)) != MP_OKAY) goto LTM_ERR;
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if (mp_cmp_d(&y, 1uL) == MP_EQ) {
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continue;
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}
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/* compute x^c mod n == x^ab mod n ; y = x^ab mod n */
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if ((err = mp_exptmod(&x, &c, &n, &y)) != MP_OKAY) goto LTM_ERR;
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/* if y == 1 loop */
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if (mp_cmp_d(&y, 1uL) == MP_EQ) {
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continue;
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}
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/* now compute (x^c mod n)^2 ; y = x^2ab mod n */
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if ((err = mp_sqrmod(&y, &n, &y)) != MP_OKAY) goto LTM_ERR;
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/* y should be 1 */
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if (mp_cmp_d(&y, 1uL) != MP_EQ) {
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continue;
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}
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break;
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}
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/* no bases worked? */
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if (ii == li) {
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goto top;
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}
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mp_print("Certificate of primality for:\n ", &n, 10, stdout);
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mp_print("A == ", &a, 10, stdout);
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mp_print("B == ", &b, 10, stdout);
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mp_print("G == ", &x, 10, stdout);
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printf("----------------------------------------------------------------\n");
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/* a = n */
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if ((err = mp_copy(&n, &a)) != MP_OKAY) goto LTM_ERR;
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}
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/* get q to be the order of the large prime subgroup */
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if ((err = mp_sub_d(&n, 1uL, q)) != MP_OKAY) goto LTM_ERR;
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if ((err = mp_div_2(q, q)) != MP_OKAY) goto LTM_ERR;
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if ((err = mp_div(q, &b, q, NULL)) != MP_OKAY) goto LTM_ERR;
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mp_exch(&n, p);
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err = MP_OKAY;
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LTM_ERR:
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mp_clear_multi(&a, &b, &c, &n, &x, &y, &z, &v, NULL);
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return err;
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}
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int main(void)
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{
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mp_int p, q;
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mp_err err;
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char buf[4096];
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int k, li;
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clock_t t1;
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printf("Enter # of bits: \n");
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fgets(buf, sizeof(buf), stdin);
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sscanf(buf, "%d", &k);
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printf("Enter number of bases to try\n");
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fgets(buf, sizeof(buf), stdin);
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sscanf(buf, "%d", &li);
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if ((err = mp_init_multi(&p, &q, NULL)) != MP_OKAY) goto LTM_ERR;
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t1 = clock();
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if ((err = pprime(k, li, &p, &q)) != MP_OKAY) {
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fprintf(stderr, "Something went wrong in function pprime: %s\n", mp_error_to_string(err));
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goto LTM_ERR;
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}
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t1 = clock() - t1;
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printf("\n\nTook %lu ticks, %d bits\n", t1, mp_count_bits(&p));
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mp_print("P == ", &p, 10, stdout);
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mp_print("Q == ", &q, 10, stdout);
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mp_clear_multi(&p, &q, NULL);
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exit(EXIT_SUCCESS);
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LTM_ERR:
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mp_clear_multi(&p, &q, NULL);
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exit(EXIT_FAILURE);
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}
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