412 lines
9.4 KiB
C
412 lines
9.4 KiB
C
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/* Generates provable primes
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*
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* See http://gmail.com:8080/papers/pp.pdf for more info.
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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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#include <stdlib.h>
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#include <time.h>
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#include "tommath_private.h"
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static int n_prime;
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static FILE *primes;
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/* fast square root */
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static mp_digit i_sqrt(mp_word x)
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{
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mp_word x1, x2;
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x2 = x;
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do {
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x1 = x2;
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x2 = x1 - ((x1 * x1) - x) / (2u * x1);
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} while (x1 != x2);
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if ((x1 * x1) > x) {
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--x1;
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}
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return x1;
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}
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/* generates a prime digit */
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static void gen_prime(void)
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{
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mp_digit r, x, y, next;
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FILE *out;
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out = fopen("pprime.dat", "wb");
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if (out != NULL) {
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/* write first set of primes */
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/* *INDENT-OFF* */
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r = 3uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 5uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 7uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 11uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 13uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 17uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 19uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 23uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 29uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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r = 31uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
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/* *INDENT-ON* */
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/* get square root, since if 'r' is composite its factors must be < than this */
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y = i_sqrt(r);
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next = (y + 1uL) * (y + 1uL);
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for (;;) {
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do {
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r += 2uL; /* next candidate */
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r &= MP_MASK;
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if (r < 31uL) break;
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/* update sqrt ? */
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if (next <= r) {
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++y;
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next = (y + 1uL) * (y + 1uL);
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}
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/* loop if divisible by 3,5,7,11,13,17,19,23,29 */
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if ((r % 3uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 5uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 7uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 11uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 13uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 17uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 19uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 23uL) == 0uL) {
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x = 0uL;
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continue;
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}
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if ((r % 29uL) == 0uL) {
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x = 0uL;
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continue;
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}
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/* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */
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for (x = 30uL; x <= y; x += 30uL) {
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if ((r % (x + 1uL)) == 0uL) {
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x = 0uL;
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break;
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}
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if ((r % (x + 7uL)) == 0uL) {
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x = 0uL;
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break;
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}
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if ((r % (x + 11uL)) == 0uL) {
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x = 0uL;
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break;
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}
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if ((r % (x + 13uL)) == 0uL) {
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x = 0uL;
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break;
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}
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if ((r % (x + 17uL)) == 0uL) {
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x = 0uL;
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break;
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}
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if ((r % (x + 19uL)) == 0uL) {
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x = 0uL;
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break;
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}
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if ((r % (x + 23uL)) == 0uL) {
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x = 0uL;
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break;
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}
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if ((r % (x + 29uL)) == 0uL) {
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x = 0uL;
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break;
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}
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}
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} while (x == 0uL);
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if (r > 31uL) {
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fwrite(&r, 1uL, sizeof(mp_digit), out);
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printf("%9lu\r", r);
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fflush(stdout);
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}
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if (r < 31uL) break;
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}
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fclose(out);
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}
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}
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static void load_tab(void)
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{
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primes = fopen("pprime.dat", "rb");
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if (primes == NULL) {
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gen_prime();
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primes = fopen("pprime.dat", "rb");
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}
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fseek(primes, 0L, SEEK_END);
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n_prime = ftell(primes) / sizeof(mp_digit);
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}
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static mp_digit prime_digit(void)
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{
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int n;
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mp_digit d;
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n = abs(rand()) % n_prime;
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fseek(primes, n * sizeof(mp_digit), SEEK_SET);
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fread(&d, 1uL, sizeof(mp_digit), primes);
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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 res;
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int ii;
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static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
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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());
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return MP_OKAY;
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}
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if ((res = mp_init(&c)) != MP_OKAY) {
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return res;
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}
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if ((res = mp_init(&v)) != MP_OKAY) {
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goto LBL_C;
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}
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/* product of first 50 primes */
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if ((res =
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mp_read_radix(&v,
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"19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
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10)) != MP_OKAY) {
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goto LBL_V;
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}
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if ((res = mp_init(&a)) != MP_OKAY) {
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goto LBL_V;
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}
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/* set the prime */
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mp_set(&a, prime_digit());
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if ((res = mp_init(&b)) != MP_OKAY) {
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goto LBL_A;
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}
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if ((res = mp_init(&n)) != MP_OKAY) {
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goto LBL_B;
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}
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if ((res = mp_init(&x)) != MP_OKAY) {
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goto LBL_N;
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}
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if ((res = mp_init(&y)) != MP_OKAY) {
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goto LBL_X;
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}
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if ((res = mp_init(&z)) != MP_OKAY) {
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goto LBL_Y;
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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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fprintf(stderr, "prime has %4d bits left\r", k - mp_count_bits(&a));
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fflush(stderr);
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top:
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mp_set(&b, prime_digit());
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/* now compute z = a * b * 2 */
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if ((res = mp_mul(&a, &b, &z)) != MP_OKAY) { /* z = a * b */
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goto LBL_Z;
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}
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if ((res = mp_copy(&z, &c)) != MP_OKAY) { /* c = a * b */
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goto LBL_Z;
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}
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if ((res = mp_mul_2(&z, &z)) != MP_OKAY) { /* z = 2 * a * b */
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goto LBL_Z;
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}
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/* n = z + 1 */
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if ((res = mp_add_d(&z, 1uL, &n)) != MP_OKAY) { /* n = z + 1 */
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goto LBL_Z;
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}
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/* check (n, v) == 1 */
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if ((res = mp_gcd(&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */
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goto LBL_Z;
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}
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if (mp_cmp_d(&y, 1uL) != MP_EQ)
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goto top;
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/* now try base x=bases[ii] */
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for (ii = 0; ii < li; ii++) {
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mp_set(&x, bases[ii]);
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/* compute x^a mod n */
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if ((res = mp_exptmod(&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */
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goto LBL_Z;
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}
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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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/* now x^2a mod n */
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if ((res = mp_sqrmod(&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */
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goto LBL_Z;
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}
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if (mp_cmp_d(&y, 1uL) == MP_EQ)
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continue;
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/* compute x^b mod n */
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if ((res = mp_exptmod(&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */
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goto LBL_Z;
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}
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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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/* now x^2b mod n */
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if ((res = mp_sqrmod(&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */
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goto LBL_Z;
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}
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if (mp_cmp_d(&y, 1uL) == MP_EQ)
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continue;
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/* compute x^c mod n == x^ab mod n */
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if ((res = mp_exptmod(&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */
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goto LBL_Z;
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}
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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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/* now compute (x^c mod n)^2 */
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if ((res = mp_sqrmod(&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */
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goto LBL_Z;
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}
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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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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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char buf[4096];
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mp_to_decimal(&n, buf, sizeof(buf));
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printf("Certificate of primality for:\n%s\n\n", buf);
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mp_to_decimal(&a, buf, sizeof(buf));
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printf("A == \n%s\n\n", buf);
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mp_to_decimal(&b, buf, sizeof(buf));
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printf("B == \n%s\n\nG == %lu\n", buf, bases[ii]);
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printf("----------------------------------------------------------------\n");
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}
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/* a = n */
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mp_copy(&n, &a);
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}
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/* get q to be the order of the large prime subgroup */
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mp_sub_d(&n, 1uL, q);
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mp_div_2(q, q);
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mp_div(q, &b, q, NULL);
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mp_exch(&n, p);
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res = MP_OKAY;
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LBL_Z:
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mp_clear(&z);
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LBL_Y:
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mp_clear(&y);
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LBL_X:
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mp_clear(&x);
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LBL_N:
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mp_clear(&n);
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LBL_B:
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mp_clear(&b);
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LBL_A:
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mp_clear(&a);
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LBL_V:
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mp_clear(&v);
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LBL_C:
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mp_clear(&c);
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return res;
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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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char buf[4096];
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int k, li;
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clock_t t1;
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srand(time(NULL));
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load_tab();
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printf("Enter # of bits: \n");
|
||
|
|
fgets(buf, sizeof(buf), stdin);
|
||
|
|
sscanf(buf, "%d", &k);
|
||
|
|
|
||
|
|
printf("Enter number of bases to try (1 to 8):\n");
|
||
|
|
fgets(buf, sizeof(buf), stdin);
|
||
|
|
sscanf(buf, "%d", &li);
|
||
|
|
|
||
|
|
|
||
|
|
mp_init(&p);
|
||
|
|
mp_init(&q);
|
||
|
|
|
||
|
|
t1 = clock();
|
||
|
|
pprime(k, li, &p, &q);
|
||
|
|
t1 = clock() - t1;
|
||
|
|
|
||
|
|
printf("\n\nTook %lu ticks, %d bits\n", t1, mp_count_bits(&p));
|
||
|
|
|
||
|
|
mp_to_decimal(&p, buf, sizeof(buf));
|
||
|
|
printf("P == %s\n", buf);
|
||
|
|
mp_to_decimal(&q, buf, sizeof(buf));
|
||
|
|
printf("Q == %s\n", buf);
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
}
|