summaryrefslogtreecommitdiffhomepage
path: root/libtommath/etc/pprime.c
diff options
context:
space:
mode:
Diffstat (limited to 'libtommath/etc/pprime.c')
-rw-r--r--libtommath/etc/pprime.c400
1 files changed, 0 insertions, 400 deletions
diff --git a/libtommath/etc/pprime.c b/libtommath/etc/pprime.c
deleted file mode 100644
index 0313948..0000000
--- a/libtommath/etc/pprime.c
+++ /dev/null
@@ -1,400 +0,0 @@
-/* Generates provable primes
- *
- * See http://gmail.com:8080/papers/pp.pdf for more info.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://tom.gmail.com
- */
-#include <time.h>
-#include "tommath.h"
-
-int n_prime;
-FILE *primes;
-
-/* fast square root */
-static mp_digit
-i_sqrt (mp_word x)
-{
- mp_word x1, x2;
-
- x2 = x;
- do {
- x1 = x2;
- x2 = x1 - ((x1 * x1) - x) / (2 * x1);
- } while (x1 != x2);
-
- if (x1 * x1 > x) {
- --x1;
- }
-
- return x1;
-}
-
-
-/* generates a prime digit */
-static void gen_prime (void)
-{
- mp_digit r, x, y, next;
- FILE *out;
-
- out = fopen("pprime.dat", "wb");
-
- /* write first set of primes */
- r = 3; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 5; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 7; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 11; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 13; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 17; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 19; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 23; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 29; fwrite(&r, 1, sizeof(mp_digit), out);
- r = 31; fwrite(&r, 1, sizeof(mp_digit), out);
-
- /* get square root, since if 'r' is composite its factors must be < than this */
- y = i_sqrt (r);
- next = (y + 1) * (y + 1);
-
- for (;;) {
- do {
- r += 2; /* next candidate */
- r &= MP_MASK;
- if (r < 31) break;
-
- /* update sqrt ? */
- if (next <= r) {
- ++y;
- next = (y + 1) * (y + 1);
- }
-
- /* loop if divisible by 3,5,7,11,13,17,19,23,29 */
- if ((r % 3) == 0) {
- x = 0;
- continue;
- }
- if ((r % 5) == 0) {
- x = 0;
- continue;
- }
- if ((r % 7) == 0) {
- x = 0;
- continue;
- }
- if ((r % 11) == 0) {
- x = 0;
- continue;
- }
- if ((r % 13) == 0) {
- x = 0;
- continue;
- }
- if ((r % 17) == 0) {
- x = 0;
- continue;
- }
- if ((r % 19) == 0) {
- x = 0;
- continue;
- }
- if ((r % 23) == 0) {
- x = 0;
- continue;
- }
- if ((r % 29) == 0) {
- x = 0;
- continue;
- }
-
- /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */
- for (x = 30; x <= y; x += 30) {
- if ((r % (x + 1)) == 0) {
- x = 0;
- break;
- }
- if ((r % (x + 7)) == 0) {
- x = 0;
- break;
- }
- if ((r % (x + 11)) == 0) {
- x = 0;
- break;
- }
- if ((r % (x + 13)) == 0) {
- x = 0;
- break;
- }
- if ((r % (x + 17)) == 0) {
- x = 0;
- break;
- }
- if ((r % (x + 19)) == 0) {
- x = 0;
- break;
- }
- if ((r % (x + 23)) == 0) {
- x = 0;
- break;
- }
- if ((r % (x + 29)) == 0) {
- x = 0;
- break;
- }
- }
- } while (x == 0);
- if (r > 31) { fwrite(&r, 1, sizeof(mp_digit), out); printf("%9d\r", r); fflush(stdout); }
- if (r < 31) break;
- }
-
- fclose(out);
-}
-
-void load_tab(void)
-{
- primes = fopen("pprime.dat", "rb");
- if (primes == NULL) {
- gen_prime();
- primes = fopen("pprime.dat", "rb");
- }
- fseek(primes, 0, SEEK_END);
- n_prime = ftell(primes) / sizeof(mp_digit);
-}
-
-mp_digit prime_digit(void)
-{
- int n;
- mp_digit d;
-
- n = abs(rand()) % n_prime;
- fseek(primes, n * sizeof(mp_digit), SEEK_SET);
- fread(&d, 1, sizeof(mp_digit), primes);
- return d;
-}
-
-
-/* makes a prime of at least k bits */
-int
-pprime (int k, int li, mp_int * p, mp_int * q)
-{
- mp_int a, b, c, n, x, y, z, v;
- int res, ii;
- static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
-
- /* single digit ? */
- if (k <= (int) DIGIT_BIT) {
- mp_set (p, prime_digit ());
- return MP_OKAY;
- }
-
- if ((res = mp_init (&c)) != MP_OKAY) {
- return res;
- }
-
- if ((res = mp_init (&v)) != MP_OKAY) {
- goto LBL_C;
- }
-
- /* product of first 50 primes */
- if ((res =
- mp_read_radix (&v,
- "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
- 10)) != MP_OKAY) {
- goto LBL_V;
- }
-
- if ((res = mp_init (&a)) != MP_OKAY) {
- goto LBL_V;
- }
-
- /* set the prime */
- mp_set (&a, prime_digit ());
-
- if ((res = mp_init (&b)) != MP_OKAY) {
- goto LBL_A;
- }
-
- if ((res = mp_init (&n)) != MP_OKAY) {
- goto LBL_B;
- }
-
- if ((res = mp_init (&x)) != MP_OKAY) {
- goto LBL_N;
- }
-
- if ((res = mp_init (&y)) != MP_OKAY) {
- goto LBL_X;
- }
-
- if ((res = mp_init (&z)) != MP_OKAY) {
- goto LBL_Y;
- }
-
- /* now loop making the single digit */
- while (mp_count_bits (&a) < k) {
- fprintf (stderr, "prime has %4d bits left\r", k - mp_count_bits (&a));
- fflush (stderr);
- top:
- mp_set (&b, prime_digit ());
-
- /* now compute z = a * b * 2 */
- if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) { /* z = a * b */
- goto LBL_Z;
- }
-
- if ((res = mp_copy (&z, &c)) != MP_OKAY) { /* c = a * b */
- goto LBL_Z;
- }
-
- if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) { /* z = 2 * a * b */
- goto LBL_Z;
- }
-
- /* n = z + 1 */
- if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) { /* n = z + 1 */
- goto LBL_Z;
- }
-
- /* check (n, v) == 1 */
- if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */
- goto LBL_Z;
- }
-
- if (mp_cmp_d (&y, 1) != MP_EQ)
- goto top;
-
- /* now try base x=bases[ii] */
- for (ii = 0; ii < li; ii++) {
- mp_set (&x, bases[ii]);
-
- /* compute x^a mod n */
- if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) { /* y = x^a mod n */
- goto LBL_Z;
- }
-
- /* if y == 1 loop */
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
-
- /* now x^2a mod n */
- if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */
- goto LBL_Z;
- }
-
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
-
- /* compute x^b mod n */
- if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */
- goto LBL_Z;
- }
-
- /* if y == 1 loop */
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
-
- /* now x^2b mod n */
- if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */
- goto LBL_Z;
- }
-
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
-
- /* compute x^c mod n == x^ab mod n */
- if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) { /* y = x^ab mod n */
- goto LBL_Z;
- }
-
- /* if y == 1 loop */
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
-
- /* now compute (x^c mod n)^2 */
- if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */
- goto LBL_Z;
- }
-
- /* y should be 1 */
- if (mp_cmp_d (&y, 1) != MP_EQ)
- continue;
- break;
- }
-
- /* no bases worked? */
- if (ii == li)
- goto top;
-
-{
- char buf[4096];
-
- mp_toradix(&n, buf, 10);
- printf("Certificate of primality for:\n%s\n\n", buf);
- mp_toradix(&a, buf, 10);
- printf("A == \n%s\n\n", buf);
- mp_toradix(&b, buf, 10);
- printf("B == \n%s\n\nG == %d\n", buf, bases[ii]);
- printf("----------------------------------------------------------------\n");
-}
-
- /* a = n */
- mp_copy (&n, &a);
- }
-
- /* get q to be the order of the large prime subgroup */
- mp_sub_d (&n, 1, q);
- mp_div_2 (q, q);
- mp_div (q, &b, q, NULL);
-
- mp_exch (&n, p);
-
- res = MP_OKAY;
-LBL_Z:mp_clear (&z);
-LBL_Y:mp_clear (&y);
-LBL_X:mp_clear (&x);
-LBL_N:mp_clear (&n);
-LBL_B:mp_clear (&b);
-LBL_A:mp_clear (&a);
-LBL_V:mp_clear (&v);
-LBL_C:mp_clear (&c);
- return res;
-}
-
-
-int
-main (void)
-{
- mp_int p, q;
- char buf[4096];
- int k, li;
- clock_t t1;
-
- srand (time (NULL));
- load_tab();
-
- 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 %ld ticks, %d bits\n", t1, mp_count_bits (&p));
-
- mp_toradix (&p, buf, 10);
- printf ("P == %s\n", buf);
- mp_toradix (&q, buf, 10);
- printf ("Q == %s\n", buf);
-
- return 0;
-}
-
-/* ref: $Format:%D$ */
-/* git commit: $Format:%H$ */
-/* commit time: $Format:%ai$ */
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-23 15:55:47 +0000