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-rw-r--r--libtommath/etc/pprime.c396
1 files changed, 396 insertions, 0 deletions
diff --git a/libtommath/etc/pprime.c b/libtommath/etc/pprime.c
new file mode 100644
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+++ b/libtommath/etc/pprime.c
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+/* Generates provable primes
+ *
+ * See http://iahu.ca:8080/papers/pp.pdf for more info.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://tom.iahu.ca
+ */
+#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;
+}
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