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author | jan.nijtmans <nijtmans@users.sourceforge.net> | 2017-04-12 12:00:11 (GMT) |
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committer | jan.nijtmans <nijtmans@users.sourceforge.net> | 2017-04-12 12:00:11 (GMT) |
commit | ece45e7fb6469e3ee3ad49f168f8711fb36f93ce (patch) | |
tree | db4a77927de2a4d6c6cf2bc672ebda4098b9b1a0 /libtommath/etc/pprime.c | |
parent | 6f3388528ef453d29fbddba3f5a054d2f5268207 (diff) | |
parent | 473bfc0f18451046035f638732a609fc86d5a0aa (diff) | |
download | tcl-initsubsystems.zip tcl-initsubsystems.tar.gz tcl-initsubsystems.tar.bz2 |
merge trunkinitsubsystems
Diffstat (limited to 'libtommath/etc/pprime.c')
-rw-r--r-- | libtommath/etc/pprime.c | 396 |
1 files changed, 0 insertions, 396 deletions
diff --git a/libtommath/etc/pprime.c b/libtommath/etc/pprime.c deleted file mode 100644 index 955f19e..0000000 --- a/libtommath/etc/pprime.c +++ /dev/null @@ -1,396 +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; -} |