*
* Tom St Denis, tomstdenis@gmail.com, http://tom.gmail.com
*/
+#include <stdlib.h>
#include <time.h>
#include "tommath.h"
-int n_prime;
-FILE *primes;
+static int n_prime;
+static FILE *primes;
/* fast square root */
-static mp_digit
-i_sqrt (mp_word x)
+static mp_digit i_sqrt(mp_word x)
{
- mp_word x1, x2;
+ mp_word x1, x2;
- x2 = x;
- do {
- x1 = x2;
- x2 = x1 - ((x1 * x1) - x) / (2 * x1);
- } while (x1 != x2);
+ x2 = x;
+ do {
+ x1 = x2;
+ x2 = x1 - ((x1 * x1) - x) / (2u * x1);
+ } while (x1 != x2);
- if (x1 * x1 > x) {
- --x1;
- }
+ if ((x1 * x1) > x) {
+ --x1;
+ }
- return x1;
+ return x1;
}
/* generates a prime digit */
-static void gen_prime (void)
+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;
+ mp_digit r, x, y, next;
+ FILE *out;
+
+ out = fopen("pprime.dat", "wb");
+ if (out != NULL) {
+
+ /* write first set of primes */
+ /* *INDENT-OFF* */
+ r = 3uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 5uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 7uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 11uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 13uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 17uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 19uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 23uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 29uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ r = 31uL; fwrite(&r, 1uL, sizeof(mp_digit), out);
+ /* *INDENT-ON* */
+
+ /* get square root, since if 'r' is composite its factors must be < than this */
+ y = i_sqrt(r);
+ next = (y + 1uL) * (y + 1uL);
+
+ for (;;) {
+ do {
+ r += 2uL; /* next candidate */
+ r &= MP_MASK;
+ if (r < 31uL) break;
+
+ /* update sqrt ? */
+ if (next <= r) {
+ ++y;
+ next = (y + 1uL) * (y + 1uL);
+ }
+
+ /* loop if divisible by 3,5,7,11,13,17,19,23,29 */
+ if ((r % 3uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 5uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 7uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 11uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 13uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 17uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 19uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 23uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+ if ((r % 29uL) == 0uL) {
+ x = 0uL;
+ continue;
+ }
+
+ /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */
+ for (x = 30uL; x <= y; x += 30uL) {
+ if ((r % (x + 1uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ if ((r % (x + 7uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ if ((r % (x + 11uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ if ((r % (x + 13uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ if ((r % (x + 17uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ if ((r % (x + 19uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ if ((r % (x + 23uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ if ((r % (x + 29uL)) == 0uL) {
+ x = 0uL;
+ break;
+ }
+ }
+ } while (x == 0uL);
+ if (r > 31uL) {
+ fwrite(&r, 1uL, sizeof(mp_digit), out);
+ printf("%9lu\r", r);
+ fflush(stdout);
+ }
+ if (r < 31uL) 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);
+ fclose(out);
+ }
}
-void load_tab(void)
+static void load_tab(void)
{
primes = fopen("pprime.dat", "rb");
if (primes == NULL) {
gen_prime();
primes = fopen("pprime.dat", "rb");
}
- fseek(primes, 0, SEEK_END);
+ fseek(primes, 0L, SEEK_END);
n_prime = ftell(primes) / sizeof(mp_digit);
}
-mp_digit prime_digit(void)
+static 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);
+ fread(&d, 1uL, 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)
+static mp_err 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;
- }
+ mp_int a, b, c, n, x, y, z, v;
+ mp_err res;
+ int ii;
+ static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
+
+ /* single digit ? */
+ if (k <= (int) MP_DIGIT_BIT) {
+ mp_set(p, prime_digit());
+ return MP_OKAY;
+ }
- /* if y == 1 loop */
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
+ if ((res = mp_init(&c)) != MP_OKAY) {
+ return res;
+ }
- /* now x^2a mod n */
- if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2a mod n */
- goto LBL_Z;
- }
+ if ((res = mp_init(&v)) != MP_OKAY) {
+ goto LBL_C;
+ }
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
+ /* product of first 50 primes */
+ if ((res =
+ mp_read_radix(&v,
+ "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
+ 10)) != MP_OKAY) {
+ goto LBL_V;
+ }
- /* compute x^b mod n */
- if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) { /* y = x^b mod n */
- goto LBL_Z;
- }
+ 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 y == 1 loop */
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
+ if ((res = mp_init(&y)) != MP_OKAY) {
+ goto LBL_X;
+ }
+
+ if ((res = mp_init(&z)) != MP_OKAY) {
+ goto LBL_Y;
+ }
- /* now x^2b mod n */
- if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2b mod n */
- goto LBL_Z;
+ /* 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 (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
+ if ((res = mp_copy(&z, &c)) != MP_OKAY) { /* c = a * b */
+ goto LBL_Z;
+ }
- /* 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 ((res = mp_mul_2(&z, &z)) != MP_OKAY) { /* z = 2 * a * b */
+ goto LBL_Z;
}
- /* if y == 1 loop */
- if (mp_cmp_d (&y, 1) == MP_EQ)
- continue;
+ /* n = z + 1 */
+ if ((res = mp_add_d(&z, 1uL, &n)) != MP_OKAY) { /* n = z + 1 */
+ goto LBL_Z;
+ }
- /* now compute (x^c mod n)^2 */
- if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) { /* y = x^2ab mod n */
- goto LBL_Z;
+ /* check (n, v) == 1 */
+ if ((res = mp_gcd(&n, &v, &y)) != MP_OKAY) { /* y = (n, v) */
+ goto LBL_Z;
}
- /* y should be 1 */
- if (mp_cmp_d (&y, 1) != MP_EQ)
- continue;
- break;
- }
+ if (mp_cmp_d(&y, 1uL) != 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, 1uL) == 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, 1uL) == 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, 1uL) == 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, 1uL) == 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, 1uL) == 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, 1uL) != MP_EQ)
+ continue;
+ break;
+ }
- /* no bases worked? */
- if (ii == li)
- goto top;
+ /* 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");
-}
+ {
+ char buf[4096];
- /* 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;
+ mp_to_decimal(&n, buf, sizeof(buf));
+ printf("Certificate of primality for:\n%s\n\n", buf);
+ mp_to_decimal(&a, buf, sizeof(buf));
+ printf("A == \n%s\n\n", buf);
+ mp_to_decimal(&b, buf, sizeof(buf));
+ printf("B == \n%s\n\nG == %lu\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, 1uL, 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)
+int main(void)
{
- mp_int p, q;
- char buf[4096];
- int k, li;
- clock_t t1;
+ mp_int p, q;
+ char buf[4096];
+ int k, li;
+ clock_t t1;
- srand (time (NULL));
- load_tab();
+ srand(time(NULL));
+ load_tab();
- printf ("Enter # of bits: \n");
- fgets (buf, sizeof (buf), stdin);
- sscanf (buf, "%d", &k);
+ 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);
+ 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);
+ mp_init(&p);
+ mp_init(&q);
- t1 = clock ();
- pprime (k, li, &p, &q);
- t1 = clock () - t1;
+ t1 = clock();
+ pprime(k, li, &p, &q);
+ t1 = clock() - t1;
- printf ("\n\nTook %ld ticks, %d bits\n", t1, mp_count_bits (&p));
+ printf("\n\nTook %d 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);
+ 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;
+ return 0;
}
-
-/* $Source: /cvs/libtom/libtommath/etc/pprime.c,v $ */
-/* $Revision: 1.3 $ */
-/* $Date: 2006/03/31 14:18:47 $ */
git.samba.org / metze / heimdal / wip.git / blobdiff