282 lines
6.4 KiB
C
282 lines
6.4 KiB
C
/* Generates provable primes
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*
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* See http://iahu.ca:8080/papers/pp.pdf for more info.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://tom.iahu.ca
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*/
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#include <time.h>
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#include "bn.h"
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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)/(2*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 mp_digit prime_digit()
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{
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mp_digit r, x, y, next;
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/* make a DIGIT_BIT-bit random number */
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for (r = x = 0; x < DIGIT_BIT; x++) {
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r = (r << 1) | (rand() & 1);
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}
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/* now force it odd */
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r |= 1;
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/* force it to be >30 */
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if (r < 30) {
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r += 30;
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}
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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+1)*(y+1);
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do {
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r += 2; /* next candidate */
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/* update sqrt ? */
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if (next <= r) {
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++y;
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next = (y+1)*(y+1);
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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 % 3) == 0) { x = 0; continue; }
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if ((r % 5) == 0) { x = 0; continue; }
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if ((r % 7) == 0) { x = 0; continue; }
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if ((r % 11) == 0) { x = 0; continue; }
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if ((r % 13) == 0) { x = 0; continue; }
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if ((r % 17) == 0) { x = 0; continue; }
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if ((r % 19) == 0) { x = 0; continue; }
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if ((r % 23) == 0) { x = 0; continue; }
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if ((r % 29) == 0) { x = 0; continue; }
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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 = 30; x <= y; x += 30) {
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if ((r % (x+1)) == 0) { x = 0; break; }
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if ((r % (x+7)) == 0) { x = 0; break; }
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if ((r % (x+11)) == 0) { x = 0; break; }
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if ((r % (x+13)) == 0) { x = 0; break; }
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if ((r % (x+17)) == 0) { x = 0; break; }
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if ((r % (x+19)) == 0) { x = 0; break; }
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if ((r % (x+23)) == 0) { x = 0; break; }
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if ((r % (x+29)) == 0) { x = 0; break; }
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}
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} while (x == 0);
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return r;
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}
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/* makes a prime of at least k bits */
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int pprime(int k, 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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int res;
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/* single digit ? */
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if (k <= (int)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 __C;
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}
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/* product of first 50 primes */
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if ((res = mp_read_radix(&v, "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190", 10)) != MP_OKAY) {
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goto __V;
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}
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if ((res = mp_init(&a)) != MP_OKAY) {
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goto __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 __A;
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}
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if ((res = mp_init(&n)) != MP_OKAY) {
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goto __B;
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}
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if ((res = mp_init(&x)) != MP_OKAY) {
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goto __N;
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}
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if ((res = mp_init(&y)) != MP_OKAY) {
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goto __X;
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}
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if ((res = mp_init(&z)) != MP_OKAY) {
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goto __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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printf("prime is %4d bits left\r", k - mp_count_bits(&a)); fflush(stdout);
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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 __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 __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 __Z;
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}
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/* n = z + 1 */
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if ((res = mp_add_d(&z, 1, &n)) != MP_OKAY) { /* n = z + 1 */
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goto __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 __Z;
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}
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if (mp_cmp_d(&y, 1) != MP_EQ) goto top;
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/* now try base x=2 */
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mp_set(&x, 2);
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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 __Z;
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}
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/* if y == 1 loop */
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if (mp_cmp_d(&y, 1) == MP_EQ) goto top;
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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 __Z;
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}
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if (mp_cmp_d(&y, 1) == MP_EQ) goto top;
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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 __Z;
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}
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/* if y == 1 loop */
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if (mp_cmp_d(&y, 1) == MP_EQ) goto top;
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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 __Z;
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}
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if (mp_cmp_d(&y, 1) == MP_EQ) goto top;
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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 __Z;
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}
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/* if y == 1 loop */
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if (mp_cmp_d(&y, 1) == MP_EQ) goto top;
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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 __Z;
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}
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/* y should be 1 */
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if (mp_cmp_d(&y, 1) != MP_EQ) goto top;
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/*
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{
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char buf[4096];
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mp_toradix(&n, buf, 10);
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printf("Certificate of primality for:\n%s\n\n", buf);
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mp_toradix(&a, buf, 10);
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printf("A == \n%s\n\n", buf);
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mp_toradix(&b, buf, 10);
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printf("B == \n%s\n", buf);
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printf("----------------------------------------------------------------\n");
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}
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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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mp_exch(&n, p);
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mp_exch(&b, q);
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res = MP_OKAY;
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__Z: mp_clear(&z);
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__Y: mp_clear(&y);
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__X: mp_clear(&x);
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__N: mp_clear(&n);
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__B: mp_clear(&b);
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__A: mp_clear(&a);
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__V: mp_clear(&v);
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__C: 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;
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clock_t t1;
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srand(time(NULL));
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printf("Enter # of bits: \n");
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scanf("%d", &k);
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mp_init(&p);
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mp_init(&q);
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t1 = clock();
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pprime(k, &p, &q);
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t1 = clock() - t1;
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printf("\n\nTook %ld ticks, %d bits\n", t1, mp_count_bits(&p));
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mp_toradix(&p, buf, 10);
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printf("P == %s\n", buf);
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mp_toradix(&q, buf, 10);
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printf("Q == %s\n", buf);
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return 0;
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}
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