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libtommath/etc/pprime.c
Daniel Mendler c4622f53c8
only include tommath_private.h
2019-10-24 21:44:55 +02:00

412 lines
9.4 KiB
C
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/* 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 <stdlib.h>
#include <time.h>
#include "tommath_private.h"
static int n_prime;
static 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) / (2u * 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");
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;
}
fclose(out);
}
}
static void load_tab(void)
{
primes = fopen("pprime.dat", "rb");
if (primes == NULL) {
gen_prime();
primes = fopen("pprime.dat", "rb");
}
fseek(primes, 0L, SEEK_END);
n_prime = ftell(primes) / sizeof(mp_digit);
}
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, 1uL, sizeof(mp_digit), primes);
return d;
}
/* makes a prime of at least k bits */
static mp_err pprime(int k, int li, mp_int *p, mp_int *q)
{
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 ((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, 1uL, &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, 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;
{
char buf[4096];
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)
{
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 %lu ticks, %d bits\n", t1, mp_count_bits(&p));
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;
}
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