369 lines
7.1 KiB
C
369 lines
7.1 KiB
C
/* Factoring with Pollard's rho method.
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Copyright 1995, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2005 Free Software
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Foundation, Inc.
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This program is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free Software
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Foundation; either version 2, or (at your option) any later version.
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This program is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
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PARTICULAR PURPOSE. See the GNU General Public License for more details.
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You should have received a copy of the GNU General Public License along with
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this program; see the file COPYING. If not, write to the Free Software
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Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
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#include <stdlib.h>
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#include <stdio.h>
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#include <string.h>
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#include "gmp.h"
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int flag_verbose = 0;
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static unsigned add[] = {4, 2, 4, 2, 4, 6, 2, 6};
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void
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factor_using_division (mpz_t t, unsigned int limit)
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{
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mpz_t q, r;
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unsigned long int f;
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int ai;
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unsigned *addv = add;
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unsigned int failures;
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if (flag_verbose)
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{
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printf ("[trial division (%u)] ", limit);
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fflush (stdout);
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}
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mpz_init (q);
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mpz_init (r);
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f = mpz_scan1 (t, 0);
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mpz_div_2exp (t, t, f);
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while (f)
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{
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printf ("2 ");
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fflush (stdout);
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--f;
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}
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for (;;)
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{
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mpz_tdiv_qr_ui (q, r, t, 3);
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if (mpz_cmp_ui (r, 0) != 0)
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break;
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mpz_set (t, q);
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printf ("3 ");
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fflush (stdout);
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}
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for (;;)
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{
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mpz_tdiv_qr_ui (q, r, t, 5);
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if (mpz_cmp_ui (r, 0) != 0)
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break;
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mpz_set (t, q);
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printf ("5 ");
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fflush (stdout);
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}
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failures = 0;
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f = 7;
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ai = 0;
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while (mpz_cmp_ui (t, 1) != 0)
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{
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mpz_tdiv_qr_ui (q, r, t, f);
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if (mpz_cmp_ui (r, 0) != 0)
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{
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f += addv[ai];
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if (mpz_cmp_ui (q, f) < 0)
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break;
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ai = (ai + 1) & 7;
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failures++;
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if (failures > limit)
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break;
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}
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else
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{
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mpz_swap (t, q);
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printf ("%lu ", f);
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fflush (stdout);
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failures = 0;
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}
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}
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mpz_clear (q);
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mpz_clear (r);
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}
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void
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factor_using_division_2kp (mpz_t t, unsigned int limit, unsigned long p)
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{
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mpz_t r;
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mpz_t f;
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unsigned int k;
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if (flag_verbose)
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{
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printf ("[trial division (%u)] ", limit);
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fflush (stdout);
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}
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mpz_init (r);
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mpz_init_set_ui (f, 2 * p);
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mpz_add_ui (f, f, 1);
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for (k = 1; k < limit; k++)
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{
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mpz_tdiv_r (r, t, f);
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while (mpz_cmp_ui (r, 0) == 0)
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{
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mpz_tdiv_q (t, t, f);
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mpz_tdiv_r (r, t, f);
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mpz_out_str (stdout, 10, f);
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fflush (stdout);
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fputc (' ', stdout);
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}
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mpz_add_ui (f, f, 2 * p);
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}
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mpz_clear (f);
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mpz_clear (r);
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}
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void
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factor_using_pollard_rho (mpz_t n, int a_int, unsigned long p)
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{
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mpz_t x, x1, y, P;
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mpz_t a;
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mpz_t g;
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mpz_t t1, t2;
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int k, l, c, i;
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if (flag_verbose)
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{
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printf ("[pollard-rho (%d)] ", a_int);
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fflush (stdout);
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}
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mpz_init (g);
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mpz_init (t1);
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mpz_init (t2);
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mpz_init_set_si (a, a_int);
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mpz_init_set_si (y, 2);
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mpz_init_set_si (x, 2);
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mpz_init_set_si (x1, 2);
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k = 1;
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l = 1;
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mpz_init_set_ui (P, 1);
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c = 0;
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while (mpz_cmp_ui (n, 1) != 0)
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{
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S2:
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if (p != 0)
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{
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mpz_powm_ui (x, x, p, n); mpz_add (x, x, a);
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}
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else
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{
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mpz_mul (x, x, x); mpz_add (x, x, a); mpz_mod (x, x, n);
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}
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mpz_sub (t1, x1, x); mpz_mul (t2, P, t1); mpz_mod (P, t2, n);
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c++;
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if (c == 20)
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{
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c = 0;
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mpz_gcd (g, P, n);
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if (mpz_cmp_ui (g, 1) != 0)
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goto S4;
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mpz_set (y, x);
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}
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S3:
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k--;
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if (k > 0)
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goto S2;
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mpz_gcd (g, P, n);
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if (mpz_cmp_ui (g, 1) != 0)
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goto S4;
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mpz_set (x1, x);
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k = l;
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l = 2 * l;
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for (i = 0; i < k; i++)
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{
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if (p != 0)
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{
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mpz_powm_ui (x, x, p, n); mpz_add (x, x, a);
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}
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else
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{
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mpz_mul (x, x, x); mpz_add (x, x, a); mpz_mod (x, x, n);
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}
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}
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mpz_set (y, x);
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c = 0;
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goto S2;
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S4:
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do
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{
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if (p != 0)
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{
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mpz_powm_ui (y, y, p, n); mpz_add (y, y, a);
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}
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else
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{
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mpz_mul (y, y, y); mpz_add (y, y, a); mpz_mod (y, y, n);
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}
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mpz_sub (t1, x1, y); mpz_gcd (g, t1, n);
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}
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while (mpz_cmp_ui (g, 1) == 0);
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mpz_div (n, n, g); /* divide by g, before g is overwritten */
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if (!mpz_probab_prime_p (g, 3))
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{
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do
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{
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mp_limb_t a_limb;
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mpn_random (&a_limb, (mp_size_t) 1);
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a_int = (int) a_limb;
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}
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while (a_int == -2 || a_int == 0);
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if (flag_verbose)
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{
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printf ("[composite factor--restarting pollard-rho] ");
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fflush (stdout);
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}
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factor_using_pollard_rho (g, a_int, p);
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}
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else
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{
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mpz_out_str (stdout, 10, g);
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fflush (stdout);
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fputc (' ', stdout);
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}
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mpz_mod (x, x, n);
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mpz_mod (x1, x1, n);
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mpz_mod (y, y, n);
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if (mpz_probab_prime_p (n, 3))
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{
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mpz_out_str (stdout, 10, n);
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fflush (stdout);
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fputc (' ', stdout);
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break;
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}
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}
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mpz_clear (g);
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mpz_clear (P);
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mpz_clear (t2);
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mpz_clear (t1);
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mpz_clear (a);
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mpz_clear (x1);
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mpz_clear (x);
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mpz_clear (y);
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}
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void
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factor (mpz_t t, unsigned long p)
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{
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unsigned int division_limit;
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if (mpz_sgn (t) == 0)
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return;
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/* Set the trial division limit according the size of t. */
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division_limit = mpz_sizeinbase (t, 2);
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if (division_limit > 1000)
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division_limit = 1000 * 1000;
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else
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division_limit = division_limit * division_limit;
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if (p != 0)
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factor_using_division_2kp (t, division_limit / 10, p);
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else
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factor_using_division (t, division_limit);
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if (mpz_cmp_ui (t, 1) != 0)
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{
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if (flag_verbose)
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{
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printf ("[is number prime?] ");
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fflush (stdout);
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}
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if (mpz_probab_prime_p (t, 3))
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mpz_out_str (stdout, 10, t);
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else
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factor_using_pollard_rho (t, 1, p);
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}
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}
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main (int argc, char *argv[])
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{
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mpz_t t;
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unsigned long p;
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int i;
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if (argc > 1 && !strcmp (argv[1], "-v"))
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{
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flag_verbose = 1;
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argv++;
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argc--;
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}
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mpz_init (t);
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if (argc > 1)
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{
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p = 0;
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for (i = 1; i < argc; i++)
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{
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if (!strncmp (argv[i], "-Mp", 3))
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{
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p = atoi (argv[i] + 3);
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mpz_set_ui (t, 1);
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mpz_mul_2exp (t, t, p);
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mpz_sub_ui (t, t, 1);
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}
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else if (!strncmp (argv[i], "-2kp", 4))
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{
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p = atoi (argv[i] + 4);
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continue;
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}
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else
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{
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mpz_set_str (t, argv[i], 0);
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}
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if (mpz_cmp_ui (t, 0) == 0)
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puts ("-");
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else
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{
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factor (t, p);
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puts ("");
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}
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}
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}
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else
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{
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for (;;)
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{
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mpz_inp_str (t, stdin, 0);
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if (feof (stdin))
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break;
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mpz_out_str (stdout, 10, t); printf (" = ");
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factor (t, 0);
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puts ("");
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}
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}
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exit (0);
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}
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