e554550755
for file in $(find -name \*.h ) ; do sed -e "s/#include \"gmp\.h\"/#include \"mpir.h\"/g" $file > temp ; mv temp $file ; done for file in $(find -name \*.cc) ; do sed -e "s/#include \"gmp\.h\"/#include \"mpir.h\"/g" $file > temp ; mv temp $file ; done
369 lines
6.7 KiB
C
369 lines
6.7 KiB
C
/* Factoring with Pollard's rho method.
|
|
|
|
Copyright 1995, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2005 Free Software
|
|
Foundation, Inc.
|
|
|
|
This program is free software; you can redistribute it and/or modify it under
|
|
the terms of the GNU General Public License as published by the Free Software
|
|
Foundation; either version 2, or (at your option) any later version.
|
|
|
|
This program is distributed in the hope that it will be useful, but WITHOUT ANY
|
|
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
|
|
PARTICULAR PURPOSE. See the GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License along with
|
|
this program; see the file COPYING. If not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
|
|
|
|
#include <stdlib.h>
|
|
#include <stdio.h>
|
|
#include <string.h>
|
|
|
|
#include "mpir.h"
|
|
|
|
int flag_verbose = 0;
|
|
|
|
static unsigned add[] = {4, 2, 4, 2, 4, 6, 2, 6};
|
|
|
|
void
|
|
factor_using_division (mpz_t t, unsigned int limit)
|
|
{
|
|
mpz_t q, r;
|
|
unsigned long int f;
|
|
int ai;
|
|
unsigned *addv = add;
|
|
unsigned int failures;
|
|
|
|
if (flag_verbose)
|
|
{
|
|
printf ("[trial division (%u)] ", limit);
|
|
fflush (stdout);
|
|
}
|
|
|
|
mpz_init (q);
|
|
mpz_init (r);
|
|
|
|
f = mpz_scan1 (t, 0);
|
|
mpz_div_2exp (t, t, f);
|
|
while (f)
|
|
{
|
|
printf ("2 ");
|
|
fflush (stdout);
|
|
--f;
|
|
}
|
|
|
|
for (;;)
|
|
{
|
|
mpz_tdiv_qr_ui (q, r, t, 3);
|
|
if (mpz_cmp_ui (r, 0) != 0)
|
|
break;
|
|
mpz_set (t, q);
|
|
printf ("3 ");
|
|
fflush (stdout);
|
|
}
|
|
|
|
for (;;)
|
|
{
|
|
mpz_tdiv_qr_ui (q, r, t, 5);
|
|
if (mpz_cmp_ui (r, 0) != 0)
|
|
break;
|
|
mpz_set (t, q);
|
|
printf ("5 ");
|
|
fflush (stdout);
|
|
}
|
|
|
|
failures = 0;
|
|
f = 7;
|
|
ai = 0;
|
|
while (mpz_cmp_ui (t, 1) != 0)
|
|
{
|
|
mpz_tdiv_qr_ui (q, r, t, f);
|
|
if (mpz_cmp_ui (r, 0) != 0)
|
|
{
|
|
f += addv[ai];
|
|
if (mpz_cmp_ui (q, f) < 0)
|
|
break;
|
|
ai = (ai + 1) & 7;
|
|
failures++;
|
|
if (failures > limit)
|
|
break;
|
|
}
|
|
else
|
|
{
|
|
mpz_swap (t, q);
|
|
printf ("%lu ", f);
|
|
fflush (stdout);
|
|
failures = 0;
|
|
}
|
|
}
|
|
|
|
mpz_clear (q);
|
|
mpz_clear (r);
|
|
}
|
|
|
|
void
|
|
factor_using_division_2kp (mpz_t t, unsigned int limit, unsigned long p)
|
|
{
|
|
mpz_t r;
|
|
mpz_t f;
|
|
unsigned int k;
|
|
|
|
if (flag_verbose)
|
|
{
|
|
printf ("[trial division (%u)] ", limit);
|
|
fflush (stdout);
|
|
}
|
|
|
|
mpz_init (r);
|
|
mpz_init_set_ui (f, 2 * p);
|
|
mpz_add_ui (f, f, 1);
|
|
for (k = 1; k < limit; k++)
|
|
{
|
|
mpz_tdiv_r (r, t, f);
|
|
while (mpz_cmp_ui (r, 0) == 0)
|
|
{
|
|
mpz_tdiv_q (t, t, f);
|
|
mpz_tdiv_r (r, t, f);
|
|
mpz_out_str (stdout, 10, f);
|
|
fflush (stdout);
|
|
fputc (' ', stdout);
|
|
}
|
|
mpz_add_ui (f, f, 2 * p);
|
|
}
|
|
|
|
mpz_clear (f);
|
|
mpz_clear (r);
|
|
}
|
|
|
|
void
|
|
factor_using_pollard_rho (mpz_t n, int a_int, unsigned long p)
|
|
{
|
|
mpz_t x, x1, y, P;
|
|
mpz_t a;
|
|
mpz_t g;
|
|
mpz_t t1, t2;
|
|
int k, l, c, i;
|
|
|
|
if (flag_verbose)
|
|
{
|
|
printf ("[pollard-rho (%d)] ", a_int);
|
|
fflush (stdout);
|
|
}
|
|
|
|
mpz_init (g);
|
|
mpz_init (t1);
|
|
mpz_init (t2);
|
|
|
|
mpz_init_set_si (a, a_int);
|
|
mpz_init_set_si (y, 2);
|
|
mpz_init_set_si (x, 2);
|
|
mpz_init_set_si (x1, 2);
|
|
k = 1;
|
|
l = 1;
|
|
mpz_init_set_ui (P, 1);
|
|
c = 0;
|
|
|
|
while (mpz_cmp_ui (n, 1) != 0)
|
|
{
|
|
S2:
|
|
if (p != 0)
|
|
{
|
|
mpz_powm_ui (x, x, p, n); mpz_add (x, x, a);
|
|
}
|
|
else
|
|
{
|
|
mpz_mul (x, x, x); mpz_add (x, x, a); mpz_mod (x, x, n);
|
|
}
|
|
mpz_sub (t1, x1, x); mpz_mul (t2, P, t1); mpz_mod (P, t2, n);
|
|
c++;
|
|
if (c == 20)
|
|
{
|
|
c = 0;
|
|
mpz_gcd (g, P, n);
|
|
if (mpz_cmp_ui (g, 1) != 0)
|
|
goto S4;
|
|
mpz_set (y, x);
|
|
}
|
|
S3:
|
|
k--;
|
|
if (k > 0)
|
|
goto S2;
|
|
|
|
mpz_gcd (g, P, n);
|
|
if (mpz_cmp_ui (g, 1) != 0)
|
|
goto S4;
|
|
|
|
mpz_set (x1, x);
|
|
k = l;
|
|
l = 2 * l;
|
|
for (i = 0; i < k; i++)
|
|
{
|
|
if (p != 0)
|
|
{
|
|
mpz_powm_ui (x, x, p, n); mpz_add (x, x, a);
|
|
}
|
|
else
|
|
{
|
|
mpz_mul (x, x, x); mpz_add (x, x, a); mpz_mod (x, x, n);
|
|
}
|
|
}
|
|
mpz_set (y, x);
|
|
c = 0;
|
|
goto S2;
|
|
S4:
|
|
do
|
|
{
|
|
if (p != 0)
|
|
{
|
|
mpz_powm_ui (y, y, p, n); mpz_add (y, y, a);
|
|
}
|
|
else
|
|
{
|
|
mpz_mul (y, y, y); mpz_add (y, y, a); mpz_mod (y, y, n);
|
|
}
|
|
mpz_sub (t1, x1, y); mpz_gcd (g, t1, n);
|
|
}
|
|
while (mpz_cmp_ui (g, 1) == 0);
|
|
|
|
mpz_div (n, n, g); /* divide by g, before g is overwritten */
|
|
|
|
if (!mpz_probab_prime_p (g, 3))
|
|
{
|
|
do
|
|
{
|
|
mp_limb_t a_limb;
|
|
mpn_random (&a_limb, (mp_size_t) 1);
|
|
a_int = (int) a_limb;
|
|
}
|
|
while (a_int == -2 || a_int == 0);
|
|
|
|
if (flag_verbose)
|
|
{
|
|
printf ("[composite factor--restarting pollard-rho] ");
|
|
fflush (stdout);
|
|
}
|
|
factor_using_pollard_rho (g, a_int, p);
|
|
}
|
|
else
|
|
{
|
|
mpz_out_str (stdout, 10, g);
|
|
fflush (stdout);
|
|
fputc (' ', stdout);
|
|
}
|
|
mpz_mod (x, x, n);
|
|
mpz_mod (x1, x1, n);
|
|
mpz_mod (y, y, n);
|
|
if (mpz_probab_prime_p (n, 3))
|
|
{
|
|
mpz_out_str (stdout, 10, n);
|
|
fflush (stdout);
|
|
fputc (' ', stdout);
|
|
break;
|
|
}
|
|
}
|
|
|
|
mpz_clear (g);
|
|
mpz_clear (P);
|
|
mpz_clear (t2);
|
|
mpz_clear (t1);
|
|
mpz_clear (a);
|
|
mpz_clear (x1);
|
|
mpz_clear (x);
|
|
mpz_clear (y);
|
|
}
|
|
|
|
void
|
|
factor (mpz_t t, unsigned long p)
|
|
{
|
|
unsigned int division_limit;
|
|
|
|
if (mpz_sgn (t) == 0)
|
|
return;
|
|
|
|
/* Set the trial division limit according the size of t. */
|
|
division_limit = mpz_sizeinbase (t, 2);
|
|
if (division_limit > 1000)
|
|
division_limit = 1000 * 1000;
|
|
else
|
|
division_limit = division_limit * division_limit;
|
|
|
|
if (p != 0)
|
|
factor_using_division_2kp (t, division_limit / 10, p);
|
|
else
|
|
factor_using_division (t, division_limit);
|
|
|
|
if (mpz_cmp_ui (t, 1) != 0)
|
|
{
|
|
if (flag_verbose)
|
|
{
|
|
printf ("[is number prime?] ");
|
|
fflush (stdout);
|
|
}
|
|
if (mpz_probab_prime_p (t, 3))
|
|
mpz_out_str (stdout, 10, t);
|
|
else
|
|
factor_using_pollard_rho (t, 1, p);
|
|
}
|
|
}
|
|
|
|
main (int argc, char *argv[])
|
|
{
|
|
mpz_t t;
|
|
unsigned long p;
|
|
int i;
|
|
|
|
if (argc > 1 && !strcmp (argv[1], "-v"))
|
|
{
|
|
flag_verbose = 1;
|
|
argv++;
|
|
argc--;
|
|
}
|
|
|
|
mpz_init (t);
|
|
if (argc > 1)
|
|
{
|
|
p = 0;
|
|
for (i = 1; i < argc; i++)
|
|
{
|
|
if (!strncmp (argv[i], "-Mp", 3))
|
|
{
|
|
p = atoi (argv[i] + 3);
|
|
mpz_set_ui (t, 1);
|
|
mpz_mul_2exp (t, t, p);
|
|
mpz_sub_ui (t, t, 1);
|
|
}
|
|
else if (!strncmp (argv[i], "-2kp", 4))
|
|
{
|
|
p = atoi (argv[i] + 4);
|
|
continue;
|
|
}
|
|
else
|
|
{
|
|
mpz_set_str (t, argv[i], 0);
|
|
}
|
|
|
|
if (mpz_cmp_ui (t, 0) == 0)
|
|
puts ("-");
|
|
else
|
|
{
|
|
factor (t, p);
|
|
puts ("");
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (;;)
|
|
{
|
|
mpz_inp_str (t, stdin, 0);
|
|
if (feof (stdin))
|
|
break;
|
|
mpz_out_str (stdout, 10, t); printf (" = ");
|
|
factor (t, 0);
|
|
puts ("");
|
|
}
|
|
}
|
|
|
|
exit (0);
|
|
}
|