mpir/mpz/probable_prime_p.c

/*
Copyright 2009 Jason Moxham

This file is part of the MPIR Library.

The MPIR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation; either version 2.1 of the License, or (at
your option) any later version.

The MPIR Library 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPIR Library; see the file COPYING.LIB.  If not, write
to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
Boston, MA 02110-1301, USA.
*/

#include "mpir.h"
#include "gmp-impl.h"

int
mpz_probable_prime_p (mpz_srcptr N, gmp_randstate_t STATE, int PROB, mpir_ui td)
{
  int d, t, i, r;
  mpz_t base, nm1, x, e, n;

  ALLOC(n) = ALLOC(N);
  SIZ(n) = ABSIZ(N);
  PTR(n) = PTR(N);		/* fake up an absolute value that we dont have de-allocate */

  /* algorithm does not handle small values, get rid of them here */
  if (mpz_cmp_ui(n, 2) == 0 || mpz_cmp_ui(n, 3) == 0)
     return 1;

  if (mpz_cmp_ui(n, 5) < 0 || mpz_even_p(n))
     return 0;

  /*
     We assume we know nothing about N, i.e. it is a random integer
     So we try here anything which speeds up the average case
     We try some trial division
  */
#define LIM 1024
  
  d = mpz_trial_division(n, 3, LIM);
  
  if (d != 0)
  {
     if (mpz_cmp_ui(n, d) == 0)
        return 1;
     
     return 0;
  }
  
  if (mpz_cmp_ui(n, LIM * LIM) < 0)
     return 1;
  
  ASSERT (mpz_odd_p(n));
  ASSERT (mpz_cmp_ui(n, 5) >= 0);

  /* now do some random strong pseudoprime tests */
  mpz_init(base);
  mpz_init_set(nm1, n);
  mpz_sub_ui(nm1, nm1, 1);
  mpz_init(e);
  mpz_init(x);

  t = mpz_scan1(nm1, 0);	/* 2^t divides nm1 */
  
  ASSERT (t > 0);
  
  mpz_tdiv_q_2exp (e, nm1, t);	/* e = nm1/2^t */
  
  r = 1;

  while (PROB > 0)
  {
     PROB -= 2;
     do
	  {
	     mpz_urandomm (base, STATE, nm1);
	  } while (mpz_cmp_ui (base, 1) <= 0);
      
     mpz_powm (x, base, e, n);	/* x = base^e mod n */

     if (mpz_cmp_ui(x, 1) == 0 || mpz_cmp(x, nm1) == 0)
	     continue;
      
     for (i = t - 1; i > 0; i--)
	  {
	     mpz_mul(x, x, x);
	     mpz_mod(x, x, n);
	     
        if (mpz_cmp(x, nm1) == 0)
	        break;
	  
        if (mpz_cmp_ui(x, 1) == 0)
	     {
	        r = 0;
	        break;
        }
     }
      
     if (i == 0 || r == 0)
     {
        r = 0;
        break;
     }
  }
  
  mpz_clear (nm1);
  mpz_clear (x);
  mpz_clear (e);
  mpz_clear (base);
  
  return r;
}