mpir/mpz/likely_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"

// could have another parameter to specify what likely means
// ie for factoring , for RSA 
// or to state that we have allready done trial div

// could call it mpz_likely_composite_p then when true we could return more info about it , ie a factor
int
mpz_likely_prime_p (mpz_srcptr N, gmp_randstate_t STATE, unsigned long td)
{
  int d, t, 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 dose 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;
// for factoring purpoises 
// we assume we know nothing about N ie it is a random integer
// therefore it has a good chance of factoring by small divisiors , so try trial division as its fast and it checks small divisors
// checking for other divisors is not worth it even if the test is fast as we have random integer so only small divisors are common
// enough , remember this is not exact so it doesn't matter if we miss a few divisors
#define LIM 255
  for (d = 2; d <= LIM; d++)
    {
      if (mpz_divisible_ui_p (n, d))
	{
	  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);	// so we can choose a base
// now do strong pseudoprime test 
// get random base , for now choose any size , later choose a small one
  mpz_init (base);
  mpz_init_set (nm1, n);
  mpz_sub_ui (nm1, nm1, 1);
  do
    {
      mpz_urandomm (base, STATE, nm1);
    }
  while (mpz_cmp_ui (base, 1) <= 0);
// so base is 2 to n-2  which implys n>=4 , only really want a small base , and ignore the rare base=n-1 condition etc
//printf("base is ");mpz_out_str(stdout,10,base);printf(" ");
  mpz_init (e);
  mpz_init (x);
  t = mpz_scan1 (nm1, 0);	// so 2^t divides nm1
  ASSERT (t > 0);
  mpz_tdiv_q_2exp (e, nm1, t);	// so e=nm1/2^t
  mpz_powm (x, base, e, n);	// x=base^e mod n
  mpz_clear (e);
  mpz_clear (base);
  if (mpz_cmp_ui (x, 1) == 0)
    {
      mpz_clear (nm1);
      mpz_clear (x);
      return 1;
    }
  if (mpz_cmp (x, nm1) == 0)
    {
      mpz_clear (nm1);
      mpz_clear (x);
      return 1;
    }
  for (r = 0, t = t - 1; t > 0; t--)
    {
      mpz_mul (x, x, x);
      mpz_mod (x, x, n);
      if (mpz_cmp (x, nm1) == 0)
	{
	  r = 1;
	  break;
	}
      if (mpz_cmp_ui (x, 1) == 0)
	break;
    }
  mpz_clear (nm1);
  mpz_clear (x);
  return r;
}