pqc/external/flint-2.4.3/ulong_extras/is_prime_pocklington.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
This file is part of FLINT.
FLINT 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 of the License, or
(at your option) any later version.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2008 Peter Shrimpton
Copyright (C) 2009 William Hart
******************************************************************************/
#include <gmp.h>
#define ulong ulongxx /* interferes with system includes */
#include <stdlib.h>
#undef ulong
#define ulong mp_limb_t
#include "flint.h"
#include "ulong_extras.h"
int
n_is_prime_pocklington(mp_limb_t n, ulong iterations)
{
int i, j, pass;
mp_limb_t n1, cofactor, b, c = 0, ninv, limit;
n_factor_t factors;
if (n % 2 == 0)
{
return (n == UWORD(2));
}
n1 = n - 1;
n_factor_init(&factors);
limit = n_sqrt(n1);
cofactor = n_factor_partial(&factors, n1, limit, 1);
if (cofactor != 1) /* check that cofactor is coprime to factors found */
{
for (i = 0; i < factors.num; i++)
{
if (factors.p[i] > FLINT_FACTOR_TRIAL_PRIMES_PRIME)
{
while (cofactor >= factors.p[i] && (cofactor % factors.p[i]) == 0)
{
factors.exp[i]++;
cofactor /= factors.p[i];
}
}
}
}
ninv = n_preinvert_limb(n);
c = 1;
for (i = factors.num - 1; i >= 0; i--)
{
mp_limb_t exp = n1 / factors.p[i];
pass = 0;
for (j = 2; j < iterations && pass == 0; j++)
{
b = n_powmod2_preinv(j, exp, n, ninv);
if (n_powmod2_ui_preinv(b, factors.p[i], n, ninv) != UWORD(1))
return 0;
b = n_submod(b, UWORD(1), n);
if (b != UWORD(0))
{
c = n_mulmod2_preinv(c, b, n, ninv);
pass = 1;
}
if (c == 0)
return 0;
}
if (j == iterations)
return -1;
}
return (n_gcd(n, c) == UWORD(1));
}