pqc/external/flint-2.4.3/fmpz/sqrtmod.c
2014-05-24 23:16:06 +02:00

174 lines
3.9 KiB
C

/*=============================================================================
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) 2009 William Hart
Copyright (C) 2011 Sebastian Pancratz
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "fmpz.h"
#include "ulong_extras.h"
/*
Assumes that p is an odd prime, and that 0 <= a < p.
Returns 1 if a is a quadratic residue and 0 otherwise.
Does not support aliasing.
*/
static int _fmpz_sqrtmod(mpz_t rop, const mpz_t a, const mpz_t p)
{
slong i, r, m;
mpz_t p1, k, exp, b, g, bpow, gpow;
if (mpz_jacobi(a, p) == -1)
return 0;
if (flint_mpz_congruent_ui_p(p, 3, 4))
{
mpz_init(exp);
flint_mpz_add_ui(exp, p, 1);
mpz_tdiv_q_2exp(exp, exp, 2);
mpz_powm(rop, a, exp, p);
mpz_clear(exp);
return 1;
}
mpz_init(p1);
mpz_init(k);
mpz_init(exp);
mpz_init(b);
mpz_init(g);
mpz_init(bpow);
mpz_init(gpow);
r = 0;
flint_mpz_sub_ui(p1, p, 1);
do {
mpz_tdiv_q_2exp(p1, p1, 1);
r++;
} while (mpz_even_p(p1));
mpz_powm(b, a, p1, p);
for (flint_mpz_set_ui(k, 2); ; flint_mpz_add_ui(k, k, 1))
{
if (mpz_jacobi(k, p) == -1) break;
}
mpz_powm(g, k, p1, p);
flint_mpz_add_ui(exp, p1, 1);
mpz_tdiv_q_2exp(exp, exp, 1);
mpz_powm(rop, a, exp, p);
while (flint_mpz_cmp_ui(b, 1))
{
mpz_set(bpow, b);
m = 0;
do
{
mpz_mul(bpow, bpow, bpow);
mpz_mod(bpow, bpow, p);
m++;
} while (m < r && flint_mpz_cmp_ui(bpow, 1));
mpz_set(gpow, g);
for (i = 1; i < r - m; i++)
{
mpz_mul(gpow, gpow, gpow);
mpz_mod(gpow, gpow, p);
}
mpz_mul(rop, rop, gpow);
mpz_mod(rop, rop, p);
mpz_mul(g, gpow, gpow);
mpz_mod(g, g, p);
mpz_mul(b, b, g);
mpz_mod(b, b, p);
r = m;
}
mpz_clear(p1);
mpz_clear(k);
mpz_clear(exp);
mpz_clear(b);
mpz_clear(g);
mpz_clear(bpow);
mpz_clear(gpow);
return mpz_sgn(rop) ? 1 : 0;
}
int fmpz_sqrtmod(fmpz_t b, const fmpz_t a, const fmpz_t p)
{
if (b == a || b == p)
{
int ans;
fmpz_t t;
fmpz_init(t);
ans = fmpz_sqrtmod(t, a, p);
fmpz_swap(b, t);
fmpz_clear(t);
return ans;
}
fmpz_mod(b, a, p);
if (fmpz_cmp_ui(b, 1) <= 0)
{
return 1;
}
if (!COEFF_IS_MPZ(*p)) /* p, and b are small */
{
mp_limb_t ans;
ans = n_sqrtmod(*b, *p);
if (ans)
fmpz_set_ui(b, ans);
return ans != 0;
}
else /* p is large */
{
int ans;
mpz_t t;
__mpz_struct *bptr;
bptr = _fmpz_promote_val(b);
mpz_init(t);
ans = _fmpz_sqrtmod(t, bptr, COEFF_TO_PTR(*p));
mpz_swap(bptr, t);
mpz_clear(t);
_fmpz_demote_val(b);
return ans;
}
}