pqc/external/flint-2.4.3/fq/norm.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) 2012 Sebastian Pancratz
Copyright (C) 2013 Mike Hansen
******************************************************************************/
#include "fq.h"
/*
Computes the characteristic polynomial of the $n \times n$ matrix $M$
modulo \code{pN} using a division-free algorithm in $O(n^4)$ ring
operations.
Only returns the determinant.
Assumes that $n$ is at least $2$.
*/
static void
_fmpz_mod_mat_det(fmpz_t rop, const fmpz * M, slong n, const fmpz_t pN)
{
if (n == 1)
{
fmpz_set(rop, M);
}
else
{
fmpz *F;
fmpz *a;
fmpz *A;
fmpz_t s;
slong t, i, j, p, k;
F = _fmpz_vec_init(n);
a = _fmpz_vec_init((n - 1) * n);
A = _fmpz_vec_init(n);
fmpz_init(s);
fmpz_neg(F + 0, M + 0 * n + 0);
for (t = 1; t < n; t++)
{
for (i = 0; i <= t; i++)
fmpz_set(a + 0 * n + i, M + i * n + t);
fmpz_set(A + 0, M + t * n + t);
for (p = 1; p < t; p++)
{
for (i = 0; i <= t; i++)
{
fmpz_zero(s);
for (j = 0; j <= t; j++)
fmpz_addmul(s, M + i * n + j, a + (p - 1) * n + j);
fmpz_mod(a + p * n + i, s, pN);
}
fmpz_set(A + p, a + p * n + t);
}
fmpz_zero(s);
for (j = 0; j <= t; j++)
fmpz_addmul(s, M + t * n + j, a + (t - 1) * n + j);
fmpz_mod(A + t, s, pN);
for (p = 0; p <= t; p++)
{
fmpz_sub(F + p, F + p, A + p);
for (k = 0; k < p; k++)
fmpz_submul(F + p, A + k, F + (p - k - 1));
fmpz_mod(F + p, F + p, pN);
}
}
/*
Now [F{n-1}, F{n-2}, ..., F{0}, 1] is the
characteristic polynomial of the matrix M.
*/
if (n % WORD(2) == 0)
{
fmpz_set(rop, F + (n - 1));
}
else
{
fmpz_neg(rop, F + (n - 1));
fmpz_mod(rop, rop, pN);
}
_fmpz_vec_clear(F, n);
_fmpz_vec_clear(a, (n - 1) * n);
_fmpz_vec_clear(A, n);
fmpz_clear(s);
}
}
/*
Computes the norm on $\mathbf{Q}_q$ to precision $N \geq 1$.
When $N = 1$, this computes the norm on $\mathbf{F}_q$.
*/
void
_fq_norm(fmpz_t rop, const fmpz * op, slong len, const fq_ctx_t ctx)
{
const slong d = fq_ctx_degree(ctx);
const slong N = 1;
fmpz *pN;
const fmpz *p = fq_ctx_prime(ctx);
if (N == 1)
{
pN = (fmpz *) p; /* XXX: Read-only */
}
else
{
pN = flint_malloc(sizeof(fmpz));
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
}
if (len == 1)
{
fmpz_powm_ui(rop, op + 0, d, pN);
}
else
{
/* Construct an ad hoc matrix M and set rop to det(M) */
{
const slong n = d + len - 1;
slong i, k;
fmpz *M;
M = flint_calloc(n * n, sizeof(fmpz));
for (k = 0; k < len - 1; k++)
{
for (i = 0; i < ctx->len; i++)
{
M[k * n + k + (d - ctx->j[i])] = ctx->a[i];
}
}
for (k = 0; k < d; k++)
{
for (i = 0; i < len; i++)
{
M[(len - 1 + k) * n + k + (len - 1 - i)] = op[i];
}
}
_fmpz_mod_mat_det(rop, M, n, pN);
flint_free(M);
}
/*
XXX: This part of the code is currently untested as the Conway
polynomials used for the extension Fq/Fp are monic.
*/
if (!fmpz_is_one(ctx->a + (ctx->len - 1)))
{
fmpz_t f;
fmpz_init(f);
fmpz_powm_ui(f, ctx->a + (ctx->len - 1), len - 1, pN);
fmpz_invmod(f, f, pN);
fmpz_mul(rop, f, rop);
fmpz_mod(rop, rop, pN);
fmpz_clear(f);
}
}
if (N > 1)
{
fmpz_clear(pN);
flint_free(pN);
}
}
void
fq_norm(fmpz_t rop, const fq_t op, const fq_ctx_t ctx)
{
if (fq_is_zero(op, ctx))
{
fmpz_zero(rop);
}
else
{
_fq_norm(rop, op->coeffs, op->length, ctx);
}
}