570 lines
11 KiB
C
570 lines
11 KiB
C
/*
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* Copyright (C) 2014 FH Bielefeld
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*
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* This file is part of a FH Bielefeld project.
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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* MA 02110-1301 USA
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*/
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/**
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* @file poly.c
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* This files purpose is to handle polynomials
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* in general, allowing modification, arithmetic
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* and common algorithms like inverting them.
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* @brief operations on polynomials
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*/
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#include "context.h"
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#include "err.h"
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#include "mem.h"
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#include "poly.h"
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#include <stdarg.h>
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#include <stdbool.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <sys/types.h>
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#include <fmpz_poly.h>
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#include <fmpz.h>
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/**
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* Find the inverse polynomial modulo a power of 2,
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* which is q.
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*
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* @param a polynomial to invert
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* @param Fq polynomial [out]
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* @param ctx NTRU context
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*/
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static
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void poly_mod2_to_modq(fmpz_poly_t a,
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fmpz_poly_t Fq,
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ntru_context *ctx);
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/*------------------------------------------------------------------------*/
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static void
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poly_mod2_to_modq(fmpz_poly_t a,
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fmpz_poly_t Fq,
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ntru_context *ctx)
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{
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int v = 2;
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fmpz_poly_t poly_tmp, two;
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fmpz_poly_init(poly_tmp);
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fmpz_poly_zero(poly_tmp);
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fmpz_poly_init(two);
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fmpz_poly_set_coeff_ui(two, 0, 2);
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while (v < (int)(ctx->q)) {
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v = v * 2;
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poly_starmultiply(a, Fq, poly_tmp, ctx, v);
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fmpz_poly_sub(poly_tmp, two, poly_tmp);
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fmpz_poly_mod_unsigned(poly_tmp, v);
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poly_starmultiply(Fq, poly_tmp, Fq, ctx, v);
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}
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fmpz_poly_clear(poly_tmp);
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fmpz_poly_clear(two);
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}
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/*------------------------------------------------------------------------*/
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void
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poly_new(fmpz_poly_t new_poly,
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int const * const c,
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const size_t len)
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{
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fmpz_poly_init(new_poly);
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for (uint32_t i = 0; i < len; i++)
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fmpz_poly_set_coeff_si(new_poly, i, c[i]);
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}
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/*------------------------------------------------------------------------*/
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void
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poly_delete(fmpz_poly_t poly)
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{
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fmpz_poly_clear(poly);
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}
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/*------------------------------------------------------------------------*/
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void
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poly_delete_array(fmpz_poly_t **poly_array)
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{
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uint32_t i = 0;
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while(poly_array[i]) {
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poly_delete(*(poly_array[i]));
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free(*(poly_array[i]));
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i++;
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}
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free(poly_array);
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}
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/*------------------------------------------------------------------------*/
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void
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poly_delete_all(fmpz_poly_t poly, ...)
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{
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fmpz_poly_struct *next_poly;
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va_list args;
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next_poly = poly;
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va_start(args, poly);
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while (next_poly != NULL) {
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poly_delete(next_poly);
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next_poly = va_arg(args, fmpz_poly_struct*);
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}
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va_end(args);
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}
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/*------------------------------------------------------------------------*/
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void
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fmpz_poly_mod_unsigned(fmpz_poly_t a,
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uint32_t mod)
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{
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nmod_poly_t nmod_tmp;
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nmod_poly_init(nmod_tmp, mod);
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fmpz_poly_get_nmod_poly(nmod_tmp, a);
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fmpz_poly_set_nmod_poly_unsigned(a, nmod_tmp);
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nmod_poly_clear(nmod_tmp);
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}
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/*------------------------------------------------------------------------*/
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void
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fmpz_poly_mod(fmpz_poly_t a,
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uint32_t mod)
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{
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nmod_poly_t nmod_tmp;
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nmod_poly_init(nmod_tmp, mod);
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fmpz_poly_get_nmod_poly(nmod_tmp, a);
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fmpz_poly_set_nmod_poly(a, nmod_tmp);
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nmod_poly_clear(nmod_tmp);
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}
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/*------------------------------------------------------------------------*/
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void
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fmpz_poly_set_coeff_fmpz_n(fmpz_poly_t poly, slong n,
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const fmpz_t x)
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{
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if (x)
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fmpz_poly_set_coeff_fmpz(poly, n, x);
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else
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fmpz_poly_set_coeff_si(poly, n, 0);
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}
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/*------------------------------------------------------------------------*/
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int
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fmpz_invmod_ui(fmpz_t f, const fmpz_t g, uint32_t mod)
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{
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fmpz_t modulus;
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fmpz_init_set_ui(modulus, mod);
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return fmpz_invmod(f, g, modulus);
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}
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/*------------------------------------------------------------------------*/
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void
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fmpz_add_n(fmpz_t f, const fmpz_t g, const fmpz_t h)
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{
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if (!g && !h) {
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fmpz_zero(f);
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} else {
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if (!g && h)
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fmpz_add_ui(f, h, 0);
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else if (g && !h)
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fmpz_add_ui(f, g, 0);
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else
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fmpz_add(f, g, h);
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}
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}
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/*------------------------------------------------------------------------*/
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void
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poly_starmultiply(fmpz_poly_t a,
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fmpz_poly_t b,
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fmpz_poly_t c,
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ntru_context *ctx,
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uint32_t modulus)
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{
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fmpz_poly_t a_tmp;
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fmpz_t c_coeff_k;
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fmpz_poly_init(a_tmp);
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fmpz_init(c_coeff_k);
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/* avoid side effects */
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fmpz_poly_set(a_tmp, a);
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fmpz_poly_zero(c);
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for (int k = ctx->N - 1; k >= 0; k--) {
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int j;
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j = k + 1;
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fmpz_set_si(c_coeff_k, 0);
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for (int i = ctx->N - 1; i >= 0; i--) {
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fmpz *a_tmp_coeff_i,
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*b_coeff_j;
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if (j == (int)(ctx->N))
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j = 0;
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a_tmp_coeff_i = fmpz_poly_get_coeff_ptr(a_tmp, i);
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b_coeff_j = fmpz_poly_get_coeff_ptr(b, j);
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if (a_tmp_coeff_i && fmpz_cmp_si(a_tmp_coeff_i, 0) &&
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b_coeff_j && fmpz_cmp_si(b_coeff_j, 0)) {
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fmpz_t fmpz_tmp;
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fmpz_init(fmpz_tmp);
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fmpz_mul(fmpz_tmp, a_tmp_coeff_i, b_coeff_j);
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fmpz_add(fmpz_tmp, fmpz_tmp, c_coeff_k);
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fmpz_mod_ui(c_coeff_k, fmpz_tmp, modulus);
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fmpz_poly_set_coeff_fmpz(c, k, c_coeff_k);
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fmpz_clear(fmpz_tmp);
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}
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j++;
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}
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fmpz_clear(c_coeff_k);
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}
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fmpz_poly_clear(a_tmp);
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}
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/*------------------------------------------------------------------------*/
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bool
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poly_inverse_poly_q(fmpz_poly_t a,
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fmpz_poly_t Fq,
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ntru_context *ctx)
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{
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bool retval = false;
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int k = 0,
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j = 0;
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fmpz *b_last;
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fmpz_poly_t a_tmp,
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b,
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c,
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f,
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g;
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/* general initialization of temp variables */
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fmpz_poly_init(b);
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fmpz_poly_set_coeff_ui(b, 0, 1);
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fmpz_poly_init(c);
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fmpz_poly_init(f);
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fmpz_poly_set(f, a);
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/* set g(x) = x^N − 1 */
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fmpz_poly_init(g);
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fmpz_poly_set_coeff_si(g, 0, -1);
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fmpz_poly_set_coeff_si(g, ctx->N, 1);
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/* avoid side effects */
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fmpz_poly_init(a_tmp);
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fmpz_poly_set(a_tmp, a);
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fmpz_poly_zero(Fq);
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while (1) {
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while (fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
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for (uint32_t i = 1; i <= ctx->N; i++) {
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fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
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fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, ctx->N - i);
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/* f(x) = f(x) / x */
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fmpz_poly_set_coeff_fmpz_n(f, i - 1,
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f_coeff);
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/* c(x) = c(x) * x */
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fmpz_poly_set_coeff_fmpz_n(c, ctx->N + 1 - i,
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c_coeff);
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}
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fmpz_poly_set_coeff_si(f, ctx->N, 0);
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fmpz_poly_set_coeff_si(c, 0, 0);
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k++;
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if (fmpz_poly_degree(f) == -1)
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goto _cleanup;
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}
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if (fmpz_poly_degree(f) == 0)
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break;
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if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
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fmpz_poly_swap(f, g);
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fmpz_poly_swap(b, c);
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}
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fmpz_poly_add(f, g, f);
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fmpz_poly_mod_unsigned(f, 2);
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fmpz_poly_add(b, c, b);
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fmpz_poly_mod_unsigned(b, 2);
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}
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k = k % ctx->N;
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b_last = fmpz_poly_get_coeff_ptr(b, ctx->N);
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if (b_last && fmpz_cmp_si(b_last, 0))
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goto _cleanup;
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/* Fq(x) = x^(N-k) * b(x) */
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for (int i = ctx->N - 1; i >= 0; i--) {
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fmpz *b_i;
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j = i - k;
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if (j < 0)
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j = j + ctx->N;
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b_i = fmpz_poly_get_coeff_ptr(b, i);
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fmpz_poly_set_coeff_fmpz_n(Fq, j, b_i);
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}
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poly_mod2_to_modq(a_tmp, Fq, ctx);
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/* check if the f * Fq = 1 (mod p) condition holds true */
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fmpz_poly_set(a_tmp, a);
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poly_starmultiply(a_tmp, Fq, a_tmp, ctx, ctx->q);
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if (fmpz_poly_is_one(a_tmp))
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retval = true;
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else
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fmpz_poly_zero(Fq);
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_cleanup:
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fmpz_poly_clear(a_tmp);
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fmpz_poly_clear(b);
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fmpz_poly_clear(c);
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fmpz_poly_clear(f);
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fmpz_poly_clear(g);
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return retval;
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}
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/*------------------------------------------------------------------------*/
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bool
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poly_inverse_poly_p(fmpz_poly_t a,
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fmpz_poly_t Fp,
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ntru_context *ctx)
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{
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bool retval = false;
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int k = 0,
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j = 0;
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fmpz *b_last;
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fmpz_poly_t a_tmp,
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b,
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c,
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f,
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g;
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/* general initialization of temp variables */
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fmpz_poly_init(b);
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fmpz_poly_set_coeff_ui(b, 0, 1);
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fmpz_poly_init(c);
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fmpz_poly_init(f);
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fmpz_poly_set(f, a);
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/* set g(x) = x^N − 1 */
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fmpz_poly_init(g);
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fmpz_poly_set_coeff_si(g, 0, -1);
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fmpz_poly_set_coeff_si(g, ctx->N, 1);
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/* avoid side effects */
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fmpz_poly_init(a_tmp);
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fmpz_poly_set(a_tmp, a);
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fmpz_poly_zero(Fp);
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while (1) {
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while (fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
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for (uint32_t i = 1; i <= ctx->N; i++) {
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fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
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fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, ctx->N - i);
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/* f(x) = f(x) / x */
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fmpz_poly_set_coeff_fmpz_n(f, i - 1,
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f_coeff);
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/* c(x) = c(x) * x */
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fmpz_poly_set_coeff_fmpz_n(c, ctx->N + 1 - i,
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c_coeff);
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}
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fmpz_poly_set_coeff_si(f, ctx->N, 0);
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fmpz_poly_set_coeff_si(c, 0, 0);
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k++;
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if (fmpz_poly_degree(f) == -1)
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goto cleanup;
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}
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if (fmpz_poly_degree(f) == 0)
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break;
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if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
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/* exchange f and g and exchange b and c */
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fmpz_poly_swap(f, g);
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fmpz_poly_swap(b, c);
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}
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{
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fmpz_poly_t c_tmp,
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g_tmp;
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fmpz_t u,
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mp_tmp;
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fmpz_init(u);
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fmpz_zero(u);
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fmpz_init_set(mp_tmp, fmpz_poly_get_coeff_ptr(f, 0));
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fmpz_poly_init(g_tmp);
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fmpz_poly_set(g_tmp, g);
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fmpz_poly_init(c_tmp);
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fmpz_poly_set(c_tmp, c);
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/* u = f[0] * g[0]^(-1) mod p */
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/* = (f[0] mod p) * (g[0] inverse mod p) mod p */
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fmpz_invmod_ui(u,
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fmpz_poly_get_coeff_ptr(g, 0),
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ctx->p);
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fmpz_mod_ui(mp_tmp, mp_tmp, ctx->p);
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fmpz_mul(u, mp_tmp, u);
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fmpz_mod_ui(u, u, ctx->p);
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/* f = f - u * g mod p */
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fmpz_poly_scalar_mul_fmpz(g_tmp, g_tmp, u);
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fmpz_poly_sub(f, g_tmp, f);
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fmpz_poly_mod_unsigned(f, ctx->p);
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/* b = b - u * c mod p */
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fmpz_poly_scalar_mul_fmpz(c_tmp, c_tmp, u);
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fmpz_poly_sub(b, c_tmp, b);
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fmpz_poly_mod_unsigned(b, ctx->p);
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fmpz_clear(u);
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fmpz_poly_clear(g_tmp);
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fmpz_poly_clear(c_tmp);
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}
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}
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k = k % ctx->N;
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b_last = fmpz_poly_get_coeff_ptr(b, ctx->N);
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if (b_last && fmpz_cmp_si(b_last, 0))
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goto cleanup;
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/* Fp(x) = x^(N-k) * b(x) */
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for (int i = ctx->N - 1; i >= 0; i--) {
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fmpz *b_i;
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/* b(X) = f[0]^(-1) * b(X) (mod p) */
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{
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fmpz_t mp_tmp;
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fmpz_init(mp_tmp);
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fmpz_invmod_ui(mp_tmp,
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fmpz_poly_get_coeff_ptr(f, 0),
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ctx->p);
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if (fmpz_poly_get_coeff_ptr(b, i)) {
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fmpz_mul(fmpz_poly_get_coeff_ptr(b, i),
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fmpz_poly_get_coeff_ptr(b, i),
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mp_tmp);
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fmpz_mod_ui(fmpz_poly_get_coeff_ptr(b, i),
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fmpz_poly_get_coeff_ptr(b, i),
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ctx->p);
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}
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}
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j = i - k;
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if (j < 0)
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j = j + ctx->N;
|
||
|
||
b_i = fmpz_poly_get_coeff_ptr(b, i);
|
||
fmpz_poly_set_coeff_fmpz_n(Fp, j, b_i);
|
||
}
|
||
|
||
/* check if the f * Fp = 1 (mod p) condition holds true */
|
||
fmpz_poly_set(a_tmp, a);
|
||
poly_starmultiply(a_tmp, Fp, a_tmp, ctx, ctx->p);
|
||
if (fmpz_poly_is_one(a_tmp))
|
||
retval = true;
|
||
else
|
||
fmpz_poly_zero(Fp);
|
||
|
||
cleanup:
|
||
fmpz_poly_clear(a_tmp);
|
||
fmpz_poly_clear(b);
|
||
fmpz_poly_clear(c);
|
||
fmpz_poly_clear(f);
|
||
fmpz_poly_clear(g);
|
||
|
||
return retval;
|
||
}
|
||
|
||
/*------------------------------------------------------------------------*/
|
||
|
||
void
|
||
poly_draw(fmpz_poly_t poly)
|
||
{
|
||
fmpz_poly_print(poly);
|
||
flint_printf("\n");
|
||
}
|
||
|
||
/*------------------------------------------------------------------------*/
|
||
|
||
void
|
||
poly_draw_pretty(fmpz_poly_t poly)
|
||
{
|
||
fmpz_poly_print_pretty(poly, "x");
|
||
flint_printf("\n");
|
||
}
|
||
|
||
/*------------------------------------------------------------------------*/
|