223 lines
5.9 KiB
C
223 lines
5.9 KiB
C
/* mpi-mpow.c - MPI functions
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* Copyright (C) 1998, 1999, 2001, 2002, 2003 Free Software Foundation, Inc.
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*
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* This file is part of Libgcrypt.
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*
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* Libgcrypt is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as
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* published by the Free Software Foundation; either version 2.1 of
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* the License, or (at your option) any later version.
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*
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* Libgcrypt 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
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* GNU 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 program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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*/
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#include <config.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include "mpi-internal.h"
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#include "longlong.h"
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#include "g10lib.h"
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/* Barrett is slower than the classical way. It can be tweaked by
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* using partial multiplications
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*/
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/*#define USE_BARRETT*/
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#ifdef USE_BARRETT
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static void barrett_mulm( gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, gcry_mpi_t m, gcry_mpi_t y, int k, gcry_mpi_t r1, gcry_mpi_t r2 );
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static gcry_mpi_t init_barrett( gcry_mpi_t m, int *k, gcry_mpi_t *r1, gcry_mpi_t *r2 );
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static int calc_barrett( gcry_mpi_t r, gcry_mpi_t x, gcry_mpi_t m, gcry_mpi_t y, int k, gcry_mpi_t r1, gcry_mpi_t r2 );
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#else
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#define barrett_mulm( w, u, v, m, y, k, r1, r2 ) gcry_mpi_mulm( (w), (u), (v), (m) )
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#endif
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static int
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build_index( gcry_mpi_t *exparray, int k, int i, int t )
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{
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int j, bitno;
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int idx = 0;
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bitno = t-i;
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for(j=k-1; j >= 0; j-- ) {
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idx <<= 1;
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if( mpi_test_bit( exparray[j], bitno ) )
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idx |= 1;
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}
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/*log_debug("t=%d i=%d idx=%d\n", t, i, idx );*/
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return idx;
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}
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/****************
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* RES = (BASE[0] ^ EXP[0]) * (BASE[1] ^ EXP[1]) * ... * mod M
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*/
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void
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_gcry_mpi_mulpowm( gcry_mpi_t res, gcry_mpi_t *basearray, gcry_mpi_t *exparray, gcry_mpi_t m)
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{
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int k; /* number of elements */
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int t; /* bit size of largest exponent */
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int i, j, idx;
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gcry_mpi_t *G; /* table with precomputed values of size 2^k */
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gcry_mpi_t tmp;
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#ifdef USE_BARRETT
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gcry_mpi_t barrett_y, barrett_r1, barrett_r2;
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int barrett_k;
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#endif
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for(k=0; basearray[k]; k++ )
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;
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gcry_assert(k);
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for(t=0, i=0; (tmp=exparray[i]); i++ ) {
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/*log_mpidump("exp: ", tmp );*/
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j = mpi_get_nbits(tmp);
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if( j > t )
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t = j;
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}
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/*log_mpidump("mod: ", m );*/
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gcry_assert (i==k);
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gcry_assert (t);
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gcry_assert (k < 10);
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G = gcry_xcalloc( (1<<k) , sizeof *G );
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#ifdef USE_BARRETT
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barrett_y = init_barrett( m, &barrett_k, &barrett_r1, &barrett_r2 );
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#endif
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/* and calculate */
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tmp = mpi_alloc( mpi_get_nlimbs(m)+1 );
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mpi_set_ui( res, 1 );
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for(i = 1; i <= t; i++ ) {
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barrett_mulm(tmp, res, res, m, barrett_y, barrett_k,
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barrett_r1, barrett_r2 );
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idx = build_index( exparray, k, i, t );
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gcry_assert (idx >= 0 && idx < (1<<k));
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if( !G[idx] ) {
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if( !idx )
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G[0] = mpi_alloc_set_ui( 1 );
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else {
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for(j=0; j < k; j++ ) {
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if( (idx & (1<<j) ) ) {
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if( !G[idx] )
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G[idx] = mpi_copy( basearray[j] );
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else
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barrett_mulm( G[idx], G[idx], basearray[j],
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m, barrett_y, barrett_k, barrett_r1, barrett_r2 );
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}
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}
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if( !G[idx] )
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G[idx] = mpi_alloc(0);
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}
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}
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barrett_mulm(res, tmp, G[idx], m, barrett_y, barrett_k, barrett_r1, barrett_r2 );
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}
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/* cleanup */
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mpi_free(tmp);
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#ifdef USE_BARRETT
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mpi_free(barrett_y);
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mpi_free(barrett_r1);
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mpi_free(barrett_r2);
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#endif
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for(i=0; i < (1<<k); i++ )
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mpi_free(G[i]);
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gcry_free(G);
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}
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#ifdef USE_BARRETT
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static void
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barrett_mulm( gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, gcry_mpi_t m, gcry_mpi_t y, int k, gcry_mpi_t r1, gcry_mpi_t r2 )
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{
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mpi_mul(w, u, v);
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if( calc_barrett( w, w, m, y, k, r1, r2 ) )
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mpi_fdiv_r( w, w, m );
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}
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/****************
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* Barrett precalculation: y = floor(b^(2k) / m)
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*/
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static gcry_mpi_t
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init_barrett( gcry_mpi_t m, int *k, gcry_mpi_t *r1, gcry_mpi_t *r2 )
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{
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gcry_mpi_t tmp;
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mpi_normalize( m );
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*k = mpi_get_nlimbs( m );
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tmp = mpi_alloc( *k + 1 );
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mpi_set_ui( tmp, 1 );
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mpi_lshift_limbs( tmp, 2 * *k );
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mpi_fdiv_q( tmp, tmp, m );
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*r1 = mpi_alloc( 2* *k + 1 );
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*r2 = mpi_alloc( 2* *k + 1 );
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return tmp;
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}
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/****************
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* Barrett reduction: We assume that these conditions are met:
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* Given x =(x_2k-1 ...x_0)_b
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* m =(m_k-1 ....m_0)_b with m_k-1 != 0
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* Output r = x mod m
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* Before using this function init_barret must be used to calucalte y and k.
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* Returns: false = no error
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* true = can't perform barret reduction
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*/
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static int
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calc_barrett( gcry_mpi_t r, gcry_mpi_t x, gcry_mpi_t m, gcry_mpi_t y, int k, gcry_mpi_t r1, gcry_mpi_t r2 )
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{
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int xx = k > 3 ? k-3:0;
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mpi_normalize( x );
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if( mpi_get_nlimbs(x) > 2*k )
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return 1; /* can't do it */
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/* 1. q1 = floor( x / b^k-1)
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* q2 = q1 * y
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* q3 = floor( q2 / b^k+1 )
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* Actually, we don't need qx, we can work direct on r2
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*/
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mpi_set( r2, x );
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mpi_rshift_limbs( r2, k-1 );
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mpi_mul( r2, r2, y );
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mpi_rshift_limbs( r2, k+1 );
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/* 2. r1 = x mod b^k+1
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* r2 = q3 * m mod b^k+1
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* r = r1 - r2
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* 3. if r < 0 then r = r + b^k+1
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*/
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mpi_set( r1, x );
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if( r1->nlimbs > k+1 ) /* quick modulo operation */
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r1->nlimbs = k+1;
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mpi_mul( r2, r2, m );
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if( r2->nlimbs > k+1 ) /* quick modulo operation */
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r2->nlimbs = k+1;
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mpi_sub( r, r1, r2 );
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if( mpi_is_neg( r ) ) {
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gcry_mpi_t tmp;
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tmp = mpi_alloc( k + 2 );
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mpi_set_ui( tmp, 1 );
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mpi_lshift_limbs( tmp, k+1 );
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mpi_add( r, r, tmp );
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mpi_free(tmp);
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}
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/* 4. while r >= m do r = r - m */
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while( mpi_cmp( r, m ) >= 0 )
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mpi_sub( r, r, m );
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return 0;
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}
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#endif /* USE_BARRETT */
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