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/* mpi-mpow.c - MPI functions
* Copyright (C) 1998, 1999 Free Software Foundation, Inc.
*
* This file is part of Libgcrypt.
*
* Libgcrypt 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.
*
* Libgcrypt 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 this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*/
#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include "mpi-internal.h"
#include "longlong.h"
#include <assert.h>
/* Barrett is slower than the classical way. It can be tweaked by
* using partial multiplications
*/
/*#define USE_BARRETT*/
#ifdef USE_BARRETT
static void barrett_mulm( MPI w, MPI u, MPI v, MPI m, MPI y, int k, MPI r1, MPI r2 );
static MPI init_barrett( MPI m, int *k, MPI *r1, MPI *r2 );
static int calc_barrett( MPI r, MPI x, MPI m, MPI y, int k, MPI r1, MPI r2 );
#else
#define barrett_mulm( w, u, v, m, y, k, r1, r2 ) mpi_mulm( (w), (u), (v), (m) )
#endif
static int
build_index( MPI *exparray, int k, int i, int t )
{
int j, bitno;
int idx = 0;
bitno = t-i;
for(j=k-1; j >= 0; j-- ) {
idx <<= 1;
if( mpi_test_bit( exparray[j], bitno ) )
idx |= 1;
}
/*log_debug("t=%d i=%d idx=%d\n", t, i, idx );*/
return idx;
}
/****************
* RES = (BASE[0] ^ EXP[0]) * (BASE[1] ^ EXP[1]) * ... * mod M
*/
void
mpi_mulpowm( MPI res, MPI *basearray, MPI *exparray, MPI m)
{
int k; /* number of elements */
int t; /* bit size of largest exponent */
int i, j, idx;
MPI *G; /* table with precomputed values of size 2^k */
MPI tmp;
#ifdef USE_BARRETT
MPI barrett_y, barrett_r1, barrett_r2;
int barrett_k;
#endif
for(k=0; basearray[k]; k++ )
;
assert(k);
for(t=0, i=0; (tmp=exparray[i]); i++ ) {
/*log_mpidump("exp: ", tmp );*/
j = mpi_get_nbits(tmp);
if( j > t )
t = j;
}
/*log_mpidump("mod: ", m );*/
assert(i==k);
assert(t);
assert( k < 10 );
G = g10_xcalloc( (1<<k) , sizeof *G );
#ifdef USE_BARRETT
barrett_y = init_barrett( m, &barrett_k, &barrett_r1, &barrett_r2 );
#endif
/* and calculate */
tmp = mpi_alloc( mpi_get_nlimbs(m)+1 );
mpi_set_ui( res, 1 );
for(i = 1; i <= t; i++ ) {
barrett_mulm(tmp, res, res, m, barrett_y, barrett_k,
barrett_r1, barrett_r2 );
idx = build_index( exparray, k, i, t );
assert( idx >= 0 && idx < (1<<k) );
if( !G[idx] ) {
if( !idx )
G[0] = mpi_alloc_set_ui( 1 );
else {
for(j=0; j < k; j++ ) {
if( (idx & (1<<j) ) ) {
if( !G[idx] )
G[idx] = mpi_copy( basearray[j] );
else
barrett_mulm( G[idx], G[idx], basearray[j],
m, barrett_y, barrett_k, barrett_r1, barrett_r2 );
}
}
if( !G[idx] )
G[idx] = mpi_alloc(0);
}
}
barrett_mulm(res, tmp, G[idx], m, barrett_y, barrett_k, barrett_r1, barrett_r2 );
}
/* cleanup */
mpi_free(tmp);
#ifdef USE_BARRETT
mpi_free(barrett_y);
mpi_free(barrett_r1);
mpi_free(barrett_r2);
#endif
for(i=0; i < (1<<k); i++ )
mpi_free(G[i]);
g10_free(G);
}
#ifdef USE_BARRETT
static void
barrett_mulm( MPI w, MPI u, MPI v, MPI m, MPI y, int k, MPI r1, MPI r2 )
{
mpi_mul(w, u, v);
if( calc_barrett( w, w, m, y, k, r1, r2 ) )
mpi_fdiv_r( w, w, m );
}
/****************
* Barrett precalculation: y = floor(b^(2k) / m)
*/
static MPI
init_barrett( MPI m, int *k, MPI *r1, MPI *r2 )
{
MPI tmp;
mpi_normalize( m );
*k = mpi_get_nlimbs( m );
tmp = mpi_alloc( *k + 1 );
mpi_set_ui( tmp, 1 );
mpi_lshift_limbs( tmp, 2 * *k );
mpi_fdiv_q( tmp, tmp, m );
*r1 = mpi_alloc( 2* *k + 1 );
*r2 = mpi_alloc( 2* *k + 1 );
return tmp;
}
/****************
* Barrett reduction: We assume that these conditions are met:
* Given x =(x_2k-1 ...x_0)_b
* m =(m_k-1 ....m_0)_b with m_k-1 != 0
* Output r = x mod m
* Before using this function init_barret must be used to calucalte y and k.
* Returns: false = no error
* true = can't perform barret reduction
*/
static int
calc_barrett( MPI r, MPI x, MPI m, MPI y, int k, MPI r1, MPI r2 )
{
int xx = k > 3 ? k-3:0;
mpi_normalize( x );
if( mpi_get_nlimbs(x) > 2*k )
return 1; /* can't do it */
/* 1. q1 = floor( x / b^k-1)
* q2 = q1 * y
* q3 = floor( q2 / b^k+1 )
* Actually, we don't need qx, we can work direct on r2
*/
mpi_set( r2, x );
mpi_rshift_limbs( r2, k-1 );
mpi_mul( r2, r2, y );
mpi_rshift_limbs( r2, k+1 );
/* 2. r1 = x mod b^k+1
* r2 = q3 * m mod b^k+1
* r = r1 - r2
* 3. if r < 0 then r = r + b^k+1
*/
mpi_set( r1, x );
if( r1->nlimbs > k+1 ) /* quick modulo operation */
r1->nlimbs = k+1;
mpi_mul( r2, r2, m );
if( r2->nlimbs > k+1 ) /* quick modulo operation */
r2->nlimbs = k+1;
mpi_sub( r, r1, r2 );
if( mpi_is_neg( r ) ) {
MPI tmp;
tmp = mpi_alloc( k + 2 );
mpi_set_ui( tmp, 1 );
mpi_lshift_limbs( tmp, k+1 );
mpi_add( r, r, tmp );
mpi_free(tmp);
}
/* 4. while r >= m do r = r - m */
while( mpi_cmp( r, m ) >= 0 )
mpi_sub( r, r, m );
return 0;
}
#endif /* USE_BARRETT */
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