Line data Source code
1 : /* mpi-mpow.c - MPI functions
2 : * Copyright (C) 1998, 1999, 2001, 2002, 2003 Free Software Foundation, Inc.
3 : *
4 : * This file is part of Libgcrypt.
5 : *
6 : * Libgcrypt is free software; you can redistribute it and/or modify
7 : * it under the terms of the GNU Lesser General Public License as
8 : * published by the Free Software Foundation; either version 2.1 of
9 : * the License, or (at your option) any later version.
10 : *
11 : * Libgcrypt is distributed in the hope that it will be useful,
12 : * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 : * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 : * GNU Lesser General Public License for more details.
15 : *
16 : * You should have received a copy of the GNU Lesser General Public
17 : * License along with this program; if not, write to the Free Software
18 : * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
19 : */
20 :
21 : #include <config.h>
22 : #include <stdio.h>
23 : #include <stdlib.h>
24 :
25 : #include "mpi-internal.h"
26 : #include "longlong.h"
27 : #include "g10lib.h"
28 :
29 :
30 : /* Barrett is slower than the classical way. It can be tweaked by
31 : * using partial multiplications
32 : */
33 : /*#define USE_BARRETT*/
34 :
35 :
36 :
37 : #ifdef USE_BARRETT
38 : 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 );
39 : static gcry_mpi_t init_barrett( gcry_mpi_t m, int *k, gcry_mpi_t *r1, gcry_mpi_t *r2 );
40 : 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 );
41 : #else
42 : #define barrett_mulm( w, u, v, m, y, k, r1, r2 ) _gcry_mpi_mulm( (w), (u), (v), (m) )
43 : #endif
44 :
45 :
46 : static int
47 0 : build_index( gcry_mpi_t *exparray, int k, int i, int t )
48 : {
49 : int j, bitno;
50 0 : int idx = 0;
51 :
52 0 : bitno = t-i;
53 0 : for(j=k-1; j >= 0; j-- ) {
54 0 : idx <<= 1;
55 0 : if( mpi_test_bit( exparray[j], bitno ) )
56 0 : idx |= 1;
57 : }
58 : /*log_debug("t=%d i=%d idx=%d\n", t, i, idx );*/
59 0 : return idx;
60 : }
61 :
62 : /****************
63 : * RES = (BASE[0] ^ EXP[0]) * (BASE[1] ^ EXP[1]) * ... * mod M
64 : */
65 : void
66 0 : _gcry_mpi_mulpowm( gcry_mpi_t res, gcry_mpi_t *basearray, gcry_mpi_t *exparray, gcry_mpi_t m)
67 : {
68 : int k; /* number of elements */
69 : int t; /* bit size of largest exponent */
70 : int i, j, idx;
71 : gcry_mpi_t *G; /* table with precomputed values of size 2^k */
72 : gcry_mpi_t tmp;
73 : #ifdef USE_BARRETT
74 : gcry_mpi_t barrett_y, barrett_r1, barrett_r2;
75 : int barrett_k;
76 : #endif
77 :
78 0 : for(k=0; basearray[k]; k++ )
79 : ;
80 0 : gcry_assert(k);
81 0 : for(t=0, i=0; (tmp=exparray[i]); i++ ) {
82 : /*log_mpidump("exp: ", tmp );*/
83 0 : j = mpi_get_nbits(tmp);
84 0 : if( j > t )
85 0 : t = j;
86 : }
87 : /*log_mpidump("mod: ", m );*/
88 0 : gcry_assert (i==k);
89 0 : gcry_assert (t);
90 0 : gcry_assert (k < 10);
91 :
92 0 : G = xcalloc( (1<<k) , sizeof *G );
93 : #ifdef USE_BARRETT
94 : barrett_y = init_barrett( m, &barrett_k, &barrett_r1, &barrett_r2 );
95 : #endif
96 : /* and calculate */
97 0 : tmp = mpi_alloc( mpi_get_nlimbs(m)+1 );
98 0 : mpi_set_ui( res, 1 );
99 0 : for(i = 1; i <= t; i++ ) {
100 0 : barrett_mulm(tmp, res, res, m, barrett_y, barrett_k,
101 : barrett_r1, barrett_r2 );
102 0 : idx = build_index( exparray, k, i, t );
103 0 : gcry_assert (idx >= 0 && idx < (1<<k));
104 0 : if( !G[idx] ) {
105 0 : if( !idx )
106 0 : G[0] = mpi_alloc_set_ui( 1 );
107 : else {
108 0 : for(j=0; j < k; j++ ) {
109 0 : if( (idx & (1<<j) ) ) {
110 0 : if( !G[idx] )
111 0 : G[idx] = mpi_copy( basearray[j] );
112 : else
113 0 : barrett_mulm( G[idx], G[idx], basearray[j],
114 : m, barrett_y, barrett_k, barrett_r1, barrett_r2 );
115 : }
116 : }
117 0 : if( !G[idx] )
118 0 : G[idx] = mpi_alloc(0);
119 : }
120 : }
121 0 : barrett_mulm(res, tmp, G[idx], m, barrett_y, barrett_k, barrett_r1, barrett_r2 );
122 : }
123 :
124 : /* cleanup */
125 0 : mpi_free(tmp);
126 : #ifdef USE_BARRETT
127 : mpi_free(barrett_y);
128 : mpi_free(barrett_r1);
129 : mpi_free(barrett_r2);
130 : #endif
131 0 : for(i=0; i < (1<<k); i++ )
132 0 : mpi_free(G[i]);
133 0 : xfree(G);
134 0 : }
135 :
136 :
137 :
138 : #ifdef USE_BARRETT
139 : static void
140 : 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 )
141 : {
142 : mpi_mul(w, u, v);
143 : if( calc_barrett( w, w, m, y, k, r1, r2 ) )
144 : mpi_fdiv_r( w, w, m );
145 : }
146 :
147 : /****************
148 : * Barrett precalculation: y = floor(b^(2k) / m)
149 : */
150 : static gcry_mpi_t
151 : init_barrett( gcry_mpi_t m, int *k, gcry_mpi_t *r1, gcry_mpi_t *r2 )
152 : {
153 : gcry_mpi_t tmp;
154 :
155 : mpi_normalize( m );
156 : *k = mpi_get_nlimbs( m );
157 : tmp = mpi_alloc( *k + 1 );
158 : mpi_set_ui( tmp, 1 );
159 : mpi_lshift_limbs( tmp, 2 * *k );
160 : mpi_fdiv_q( tmp, tmp, m );
161 : *r1 = mpi_alloc( 2* *k + 1 );
162 : *r2 = mpi_alloc( 2* *k + 1 );
163 : return tmp;
164 : }
165 :
166 : /****************
167 : * Barrett reduction: We assume that these conditions are met:
168 : * Given x =(x_2k-1 ...x_0)_b
169 : * m =(m_k-1 ....m_0)_b with m_k-1 != 0
170 : * Output r = x mod m
171 : * Before using this function init_barret must be used to calucalte y and k.
172 : * Returns: false = no error
173 : * true = can't perform barret reduction
174 : */
175 : static int
176 : 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 )
177 : {
178 : int xx = k > 3 ? k-3:0;
179 :
180 : mpi_normalize( x );
181 : if( mpi_get_nlimbs(x) > 2*k )
182 : return 1; /* can't do it */
183 :
184 : /* 1. q1 = floor( x / b^k-1)
185 : * q2 = q1 * y
186 : * q3 = floor( q2 / b^k+1 )
187 : * Actually, we don't need qx, we can work direct on r2
188 : */
189 : mpi_set( r2, x );
190 : mpi_rshift_limbs( r2, k-1 );
191 : mpi_mul( r2, r2, y );
192 : mpi_rshift_limbs( r2, k+1 );
193 :
194 : /* 2. r1 = x mod b^k+1
195 : * r2 = q3 * m mod b^k+1
196 : * r = r1 - r2
197 : * 3. if r < 0 then r = r + b^k+1
198 : */
199 : mpi_set( r1, x );
200 : if( r1->nlimbs > k+1 ) /* quick modulo operation */
201 : r1->nlimbs = k+1;
202 : mpi_mul( r2, r2, m );
203 : if( r2->nlimbs > k+1 ) /* quick modulo operation */
204 : r2->nlimbs = k+1;
205 : mpi_sub( r, r1, r2 );
206 :
207 : if( mpi_has_sign (r) ) {
208 : gcry_mpi_t tmp;
209 :
210 : tmp = mpi_alloc( k + 2 );
211 : mpi_set_ui( tmp, 1 );
212 : mpi_lshift_limbs( tmp, k+1 );
213 : mpi_add( r, r, tmp );
214 : mpi_free(tmp);
215 : }
216 :
217 : /* 4. while r >= m do r = r - m */
218 : while( mpi_cmp( r, m ) >= 0 )
219 : mpi_sub( r, r, m );
220 :
221 : return 0;
222 : }
223 : #endif /* USE_BARRETT */
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