1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
|
/* mpi-mpow.c - MPI functions
* Copyright (C) 1998, 1999, 2001, 2002, 2003 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 Lesser General Public License as
* published by the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser 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 "g10lib.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( 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 );
static gcry_mpi_t init_barrett( gcry_mpi_t m, int *k, gcry_mpi_t *r1, gcry_mpi_t *r2 );
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 );
#else
#define barrett_mulm( w, u, v, m, y, k, r1, r2 ) _gcry_mpi_mulm( (w), (u), (v), (m) )
#endif
static int
build_index( gcry_mpi_t *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
_gcry_mpi_mulpowm( gcry_mpi_t res, gcry_mpi_t *basearray, gcry_mpi_t *exparray, gcry_mpi_t m)
{
int k; /* number of elements */
int t; /* bit size of largest exponent */
int i, j, idx;
gcry_mpi_t *G; /* table with precomputed values of size 2^k */
gcry_mpi_t tmp;
#ifdef USE_BARRETT
gcry_mpi_t barrett_y, barrett_r1, barrett_r2;
int barrett_k;
#endif
for(k=0; basearray[k]; k++ )
;
gcry_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 );*/
gcry_assert (i==k);
gcry_assert (t);
gcry_assert (k < 10);
G = 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 );
gcry_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]);
xfree(G);
}
#ifdef USE_BARRETT
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 )
{
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 gcry_mpi_t
init_barrett( gcry_mpi_t m, int *k, gcry_mpi_t *r1, gcry_mpi_t *r2 )
{
gcry_mpi_t 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( 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 )
{
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_has_sign (r) ) {
gcry_mpi_t 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 */
|
