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
|
/* primegen.c - prime number generator
* Copyright (c) 1997 by Werner Koch (dd9jn)
*
* This file is part of G10.
*
* G10 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.
*
* G10 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 <string.h>
#include <assert.h>
#include "util.h"
#include "mpi.h"
#include "cipher.h"
static int no_of_small_prime_numbers;
static int rabin_miller( MPI n );
static MPI gen_prime( unsigned nbits, int mode );
/****************
* Generate a prime number (stored in secure memory)
*/
MPI
generate_secret_prime( unsigned nbits )
{
return gen_prime( nbits, 1 );
}
MPI
generate_public_prime( unsigned nbits )
{
return gen_prime( nbits, 0 );
}
static MPI
gen_prime( unsigned nbits, int secret )
{
unsigned nlimbs;
MPI prime, val_2, val_3, result;
int i;
unsigned x, step;
unsigned count1, count2;
int *mods;
if( DBG_CIPHER )
log_debug("generate a prime of %u bits ", nbits );
if( !no_of_small_prime_numbers ) {
for(i=0; small_prime_numbers[i]; i++ )
no_of_small_prime_numbers++;
}
mods = m_alloc( no_of_small_prime_numbers * sizeof *mods );
/* make nbits fit into MPI implementation */
nlimbs = (nbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB;
assert( nlimbs );
val_2 = mpi_alloc( nlimbs );
mpi_set_ui(val_2, 2);
val_3 = mpi_alloc( nlimbs );
mpi_set_ui(val_3, 3);
result = mpi_alloc( nlimbs );
prime = secret? mpi_alloc_secure( nlimbs ): mpi_alloc( nlimbs );
count1 = count2 = 0;
/* enter (endless) loop */
for(;;) {
/* generate a random number */
mpi_set_bytes( prime, nbits, get_random_byte, 2 );
/* set high order bit to 1, set low order bit to 1 */
mpi_set_bit( prime, nbits-1 );
mpi_set_bit( prime, 0 );
/* calculate all remainders */
for(i=0; (x = small_prime_numbers[i]); i++ )
mods[i] = mpi_fdiv_r_ui(NULL, prime, x);
for(step=0; step < 20000; step += 2 ) {
/* check against all the small primes we have in mods */
count1++;
for(i=0; (x = small_prime_numbers[i]); i++ ) {
while( mods[i] + step >= x )
mods[i] -= x;
if( !(mods[i] + step) )
break;
}
if( x )
continue; /* found a multiple of a already known prime */
if( DBG_CIPHER )
fputc('.', stderr);
mpi_add_ui( prime, prime, step );
/* do a Fermat test */
count2++;
mpi_powm( result, val_2, prime, prime );
if( mpi_cmp_ui(result, 2) )
continue; /* stepping (fermat test failed) */
if( DBG_CIPHER )
fputc('+', stderr);
/* and a second one */
count2++;
mpi_powm( result, val_3, prime, prime );
if( mpi_cmp_ui(result, 3) )
continue; /* stepping (fermat test failed) */
if( DBG_CIPHER )
fputc('+', stderr);
/* perform Rabin-Miller tests */
for(i=5; i > 0; i-- ) {
if( DBG_CIPHER )
fputc('+', stderr);
if( rabin_miller(prime) )
break;
}
if( !i ) {
if( !mpi_test_bit( prime, nbits-1 ) ) {
if( DBG_CIPHER ) {
fputc('\n', stderr);
log_debug("overflow in prime generation\n");
break; /* step loop, cont with a new prime */
}
}
if( DBG_CIPHER ) {
fputc('\n', stderr);
log_debug("performed %u simple and %u Fermat/Rabin-Miller tests\n",
count1, count2 );
log_mpidump("found prime: ", prime );
}
mpi_free(val_2);
mpi_free(val_3);
mpi_free(result);
m_free(mods);
return prime;
}
}
if( DBG_CIPHER )
fputc(':', stderr); /* restart with a new random value */
}
}
/****************
* Return 1 if n is not a prime
*/
static int
rabin_miller( MPI n )
{
return 0;
}
|
