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
|
/* rsa.c
*
* The RSA publickey algorithm.
*/
/* nettle, low-level cryptographics library
*
* Copyright (C) 2001 Niels Möller
*
* The nettle library 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.
*
* The nettle library 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 the nettle library; see the file COPYING.LIB. If not, write to
* the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
#if HAVE_CONFIG_H
#include "config.h"
#endif
#if HAVE_LIBGMP
#include "rsa.h"
#include "bignum.h"
/* FIXME: Perhaps we should split this into several functions, so that
* one can link in the signature functions without also getting the
* verify functions. */
int
rsa_init_public_key(struct rsa_public_key *key)
{
unsigned size = (mpz_sizeinbase(key->n, 2) + 7) / 8;
/* For PKCS#1 to make sense, the size of the modulo, in octets, must
* be at least 11 + the length of the DER-encoded Digest Info.
*
* And a DigestInfo is 34 octets for md5, and 35 octets for sha1.
* 46 octets is 368 bits. */
if (size < 46)
{
/* Make sure the signing and verification functions doesn't
* try to use this key. */
key->size = 0;
return 0;
}
else
{
key->size = size;
return 1;
}
}
int
rsa_init_private_key(struct rsa_private_key *key)
{
return rsa_init_public_key(&key->pub);
}
#ifndef RSA_CRT
#define RSA_CRT 1
#endif
/* Internal function for computing an rsa root.
*
* NOTE: We don't really need n not e, so we could delete the public
* key info from struct rsa_private_key. We do need the size,
* though. */
void
rsa_compute_root(struct rsa_private_key *key, mpz_t x, mpz_t m)
{
#if RSA_CRT
{
mpz_t xp; /* modulo p */
mpz_t xq; /* modulo q */
mpz_init(xp); mpz_init(xq);
/* Compute xq = m^d % q = (m%q)^b % q */
mpz_fdiv_r(xq, m, key->q);
mpz_powm(xq, xq, key->b, key->q);
/* Compute xp = m^d % p = (m%p)^a % p */
mpz_fdiv_r(xp, m, key->p);
mpz_powm(xp, xp, key->a, key->p);
/* Set xp' = (xp - xq) c % p. */
mpz_sub(xp, xp, xq);
mpz_mul(xp, xp, key->c);
mpz_fdiv_r(xp, xp, key->p);
/* Finally, compute x = xq + q xp'
*
* To prove that this works, note that
*
* xp = x + i p,
* xq = x + j q,
* c q = 1 + k p
*
* for some integers i, j and k. Now, for some integer l,
*
* xp' = (xp - xq) c + l p
* = (x + i p - (x + j q)) c + l p
* = (i p - j q) c + l p
* = (i c + l) p - j (c q)
* = (i c + l) p - j (1 + kp)
* = (i c + l - j k) p - j
*
* which shows that xp' = -j (mod p). We get
*
* xq + q xp' = x + j q + (i c + l - j k) p q - j q
* = x + (i c + l - j k) p q
*
* so that
*
* xq + q xp' = x (mod pq)
*
* We also get 0 <= xq + q xp' < p q, because
*
* 0 <= xq < q and 0 <= xp' < p.
*/
mpz_mul(x, key->q, xp);
mpz_add(x, x, xq);
mpz_clear(xp); mpz_clear(xq);
}
#else /* !RSA_CRT */
mpz_powm(x, m, key->d, key->pub->n);
#endif /* !RSA_CRT */
}
#endif /* HAVE_LIBGMP */
|
