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
|
#include <machine/rtems-bsd-user-space.h>
/*
* Copyright 1995-2019 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
/*
* NB: These functions have been upgraded - the previous prototypes are in
* dh_depr.c as wrappers to these ones. - Geoff
*/
#include <stdio.h>
#include "internal/cryptlib.h"
#include <openssl/bn.h>
#include "dh_locl.h"
static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
BN_GENCB *cb);
int DH_generate_parameters_ex(DH *ret, int prime_len, int generator,
BN_GENCB *cb)
{
if (ret->meth->generate_params)
return ret->meth->generate_params(ret, prime_len, generator, cb);
return dh_builtin_genparams(ret, prime_len, generator, cb);
}
/*-
* We generate DH parameters as follows
* find a prime p which is prime_len bits long,
* where q=(p-1)/2 is also prime.
* In the following we assume that g is not 0, 1 or p-1, since it
* would generate only trivial subgroups.
* For this case, g is a generator of the order-q subgroup if
* g^q mod p == 1.
* Or in terms of the Legendre symbol: (g/p) == 1.
*
* Having said all that,
* there is another special case method for the generators 2, 3 and 5.
* Using the quadratic reciprocity law it is possible to solve
* (g/p) == 1 for the special values 2, 3, 5:
* (2/p) == 1 if p mod 8 == 1 or 7.
* (3/p) == 1 if p mod 12 == 1 or 11.
* (5/p) == 1 if p mod 5 == 1 or 4.
* See for instance: https://en.wikipedia.org/wiki/Legendre_symbol
*
* Since all safe primes > 7 must satisfy p mod 12 == 11
* and all safe primes > 11 must satisfy p mod 5 != 1
* we can further improve the condition for g = 2, 3 and 5:
* for 2, p mod 24 == 23
* for 3, p mod 12 == 11
* for 5, p mod 60 == 59
*
* However for compatibilty with previous versions we use:
* for 2, p mod 24 == 11
* for 5, p mod 60 == 23
*/
static int dh_builtin_genparams(DH *ret, int prime_len, int generator,
BN_GENCB *cb)
{
BIGNUM *t1, *t2;
int g, ok = -1;
BN_CTX *ctx = NULL;
ctx = BN_CTX_new();
if (ctx == NULL)
goto err;
BN_CTX_start(ctx);
t1 = BN_CTX_get(ctx);
t2 = BN_CTX_get(ctx);
if (t2 == NULL)
goto err;
/* Make sure 'ret' has the necessary elements */
if (!ret->p && ((ret->p = BN_new()) == NULL))
goto err;
if (!ret->g && ((ret->g = BN_new()) == NULL))
goto err;
if (generator <= 1) {
DHerr(DH_F_DH_BUILTIN_GENPARAMS, DH_R_BAD_GENERATOR);
goto err;
}
if (generator == DH_GENERATOR_2) {
if (!BN_set_word(t1, 24))
goto err;
if (!BN_set_word(t2, 11))
goto err;
g = 2;
} else if (generator == DH_GENERATOR_5) {
if (!BN_set_word(t1, 60))
goto err;
if (!BN_set_word(t2, 23))
goto err;
g = 5;
} else {
/*
* in the general case, don't worry if 'generator' is a generator or
* not: since we are using safe primes, it will generate either an
* order-q or an order-2q group, which both is OK
*/
if (!BN_set_word(t1, 12))
goto err;
if (!BN_set_word(t2, 11))
goto err;
g = generator;
}
if (!BN_generate_prime_ex(ret->p, prime_len, 1, t1, t2, cb))
goto err;
if (!BN_GENCB_call(cb, 3, 0))
goto err;
if (!BN_set_word(ret->g, g))
goto err;
ok = 1;
err:
if (ok == -1) {
DHerr(DH_F_DH_BUILTIN_GENPARAMS, ERR_R_BN_LIB);
ok = 0;
}
BN_CTX_end(ctx);
BN_CTX_free(ctx);
return ok;
}
|
