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
|
/*
* Copyright 1995-2023 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the Apache License 2.0 (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
*/
#include "internal/cryptlib.h"
#include "bn_local.h"
void BN_RECP_CTX_init(BN_RECP_CTX *recp)
{
memset(recp, 0, sizeof(*recp));
bn_init(&(recp->N));
bn_init(&(recp->Nr));
}
BN_RECP_CTX *BN_RECP_CTX_new(void)
{
BN_RECP_CTX *ret;
if ((ret = OPENSSL_zalloc(sizeof(*ret))) == NULL) {
ERR_raise(ERR_LIB_BN, ERR_R_MALLOC_FAILURE);
return NULL;
}
bn_init(&(ret->N));
bn_init(&(ret->Nr));
ret->flags = BN_FLG_MALLOCED;
return ret;
}
void BN_RECP_CTX_free(BN_RECP_CTX *recp)
{
if (recp == NULL)
return;
BN_free(&recp->N);
BN_free(&recp->Nr);
if (recp->flags & BN_FLG_MALLOCED)
OPENSSL_free(recp);
}
int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)
{
if (BN_is_zero(d) || !BN_copy(&(recp->N), d))
return 0;
BN_zero(&(recp->Nr));
recp->num_bits = BN_num_bits(d);
recp->shift = 0;
return 1;
}
int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
BN_RECP_CTX *recp, BN_CTX *ctx)
{
int ret = 0;
BIGNUM *a;
const BIGNUM *ca;
BN_CTX_start(ctx);
if ((a = BN_CTX_get(ctx)) == NULL)
goto err;
if (y != NULL) {
if (x == y) {
if (!BN_sqr(a, x, ctx))
goto err;
} else {
if (!BN_mul(a, x, y, ctx))
goto err;
}
ca = a;
} else
ca = x; /* Just do the mod */
ret = BN_div_recp(NULL, r, ca, recp, ctx);
err:
BN_CTX_end(ctx);
bn_check_top(r);
return ret;
}
int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
BN_RECP_CTX *recp, BN_CTX *ctx)
{
int i, j, ret = 0;
BIGNUM *a, *b, *d, *r;
BN_CTX_start(ctx);
d = (dv != NULL) ? dv : BN_CTX_get(ctx);
r = (rem != NULL) ? rem : BN_CTX_get(ctx);
a = BN_CTX_get(ctx);
b = BN_CTX_get(ctx);
if (b == NULL)
goto err;
if (BN_ucmp(m, &(recp->N)) < 0) {
BN_zero(d);
if (!BN_copy(r, m)) {
BN_CTX_end(ctx);
return 0;
}
BN_CTX_end(ctx);
return 1;
}
/*
* We want the remainder Given input of ABCDEF / ab we need multiply
* ABCDEF by 3 digests of the reciprocal of ab
*/
/* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
i = BN_num_bits(m);
j = recp->num_bits << 1;
if (j > i)
i = j;
/* Nr := round(2^i / N) */
if (i != recp->shift)
recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);
/* BN_reciprocal could have returned -1 for an error */
if (recp->shift == -1)
goto err;
/*-
* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
* = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
* <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
* = |m/N|
*/
if (!BN_rshift(a, m, recp->num_bits))
goto err;
if (!BN_mul(b, a, &(recp->Nr), ctx))
goto err;
if (!BN_rshift(d, b, i - recp->num_bits))
goto err;
d->neg = 0;
if (!BN_mul(b, &(recp->N), d, ctx))
goto err;
if (!BN_usub(r, m, b))
goto err;
r->neg = 0;
j = 0;
while (BN_ucmp(r, &(recp->N)) >= 0) {
if (j++ > 2) {
ERR_raise(ERR_LIB_BN, BN_R_BAD_RECIPROCAL);
goto err;
}
if (!BN_usub(r, r, &(recp->N)))
goto err;
if (!BN_add_word(d, 1))
goto err;
}
r->neg = BN_is_zero(r) ? 0 : m->neg;
d->neg = m->neg ^ recp->N.neg;
ret = 1;
err:
BN_CTX_end(ctx);
bn_check_top(dv);
bn_check_top(rem);
return ret;
}
/*
* len is the expected size of the result We actually calculate with an extra
* word of precision, so we can do faster division if the remainder is not
* required.
*/
/* r := 2^len / m */
int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)
{
int ret = -1;
BIGNUM *t;
BN_CTX_start(ctx);
if ((t = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_set_bit(t, len))
goto err;
if (!BN_div(r, NULL, t, m, ctx))
goto err;
ret = len;
err:
bn_check_top(r);
BN_CTX_end(ctx);
return ret;
}
|