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d02b48c6 1/* crypto/bn/bn_recp.c */
58964a49 2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
d02b48c6
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3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
0f113f3e 8 *
d02b48c6
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9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
0f113f3e 15 *
d02b48c6
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16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
0f113f3e 22 *
d02b48c6
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23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
0f113f3e 37 * 4. If you include any Windows specific code (or a derivative thereof) from
d02b48c6
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38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
0f113f3e 40 *
d02b48c6
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41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
0f113f3e 52 *
d02b48c6
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53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58
b39fc560 59#include "internal/cryptlib.h"
d02b48c6
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60#include "bn_lcl.h"
61
6b691a5c 62void BN_RECP_CTX_init(BN_RECP_CTX *recp)
0f113f3e
MC
63{
64 BN_init(&(recp->N));
65 BN_init(&(recp->Nr));
66 recp->num_bits = 0;
67 recp->flags = 0;
68}
dfeab068 69
6b691a5c 70BN_RECP_CTX *BN_RECP_CTX_new(void)
0f113f3e
MC
71{
72 BN_RECP_CTX *ret;
dfeab068 73
b4faea50 74 if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
0f113f3e 75 return (NULL);
dfeab068 76
0f113f3e
MC
77 BN_RECP_CTX_init(ret);
78 ret->flags = BN_FLG_MALLOCED;
79 return (ret);
80}
dfeab068 81
6b691a5c 82void BN_RECP_CTX_free(BN_RECP_CTX *recp)
0f113f3e
MC
83{
84 if (recp == NULL)
85 return;
e03ddfae 86
0f113f3e
MC
87 BN_free(&(recp->N));
88 BN_free(&(recp->Nr));
89 if (recp->flags & BN_FLG_MALLOCED)
90 OPENSSL_free(recp);
91}
dfeab068 92
84c15db5 93int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)
0f113f3e
MC
94{
95 if (!BN_copy(&(recp->N), d))
96 return 0;
97 BN_zero(&(recp->Nr));
98 recp->num_bits = BN_num_bits(d);
99 recp->shift = 0;
100 return (1);
101}
dfeab068 102
020fc820 103int BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
0f113f3e
MC
104 BN_RECP_CTX *recp, BN_CTX *ctx)
105{
106 int ret = 0;
107 BIGNUM *a;
108 const BIGNUM *ca;
109
110 BN_CTX_start(ctx);
111 if ((a = BN_CTX_get(ctx)) == NULL)
112 goto err;
113 if (y != NULL) {
114 if (x == y) {
115 if (!BN_sqr(a, x, ctx))
116 goto err;
117 } else {
118 if (!BN_mul(a, x, y, ctx))
119 goto err;
120 }
121 ca = a;
122 } else
123 ca = x; /* Just do the mod */
124
125 ret = BN_div_recp(NULL, r, ca, recp, ctx);
126 err:
127 BN_CTX_end(ctx);
128 bn_check_top(r);
129 return (ret);
130}
dfeab068 131
020fc820 132int BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m,
0f113f3e
MC
133 BN_RECP_CTX *recp, BN_CTX *ctx)
134{
135 int i, j, ret = 0;
136 BIGNUM *a, *b, *d, *r;
137
138 BN_CTX_start(ctx);
139 a = BN_CTX_get(ctx);
140 b = BN_CTX_get(ctx);
141 if (dv != NULL)
142 d = dv;
143 else
144 d = BN_CTX_get(ctx);
145 if (rem != NULL)
146 r = rem;
147 else
148 r = BN_CTX_get(ctx);
149 if (a == NULL || b == NULL || d == NULL || r == NULL)
150 goto err;
151
152 if (BN_ucmp(m, &(recp->N)) < 0) {
153 BN_zero(d);
154 if (!BN_copy(r, m))
155 return 0;
156 BN_CTX_end(ctx);
157 return (1);
158 }
159
160 /*
161 * We want the remainder Given input of ABCDEF / ab we need multiply
162 * ABCDEF by 3 digests of the reciprocal of ab
163 */
164
165 /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
166 i = BN_num_bits(m);
167 j = recp->num_bits << 1;
168 if (j > i)
169 i = j;
170
171 /* Nr := round(2^i / N) */
172 if (i != recp->shift)
173 recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);
174 /* BN_reciprocal could have returned -1 for an error */
175 if (recp->shift == -1)
176 goto err;
dfeab068 177
e95bbc3c
AP
178 /*-
179 * d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
180 * = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
181 * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
182 * = |m/N|
183 */
0f113f3e
MC
184 if (!BN_rshift(a, m, recp->num_bits))
185 goto err;
186 if (!BN_mul(b, a, &(recp->Nr), ctx))
187 goto err;
188 if (!BN_rshift(d, b, i - recp->num_bits))
189 goto err;
190 d->neg = 0;
191
192 if (!BN_mul(b, &(recp->N), d, ctx))
193 goto err;
194 if (!BN_usub(r, m, b))
195 goto err;
196 r->neg = 0;
dfeab068 197
0f113f3e
MC
198 j = 0;
199 while (BN_ucmp(r, &(recp->N)) >= 0) {
200 if (j++ > 2) {
201 BNerr(BN_F_BN_DIV_RECP, BN_R_BAD_RECIPROCAL);
202 goto err;
203 }
204 if (!BN_usub(r, r, &(recp->N)))
205 goto err;
206 if (!BN_add_word(d, 1))
207 goto err;
208 }
d02b48c6 209
0f113f3e
MC
210 r->neg = BN_is_zero(r) ? 0 : m->neg;
211 d->neg = m->neg ^ recp->N.neg;
212 ret = 1;
213 err:
214 BN_CTX_end(ctx);
215 bn_check_top(dv);
216 bn_check_top(rem);
217 return (ret);
218}
219
220/*
221 * len is the expected size of the result We actually calculate with an extra
222 * word of precision, so we can do faster division if the remainder is not
223 * required.
dfeab068 224 */
78a0c1f1 225/* r := 2^len / m */
6343829a 226int BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)
0f113f3e
MC
227{
228 int ret = -1;
229 BIGNUM *t;
230
231 BN_CTX_start(ctx);
232 if ((t = BN_CTX_get(ctx)) == NULL)
233 goto err;
234
235 if (!BN_set_bit(t, len))
236 goto err;
237
238 if (!BN_div(r, NULL, t, m, ctx))
239 goto err;
240
241 ret = len;
242 err:
243 bn_check_top(r);
244 BN_CTX_end(ctx);
245 return (ret);
246}