1 /* $OpenBSD: bn_recp.c,v 1.15 2017/01/29 17:49:22 beck Exp $ */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
8 *
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).
15 *
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.
22 *
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 :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
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.
52 *
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
59 #include <stdio.h>
60
61 #include <openssl/err.h>
62
63 #include "bn_lcl.h"
64
65 void
BN_RECP_CTX_init(BN_RECP_CTX * recp)66 BN_RECP_CTX_init(BN_RECP_CTX *recp)
67 {
68 BN_init(&(recp->N));
69 BN_init(&(recp->Nr));
70 recp->num_bits = 0;
71 recp->flags = 0;
72 }
73
74 BN_RECP_CTX *
BN_RECP_CTX_new(void)75 BN_RECP_CTX_new(void)
76 {
77 BN_RECP_CTX *ret;
78
79 if ((ret = malloc(sizeof(BN_RECP_CTX))) == NULL)
80 return (NULL);
81
82 BN_RECP_CTX_init(ret);
83 ret->flags = BN_FLG_MALLOCED;
84 return (ret);
85 }
86
87 void
BN_RECP_CTX_free(BN_RECP_CTX * recp)88 BN_RECP_CTX_free(BN_RECP_CTX *recp)
89 {
90 if (recp == NULL)
91 return;
92
93 BN_free(&(recp->N));
94 BN_free(&(recp->Nr));
95 if (recp->flags & BN_FLG_MALLOCED)
96 free(recp);
97 }
98
99 int
BN_RECP_CTX_set(BN_RECP_CTX * recp,const BIGNUM * d,BN_CTX * ctx)100 BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)
101 {
102 if (!BN_copy(&(recp->N), d))
103 return 0;
104 BN_zero(&(recp->Nr));
105 recp->num_bits = BN_num_bits(d);
106 recp->shift = 0;
107 return (1);
108 }
109
110 int
BN_mod_mul_reciprocal(BIGNUM * r,const BIGNUM * x,const BIGNUM * y,BN_RECP_CTX * recp,BN_CTX * ctx)111 BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,
112 BN_RECP_CTX *recp, BN_CTX *ctx)
113 {
114 int ret = 0;
115 BIGNUM *a;
116 const BIGNUM *ca;
117
118 BN_CTX_start(ctx);
119 if ((a = BN_CTX_get(ctx)) == NULL)
120 goto err;
121 if (y != NULL) {
122 if (x == y) {
123 if (!BN_sqr(a, x, ctx))
124 goto err;
125 } else {
126 if (!BN_mul(a, x, y, ctx))
127 goto err;
128 }
129 ca = a;
130 } else
131 ca = x; /* Just do the mod */
132
133 ret = BN_div_recp(NULL, r, ca, recp, ctx);
134
135 err:
136 BN_CTX_end(ctx);
137 bn_check_top(r);
138 return (ret);
139 }
140
141 int
BN_div_recp(BIGNUM * dv,BIGNUM * rem,const BIGNUM * m,BN_RECP_CTX * recp,BN_CTX * ctx)142 BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, BN_RECP_CTX *recp,
143 BN_CTX *ctx)
144 {
145 int i, j, ret = 0;
146 BIGNUM *a, *b, *d, *r;
147
148 BN_CTX_start(ctx);
149 a = BN_CTX_get(ctx);
150 b = BN_CTX_get(ctx);
151 if (dv != NULL)
152 d = dv;
153 else
154 d = BN_CTX_get(ctx);
155 if (rem != NULL)
156 r = rem;
157 else
158 r = BN_CTX_get(ctx);
159 if (a == NULL || b == NULL || d == NULL || r == NULL)
160 goto err;
161
162 if (BN_ucmp(m, &(recp->N)) < 0) {
163 BN_zero(d);
164 if (!BN_copy(r, m)) {
165 BN_CTX_end(ctx);
166 return 0;
167 }
168 BN_CTX_end(ctx);
169 return (1);
170 }
171
172 /* We want the remainder
173 * Given input of ABCDEF / ab
174 * we need multiply ABCDEF by 3 digests of the reciprocal of ab
175 *
176 */
177
178 /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */
179 i = BN_num_bits(m);
180 j = recp->num_bits << 1;
181 if (j > i)
182 i = j;
183
184 /* Nr := round(2^i / N) */
185 if (i != recp->shift)
186 recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);
187
188 /* BN_reciprocal returns i, or -1 for an error */
189 if (recp->shift == -1)
190 goto err;
191
192 /* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|
193 * = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|
194 * <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|
195 * = |m/N|
196 */
197 if (!BN_rshift(a, m, recp->num_bits))
198 goto err;
199 if (!BN_mul(b, a,&(recp->Nr), ctx))
200 goto err;
201 if (!BN_rshift(d, b, i - recp->num_bits))
202 goto err;
203 d->neg = 0;
204
205 if (!BN_mul(b, &(recp->N), d, ctx))
206 goto err;
207 if (!BN_usub(r, m, b))
208 goto err;
209 r->neg = 0;
210
211 #if 1
212 j = 0;
213 while (BN_ucmp(r, &(recp->N)) >= 0) {
214 if (j++ > 2) {
215 BNerror(BN_R_BAD_RECIPROCAL);
216 goto err;
217 }
218 if (!BN_usub(r, r, &(recp->N)))
219 goto err;
220 if (!BN_add_word(d, 1))
221 goto err;
222 }
223 #endif
224
225 r->neg = BN_is_zero(r) ? 0 : m->neg;
226 d->neg = m->neg^recp->N.neg;
227 ret = 1;
228
229 err:
230 BN_CTX_end(ctx);
231 bn_check_top(dv);
232 bn_check_top(rem);
233 return (ret);
234 }
235
236 /* len is the expected size of the result
237 * We actually calculate with an extra word of precision, so
238 * we can do faster division if the remainder is not required.
239 */
240 /* r := 2^len / m */
241 int
BN_reciprocal(BIGNUM * r,const BIGNUM * m,int len,BN_CTX * ctx)242 BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)
243 {
244 int ret = -1;
245 BIGNUM *t;
246
247 BN_CTX_start(ctx);
248 if ((t = BN_CTX_get(ctx)) == NULL)
249 goto err;
250
251 if (!BN_set_bit(t, len))
252 goto err;
253
254 if (!BN_div_ct(r, NULL, t,m, ctx))
255 goto err;
256
257 ret = len;
258
259 err:
260 bn_check_top(r);
261 BN_CTX_end(ctx);
262 return (ret);
263 }
264