1 /* $OpenBSD: bn_exp2.c,v 1.13 2022/02/07 19:49:56 tb 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 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
111
112 #include <stdio.h>
113
114 #include <openssl/err.h>
115
116 #include "bn_lcl.h"
117
118 #define TABLE_SIZE 32
119
120 int
BN_mod_exp2_mont(BIGNUM * rr,const BIGNUM * a1,const BIGNUM * p1,const BIGNUM * a2,const BIGNUM * p2,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)121 BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
122 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m, BN_CTX *ctx,
123 BN_MONT_CTX *in_mont)
124 {
125 int i, j, bits, b, bits1, bits2, ret = 0, wpos1, wpos2, window1, window2, wvalue1, wvalue2;
126 int r_is_one = 1;
127 BIGNUM *d, *r;
128 const BIGNUM *a_mod_m;
129 /* Tables of variables obtained from 'ctx' */
130 BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
131 BN_MONT_CTX *mont = NULL;
132
133 bn_check_top(a1);
134 bn_check_top(p1);
135 bn_check_top(a2);
136 bn_check_top(p2);
137 bn_check_top(m);
138
139 if (!BN_is_odd(m)) {
140 BNerror(BN_R_CALLED_WITH_EVEN_MODULUS);
141 return (0);
142 }
143 bits1 = BN_num_bits(p1);
144 bits2 = BN_num_bits(p2);
145 if ((bits1 == 0) && (bits2 == 0)) {
146 ret = BN_one(rr);
147 return ret;
148 }
149
150 bits = (bits1 > bits2) ? bits1 : bits2;
151
152 BN_CTX_start(ctx);
153 if ((d = BN_CTX_get(ctx)) == NULL)
154 goto err;
155 if ((r = BN_CTX_get(ctx)) == NULL)
156 goto err;
157 if ((val1[0] = BN_CTX_get(ctx)) == NULL)
158 goto err;
159 if ((val2[0] = BN_CTX_get(ctx)) == NULL)
160 goto err;
161
162 if (in_mont != NULL)
163 mont = in_mont;
164 else {
165 if ((mont = BN_MONT_CTX_new()) == NULL)
166 goto err;
167 if (!BN_MONT_CTX_set(mont, m, ctx))
168 goto err;
169 }
170
171 window1 = BN_window_bits_for_exponent_size(bits1);
172 window2 = BN_window_bits_for_exponent_size(bits2);
173
174 /*
175 * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1)
176 */
177 if (a1->neg || BN_ucmp(a1, m) >= 0) {
178 if (!BN_mod_ct(val1[0], a1, m, ctx))
179 goto err;
180 a_mod_m = val1[0];
181 } else
182 a_mod_m = a1;
183 if (BN_is_zero(a_mod_m)) {
184 BN_zero(rr);
185 ret = 1;
186 goto err;
187 }
188
189 if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx))
190 goto err;
191 if (window1 > 1) {
192 if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx))
193 goto err;
194
195 j = 1 << (window1 - 1);
196 for (i = 1; i < j; i++) {
197 if (((val1[i] = BN_CTX_get(ctx)) == NULL) ||
198 !BN_mod_mul_montgomery(val1[i], val1[i - 1],
199 d, mont, ctx))
200 goto err;
201 }
202 }
203
204
205 /*
206 * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1)
207 */
208 if (a2->neg || BN_ucmp(a2, m) >= 0) {
209 if (!BN_mod_ct(val2[0], a2, m, ctx))
210 goto err;
211 a_mod_m = val2[0];
212 } else
213 a_mod_m = a2;
214 if (BN_is_zero(a_mod_m)) {
215 BN_zero(rr);
216 ret = 1;
217 goto err;
218 }
219 if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx))
220 goto err;
221 if (window2 > 1) {
222 if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx))
223 goto err;
224
225 j = 1 << (window2 - 1);
226 for (i = 1; i < j; i++) {
227 if (((val2[i] = BN_CTX_get(ctx)) == NULL) ||
228 !BN_mod_mul_montgomery(val2[i], val2[i - 1],
229 d, mont, ctx))
230 goto err;
231 }
232 }
233
234
235 /* Now compute the power product, using independent windows. */
236 r_is_one = 1;
237 wvalue1 = 0; /* The 'value' of the first window */
238 wvalue2 = 0; /* The 'value' of the second window */
239 wpos1 = 0; /* If wvalue1 > 0, the bottom bit of the first window */
240 wpos2 = 0; /* If wvalue2 > 0, the bottom bit of the second window */
241
242 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
243 goto err;
244 for (b = bits - 1; b >= 0; b--) {
245 if (!r_is_one) {
246 if (!BN_mod_mul_montgomery(r, r,r, mont, ctx))
247 goto err;
248 }
249
250 if (!wvalue1)
251 if (BN_is_bit_set(p1, b)) {
252 /* consider bits b-window1+1 .. b for this window */
253 i = b - window1 + 1;
254 while (!BN_is_bit_set(p1, i)) /* works for i<0 */
255 i++;
256 wpos1 = i;
257 wvalue1 = 1;
258 for (i = b - 1; i >= wpos1; i--) {
259 wvalue1 <<= 1;
260 if (BN_is_bit_set(p1, i))
261 wvalue1++;
262 }
263 }
264
265 if (!wvalue2)
266 if (BN_is_bit_set(p2, b)) {
267 /* consider bits b-window2+1 .. b for this window */
268 i = b - window2 + 1;
269 while (!BN_is_bit_set(p2, i))
270 i++;
271 wpos2 = i;
272 wvalue2 = 1;
273 for (i = b - 1; i >= wpos2; i--) {
274 wvalue2 <<= 1;
275 if (BN_is_bit_set(p2, i))
276 wvalue2++;
277 }
278 }
279
280 if (wvalue1 && b == wpos1) {
281 /* wvalue1 is odd and < 2^window1 */
282 if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1],
283 mont, ctx))
284 goto err;
285 wvalue1 = 0;
286 r_is_one = 0;
287 }
288
289 if (wvalue2 && b == wpos2) {
290 /* wvalue2 is odd and < 2^window2 */
291 if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1],
292 mont, ctx))
293 goto err;
294 wvalue2 = 0;
295 r_is_one = 0;
296 }
297 }
298 if (!BN_from_montgomery(rr, r,mont, ctx))
299 goto err;
300 ret = 1;
301
302 err:
303 if ((in_mont == NULL) && (mont != NULL))
304 BN_MONT_CTX_free(mont);
305 BN_CTX_end(ctx);
306 bn_check_top(rr);
307 return (ret);
308 }
309