1/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
2 * All rights reserved.
3 *
4 * This package is an SSL implementation written
5 * by Eric Young (eay@cryptsoft.com).
6 * The implementation was written so as to conform with Netscapes SSL.
7 *
8 * This library is free for commercial and non-commercial use as long as
9 * the following conditions are aheared to. The following conditions
10 * apply to all code found in this distribution, be it the RC4, RSA,
11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
12 * included with this distribution is covered by the same copyright terms
13 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
14 *
15 * Copyright remains Eric Young's, and as such any Copyright notices in
16 * the code are not to be removed.
17 * If this package is used in a product, Eric Young should be given attribution
18 * as the author of the parts of the library used.
19 * This can be in the form of a textual message at program startup or
20 * in documentation (online or textual) provided with the package.
21 *
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
24 * are met:
25 * 1. Redistributions of source code must retain the copyright
26 * notice, this list of conditions and the following disclaimer.
27 * 2. Redistributions in binary form must reproduce the above copyright
28 * notice, this list of conditions and the following disclaimer in the
29 * documentation and/or other materials provided with the distribution.
30 * 3. All advertising materials mentioning features or use of this software
31 * must display the following acknowledgement:
32 * "This product includes cryptographic software written by
33 * Eric Young (eay@cryptsoft.com)"
34 * The word 'cryptographic' can be left out if the rouines from the library
35 * being used are not cryptographic related :-).
36 * 4. If you include any Windows specific code (or a derivative thereof) from
37 * the apps directory (application code) you must include an acknowledgement:
38 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
39 *
40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
50 * SUCH DAMAGE.
51 *
52 * The licence and distribution terms for any publically available version or
53 * derivative of this code cannot be changed. i.e. this code cannot simply be
54 * copied and put under another distribution licence
55 * [including the GNU Public Licence.]
56 */
57/* ====================================================================
58 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
59 *
60 * Redistribution and use in source and binary forms, with or without
61 * modification, are permitted provided that the following conditions
62 * are met:
63 *
64 * 1. Redistributions of source code must retain the above copyright
65 * notice, this list of conditions and the following disclaimer.
66 *
67 * 2. Redistributions in binary form must reproduce the above copyright
68 * notice, this list of conditions and the following disclaimer in
69 * the documentation and/or other materials provided with the
70 * distribution.
71 *
72 * 3. All advertising materials mentioning features or use of this
73 * software must display the following acknowledgment:
74 * "This product includes software developed by the OpenSSL Project
75 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
76 *
77 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
78 * endorse or promote products derived from this software without
79 * prior written permission. For written permission, please contact
80 * openssl-core@openssl.org.
81 *
82 * 5. Products derived from this software may not be called "OpenSSL"
83 * nor may "OpenSSL" appear in their names without prior written
84 * permission of the OpenSSL Project.
85 *
86 * 6. Redistributions of any form whatsoever must retain the following
87 * acknowledgment:
88 * "This product includes software developed by the OpenSSL Project
89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
90 *
91 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
92 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
93 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
94 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
95 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
96 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
97 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
98 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
99 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
100 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
101 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
102 * OF THE POSSIBILITY OF SUCH DAMAGE.
103 * ====================================================================
104 *
105 * This product includes cryptographic software written by Eric Young
106 * (eay@cryptsoft.com). This product includes software written by Tim
107 * Hudson (tjh@cryptsoft.com). */
108
109#include <openssl/bn.h>
110
111#include <limits.h>
112#include <string.h>
113
114#include <openssl/err.h>
115#include <openssl/rand.h>
116#include <openssl/type_check.h>
117
118#include "internal.h"
119#include "../../internal.h"
120#include "../rand/internal.h"
121
122
123int BN_rand(BIGNUM *rnd, int bits, int top, int bottom) {
124 if (rnd == NULL) {
125 return 0;
126 }
127
128 if (top != BN_RAND_TOP_ANY && top != BN_RAND_TOP_ONE &&
129 top != BN_RAND_TOP_TWO) {
130 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
131 return 0;
132 }
133
134 if (bottom != BN_RAND_BOTTOM_ANY && bottom != BN_RAND_BOTTOM_ODD) {
135 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
136 return 0;
137 }
138
139 if (bits == 0) {
140 BN_zero(rnd);
141 return 1;
142 }
143
144 if (bits > INT_MAX - (BN_BITS2 - 1)) {
145 OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
146 return 0;
147 }
148
149 int words = (bits + BN_BITS2 - 1) / BN_BITS2;
150 int bit = (bits - 1) % BN_BITS2;
151 const BN_ULONG kOne = 1;
152 const BN_ULONG kThree = 3;
153 BN_ULONG mask = bit < BN_BITS2 - 1 ? (kOne << (bit + 1)) - 1 : BN_MASK2;
154 if (!bn_wexpand(rnd, words)) {
155 return 0;
156 }
157
158 RAND_bytes((uint8_t *)rnd->d, words * sizeof(BN_ULONG));
159 rnd->d[words - 1] &= mask;
160 if (top != BN_RAND_TOP_ANY) {
161 if (top == BN_RAND_TOP_TWO && bits > 1) {
162 if (bit == 0) {
163 rnd->d[words - 1] |= 1;
164 rnd->d[words - 2] |= kOne << (BN_BITS2 - 1);
165 } else {
166 rnd->d[words - 1] |= kThree << (bit - 1);
167 }
168 } else {
169 rnd->d[words - 1] |= kOne << bit;
170 }
171 }
172 if (bottom == BN_RAND_BOTTOM_ODD) {
173 rnd->d[0] |= 1;
174 }
175
176 rnd->neg = 0;
177 rnd->width = words;
178 return 1;
179}
180
181int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom) {
182 return BN_rand(rnd, bits, top, bottom);
183}
184
185// bn_less_than_word_mask returns a mask of all ones if the number represented
186// by |len| words at |a| is less than |b| and zero otherwise. It performs this
187// computation in time independent of the value of |a|. |b| is assumed public.
188static crypto_word_t bn_less_than_word_mask(const BN_ULONG *a, size_t len,
189 BN_ULONG b) {
190 if (b == 0) {
191 return CONSTTIME_FALSE_W;
192 }
193 if (len == 0) {
194 return CONSTTIME_TRUE_W;
195 }
196
197 // |a| < |b| iff a[1..len-1] are all zero and a[0] < b.
198 OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
199 "crypto_word_t is too small");
200 crypto_word_t mask = 0;
201 for (size_t i = 1; i < len; i++) {
202 mask |= a[i];
203 }
204 // |mask| is now zero iff a[1..len-1] are all zero.
205 mask = constant_time_is_zero_w(mask);
206 mask &= constant_time_lt_w(a[0], b);
207 return mask;
208}
209
210int bn_in_range_words(const BN_ULONG *a, BN_ULONG min_inclusive,
211 const BN_ULONG *max_exclusive, size_t len) {
212 crypto_word_t mask = ~bn_less_than_word_mask(a, len, min_inclusive);
213 return mask & bn_less_than_words(a, max_exclusive, len);
214}
215
216static int bn_range_to_mask(size_t *out_words, BN_ULONG *out_mask,
217 size_t min_inclusive, const BN_ULONG *max_exclusive,
218 size_t len) {
219 // The magnitude of |max_exclusive| is assumed public.
220 size_t words = len;
221 while (words > 0 && max_exclusive[words - 1] == 0) {
222 words--;
223 }
224 if (words == 0 ||
225 (words == 1 && max_exclusive[0] <= min_inclusive)) {
226 OPENSSL_PUT_ERROR(BN, BN_R_INVALID_RANGE);
227 return 0;
228 }
229 BN_ULONG mask = max_exclusive[words - 1];
230 // This sets all bits in |mask| below the most significant bit.
231 mask |= mask >> 1;
232 mask |= mask >> 2;
233 mask |= mask >> 4;
234 mask |= mask >> 8;
235 mask |= mask >> 16;
236#if defined(OPENSSL_64_BIT)
237 mask |= mask >> 32;
238#endif
239
240 *out_words = words;
241 *out_mask = mask;
242 return 1;
243}
244
245int bn_rand_range_words(BN_ULONG *out, BN_ULONG min_inclusive,
246 const BN_ULONG *max_exclusive, size_t len,
247 const uint8_t additional_data[32]) {
248 // This function implements the equivalent of steps 4 through 7 of FIPS 186-4
249 // appendices B.4.2 and B.5.2. When called in those contexts, |max_exclusive|
250 // is n and |min_inclusive| is one.
251
252 // Compute the bit length of |max_exclusive| (step 1), in terms of a number of
253 // |words| worth of entropy to fill and a mask of bits to clear in the top
254 // word.
255 size_t words;
256 BN_ULONG mask;
257 if (!bn_range_to_mask(&words, &mask, min_inclusive, max_exclusive, len)) {
258 return 0;
259 }
260
261 // Fill any unused words with zero.
262 OPENSSL_memset(out + words, 0, (len - words) * sizeof(BN_ULONG));
263
264 unsigned count = 100;
265 do {
266 if (!--count) {
267 OPENSSL_PUT_ERROR(BN, BN_R_TOO_MANY_ITERATIONS);
268 return 0;
269 }
270
271 // Steps 4 and 5. Use |words| and |mask| together to obtain a string of N
272 // bits, where N is the bit length of |max_exclusive|.
273 RAND_bytes_with_additional_data((uint8_t *)out, words * sizeof(BN_ULONG),
274 additional_data);
275 out[words - 1] &= mask;
276
277 // If out >= max_exclusive or out < min_inclusive, retry. This implements
278 // the equivalent of steps 6 and 7 without leaking the value of |out|.
279 } while (!bn_in_range_words(out, min_inclusive, max_exclusive, words));
280 return 1;
281}
282
283int BN_rand_range_ex(BIGNUM *r, BN_ULONG min_inclusive,
284 const BIGNUM *max_exclusive) {
285 static const uint8_t kDefaultAdditionalData[32] = {0};
286 if (!bn_wexpand(r, max_exclusive->width) ||
287 !bn_rand_range_words(r->d, min_inclusive, max_exclusive->d,
288 max_exclusive->width, kDefaultAdditionalData)) {
289 return 0;
290 }
291
292 r->neg = 0;
293 r->width = max_exclusive->width;
294 return 1;
295}
296
297int bn_rand_secret_range(BIGNUM *r, int *out_is_uniform, BN_ULONG min_inclusive,
298 const BIGNUM *max_exclusive) {
299 size_t words;
300 BN_ULONG mask;
301 if (!bn_range_to_mask(&words, &mask, min_inclusive, max_exclusive->d,
302 max_exclusive->width) ||
303 !bn_wexpand(r, words)) {
304 return 0;
305 }
306
307 assert(words > 0);
308 assert(mask != 0);
309 // The range must be large enough for bit tricks to fix invalid values.
310 if (words == 1 && min_inclusive > mask >> 1) {
311 OPENSSL_PUT_ERROR(BN, BN_R_INVALID_RANGE);
312 return 0;
313 }
314
315 // Select a uniform random number with num_bits(max_exclusive) bits.
316 RAND_bytes((uint8_t *)r->d, words * sizeof(BN_ULONG));
317 r->d[words - 1] &= mask;
318
319 // Check, in constant-time, if the value is in range.
320 *out_is_uniform =
321 bn_in_range_words(r->d, min_inclusive, max_exclusive->d, words);
322 crypto_word_t in_range = *out_is_uniform;
323 in_range = 0 - in_range;
324
325 // If the value is not in range, force it to be in range.
326 r->d[0] |= constant_time_select_w(in_range, 0, min_inclusive);
327 r->d[words - 1] &= constant_time_select_w(in_range, BN_MASK2, mask >> 1);
328 assert(bn_in_range_words(r->d, min_inclusive, max_exclusive->d, words));
329
330 r->neg = 0;
331 r->width = words;
332 return 1;
333}
334
335int BN_rand_range(BIGNUM *r, const BIGNUM *range) {
336 return BN_rand_range_ex(r, 0, range);
337}
338
339int BN_pseudo_rand_range(BIGNUM *r, const BIGNUM *range) {
340 return BN_rand_range(r, range);
341}
342