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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 
BN_rand(BIGNUM * rnd,int bits,int top,int bottom)123 int 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 
BN_pseudo_rand(BIGNUM * rnd,int bits,int top,int bottom)181 int 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.
bn_less_than_word_mask(const BN_ULONG * a,size_t len,BN_ULONG b)188 static 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 
bn_in_range_words(const BN_ULONG * a,BN_ULONG min_inclusive,const BN_ULONG * max_exclusive,size_t len)210 int 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 
bn_range_to_mask(size_t * out_words,BN_ULONG * out_mask,size_t min_inclusive,const BN_ULONG * max_exclusive,size_t len)216 static 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 
bn_rand_range_words(BN_ULONG * out,BN_ULONG min_inclusive,const BN_ULONG * max_exclusive,size_t len,const uint8_t additional_data[32])245 int 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 
BN_rand_range_ex(BIGNUM * r,BN_ULONG min_inclusive,const BIGNUM * max_exclusive)283 int 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 
bn_rand_secret_range(BIGNUM * r,int * out_is_uniform,BN_ULONG min_inclusive,const BIGNUM * max_exclusive)297 int 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 
BN_rand_range(BIGNUM * r,const BIGNUM * range)335 int BN_rand_range(BIGNUM *r, const BIGNUM *range) {
336   return BN_rand_range_ex(r, 0, range);
337 }
338 
BN_pseudo_rand_range(BIGNUM * r,const BIGNUM * range)339 int BN_pseudo_rand_range(BIGNUM *r, const BIGNUM *range) {
340   return BN_rand_range(r, range);
341 }
342