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) 1998-2006 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 <assert.h>
112#include <stdio.h>
113#include <stdlib.h>
114#include <string.h>
115
116#include <openssl/err.h>
117#include <openssl/mem.h>
118#include <openssl/thread.h>
119#include <openssl/type_check.h>
120
121#include "internal.h"
122#include "../../internal.h"
123
124
125BN_MONT_CTX *BN_MONT_CTX_new(void) {
126 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));
127
128 if (ret == NULL) {
129 return NULL;
130 }
131
132 OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX));
133 BN_init(&ret->RR);
134 BN_init(&ret->N);
135
136 return ret;
137}
138
139void BN_MONT_CTX_free(BN_MONT_CTX *mont) {
140 if (mont == NULL) {
141 return;
142 }
143
144 BN_free(&mont->RR);
145 BN_free(&mont->N);
146 OPENSSL_free(mont);
147}
148
149BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) {
150 if (to == from) {
151 return to;
152 }
153
154 if (!BN_copy(&to->RR, &from->RR) ||
155 !BN_copy(&to->N, &from->N)) {
156 return NULL;
157 }
158 to->n0[0] = from->n0[0];
159 to->n0[1] = from->n0[1];
160 return to;
161}
162
163static int bn_mont_ctx_set_N_and_n0(BN_MONT_CTX *mont, const BIGNUM *mod) {
164 if (BN_is_zero(mod)) {
165 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
166 return 0;
167 }
168 if (!BN_is_odd(mod)) {
169 OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
170 return 0;
171 }
172 if (BN_is_negative(mod)) {
173 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
174 return 0;
175 }
176
177 // Save the modulus.
178 if (!BN_copy(&mont->N, mod)) {
179 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
180 return 0;
181 }
182 // |mont->N| is always stored minimally. Computing RR efficiently leaks the
183 // size of the modulus. While the modulus may be private in RSA (one of the
184 // primes), their sizes are public, so this is fine.
185 bn_set_minimal_width(&mont->N);
186
187 // Find n0 such that n0 * N == -1 (mod r).
188 //
189 // Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the
190 // others, we could use a shorter R value and use faster |BN_ULONG|-based
191 // math instead of |uint64_t|-based math, which would be double-precision.
192 // However, currently only the assembler files know which is which.
193 OPENSSL_STATIC_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2,
194 "BN_MONT_CTX_N0_LIMBS value is invalid");
195 OPENSSL_STATIC_ASSERT(
196 sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS == sizeof(uint64_t),
197 "uint64_t is insufficient precision for n0");
198 uint64_t n0 = bn_mont_n0(&mont->N);
199 mont->n0[0] = (BN_ULONG)n0;
200#if BN_MONT_CTX_N0_LIMBS == 2
201 mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2);
202#else
203 mont->n0[1] = 0;
204#endif
205 return 1;
206}
207
208int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) {
209 if (!bn_mont_ctx_set_N_and_n0(mont, mod)) {
210 return 0;
211 }
212
213 BN_CTX *new_ctx = NULL;
214 if (ctx == NULL) {
215 new_ctx = BN_CTX_new();
216 if (new_ctx == NULL) {
217 return 0;
218 }
219 ctx = new_ctx;
220 }
221
222 // Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS2 such that R
223 // > mod. Even though the assembly on some 32-bit platforms works with 64-bit
224 // values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS *
225 // BN_BITS2|, is correct because R**2 will still be a multiple of the latter
226 // as |BN_MONT_CTX_N0_LIMBS| is either one or two.
227 unsigned lgBigR = mont->N.width * BN_BITS2;
228 BN_zero(&mont->RR);
229 int ok = BN_set_bit(&mont->RR, lgBigR * 2) &&
230 BN_mod(&mont->RR, &mont->RR, &mont->N, ctx) &&
231 bn_resize_words(&mont->RR, mont->N.width);
232 BN_CTX_free(new_ctx);
233 return ok;
234}
235
236BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, BN_CTX *ctx) {
237 BN_MONT_CTX *mont = BN_MONT_CTX_new();
238 if (mont == NULL ||
239 !BN_MONT_CTX_set(mont, mod, ctx)) {
240 BN_MONT_CTX_free(mont);
241 return NULL;
242 }
243 return mont;
244}
245
246BN_MONT_CTX *BN_MONT_CTX_new_consttime(const BIGNUM *mod, BN_CTX *ctx) {
247 BN_MONT_CTX *mont = BN_MONT_CTX_new();
248 if (mont == NULL ||
249 !bn_mont_ctx_set_N_and_n0(mont, mod)) {
250 goto err;
251 }
252 unsigned lgBigR = mont->N.width * BN_BITS2;
253 if (!bn_mod_exp_base_2_consttime(&mont->RR, lgBigR * 2, &mont->N, ctx) ||
254 !bn_resize_words(&mont->RR, mont->N.width)) {
255 goto err;
256 }
257 return mont;
258
259err:
260 BN_MONT_CTX_free(mont);
261 return NULL;
262}
263
264int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
265 const BIGNUM *mod, BN_CTX *bn_ctx) {
266 CRYPTO_MUTEX_lock_read(lock);
267 BN_MONT_CTX *ctx = *pmont;
268 CRYPTO_MUTEX_unlock_read(lock);
269
270 if (ctx) {
271 return 1;
272 }
273
274 CRYPTO_MUTEX_lock_write(lock);
275 if (*pmont == NULL) {
276 *pmont = BN_MONT_CTX_new_for_modulus(mod, bn_ctx);
277 }
278 const int ok = *pmont != NULL;
279 CRYPTO_MUTEX_unlock_write(lock);
280 return ok;
281}
282
283int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
284 BN_CTX *ctx) {
285 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
286}
287
288static int bn_from_montgomery_in_place(BN_ULONG *r, size_t num_r, BN_ULONG *a,
289 size_t num_a, const BN_MONT_CTX *mont) {
290 const BN_ULONG *n = mont->N.d;
291 size_t num_n = mont->N.width;
292 if (num_r != num_n || num_a != 2 * num_n) {
293 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
294 return 0;
295 }
296
297 // Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
298 // input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
299 // includes |carry| which is stored separately.
300 BN_ULONG n0 = mont->n0[0];
301 BN_ULONG carry = 0;
302 for (size_t i = 0; i < num_n; i++) {
303 BN_ULONG v = bn_mul_add_words(a + i, n, num_n, a[i] * n0);
304 v += carry + a[i + num_n];
305 carry |= (v != a[i + num_n]);
306 carry &= (v <= a[i + num_n]);
307 a[i + num_n] = v;
308 }
309
310 // Shift |num_n| words to divide by R. We have |a| < 2 * |n|. Note that |a|
311 // includes |carry| which is stored separately.
312 a += num_n;
313
314 // |a| thus requires at most one additional subtraction |n| to be reduced.
315 bn_reduce_once(r, a, carry, n, num_n);
316 return 1;
317}
318
319static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r,
320 const BN_MONT_CTX *mont) {
321 if (r->neg) {
322 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
323 return 0;
324 }
325
326 const BIGNUM *n = &mont->N;
327 if (n->width == 0) {
328 ret->width = 0;
329 return 1;
330 }
331
332 int max = 2 * n->width; // carry is stored separately
333 if (!bn_resize_words(r, max) ||
334 !bn_wexpand(ret, n->width)) {
335 return 0;
336 }
337
338 ret->width = n->width;
339 ret->neg = 0;
340 return bn_from_montgomery_in_place(ret->d, ret->width, r->d, r->width, mont);
341}
342
343int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont,
344 BN_CTX *ctx) {
345 int ret = 0;
346 BIGNUM *t;
347
348 BN_CTX_start(ctx);
349 t = BN_CTX_get(ctx);
350 if (t == NULL ||
351 !BN_copy(t, a)) {
352 goto err;
353 }
354
355 ret = BN_from_montgomery_word(r, t, mont);
356
357err:
358 BN_CTX_end(ctx);
359
360 return ret;
361}
362
363int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx) {
364 // If the high bit of |n| is set, R = 2^(width*BN_BITS2) < 2 * |n|, so we
365 // compute R - |n| rather than perform Montgomery reduction.
366 const BIGNUM *n = &mont->N;
367 if (n->width > 0 && (n->d[n->width - 1] >> (BN_BITS2 - 1)) != 0) {
368 if (!bn_wexpand(r, n->width)) {
369 return 0;
370 }
371 r->d[0] = 0 - n->d[0];
372 for (int i = 1; i < n->width; i++) {
373 r->d[i] = ~n->d[i];
374 }
375 r->width = n->width;
376 r->neg = 0;
377 return 1;
378 }
379
380 return BN_from_montgomery(r, &mont->RR, mont, ctx);
381}
382
383static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a,
384 const BIGNUM *b,
385 const BN_MONT_CTX *mont,
386 BN_CTX *ctx) {
387 int ret = 0;
388
389 BN_CTX_start(ctx);
390 BIGNUM *tmp = BN_CTX_get(ctx);
391 if (tmp == NULL) {
392 goto err;
393 }
394
395 if (a == b) {
396 if (!bn_sqr_consttime(tmp, a, ctx)) {
397 goto err;
398 }
399 } else {
400 if (!bn_mul_consttime(tmp, a, b, ctx)) {
401 goto err;
402 }
403 }
404
405 // reduce from aRR to aR
406 if (!BN_from_montgomery_word(r, tmp, mont)) {
407 goto err;
408 }
409
410 ret = 1;
411
412err:
413 BN_CTX_end(ctx);
414 return ret;
415}
416
417int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
418 const BN_MONT_CTX *mont, BN_CTX *ctx) {
419 if (a->neg || b->neg) {
420 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
421 return 0;
422 }
423
424#if defined(OPENSSL_BN_ASM_MONT)
425 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86.
426 int num = mont->N.width;
427 if (num >= (128 / BN_BITS2) &&
428 a->width == num &&
429 b->width == num) {
430 if (!bn_wexpand(r, num)) {
431 return 0;
432 }
433 if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
434 // The check above ensures this won't happen.
435 assert(0);
436 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
437 return 0;
438 }
439 r->neg = 0;
440 r->width = num;
441 return 1;
442 }
443#endif
444
445 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx);
446}
447
448int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont) {
449 return !BN_is_negative(bn) &&
450 bn_fits_in_words(bn, mont->N.width);
451}
452
453void bn_to_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num,
454 const BN_MONT_CTX *mont) {
455 bn_mod_mul_montgomery_small(r, a, mont->RR.d, num, mont);
456}
457
458void bn_from_montgomery_small(BN_ULONG *r, const BN_ULONG *a, size_t num,
459 const BN_MONT_CTX *mont) {
460 if (num != (size_t)mont->N.width || num > BN_SMALL_MAX_WORDS) {
461 abort();
462 }
463 BN_ULONG tmp[BN_SMALL_MAX_WORDS * 2];
464 OPENSSL_memcpy(tmp, a, num * sizeof(BN_ULONG));
465 OPENSSL_memset(tmp + num, 0, num * sizeof(BN_ULONG));
466 if (!bn_from_montgomery_in_place(r, num, tmp, 2 * num, mont)) {
467 abort();
468 }
469 OPENSSL_cleanse(tmp, 2 * num * sizeof(BN_ULONG));
470}
471
472void bn_mod_mul_montgomery_small(BN_ULONG *r, const BN_ULONG *a,
473 const BN_ULONG *b, size_t num,
474 const BN_MONT_CTX *mont) {
475 if (num != (size_t)mont->N.width || num > BN_SMALL_MAX_WORDS) {
476 abort();
477 }
478
479#if defined(OPENSSL_BN_ASM_MONT)
480 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86.
481 if (num >= (128 / BN_BITS2)) {
482 if (!bn_mul_mont(r, a, b, mont->N.d, mont->n0, num)) {
483 abort(); // The check above ensures this won't happen.
484 }
485 return;
486 }
487#endif
488
489 // Compute the product.
490 BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];
491 if (a == b) {
492 bn_sqr_small(tmp, 2 * num, a, num);
493 } else {
494 bn_mul_small(tmp, 2 * num, a, num, b, num);
495 }
496
497 // Reduce.
498 if (!bn_from_montgomery_in_place(r, num, tmp, 2 * num, mont)) {
499 abort();
500 }
501 OPENSSL_cleanse(tmp, 2 * num * sizeof(BN_ULONG));
502}
503