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 <string.h>
113
114 #include <openssl/err.h>
115 #include <openssl/mem.h>
116 #include <openssl/thread.h>
117 #include <openssl/type_check.h>
118
119 #include "internal.h"
120 #include "../../internal.h"
121
122
123 #if !defined(OPENSSL_NO_ASM) && \
124 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \
125 defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64))
126 #define OPENSSL_BN_ASM_MONT
127 #endif
128
129
BN_MONT_CTX_new(void)130 BN_MONT_CTX *BN_MONT_CTX_new(void) {
131 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));
132
133 if (ret == NULL) {
134 return NULL;
135 }
136
137 OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX));
138 BN_init(&ret->RR);
139 BN_init(&ret->N);
140
141 return ret;
142 }
143
BN_MONT_CTX_free(BN_MONT_CTX * mont)144 void BN_MONT_CTX_free(BN_MONT_CTX *mont) {
145 if (mont == NULL) {
146 return;
147 }
148
149 BN_free(&mont->RR);
150 BN_free(&mont->N);
151 OPENSSL_free(mont);
152 }
153
BN_MONT_CTX_copy(BN_MONT_CTX * to,const BN_MONT_CTX * from)154 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) {
155 if (to == from) {
156 return to;
157 }
158
159 if (!BN_copy(&to->RR, &from->RR) ||
160 !BN_copy(&to->N, &from->N)) {
161 return NULL;
162 }
163 to->n0[0] = from->n0[0];
164 to->n0[1] = from->n0[1];
165 return to;
166 }
167
168 OPENSSL_COMPILE_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2,
169 BN_MONT_CTX_N0_LIMBS_VALUE_INVALID);
170 OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS ==
171 sizeof(uint64_t), BN_MONT_CTX_set_64_bit_mismatch);
172
BN_MONT_CTX_set(BN_MONT_CTX * mont,const BIGNUM * mod,BN_CTX * ctx)173 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) {
174 if (BN_is_zero(mod)) {
175 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
176 return 0;
177 }
178 if (!BN_is_odd(mod)) {
179 OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
180 return 0;
181 }
182 if (BN_is_negative(mod)) {
183 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
184 return 0;
185 }
186
187 // Save the modulus.
188 if (!BN_copy(&mont->N, mod)) {
189 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
190 return 0;
191 }
192 // |mont->N| is always stored minimally. Computing RR efficiently leaks the
193 // size of the modulus. While the modulus may be private in RSA (one of the
194 // primes), their sizes are public, so this is fine.
195 bn_correct_top(&mont->N);
196
197 // Find n0 such that n0 * N == -1 (mod r).
198 //
199 // Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the
200 // others, we could use a shorter R value and use faster |BN_ULONG|-based
201 // math instead of |uint64_t|-based math, which would be double-precision.
202 // However, currently only the assembler files know which is which.
203 uint64_t n0 = bn_mont_n0(&mont->N);
204 mont->n0[0] = (BN_ULONG)n0;
205 #if BN_MONT_CTX_N0_LIMBS == 2
206 mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2);
207 #else
208 mont->n0[1] = 0;
209 #endif
210
211 // Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS2 such that R
212 // > mod. Even though the assembly on some 32-bit platforms works with 64-bit
213 // values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS *
214 // BN_BITS2|, is correct because R**2 will still be a multiple of the latter
215 // as |BN_MONT_CTX_N0_LIMBS| is either one or two.
216 //
217 // XXX: This is not constant time with respect to |mont->N|, but it should be.
218 unsigned lgBigR = mont->N.top * BN_BITS2;
219 if (!bn_mod_exp_base_2_vartime(&mont->RR, lgBigR * 2, &mont->N)) {
220 return 0;
221 }
222
223 return 1;
224 }
225
BN_MONT_CTX_new_for_modulus(const BIGNUM * mod,BN_CTX * ctx)226 BN_MONT_CTX *BN_MONT_CTX_new_for_modulus(const BIGNUM *mod, BN_CTX *ctx) {
227 BN_MONT_CTX *mont = BN_MONT_CTX_new();
228 if (mont == NULL ||
229 !BN_MONT_CTX_set(mont, mod, ctx)) {
230 BN_MONT_CTX_free(mont);
231 return NULL;
232 }
233 return mont;
234 }
235
BN_MONT_CTX_set_locked(BN_MONT_CTX ** pmont,CRYPTO_MUTEX * lock,const BIGNUM * mod,BN_CTX * bn_ctx)236 int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
237 const BIGNUM *mod, BN_CTX *bn_ctx) {
238 CRYPTO_MUTEX_lock_read(lock);
239 BN_MONT_CTX *ctx = *pmont;
240 CRYPTO_MUTEX_unlock_read(lock);
241
242 if (ctx) {
243 return 1;
244 }
245
246 CRYPTO_MUTEX_lock_write(lock);
247 if (*pmont == NULL) {
248 *pmont = BN_MONT_CTX_new_for_modulus(mod, bn_ctx);
249 }
250 const int ok = *pmont != NULL;
251 CRYPTO_MUTEX_unlock_write(lock);
252 return ok;
253 }
254
BN_to_montgomery(BIGNUM * ret,const BIGNUM * a,const BN_MONT_CTX * mont,BN_CTX * ctx)255 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
256 BN_CTX *ctx) {
257 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
258 }
259
bn_from_montgomery_in_place(BN_ULONG * r,size_t num_r,BN_ULONG * a,size_t num_a,const BN_MONT_CTX * mont)260 static int bn_from_montgomery_in_place(BN_ULONG *r, size_t num_r, BN_ULONG *a,
261 size_t num_a, const BN_MONT_CTX *mont) {
262 const BN_ULONG *n = mont->N.d;
263 size_t num_n = mont->N.top;
264 if (num_r != num_n || num_a != 2 * num_n) {
265 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
266 return 0;
267 }
268
269 // Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
270 // input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
271 // includes |carry| which is stored separately.
272 BN_ULONG n0 = mont->n0[0];
273 BN_ULONG carry = 0;
274 for (size_t i = 0; i < num_n; i++) {
275 BN_ULONG v = bn_mul_add_words(a + i, n, num_n, a[i] * n0);
276 v += carry + a[i + num_n];
277 carry |= (v != a[i + num_n]);
278 carry &= (v <= a[i + num_n]);
279 a[i + num_n] = v;
280 }
281
282 // Shift |num_n| words to divide by R. We have |a| < 2 * |n|. Note that |a|
283 // includes |carry| which is stored separately.
284 a += num_n;
285
286 // |a| thus requires at most one additional subtraction |n| to be reduced.
287 // Subtract |n| and select the answer in constant time.
288 OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
289 crypto_word_t_too_small);
290 BN_ULONG v = bn_sub_words(r, a, n, num_n) - carry;
291 // |v| is one if |a| - |n| underflowed or zero if it did not. Note |v| cannot
292 // be -1. That would imply the subtraction did not fit in |num_n| words, and
293 // we know at most one subtraction is needed.
294 v = 0u - v;
295 for (size_t i = 0; i < num_n; i++) {
296 r[i] = constant_time_select_w(v, a[i], r[i]);
297 a[i] = 0;
298 }
299 return 1;
300 }
301
BN_from_montgomery_word(BIGNUM * ret,BIGNUM * r,const BN_MONT_CTX * mont)302 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r,
303 const BN_MONT_CTX *mont) {
304 if (r->neg) {
305 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
306 return 0;
307 }
308
309 const BIGNUM *n = &mont->N;
310 if (n->top == 0) {
311 ret->top = 0;
312 return 1;
313 }
314
315 int max = (2 * n->top); // carry is stored separately
316 if (!bn_resize_words(r, max) ||
317 !bn_wexpand(ret, n->top)) {
318 return 0;
319 }
320 ret->top = n->top;
321
322 if (!bn_from_montgomery_in_place(ret->d, ret->top, r->d, r->top, mont)) {
323 return 0;
324 }
325 ret->neg = 0;
326
327 bn_correct_top(r);
328 bn_correct_top(ret);
329 return 1;
330 }
331
BN_from_montgomery(BIGNUM * r,const BIGNUM * a,const BN_MONT_CTX * mont,BN_CTX * ctx)332 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont,
333 BN_CTX *ctx) {
334 int ret = 0;
335 BIGNUM *t;
336
337 BN_CTX_start(ctx);
338 t = BN_CTX_get(ctx);
339 if (t == NULL ||
340 !BN_copy(t, a)) {
341 goto err;
342 }
343
344 ret = BN_from_montgomery_word(r, t, mont);
345
346 err:
347 BN_CTX_end(ctx);
348
349 return ret;
350 }
351
bn_one_to_montgomery(BIGNUM * r,const BN_MONT_CTX * mont,BN_CTX * ctx)352 int bn_one_to_montgomery(BIGNUM *r, const BN_MONT_CTX *mont, BN_CTX *ctx) {
353 // If the high bit of |n| is set, R = 2^(top*BN_BITS2) < 2 * |n|, so we
354 // compute R - |n| rather than perform Montgomery reduction.
355 const BIGNUM *n = &mont->N;
356 if (n->top > 0 && (n->d[n->top - 1] >> (BN_BITS2 - 1)) != 0) {
357 if (!bn_wexpand(r, n->top)) {
358 return 0;
359 }
360 r->d[0] = 0 - n->d[0];
361 for (int i = 1; i < n->top; i++) {
362 r->d[i] = ~n->d[i];
363 }
364 r->top = n->top;
365 r->neg = 0;
366 // The upper words will be zero if the corresponding words of |n| were
367 // 0xfff[...], so call |bn_correct_top|.
368 bn_correct_top(r);
369 return 1;
370 }
371
372 return BN_from_montgomery(r, &mont->RR, mont, ctx);
373 }
374
bn_mod_mul_montgomery_fallback(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BN_MONT_CTX * mont,BN_CTX * ctx)375 static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a,
376 const BIGNUM *b,
377 const BN_MONT_CTX *mont,
378 BN_CTX *ctx) {
379 int ret = 0;
380
381 BN_CTX_start(ctx);
382 BIGNUM *tmp = BN_CTX_get(ctx);
383 if (tmp == NULL) {
384 goto err;
385 }
386
387 if (a == b) {
388 if (!BN_sqr(tmp, a, ctx)) {
389 goto err;
390 }
391 } else {
392 if (!BN_mul(tmp, a, b, ctx)) {
393 goto err;
394 }
395 }
396
397 // reduce from aRR to aR
398 if (!BN_from_montgomery_word(r, tmp, mont)) {
399 goto err;
400 }
401
402 ret = 1;
403
404 err:
405 BN_CTX_end(ctx);
406 return ret;
407 }
408
BN_mod_mul_montgomery(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BN_MONT_CTX * mont,BN_CTX * ctx)409 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
410 const BN_MONT_CTX *mont, BN_CTX *ctx) {
411 if (a->neg || b->neg) {
412 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
413 return 0;
414 }
415
416 #if defined(OPENSSL_BN_ASM_MONT)
417 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86.
418 int num = mont->N.top;
419 if (num >= (128 / BN_BITS2) &&
420 a->top == num &&
421 b->top == num) {
422 if (!bn_wexpand(r, num)) {
423 return 0;
424 }
425 if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
426 // The check above ensures this won't happen.
427 assert(0);
428 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
429 return 0;
430 }
431 r->neg = 0;
432 r->top = num;
433 bn_correct_top(r);
434
435 return 1;
436 }
437 #endif
438
439 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx);
440 }
441
bn_less_than_montgomery_R(const BIGNUM * bn,const BN_MONT_CTX * mont)442 int bn_less_than_montgomery_R(const BIGNUM *bn, const BN_MONT_CTX *mont) {
443 return !BN_is_negative(bn) &&
444 bn_fits_in_words(bn, mont->N.top);
445 }
446
bn_to_montgomery_small(BN_ULONG * r,size_t num_r,const BN_ULONG * a,size_t num_a,const BN_MONT_CTX * mont)447 int bn_to_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
448 size_t num_a, const BN_MONT_CTX *mont) {
449 return bn_mod_mul_montgomery_small(r, num_r, a, num_a, mont->RR.d,
450 mont->RR.top, mont);
451 }
452
bn_from_montgomery_small(BN_ULONG * r,size_t num_r,const BN_ULONG * a,size_t num_a,const BN_MONT_CTX * mont)453 int bn_from_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
454 size_t num_a, const BN_MONT_CTX *mont) {
455 size_t num_n = mont->N.top;
456 if (num_a > 2 * num_n || num_r != num_n || num_n > BN_SMALL_MAX_WORDS) {
457 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
458 return 0;
459 }
460 BN_ULONG tmp[BN_SMALL_MAX_WORDS * 2];
461 size_t num_tmp = 2 * num_n;
462 OPENSSL_memcpy(tmp, a, num_a * sizeof(BN_ULONG));
463 OPENSSL_memset(tmp + num_a, 0, (num_tmp - num_a) * sizeof(BN_ULONG));
464 int ret = bn_from_montgomery_in_place(r, num_r, tmp, num_tmp, mont);
465 OPENSSL_cleanse(tmp, num_tmp * sizeof(BN_ULONG));
466 return ret;
467 }
468
bn_one_to_montgomery_small(BN_ULONG * r,size_t num_r,const BN_MONT_CTX * mont)469 int bn_one_to_montgomery_small(BN_ULONG *r, size_t num_r,
470 const BN_MONT_CTX *mont) {
471 const BN_ULONG *n = mont->N.d;
472 size_t num_n = mont->N.top;
473 if (num_n == 0 || num_r != num_n) {
474 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
475 return 0;
476 }
477
478 // If the high bit of |n| is set, R = 2^(num_n*BN_BITS2) < 2 * |n|, so we
479 // compute R - |n| rather than perform Montgomery reduction.
480 if (num_n > 0 && (n[num_n - 1] >> (BN_BITS2 - 1)) != 0) {
481 r[0] = 0 - n[0];
482 for (size_t i = 1; i < num_n; i++) {
483 r[i] = ~n[i];
484 }
485 return 1;
486 }
487
488 return bn_from_montgomery_small(r, num_r, mont->RR.d, mont->RR.top, mont);
489 }
490
bn_mod_mul_montgomery_small(BN_ULONG * r,size_t num_r,const BN_ULONG * a,size_t num_a,const BN_ULONG * b,size_t num_b,const BN_MONT_CTX * mont)491 int bn_mod_mul_montgomery_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a,
492 size_t num_a, const BN_ULONG *b, size_t num_b,
493 const BN_MONT_CTX *mont) {
494 size_t num_n = mont->N.top;
495 if (num_r != num_n || num_a + num_b > 2 * num_n ||
496 num_n > BN_SMALL_MAX_WORDS) {
497 OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
498 return 0;
499 }
500
501 #if defined(OPENSSL_BN_ASM_MONT)
502 // |bn_mul_mont| requires at least 128 bits of limbs, at least for x86.
503 if (num_n >= (128 / BN_BITS2) &&
504 num_a == num_n &&
505 num_b == num_n) {
506 if (!bn_mul_mont(r, a, b, mont->N.d, mont->n0, num_n)) {
507 assert(0); // The check above ensures this won't happen.
508 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
509 return 0;
510 }
511 return 1;
512 }
513 #endif
514
515 // Compute the product.
516 BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];
517 size_t num_tmp = 2 * num_n;
518 size_t num_ab = num_a + num_b;
519 if (a == b && num_a == num_b) {
520 if (!bn_sqr_small(tmp, num_ab, a, num_a)) {
521 return 0;
522 }
523 } else if (!bn_mul_small(tmp, num_ab, a, num_a, b, num_b)) {
524 return 0;
525 }
526
527 // Zero-extend to full width and reduce.
528 OPENSSL_memset(tmp + num_ab, 0, (num_tmp - num_ab) * sizeof(BN_ULONG));
529 int ret = bn_from_montgomery_in_place(r, num_r, tmp, num_tmp, mont);
530 OPENSSL_cleanse(tmp, num_tmp * sizeof(BN_ULONG));
531 return ret;
532 }
533