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
118 #include "internal.h"
119 #include "../../internal.h"
120
121
122 #if !defined(OPENSSL_NO_ASM) && \
123 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64) || \
124 defined(OPENSSL_ARM) || defined(OPENSSL_AARCH64))
125 #define OPENSSL_BN_ASM_MONT
126 #endif
127
128 static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a,
129 const BIGNUM *b,
130 const BN_MONT_CTX *mont, BN_CTX *ctx);
131
132
BN_MONT_CTX_new(void)133 BN_MONT_CTX *BN_MONT_CTX_new(void) {
134 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));
135
136 if (ret == NULL) {
137 return NULL;
138 }
139
140 OPENSSL_memset(ret, 0, sizeof(BN_MONT_CTX));
141 BN_init(&ret->RR);
142 BN_init(&ret->N);
143
144 return ret;
145 }
146
BN_MONT_CTX_free(BN_MONT_CTX * mont)147 void BN_MONT_CTX_free(BN_MONT_CTX *mont) {
148 if (mont == NULL) {
149 return;
150 }
151
152 BN_free(&mont->RR);
153 BN_free(&mont->N);
154 OPENSSL_free(mont);
155 }
156
BN_MONT_CTX_copy(BN_MONT_CTX * to,const BN_MONT_CTX * from)157 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, const BN_MONT_CTX *from) {
158 if (to == from) {
159 return to;
160 }
161
162 if (!BN_copy(&to->RR, &from->RR) ||
163 !BN_copy(&to->N, &from->N)) {
164 return NULL;
165 }
166 to->n0[0] = from->n0[0];
167 to->n0[1] = from->n0[1];
168 return to;
169 }
170
171 OPENSSL_COMPILE_ASSERT(BN_MONT_CTX_N0_LIMBS == 1 || BN_MONT_CTX_N0_LIMBS == 2,
172 BN_MONT_CTX_N0_LIMBS_VALUE_INVALID);
173 OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) * BN_MONT_CTX_N0_LIMBS ==
174 sizeof(uint64_t), BN_MONT_CTX_set_64_bit_mismatch);
175
BN_MONT_CTX_set(BN_MONT_CTX * mont,const BIGNUM * mod,BN_CTX * ctx)176 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) {
177 if (BN_is_zero(mod)) {
178 OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
179 return 0;
180 }
181 if (!BN_is_odd(mod)) {
182 OPENSSL_PUT_ERROR(BN, BN_R_CALLED_WITH_EVEN_MODULUS);
183 return 0;
184 }
185 if (BN_is_negative(mod)) {
186 OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
187 return 0;
188 }
189
190 /* Save the modulus. */
191 if (!BN_copy(&mont->N, mod)) {
192 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
193 return 0;
194 }
195
196 /* Find n0 such that n0 * N == -1 (mod r).
197 *
198 * Only certain BN_BITS2<=32 platforms actually make use of n0[1]. For the
199 * others, we could use a shorter R value and use faster |BN_ULONG|-based
200 * math instead of |uint64_t|-based math, which would be double-precision.
201 * However, currently only the assembler files know which is which. */
202 uint64_t n0 = bn_mont_n0(mod);
203 mont->n0[0] = (BN_ULONG)n0;
204 #if BN_MONT_CTX_N0_LIMBS == 2
205 mont->n0[1] = (BN_ULONG)(n0 >> BN_BITS2);
206 #else
207 mont->n0[1] = 0;
208 #endif
209
210 /* Save RR = R**2 (mod N). R is the smallest power of 2**BN_BITS such that R
211 * > mod. Even though the assembly on some 32-bit platforms works with 64-bit
212 * values, using |BN_BITS2| here, rather than |BN_MONT_CTX_N0_LIMBS *
213 * BN_BITS2|, is correct because R**2 will still be a multiple of the latter
214 * as |BN_MONT_CTX_N0_LIMBS| is either one or two.
215 *
216 * XXX: This is not constant time with respect to |mont->N|, but it should
217 * be. */
218 unsigned lgBigR = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * 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_set_locked(BN_MONT_CTX ** pmont,CRYPTO_MUTEX * lock,const BIGNUM * mod,BN_CTX * bn_ctx)226 int BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, CRYPTO_MUTEX *lock,
227 const BIGNUM *mod, BN_CTX *bn_ctx) {
228 CRYPTO_MUTEX_lock_read(lock);
229 BN_MONT_CTX *ctx = *pmont;
230 CRYPTO_MUTEX_unlock_read(lock);
231
232 if (ctx) {
233 return 1;
234 }
235
236 CRYPTO_MUTEX_lock_write(lock);
237 ctx = *pmont;
238 if (ctx) {
239 goto out;
240 }
241
242 ctx = BN_MONT_CTX_new();
243 if (ctx == NULL) {
244 goto out;
245 }
246 if (!BN_MONT_CTX_set(ctx, mod, bn_ctx)) {
247 BN_MONT_CTX_free(ctx);
248 ctx = NULL;
249 goto out;
250 }
251 *pmont = ctx;
252
253 out:
254 CRYPTO_MUTEX_unlock_write(lock);
255 return ctx != NULL;
256 }
257
BN_to_montgomery(BIGNUM * ret,const BIGNUM * a,const BN_MONT_CTX * mont,BN_CTX * ctx)258 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
259 BN_CTX *ctx) {
260 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
261 }
262
BN_from_montgomery_word(BIGNUM * ret,BIGNUM * r,const BN_MONT_CTX * mont)263 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r,
264 const BN_MONT_CTX *mont) {
265 BN_ULONG *ap, *np, *rp, n0, v, carry;
266 int nl, max, i;
267
268 const BIGNUM *n = &mont->N;
269 nl = n->top;
270 if (nl == 0) {
271 ret->top = 0;
272 return 1;
273 }
274
275 max = (2 * nl); /* carry is stored separately */
276 if (!bn_wexpand(r, max)) {
277 return 0;
278 }
279
280 r->neg ^= n->neg;
281 np = n->d;
282 rp = r->d;
283
284 /* clear the top words of T */
285 if (max > r->top) {
286 OPENSSL_memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG));
287 }
288
289 r->top = max;
290 n0 = mont->n0[0];
291
292 for (carry = 0, i = 0; i < nl; i++, rp++) {
293 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
294 v = (v + carry + rp[nl]) & BN_MASK2;
295 carry |= (v != rp[nl]);
296 carry &= (v <= rp[nl]);
297 rp[nl] = v;
298 }
299
300 if (!bn_wexpand(ret, nl)) {
301 return 0;
302 }
303 ret->top = nl;
304 ret->neg = r->neg;
305
306 rp = ret->d;
307 ap = &(r->d[nl]);
308
309 {
310 BN_ULONG *nrp;
311 uintptr_t m;
312
313 v = bn_sub_words(rp, ap, np, nl) - carry;
314 /* if subtraction result is real, then trick unconditional memcpy below to
315 * perform in-place "refresh" instead of actual copy. */
316 m = (0u - (uintptr_t)v);
317 nrp = (BN_ULONG *)(((uintptr_t)rp & ~m) | ((uintptr_t)ap & m));
318
319 for (i = 0, nl -= 4; i < nl; i += 4) {
320 BN_ULONG t1, t2, t3, t4;
321
322 t1 = nrp[i + 0];
323 t2 = nrp[i + 1];
324 t3 = nrp[i + 2];
325 ap[i + 0] = 0;
326 t4 = nrp[i + 3];
327 ap[i + 1] = 0;
328 rp[i + 0] = t1;
329 ap[i + 2] = 0;
330 rp[i + 1] = t2;
331 ap[i + 3] = 0;
332 rp[i + 2] = t3;
333 rp[i + 3] = t4;
334 }
335
336 for (nl += 4; i < nl; i++) {
337 rp[i] = nrp[i], ap[i] = 0;
338 }
339 }
340
341 bn_correct_top(r);
342 bn_correct_top(ret);
343
344 return 1;
345 }
346
BN_from_montgomery(BIGNUM * r,const BIGNUM * a,const BN_MONT_CTX * mont,BN_CTX * ctx)347 int BN_from_montgomery(BIGNUM *r, const BIGNUM *a, const BN_MONT_CTX *mont,
348 BN_CTX *ctx) {
349 int ret = 0;
350 BIGNUM *t;
351
352 BN_CTX_start(ctx);
353 t = BN_CTX_get(ctx);
354 if (t == NULL ||
355 !BN_copy(t, a)) {
356 goto err;
357 }
358
359 ret = BN_from_montgomery_word(r, t, mont);
360
361 err:
362 BN_CTX_end(ctx);
363
364 return ret;
365 }
366
BN_mod_mul_montgomery(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BN_MONT_CTX * mont,BN_CTX * ctx)367 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
368 const BN_MONT_CTX *mont, BN_CTX *ctx) {
369 #if !defined(OPENSSL_BN_ASM_MONT)
370 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx);
371 #else
372 int num = mont->N.top;
373
374 /* |bn_mul_mont| requires at least 128 bits of limbs, at least for x86. */
375 if (num < (128 / BN_BITS2) ||
376 a->top != num ||
377 b->top != num) {
378 return bn_mod_mul_montgomery_fallback(r, a, b, mont, ctx);
379 }
380
381 if (!bn_wexpand(r, num)) {
382 return 0;
383 }
384 if (!bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
385 /* The check above ensures this won't happen. */
386 assert(0);
387 OPENSSL_PUT_ERROR(BN, ERR_R_INTERNAL_ERROR);
388 return 0;
389 }
390 r->neg = a->neg ^ b->neg;
391 r->top = num;
392 bn_correct_top(r);
393
394 return 1;
395 #endif
396 }
397
bn_mod_mul_montgomery_fallback(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BN_MONT_CTX * mont,BN_CTX * ctx)398 static int bn_mod_mul_montgomery_fallback(BIGNUM *r, const BIGNUM *a,
399 const BIGNUM *b,
400 const BN_MONT_CTX *mont,
401 BN_CTX *ctx) {
402 int ret = 0;
403
404 BN_CTX_start(ctx);
405 BIGNUM *tmp = BN_CTX_get(ctx);
406 if (tmp == NULL) {
407 goto err;
408 }
409
410 if (a == b) {
411 if (!BN_sqr(tmp, a, ctx)) {
412 goto err;
413 }
414 } else {
415 if (!BN_mul(tmp, a, b, ctx)) {
416 goto err;
417 }
418 }
419
420 /* reduce from aRR to aR */
421 if (!BN_from_montgomery_word(r, tmp, mont)) {
422 goto err;
423 }
424
425 ret = 1;
426
427 err:
428 BN_CTX_end(ctx);
429 return ret;
430 }
431