1 /* crypto/bn/bn_mont.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58 /* ====================================================================
59 * Copyright (c) 1998-2018 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
111
112 /*
113 * Details about Montgomery multiplication algorithms can be found at
114 * http://security.ece.orst.edu/publications.html, e.g.
115 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
116 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
117 */
118
119 #include <stdio.h>
120 #include "cryptlib.h"
121 #include "bn_lcl.h"
122
123 #define MONT_WORD /* use the faster word-based algorithm */
124
125 #ifdef MONT_WORD
126 static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
127 #endif
128
BN_mod_mul_montgomery(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_MONT_CTX * mont,BN_CTX * ctx)129 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
130 BN_MONT_CTX *mont, BN_CTX *ctx)
131 {
132 int ret = bn_mul_mont_fixed_top(r, a, b, mont, ctx);
133
134 bn_correct_top(r);
135 bn_check_top(r);
136
137 return ret;
138 }
139
bn_mul_mont_fixed_top(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_MONT_CTX * mont,BN_CTX * ctx)140 int bn_mul_mont_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
141 BN_MONT_CTX *mont, BN_CTX *ctx)
142 {
143 BIGNUM *tmp;
144 int ret = 0;
145 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
146 int num = mont->N.top;
147
148 if (num > 1 && a->top == num && b->top == num) {
149 if (bn_wexpand(r, num) == NULL)
150 return (0);
151 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
152 r->neg = a->neg ^ b->neg;
153 r->top = num;
154 r->flags |= BN_FLG_FIXED_TOP;
155 return 1;
156 }
157 }
158 #endif
159
160 BN_CTX_start(ctx);
161 tmp = BN_CTX_get(ctx);
162 if (tmp == NULL)
163 goto err;
164
165 bn_check_top(tmp);
166 if (a == b) {
167 if (!bn_sqr_fixed_top(tmp, a, ctx))
168 goto err;
169 } else {
170 if (!bn_mul_fixed_top(tmp, a, b, ctx))
171 goto err;
172 }
173 /* reduce from aRR to aR */
174 #ifdef MONT_WORD
175 if (!bn_from_montgomery_word(r, tmp, mont))
176 goto err;
177 #else
178 if (!BN_from_montgomery(r, tmp, mont, ctx))
179 goto err;
180 #endif
181 ret = 1;
182 err:
183 BN_CTX_end(ctx);
184 return (ret);
185 }
186
187 #ifdef MONT_WORD
bn_from_montgomery_word(BIGNUM * ret,BIGNUM * r,BN_MONT_CTX * mont)188 static int bn_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
189 {
190 BIGNUM *n;
191 BN_ULONG *ap, *np, *rp, n0, v, carry;
192 int nl, max, i;
193 unsigned int rtop;
194
195 n = &(mont->N);
196 nl = n->top;
197 if (nl == 0) {
198 ret->top = 0;
199 return (1);
200 }
201
202 max = (2 * nl); /* carry is stored separately */
203 if (bn_wexpand(r, max) == NULL)
204 return (0);
205
206 r->neg ^= n->neg;
207 np = n->d;
208 rp = r->d;
209
210 /* clear the top words of T */
211 for (rtop = r->top, i = 0; i < max; i++) {
212 v = (BN_ULONG)0 - ((i - rtop) >> (8 * sizeof(rtop) - 1));
213 rp[i] &= v;
214 }
215
216 r->top = max;
217 r->flags |= BN_FLG_FIXED_TOP;
218 n0 = mont->n0[0];
219
220 /*
221 * Add multiples of |n| to |r| until R = 2^(nl * BN_BITS2) divides it. On
222 * input, we had |r| < |n| * R, so now |r| < 2 * |n| * R. Note that |r|
223 * includes |carry| which is stored separately.
224 */
225 for (carry = 0, i = 0; i < nl; i++, rp++) {
226 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
227 v = (v + carry + rp[nl]) & BN_MASK2;
228 carry |= (v != rp[nl]);
229 carry &= (v <= rp[nl]);
230 rp[nl] = v;
231 }
232
233 if (bn_wexpand(ret, nl) == NULL)
234 return (0);
235 ret->top = nl;
236 ret->flags |= BN_FLG_FIXED_TOP;
237 ret->neg = r->neg;
238
239 rp = ret->d;
240
241 /*
242 * Shift |nl| words to divide by R. We have |ap| < 2 * |n|. Note that |ap|
243 * includes |carry| which is stored separately.
244 */
245 ap = &(r->d[nl]);
246
247 carry -= bn_sub_words(rp, ap, np, nl);
248 /*
249 * |carry| is -1 if |ap| - |np| underflowed or zero if it did not. Note
250 * |carry| cannot be 1. That would imply the subtraction did not fit in
251 * |nl| words, and we know at most one subtraction is needed.
252 */
253 for (i = 0; i < nl; i++) {
254 rp[i] = (carry & ap[i]) | (~carry & rp[i]);
255 ap[i] = 0;
256 }
257
258 return (1);
259 }
260 #endif /* MONT_WORD */
261
BN_from_montgomery(BIGNUM * ret,const BIGNUM * a,BN_MONT_CTX * mont,BN_CTX * ctx)262 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
263 BN_CTX *ctx)
264 {
265 int retn;
266
267 retn = bn_from_mont_fixed_top(ret, a, mont, ctx);
268 bn_correct_top(ret);
269 bn_check_top(ret);
270
271 return retn;
272 }
273
bn_from_mont_fixed_top(BIGNUM * ret,const BIGNUM * a,BN_MONT_CTX * mont,BN_CTX * ctx)274 int bn_from_mont_fixed_top(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
275 BN_CTX *ctx)
276 {
277 int retn = 0;
278 #ifdef MONT_WORD
279 BIGNUM *t;
280
281 BN_CTX_start(ctx);
282 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a)) {
283 retn = bn_from_montgomery_word(ret, t, mont);
284 }
285 BN_CTX_end(ctx);
286 #else /* !MONT_WORD */
287 BIGNUM *t1, *t2;
288
289 BN_CTX_start(ctx);
290 t1 = BN_CTX_get(ctx);
291 t2 = BN_CTX_get(ctx);
292 if (t1 == NULL || t2 == NULL)
293 goto err;
294
295 if (!BN_copy(t1, a))
296 goto err;
297 BN_mask_bits(t1, mont->ri);
298
299 if (!BN_mul(t2, t1, &mont->Ni, ctx))
300 goto err;
301 BN_mask_bits(t2, mont->ri);
302
303 if (!BN_mul(t1, t2, &mont->N, ctx))
304 goto err;
305 if (!BN_add(t2, a, t1))
306 goto err;
307 if (!BN_rshift(ret, t2, mont->ri))
308 goto err;
309
310 if (BN_ucmp(ret, &(mont->N)) >= 0) {
311 if (!BN_usub(ret, ret, &(mont->N)))
312 goto err;
313 }
314 retn = 1;
315 bn_check_top(ret);
316 err:
317 BN_CTX_end(ctx);
318 #endif /* MONT_WORD */
319 return (retn);
320 }
321
bn_to_mont_fixed_top(BIGNUM * r,const BIGNUM * a,BN_MONT_CTX * mont,BN_CTX * ctx)322 int bn_to_mont_fixed_top(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
323 BN_CTX *ctx)
324 {
325 return bn_mul_mont_fixed_top(r, a, &(mont->RR), mont, ctx);
326 }
327
BN_MONT_CTX_new(void)328 BN_MONT_CTX *BN_MONT_CTX_new(void)
329 {
330 BN_MONT_CTX *ret;
331
332 if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
333 return (NULL);
334
335 BN_MONT_CTX_init(ret);
336 ret->flags = BN_FLG_MALLOCED;
337 return (ret);
338 }
339
BN_MONT_CTX_init(BN_MONT_CTX * ctx)340 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
341 {
342 ctx->ri = 0;
343 BN_init(&(ctx->RR));
344 BN_init(&(ctx->N));
345 BN_init(&(ctx->Ni));
346 ctx->n0[0] = ctx->n0[1] = 0;
347 ctx->flags = 0;
348 }
349
BN_MONT_CTX_free(BN_MONT_CTX * mont)350 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
351 {
352 if (mont == NULL)
353 return;
354
355 BN_clear_free(&(mont->RR));
356 BN_clear_free(&(mont->N));
357 BN_clear_free(&(mont->Ni));
358 if (mont->flags & BN_FLG_MALLOCED)
359 OPENSSL_free(mont);
360 }
361
BN_MONT_CTX_set(BN_MONT_CTX * mont,const BIGNUM * mod,BN_CTX * ctx)362 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
363 {
364 int i, ret = 0;
365 BIGNUM *Ri, *R;
366
367 if (BN_is_zero(mod))
368 return 0;
369
370 BN_CTX_start(ctx);
371 if ((Ri = BN_CTX_get(ctx)) == NULL)
372 goto err;
373 R = &(mont->RR); /* grab RR as a temp */
374 if (!BN_copy(&(mont->N), mod))
375 goto err; /* Set N */
376 if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
377 BN_set_flags(&(mont->N), BN_FLG_CONSTTIME);
378 mont->N.neg = 0;
379
380 #ifdef MONT_WORD
381 {
382 BIGNUM tmod;
383 BN_ULONG buf[2];
384
385 BN_init(&tmod);
386 tmod.d = buf;
387 tmod.dmax = 2;
388 tmod.neg = 0;
389
390 if (BN_get_flags(mod, BN_FLG_CONSTTIME) != 0)
391 BN_set_flags(&tmod, BN_FLG_CONSTTIME);
392
393 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
394
395 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
396 /*
397 * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
398 * and we could use the #else case (with a shorter R value) for the
399 * others. However, currently only the assembler files do know which
400 * is which.
401 */
402
403 BN_zero(R);
404 if (!(BN_set_bit(R, 2 * BN_BITS2)))
405 goto err;
406
407 tmod.top = 0;
408 if ((buf[0] = mod->d[0]))
409 tmod.top = 1;
410 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
411 tmod.top = 2;
412
413 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
414 goto err;
415 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
416 goto err; /* R*Ri */
417 if (!BN_is_zero(Ri)) {
418 if (!BN_sub_word(Ri, 1))
419 goto err;
420 } else { /* if N mod word size == 1 */
421
422 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
423 goto err;
424 /* Ri-- (mod double word size) */
425 Ri->neg = 0;
426 Ri->d[0] = BN_MASK2;
427 Ri->d[1] = BN_MASK2;
428 Ri->top = 2;
429 }
430 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
431 goto err;
432 /*
433 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
434 */
435 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
436 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
437 # else
438 BN_zero(R);
439 if (!(BN_set_bit(R, BN_BITS2)))
440 goto err; /* R */
441
442 buf[0] = mod->d[0]; /* tmod = N mod word size */
443 buf[1] = 0;
444 tmod.top = buf[0] != 0 ? 1 : 0;
445 /* Ri = R^-1 mod N */
446 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
447 goto err;
448 if (!BN_lshift(Ri, Ri, BN_BITS2))
449 goto err; /* R*Ri */
450 if (!BN_is_zero(Ri)) {
451 if (!BN_sub_word(Ri, 1))
452 goto err;
453 } else { /* if N mod word size == 1 */
454
455 if (!BN_set_word(Ri, BN_MASK2))
456 goto err; /* Ri-- (mod word size) */
457 }
458 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
459 goto err;
460 /*
461 * Ni = (R*Ri-1)/N, keep only least significant word:
462 */
463 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
464 mont->n0[1] = 0;
465 # endif
466 }
467 #else /* !MONT_WORD */
468 { /* bignum version */
469 mont->ri = BN_num_bits(&mont->N);
470 BN_zero(R);
471 if (!BN_set_bit(R, mont->ri))
472 goto err; /* R = 2^ri */
473 /* Ri = R^-1 mod N */
474 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
475 goto err;
476 if (!BN_lshift(Ri, Ri, mont->ri))
477 goto err; /* R*Ri */
478 if (!BN_sub_word(Ri, 1))
479 goto err;
480 /*
481 * Ni = (R*Ri-1) / N
482 */
483 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
484 goto err;
485 }
486 #endif
487
488 /* setup RR for conversions */
489 BN_zero(&(mont->RR));
490 if (!BN_set_bit(&(mont->RR), mont->ri * 2))
491 goto err;
492 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
493 goto err;
494
495 for (i = mont->RR.top, ret = mont->N.top; i < ret; i++)
496 mont->RR.d[i] = 0;
497 mont->RR.top = ret;
498 mont->RR.flags |= BN_FLG_FIXED_TOP;
499
500 ret = 1;
501 err:
502 BN_CTX_end(ctx);
503 return ret;
504 }
505
BN_MONT_CTX_copy(BN_MONT_CTX * to,BN_MONT_CTX * from)506 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
507 {
508 if (to == from)
509 return (to);
510
511 if (!BN_copy(&(to->RR), &(from->RR)))
512 return NULL;
513 if (!BN_copy(&(to->N), &(from->N)))
514 return NULL;
515 if (!BN_copy(&(to->Ni), &(from->Ni)))
516 return NULL;
517 to->ri = from->ri;
518 to->n0[0] = from->n0[0];
519 to->n0[1] = from->n0[1];
520 return (to);
521 }
522
BN_MONT_CTX_set_locked(BN_MONT_CTX ** pmont,int lock,const BIGNUM * mod,BN_CTX * ctx)523 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
524 const BIGNUM *mod, BN_CTX *ctx)
525 {
526 BN_MONT_CTX *ret;
527
528 CRYPTO_r_lock(lock);
529 ret = *pmont;
530 CRYPTO_r_unlock(lock);
531 if (ret)
532 return ret;
533
534 /*
535 * We don't want to serialise globally while doing our lazy-init math in
536 * BN_MONT_CTX_set. That punishes threads that are doing independent
537 * things. Instead, punish the case where more than one thread tries to
538 * lazy-init the same 'pmont', by having each do the lazy-init math work
539 * independently and only use the one from the thread that wins the race
540 * (the losers throw away the work they've done).
541 */
542 ret = BN_MONT_CTX_new();
543 if (!ret)
544 return NULL;
545 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
546 BN_MONT_CTX_free(ret);
547 return NULL;
548 }
549
550 /* The locked compare-and-set, after the local work is done. */
551 CRYPTO_w_lock(lock);
552 if (*pmont) {
553 BN_MONT_CTX_free(ret);
554 ret = *pmont;
555 } else
556 *pmont = ret;
557 CRYPTO_w_unlock(lock);
558 return ret;
559 }
560