Line data Source code
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) 1998-2006 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 :
129 537548 : int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
130 : BN_MONT_CTX *mont, BN_CTX *ctx)
131 : {
132 : BIGNUM *tmp;
133 : int ret = 0;
134 : #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
135 : int num = mont->N.top;
136 :
137 : if (num > 1 && a->top == num && b->top == num) {
138 : if (bn_wexpand(r, num) == NULL)
139 : return (0);
140 : if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
141 : r->neg = a->neg ^ b->neg;
142 : r->top = num;
143 : bn_correct_top(r);
144 : return (1);
145 : }
146 : }
147 : #endif
148 :
149 537548 : BN_CTX_start(ctx);
150 537548 : tmp = BN_CTX_get(ctx);
151 537548 : if (tmp == NULL)
152 : goto err;
153 :
154 : bn_check_top(tmp);
155 537548 : if (a == b) {
156 429303 : if (!BN_sqr(tmp, a, ctx))
157 : goto err;
158 : } else {
159 108245 : if (!BN_mul(tmp, a, b, ctx))
160 : goto err;
161 : }
162 : /* reduce from aRR to aR */
163 : #ifdef MONT_WORD
164 537548 : if (!BN_from_montgomery_word(r, tmp, mont))
165 : goto err;
166 : #else
167 : if (!BN_from_montgomery(r, tmp, mont, ctx))
168 : goto err;
169 : #endif
170 : bn_check_top(r);
171 : ret = 1;
172 : err:
173 537548 : BN_CTX_end(ctx);
174 537548 : return (ret);
175 : }
176 :
177 : #ifdef MONT_WORD
178 539818 : static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
179 : {
180 : BIGNUM *n;
181 : BN_ULONG *ap, *np, *rp, n0, v, carry;
182 : int nl, max, i;
183 :
184 : n = &(mont->N);
185 539818 : nl = n->top;
186 539818 : if (nl == 0) {
187 0 : ret->top = 0;
188 0 : return (1);
189 : }
190 :
191 539818 : max = (2 * nl); /* carry is stored separately */
192 539818 : if (bn_wexpand(r, max) == NULL)
193 : return (0);
194 :
195 539818 : r->neg ^= n->neg;
196 539818 : np = n->d;
197 539818 : rp = r->d;
198 :
199 : /* clear the top words of T */
200 : # if 1
201 569754 : for (i = r->top; i < max; i++) /* memset? XXX */
202 29936 : rp[i] = 0;
203 : # else
204 : memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
205 : # endif
206 :
207 539818 : r->top = max;
208 539818 : n0 = mont->n0[0];
209 :
210 : # ifdef BN_COUNT
211 : fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);
212 : # endif
213 5093882 : for (carry = 0, i = 0; i < nl; i++, rp++) {
214 : # ifdef __TANDEM
215 : {
216 : long long t1;
217 : long long t2;
218 : long long t3;
219 : t1 = rp[0] * (n0 & 0177777);
220 : t2 = 037777600000l;
221 : t2 = n0 & t2;
222 : t3 = rp[0] & 0177777;
223 : t2 = (t3 * t2) & BN_MASK2;
224 : t1 = t1 + t2;
225 : v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
226 : }
227 : # else
228 4554064 : v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
229 : # endif
230 4554064 : v = (v + carry + rp[nl]) & BN_MASK2;
231 4554064 : carry |= (v != rp[nl]);
232 4554064 : carry &= (v <= rp[nl]);
233 4554064 : rp[nl] = v;
234 : }
235 :
236 539818 : if (bn_wexpand(ret, nl) == NULL)
237 : return (0);
238 539818 : ret->top = nl;
239 539818 : ret->neg = r->neg;
240 :
241 539818 : rp = ret->d;
242 539818 : ap = &(r->d[nl]);
243 :
244 : # define BRANCH_FREE 1
245 : # if BRANCH_FREE
246 : {
247 : BN_ULONG *nrp;
248 : size_t m;
249 :
250 539818 : v = bn_sub_words(rp, ap, np, nl) - carry;
251 : /*
252 : * if subtraction result is real, then trick unconditional memcpy
253 : * below to perform in-place "refresh" instead of actual copy.
254 : */
255 539818 : m = (0 - (size_t)v);
256 539818 : nrp =
257 539818 : (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
258 :
259 1138516 : for (i = 0, nl -= 4; i < nl; i += 4) {
260 : BN_ULONG t1, t2, t3, t4;
261 :
262 598698 : t1 = nrp[i + 0];
263 598698 : t2 = nrp[i + 1];
264 598698 : t3 = nrp[i + 2];
265 598698 : ap[i + 0] = 0;
266 598698 : t4 = nrp[i + 3];
267 598698 : ap[i + 1] = 0;
268 598698 : rp[i + 0] = t1;
269 598698 : ap[i + 2] = 0;
270 598698 : rp[i + 1] = t2;
271 598698 : ap[i + 3] = 0;
272 598698 : rp[i + 2] = t3;
273 598698 : rp[i + 3] = t4;
274 : }
275 2159272 : for (nl += 4; i < nl; i++)
276 2159272 : rp[i] = nrp[i], ap[i] = 0;
277 : }
278 : # else
279 : if (bn_sub_words(rp, ap, np, nl) - carry)
280 : memcpy(rp, ap, nl * sizeof(BN_ULONG));
281 : # endif
282 539818 : bn_correct_top(r);
283 539818 : bn_correct_top(ret);
284 : bn_check_top(ret);
285 :
286 : return (1);
287 : }
288 : #endif /* MONT_WORD */
289 :
290 2270 : int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
291 : BN_CTX *ctx)
292 : {
293 : int retn = 0;
294 : #ifdef MONT_WORD
295 : BIGNUM *t;
296 :
297 2270 : BN_CTX_start(ctx);
298 2270 : if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
299 2270 : retn = BN_from_montgomery_word(ret, t, mont);
300 2270 : BN_CTX_end(ctx);
301 : #else /* !MONT_WORD */
302 : BIGNUM *t1, *t2;
303 :
304 : BN_CTX_start(ctx);
305 : t1 = BN_CTX_get(ctx);
306 : t2 = BN_CTX_get(ctx);
307 : if (t1 == NULL || t2 == NULL)
308 : goto err;
309 :
310 : if (!BN_copy(t1, a))
311 : goto err;
312 : BN_mask_bits(t1, mont->ri);
313 :
314 : if (!BN_mul(t2, t1, &mont->Ni, ctx))
315 : goto err;
316 : BN_mask_bits(t2, mont->ri);
317 :
318 : if (!BN_mul(t1, t2, &mont->N, ctx))
319 : goto err;
320 : if (!BN_add(t2, a, t1))
321 : goto err;
322 : if (!BN_rshift(ret, t2, mont->ri))
323 : goto err;
324 :
325 : if (BN_ucmp(ret, &(mont->N)) >= 0) {
326 : if (!BN_usub(ret, ret, &(mont->N)))
327 : goto err;
328 : }
329 : retn = 1;
330 : bn_check_top(ret);
331 : err:
332 : BN_CTX_end(ctx);
333 : #endif /* MONT_WORD */
334 2270 : return (retn);
335 : }
336 :
337 6434 : BN_MONT_CTX *BN_MONT_CTX_new(void)
338 : {
339 : BN_MONT_CTX *ret;
340 :
341 6434 : if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
342 : return (NULL);
343 :
344 6434 : BN_MONT_CTX_init(ret);
345 6434 : ret->flags = BN_FLG_MALLOCED;
346 6434 : return (ret);
347 : }
348 :
349 6434 : void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
350 : {
351 6434 : ctx->ri = 0;
352 6434 : BN_init(&(ctx->RR));
353 6434 : BN_init(&(ctx->N));
354 6434 : BN_init(&(ctx->Ni));
355 6434 : ctx->n0[0] = ctx->n0[1] = 0;
356 6434 : ctx->flags = 0;
357 6434 : }
358 :
359 6434 : void BN_MONT_CTX_free(BN_MONT_CTX *mont)
360 : {
361 6434 : if (mont == NULL)
362 6434 : return;
363 :
364 6434 : BN_free(&(mont->RR));
365 6434 : BN_free(&(mont->N));
366 6434 : BN_free(&(mont->Ni));
367 6434 : if (mont->flags & BN_FLG_MALLOCED)
368 6434 : OPENSSL_free(mont);
369 : }
370 :
371 3332 : int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
372 : {
373 : int ret = 0;
374 : BIGNUM *Ri, *R;
375 :
376 3332 : BN_CTX_start(ctx);
377 3332 : if ((Ri = BN_CTX_get(ctx)) == NULL)
378 : goto err;
379 3332 : R = &(mont->RR); /* grab RR as a temp */
380 3332 : if (!BN_copy(&(mont->N), mod))
381 : goto err; /* Set N */
382 3332 : mont->N.neg = 0;
383 :
384 : #ifdef MONT_WORD
385 : {
386 : BIGNUM tmod;
387 : BN_ULONG buf[2];
388 :
389 3332 : BN_init(&tmod);
390 3332 : tmod.d = buf;
391 3332 : tmod.dmax = 2;
392 3332 : tmod.neg = 0;
393 :
394 3332 : mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
395 :
396 : # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
397 : /*
398 : * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
399 : * and we could use the #else case (with a shorter R value) for the
400 : * others. However, currently only the assembler files do know which
401 : * is which.
402 : */
403 :
404 : BN_zero(R);
405 : if (!(BN_set_bit(R, 2 * BN_BITS2)))
406 : goto err;
407 :
408 : tmod.top = 0;
409 : if ((buf[0] = mod->d[0]))
410 : tmod.top = 1;
411 : if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
412 : tmod.top = 2;
413 :
414 : if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
415 : goto err;
416 : if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
417 : goto err; /* R*Ri */
418 : if (!BN_is_zero(Ri)) {
419 : if (!BN_sub_word(Ri, 1))
420 : goto err;
421 : } else { /* if N mod word size == 1 */
422 :
423 : if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
424 : goto err;
425 : /* Ri-- (mod double word size) */
426 : Ri->neg = 0;
427 : Ri->d[0] = BN_MASK2;
428 : Ri->d[1] = BN_MASK2;
429 : Ri->top = 2;
430 : }
431 : if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
432 : goto err;
433 : /*
434 : * Ni = (R*Ri-1)/N, keep only couple of least significant words:
435 : */
436 : mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
437 : mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
438 : # else
439 3332 : BN_zero(R);
440 3332 : if (!(BN_set_bit(R, BN_BITS2)))
441 : goto err; /* R */
442 :
443 3332 : buf[0] = mod->d[0]; /* tmod = N mod word size */
444 3332 : buf[1] = 0;
445 3332 : tmod.top = buf[0] != 0 ? 1 : 0;
446 : /* Ri = R^-1 mod N */
447 3332 : if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
448 : goto err;
449 3332 : if (!BN_lshift(Ri, Ri, BN_BITS2))
450 : goto err; /* R*Ri */
451 3332 : if (!BN_is_zero(Ri)) {
452 3332 : if (!BN_sub_word(Ri, 1))
453 : goto err;
454 : } else { /* if N mod word size == 1 */
455 :
456 0 : if (!BN_set_word(Ri, BN_MASK2))
457 : goto err; /* Ri-- (mod word size) */
458 : }
459 3332 : if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
460 : goto err;
461 : /*
462 : * Ni = (R*Ri-1)/N, keep only least significant word:
463 : */
464 3332 : mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
465 3332 : mont->n0[1] = 0;
466 : # endif
467 : }
468 : #else /* !MONT_WORD */
469 : { /* bignum version */
470 : mont->ri = BN_num_bits(&mont->N);
471 : BN_zero(R);
472 : if (!BN_set_bit(R, mont->ri))
473 : goto err; /* R = 2^ri */
474 : /* Ri = R^-1 mod N */
475 : if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
476 : goto err;
477 : if (!BN_lshift(Ri, Ri, mont->ri))
478 : goto err; /* R*Ri */
479 : if (!BN_sub_word(Ri, 1))
480 : goto err;
481 : /*
482 : * Ni = (R*Ri-1) / N
483 : */
484 : if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
485 : goto err;
486 : }
487 : #endif
488 :
489 : /* setup RR for conversions */
490 3332 : BN_zero(&(mont->RR));
491 3332 : if (!BN_set_bit(&(mont->RR), mont->ri * 2))
492 : goto err;
493 3332 : if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
494 : goto err;
495 :
496 : ret = 1;
497 : err:
498 3332 : BN_CTX_end(ctx);
499 3332 : return ret;
500 : }
501 :
502 3102 : BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
503 : {
504 3102 : if (to == from)
505 : return (to);
506 :
507 3102 : if (!BN_copy(&(to->RR), &(from->RR)))
508 : return NULL;
509 3102 : if (!BN_copy(&(to->N), &(from->N)))
510 : return NULL;
511 3102 : if (!BN_copy(&(to->Ni), &(from->Ni)))
512 : return NULL;
513 3102 : to->ri = from->ri;
514 3102 : to->n0[0] = from->n0[0];
515 3102 : to->n0[1] = from->n0[1];
516 3102 : return (to);
517 : }
518 :
519 1889 : BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
520 : const BIGNUM *mod, BN_CTX *ctx)
521 : {
522 : BN_MONT_CTX *ret;
523 :
524 1889 : CRYPTO_r_lock(lock);
525 1889 : ret = *pmont;
526 1889 : CRYPTO_r_unlock(lock);
527 1889 : if (ret)
528 : return ret;
529 :
530 : /*
531 : * We don't want to serialise globally while doing our lazy-init math in
532 : * BN_MONT_CTX_set. That punishes threads that are doing independent
533 : * things. Instead, punish the case where more than one thread tries to
534 : * lazy-init the same 'pmont', by having each do the lazy-init math work
535 : * independently and only use the one from the thread that wins the race
536 : * (the losers throw away the work they've done).
537 : */
538 1739 : ret = BN_MONT_CTX_new();
539 1739 : if (!ret)
540 : return NULL;
541 1739 : if (!BN_MONT_CTX_set(ret, mod, ctx)) {
542 0 : BN_MONT_CTX_free(ret);
543 0 : return NULL;
544 : }
545 :
546 : /* The locked compare-and-set, after the local work is done. */
547 1739 : CRYPTO_w_lock(lock);
548 1739 : if (*pmont) {
549 0 : BN_MONT_CTX_free(ret);
550 0 : ret = *pmont;
551 : } else
552 1739 : *pmont = ret;
553 1739 : CRYPTO_w_unlock(lock);
554 1739 : return ret;
555 : }
|
