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 <openssl/mem.h>
112 #include <openssl/thread.h>
113
114 #include "internal.h"
115
116
117 #if !defined(OPENSSL_NO_ASM) && \
118 (defined(OPENSSL_X86) || defined(OPENSSL_X86_64))
119 #define OPENSSL_BN_ASM_MONT
120 #endif
121
BN_MONT_CTX_new(void)122 BN_MONT_CTX *BN_MONT_CTX_new(void) {
123 BN_MONT_CTX *ret = OPENSSL_malloc(sizeof(BN_MONT_CTX));
124
125 if (ret == NULL) {
126 return NULL;
127 }
128
129 BN_MONT_CTX_init(ret);
130 ret->flags = BN_FLG_MALLOCED;
131 return ret;
132 }
133
BN_MONT_CTX_init(BN_MONT_CTX * mont)134 void BN_MONT_CTX_init(BN_MONT_CTX *mont) {
135 memset(mont, 0, sizeof(BN_MONT_CTX));
136 BN_init(&mont->RR);
137 BN_init(&mont->N);
138 BN_init(&mont->Ni);
139 }
140
BN_MONT_CTX_free(BN_MONT_CTX * mont)141 void BN_MONT_CTX_free(BN_MONT_CTX *mont) {
142 if (mont == NULL) {
143 return;
144 }
145
146 BN_free(&mont->RR);
147 BN_free(&mont->N);
148 BN_free(&mont->Ni);
149 if (mont->flags & BN_FLG_MALLOCED) {
150 OPENSSL_free(mont);
151 }
152 }
153
BN_MONT_CTX_copy(BN_MONT_CTX * to,BN_MONT_CTX * from)154 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, 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 !BN_copy(&to->Ni, &from->Ni)) {
162 return NULL;
163 }
164 to->ri = from->ri;
165 to->n0[0] = from->n0[0];
166 to->n0[1] = from->n0[1];
167 return to;
168 }
169
BN_MONT_CTX_set(BN_MONT_CTX * mont,const BIGNUM * mod,BN_CTX * ctx)170 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) {
171 int ret = 0;
172 BIGNUM *Ri, *R;
173 BIGNUM tmod;
174 BN_ULONG buf[2];
175
176 BN_CTX_start(ctx);
177 Ri = BN_CTX_get(ctx);
178 if (Ri == NULL) {
179 goto err;
180 }
181 R = &mont->RR; /* grab RR as a temp */
182 if (!BN_copy(&mont->N, mod)) {
183 goto err; /* Set N */
184 }
185 mont->N.neg = 0;
186
187 BN_init(&tmod);
188 tmod.d = buf;
189 tmod.dmax = 2;
190 tmod.neg = 0;
191
192 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
193
194 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2 <= 32)
195 /* Only certain BN_BITS2<=32 platforms actually make use of
196 * n0[1], and we could use the #else case (with a shorter R
197 * value) for the others. However, currently only the assembler
198 * files do know which is which. */
199
200 BN_zero(R);
201 if (!BN_set_bit(R, 2 * BN_BITS2)) {
202 goto err;
203 }
204
205 tmod.top = 0;
206 if ((buf[0] = mod->d[0])) {
207 tmod.top = 1;
208 }
209 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0)) {
210 tmod.top = 2;
211 }
212
213 if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) {
214 goto err;
215 }
216 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2)) {
217 goto err; /* R*Ri */
218 }
219 if (!BN_is_zero(Ri)) {
220 if (!BN_sub_word(Ri, 1)) {
221 goto err;
222 }
223 } else {
224 /* if N mod word size == 1 */
225 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL) {
226 goto err;
227 }
228 /* Ri-- (mod double word size) */
229 Ri->neg = 0;
230 Ri->d[0] = BN_MASK2;
231 Ri->d[1] = BN_MASK2;
232 Ri->top = 2;
233 }
234
235 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) {
236 goto err;
237 }
238 /* Ni = (R*Ri-1)/N,
239 * keep only couple of least significant words: */
240 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
241 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
242 #else
243 BN_zero(R);
244 if (!BN_set_bit(R, BN_BITS2)) {
245 goto err; /* R */
246 }
247
248 buf[0] = mod->d[0]; /* tmod = N mod word size */
249 buf[1] = 0;
250 tmod.top = buf[0] != 0 ? 1 : 0;
251 /* Ri = R^-1 mod N*/
252 if (BN_mod_inverse(Ri, R, &tmod, ctx) == NULL) {
253 goto err;
254 }
255 if (!BN_lshift(Ri, Ri, BN_BITS2)) {
256 goto err; /* R*Ri */
257 }
258 if (!BN_is_zero(Ri)) {
259 if (!BN_sub_word(Ri, 1)) {
260 goto err;
261 }
262 } else {
263 /* if N mod word size == 1 */
264 if (!BN_set_word(Ri, BN_MASK2)) {
265 goto err; /* Ri-- (mod word size) */
266 }
267 }
268 if (!BN_div(Ri, NULL, Ri, &tmod, ctx)) {
269 goto err;
270 }
271 /* Ni = (R*Ri-1)/N,
272 * keep only least significant word: */
273 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
274 mont->n0[1] = 0;
275 #endif
276
277 /* setup RR for conversions */
278 BN_zero(&(mont->RR));
279 if (!BN_set_bit(&(mont->RR), mont->ri * 2)) {
280 goto err;
281 }
282 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx)) {
283 goto err;
284 }
285
286 ret = 1;
287
288 err:
289 BN_CTX_end(ctx);
290 return ret;
291 }
292
BN_MONT_CTX_set_locked(BN_MONT_CTX ** pmont,int lock,const BIGNUM * mod,BN_CTX * ctx)293 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
294 const BIGNUM *mod, BN_CTX *ctx) {
295 BN_MONT_CTX *ret;
296
297 CRYPTO_r_lock(lock);
298 ret = *pmont;
299 CRYPTO_r_unlock(lock);
300 if (ret) {
301 return ret;
302 }
303
304 /* We don't want to serialise globally while doing our lazy-init math in
305 * BN_MONT_CTX_set. That punishes threads that are doing independent
306 * things. Instead, punish the case where more than one thread tries to
307 * lazy-init the same 'pmont', by having each do the lazy-init math work
308 * independently and only use the one from the thread that wins the race
309 * (the losers throw away the work they've done). */
310 ret = BN_MONT_CTX_new();
311 if (!ret) {
312 return NULL;
313 }
314 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
315 BN_MONT_CTX_free(ret);
316 return NULL;
317 }
318
319 /* The locked compare-and-set, after the local work is done. */
320 CRYPTO_w_lock(lock);
321 if (*pmont) {
322 BN_MONT_CTX_free(ret);
323 ret = *pmont;
324 } else {
325 *pmont = ret;
326 }
327
328 CRYPTO_w_unlock(lock);
329
330 return ret;
331 }
332
BN_to_montgomery(BIGNUM * ret,const BIGNUM * a,const BN_MONT_CTX * mont,BN_CTX * ctx)333 int BN_to_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
334 BN_CTX *ctx) {
335 return BN_mod_mul_montgomery(ret, a, &mont->RR, mont, ctx);
336 }
337
338 #if 0
339 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r,
340 const BN_MONT_CTX *mont) {
341 const BIGNUM *n;
342 BN_ULONG *ap, *np, *rp, n0, v, carry;
343 int nl, max, i;
344
345 n = &mont->N;
346 nl = n->top;
347 if (nl == 0) {
348 ret->top = 0;
349 return 1;
350 }
351
352 max = (2 * nl); /* carry is stored separately */
353 if (bn_wexpand(r, max) == NULL) {
354 return 0;
355 }
356
357 r->neg ^= n->neg;
358 np = n->d;
359 rp = r->d;
360
361 /* clear the top words of T */
362 if (max > r->top) {
363 memset(&rp[r->top], 0, (max - r->top) * sizeof(BN_ULONG));
364 }
365
366 r->top = max;
367 n0 = mont->n0[0];
368
369 for (carry = 0, i = 0; i < nl; i++, rp++) {
370 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
371 v = (v + carry + rp[nl]) & BN_MASK2;
372 carry |= (v != rp[nl]);
373 carry &= (v <= rp[nl]);
374 rp[nl] = v;
375 }
376
377 if (bn_wexpand(ret, nl) == NULL) {
378 return 0;
379 }
380 ret->top = nl;
381 ret->neg = r->neg;
382
383 rp = ret->d;
384 ap = &(r->d[nl]);
385
386 {
387 BN_ULONG *nrp;
388 size_t m;
389
390 v = bn_sub_words(rp, ap, np, nl) - carry;
391 /* if subtraction result is real, then trick unconditional memcpy below to
392 * perform in-place "refresh" instead of actual copy. */
393 m = (0 - (size_t)v);
394 nrp = (BN_ULONG *)(((intptr_t)rp & ~m) | ((intptr_t)ap & m));
395
396 for (i = 0, nl -= 4; i < nl; i += 4) {
397 BN_ULONG t1, t2, t3, t4;
398
399 t1 = nrp[i + 0];
400 t2 = nrp[i + 1];
401 t3 = nrp[i + 2];
402 ap[i + 0] = 0;
403 t4 = nrp[i + 3];
404 ap[i + 1] = 0;
405 rp[i + 0] = t1;
406 ap[i + 2] = 0;
407 rp[i + 1] = t2;
408 ap[i + 3] = 0;
409 rp[i + 2] = t3;
410 rp[i + 3] = t4;
411 }
412
413 for (nl += 4; i < nl; i++) {
414 rp[i] = nrp[i], ap[i] = 0;
415 }
416 }
417
418 bn_correct_top(r);
419 bn_correct_top(ret);
420
421 return 1;
422 }
423 #endif
424
425 #define PTR_SIZE_INT size_t
426
BN_from_montgomery_word(BIGNUM * ret,BIGNUM * r,const BN_MONT_CTX * mont)427 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, const BN_MONT_CTX *mont)
428 {
429 BIGNUM *n;
430 BN_ULONG *ap,*np,*rp,n0,v,carry;
431 int nl,max,i;
432
433 n= (BIGNUM*) &(mont->N);
434 nl=n->top;
435 if (nl == 0) { ret->top=0; return(1); }
436
437 max=(2*nl); /* carry is stored separately */
438 if (bn_wexpand(r,max) == NULL) return(0);
439
440 r->neg^=n->neg;
441 np=n->d;
442 rp=r->d;
443
444 /* clear the top words of T */
445 #if 1
446 for (i=r->top; i<max; i++) /* memset? XXX */
447 rp[i]=0;
448 #else
449 memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
450 #endif
451
452 r->top=max;
453 n0=mont->n0[0];
454
455 for (carry=0, i=0; i<nl; i++, rp++)
456 {
457 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
458 v = (v+carry+rp[nl])&BN_MASK2;
459 carry |= (v != rp[nl]);
460 carry &= (v <= rp[nl]);
461 rp[nl]=v;
462 }
463
464 if (bn_wexpand(ret,nl) == NULL) return(0);
465 ret->top=nl;
466 ret->neg=r->neg;
467
468 rp=ret->d;
469 ap=&(r->d[nl]);
470
471 {
472 BN_ULONG *nrp;
473 size_t m;
474
475 v=bn_sub_words(rp,ap,np,nl)-carry;
476 /* if subtraction result is real, then
477 * trick unconditional memcpy below to perform in-place
478 * "refresh" instead of actual copy. */
479 m=(0-(size_t)v);
480 nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m));
481
482 for (i=0,nl-=4; i<nl; i+=4)
483 {
484 BN_ULONG t1,t2,t3,t4;
485
486 t1=nrp[i+0];
487 t2=nrp[i+1];
488 t3=nrp[i+2]; ap[i+0]=0;
489 t4=nrp[i+3]; ap[i+1]=0;
490 rp[i+0]=t1; ap[i+2]=0;
491 rp[i+1]=t2; ap[i+3]=0;
492 rp[i+2]=t3;
493 rp[i+3]=t4;
494 }
495 for (nl+=4; i<nl; i++)
496 rp[i]=nrp[i], ap[i]=0;
497 }
498 bn_correct_top(r);
499 bn_correct_top(ret);
500
501 return(1);
502 }
503
BN_from_montgomery(BIGNUM * ret,const BIGNUM * a,const BN_MONT_CTX * mont,BN_CTX * ctx)504 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, const BN_MONT_CTX *mont,
505 BN_CTX *ctx) {
506 int retn = 0;
507 BIGNUM *t;
508
509 BN_CTX_start(ctx);
510 t = BN_CTX_get(ctx);
511 if (t == NULL) {
512 return 0;
513 }
514
515 if (BN_copy(t, a))
516 retn = BN_from_montgomery_word(ret, t, mont);
517 BN_CTX_end(ctx);
518
519 return retn;
520 }
521
BN_mod_mul_montgomery(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BN_MONT_CTX * mont,BN_CTX * ctx)522 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
523 const BN_MONT_CTX *mont, BN_CTX *ctx) {
524 BIGNUM *tmp;
525 int ret = 0;
526
527 #if defined(OPENSSL_BN_ASM_MONT)
528 int num = mont->N.top;
529
530 if (num > 1 && a->top == num && b->top == num) {
531 if (bn_wexpand(r, num) == NULL) {
532 return 0;
533 }
534 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
535 r->neg = a->neg ^ b->neg;
536 r->top = num;
537 bn_correct_top(r);
538 return 1;
539 }
540 }
541 #endif
542
543 BN_CTX_start(ctx);
544 tmp = BN_CTX_get(ctx);
545 if (tmp == NULL) {
546 goto err;
547 }
548
549 if (a == b) {
550 if (!BN_sqr(tmp, a, ctx)) {
551 goto err;
552 }
553 } else {
554 if (!BN_mul(tmp, a, b, ctx)) {
555 goto err;
556 }
557 }
558
559 /* reduce from aRR to aR */
560 if (!BN_from_montgomery_word(r, tmp, mont)) {
561 goto err;
562 }
563
564 ret = 1;
565
566 err:
567 BN_CTX_end(ctx);
568 return ret;
569 }
570