1 /* $OpenBSD: bn_mont.c,v 1.28 2022/02/07 19:44:23 tb Exp $ */
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 <stdint.h>
121
122 #include "bn_lcl.h"
123
124 #define MONT_WORD /* use the faster word-based algorithm */
125
126 #ifdef MONT_WORD
127 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
128 #endif
129
130 int
BN_mod_mul_montgomery(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,BN_MONT_CTX * mont,BN_CTX * ctx)131 BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
132 BN_MONT_CTX *mont, BN_CTX *ctx)
133 {
134 BIGNUM *tmp;
135 int ret = 0;
136 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
137 int num = mont->N.top;
138
139 if (num > 1 && a->top == num && b->top == num) {
140 if (bn_wexpand(r, num) == NULL)
141 return (0);
142 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
143 r->neg = a->neg^b->neg;
144 r->top = num;
145 bn_correct_top(r);
146 return (1);
147 }
148 }
149 #endif
150
151 BN_CTX_start(ctx);
152 if ((tmp = BN_CTX_get(ctx)) == NULL)
153 goto err;
154
155 bn_check_top(tmp);
156 if (a == b) {
157 if (!BN_sqr(tmp, a, ctx))
158 goto err;
159 } else {
160 if (!BN_mul(tmp, a,b, ctx))
161 goto err;
162 }
163 /* reduce from aRR to aR */
164 #ifdef MONT_WORD
165 if (!BN_from_montgomery_word(r, tmp, mont))
166 goto err;
167 #else
168 if (!BN_from_montgomery(r, tmp, mont, ctx))
169 goto err;
170 #endif
171 bn_check_top(r);
172 ret = 1;
173 err:
174 BN_CTX_end(ctx);
175 return (ret);
176 }
177
178 int
BN_to_montgomery(BIGNUM * r,const BIGNUM * a,BN_MONT_CTX * mont,BN_CTX * ctx)179 BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx)
180 {
181 return BN_mod_mul_montgomery(r, a, &mont->RR, mont, ctx);
182 }
183
184 #ifdef MONT_WORD
185 static int
BN_from_montgomery_word(BIGNUM * ret,BIGNUM * r,BN_MONT_CTX * mont)186 BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
187 {
188 BIGNUM *n;
189 BN_ULONG *ap, *np, *rp, n0, v, carry;
190 int nl, max, i;
191
192 n = &(mont->N);
193 nl = n->top;
194 if (nl == 0) {
195 ret->top = 0;
196 return (1);
197 }
198
199 max = (2 * nl); /* carry is stored separately */
200 if (bn_wexpand(r, max) == NULL)
201 return (0);
202
203 r->neg ^= n->neg;
204 np = n->d;
205 rp = r->d;
206
207 /* clear the top words of T */
208 #if 1
209 for (i=r->top; i<max; i++) /* memset? XXX */
210 rp[i] = 0;
211 #else
212 memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
213 #endif
214
215 r->top = max;
216 n0 = mont->n0[0];
217
218 #ifdef BN_COUNT
219 fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);
220 #endif
221 for (carry = 0, i = 0; i < nl; i++, rp++) {
222 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
223 v = (v + carry + rp[nl]) & BN_MASK2;
224 carry |= (v != rp[nl]);
225 carry &= (v <= rp[nl]);
226 rp[nl] = v;
227 }
228
229 if (bn_wexpand(ret, nl) == NULL)
230 return (0);
231 ret->top = nl;
232 ret->neg = r->neg;
233
234 rp = ret->d;
235 ap = &(r->d[nl]);
236
237 #define BRANCH_FREE 1
238 #if BRANCH_FREE
239 {
240 BN_ULONG *nrp;
241 size_t m;
242
243 v = bn_sub_words(rp, ap, np, nl) - carry;
244 /* if subtraction result is real, then
245 * trick unconditional memcpy below to perform in-place
246 * "refresh" instead of actual copy. */
247 m = (0 - (size_t)v);
248 nrp = (BN_ULONG *)(((uintptr_t)rp & ~m)|((uintptr_t)ap & m));
249
250 for (i = 0, nl -= 4; i < nl; i += 4) {
251 BN_ULONG t1, t2, t3, t4;
252
253 t1 = nrp[i + 0];
254 t2 = nrp[i + 1];
255 t3 = nrp[i + 2];
256 ap[i + 0] = 0;
257 t4 = nrp[i + 3];
258 ap[i + 1] = 0;
259 rp[i + 0] = t1;
260 ap[i + 2] = 0;
261 rp[i + 1] = t2;
262 ap[i + 3] = 0;
263 rp[i + 2] = t3;
264 rp[i + 3] = t4;
265 }
266 for (nl += 4; i < nl; i++)
267 rp[i] = nrp[i], ap[i] = 0;
268 }
269 #else
270 if (bn_sub_words (rp, ap, np, nl) - carry)
271 memcpy(rp, ap, nl*sizeof(BN_ULONG));
272 #endif
273 bn_correct_top(r);
274 bn_correct_top(ret);
275 bn_check_top(ret);
276
277 return (1);
278 }
279 #endif /* MONT_WORD */
280
281 int
BN_from_montgomery(BIGNUM * ret,const BIGNUM * a,BN_MONT_CTX * mont,BN_CTX * ctx)282 BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx)
283 {
284 int retn = 0;
285 #ifdef MONT_WORD
286 BIGNUM *t;
287
288 BN_CTX_start(ctx);
289 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
290 retn = BN_from_montgomery_word(ret, t, mont);
291 BN_CTX_end(ctx);
292 #else /* !MONT_WORD */
293 BIGNUM *t1, *t2;
294
295 BN_CTX_start(ctx);
296 if ((t1 = BN_CTX_get(ctx)) == NULL)
297 goto err;
298 if ((t2 = BN_CTX_get(ctx)) == NULL)
299 goto err;
300
301 if (!BN_copy(t1, a))
302 goto err;
303 BN_mask_bits(t1, mont->ri);
304
305 if (!BN_mul(t2, t1, &mont->Ni, ctx))
306 goto err;
307 BN_mask_bits(t2, mont->ri);
308
309 if (!BN_mul(t1, t2, &mont->N, ctx))
310 goto err;
311 if (!BN_add(t2, a, t1))
312 goto err;
313 if (!BN_rshift(ret, t2, mont->ri))
314 goto err;
315
316 if (BN_ucmp(ret, &(mont->N)) >= 0) {
317 if (!BN_usub(ret, ret, &(mont->N)))
318 goto err;
319 }
320 retn = 1;
321 bn_check_top(ret);
322
323 err:
324 BN_CTX_end(ctx);
325 #endif /* MONT_WORD */
326 return (retn);
327 }
328
329 BN_MONT_CTX *
BN_MONT_CTX_new(void)330 BN_MONT_CTX_new(void)
331 {
332 BN_MONT_CTX *ret;
333
334 if ((ret = malloc(sizeof(BN_MONT_CTX))) == NULL)
335 return (NULL);
336
337 BN_MONT_CTX_init(ret);
338 ret->flags = BN_FLG_MALLOCED;
339 return (ret);
340 }
341
342 void
BN_MONT_CTX_init(BN_MONT_CTX * ctx)343 BN_MONT_CTX_init(BN_MONT_CTX *ctx)
344 {
345 ctx->ri = 0;
346 BN_init(&(ctx->RR));
347 BN_init(&(ctx->N));
348 BN_init(&(ctx->Ni));
349 ctx->n0[0] = ctx->n0[1] = 0;
350 ctx->flags = 0;
351 }
352
353 void
BN_MONT_CTX_free(BN_MONT_CTX * mont)354 BN_MONT_CTX_free(BN_MONT_CTX *mont)
355 {
356 if (mont == NULL)
357 return;
358
359 BN_clear_free(&(mont->RR));
360 BN_clear_free(&(mont->N));
361 BN_clear_free(&(mont->Ni));
362 if (mont->flags & BN_FLG_MALLOCED)
363 free(mont);
364 }
365
366 int
BN_MONT_CTX_set(BN_MONT_CTX * mont,const BIGNUM * mod,BN_CTX * ctx)367 BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
368 {
369 int ret = 0;
370 BIGNUM *Ri, *R;
371
372 if (BN_is_zero(mod))
373 return 0;
374
375 BN_CTX_start(ctx);
376 if ((Ri = BN_CTX_get(ctx)) == NULL)
377 goto err;
378 R = &(mont->RR); /* grab RR as a temp */
379 if (!BN_copy(&(mont->N), mod))
380 goto err; /* Set N */
381 mont->N.neg = 0;
382
383 #ifdef MONT_WORD
384 {
385 BIGNUM tmod;
386 BN_ULONG buf[2];
387
388 BN_init(&tmod);
389 tmod.d = buf;
390 tmod.dmax = 2;
391 tmod.neg = 0;
392
393 mont->ri = (BN_num_bits(mod) +
394 (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
395
396 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
397 /* Only certain BN_BITS2<=32 platforms actually make use of
398 * n0[1], and we could use the #else case (with a shorter R
399 * value) for the others. However, currently only the assembler
400 * files do know which is which. */
401
402 BN_zero(R);
403 if (!(BN_set_bit(R, 2 * BN_BITS2)))
404 goto err;
405
406 tmod.top = 0;
407 if ((buf[0] = mod->d[0]))
408 tmod.top = 1;
409 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
410 tmod.top = 2;
411
412 if ((BN_mod_inverse_ct(Ri, R, &tmod, ctx)) == NULL)
413 goto err;
414 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
415 goto err; /* R*Ri */
416 if (!BN_is_zero(Ri)) {
417 if (!BN_sub_word(Ri, 1))
418 goto err;
419 }
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_ct(Ri, NULL, Ri, &tmod, ctx))
431 goto err;
432 /* Ni = (R*Ri-1)/N,
433 * keep only couple of least significant words: */
434 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
435 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
436 #else
437 BN_zero(R);
438 if (!(BN_set_bit(R, BN_BITS2)))
439 goto err; /* R */
440
441 buf[0] = mod->d[0]; /* tmod = N mod word size */
442 buf[1] = 0;
443 tmod.top = buf[0] != 0 ? 1 : 0;
444 /* Ri = R^-1 mod N*/
445 if ((BN_mod_inverse_ct(Ri, R, &tmod, ctx)) == NULL)
446 goto err;
447 if (!BN_lshift(Ri, Ri, BN_BITS2))
448 goto err; /* R*Ri */
449 if (!BN_is_zero(Ri)) {
450 if (!BN_sub_word(Ri, 1))
451 goto err;
452 }
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_ct(Ri, NULL, Ri, &tmod, ctx))
459 goto err;
460 /* Ni = (R*Ri-1)/N,
461 * keep only least significant word: */
462 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
463 mont->n0[1] = 0;
464 #endif
465 }
466 #else /* !MONT_WORD */
467 { /* bignum version */
468 mont->ri = BN_num_bits(&mont->N);
469 BN_zero(R);
470 if (!BN_set_bit(R, mont->ri))
471 goto err; /* R = 2^ri */
472 /* Ri = R^-1 mod N*/
473 if ((BN_mod_inverse_ct(Ri, R, &mont->N, ctx)) == NULL)
474 goto err;
475 if (!BN_lshift(Ri, Ri, mont->ri))
476 goto err; /* R*Ri */
477 if (!BN_sub_word(Ri, 1))
478 goto err;
479 /* Ni = (R*Ri-1) / N */
480 if (!BN_div_ct(&(mont->Ni), NULL, Ri, &mont->N, ctx))
481 goto err;
482 }
483 #endif
484
485 /* setup RR for conversions */
486 BN_zero(&(mont->RR));
487 if (!BN_set_bit(&(mont->RR), mont->ri*2))
488 goto err;
489 if (!BN_mod_ct(&(mont->RR), &(mont->RR), &(mont->N), ctx))
490 goto err;
491
492 ret = 1;
493
494 err:
495 BN_CTX_end(ctx);
496 return ret;
497 }
498
499 BN_MONT_CTX *
BN_MONT_CTX_copy(BN_MONT_CTX * to,BN_MONT_CTX * from)500 BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
501 {
502 if (to == from)
503 return (to);
504
505 if (!BN_copy(&(to->RR), &(from->RR)))
506 return NULL;
507 if (!BN_copy(&(to->N), &(from->N)))
508 return NULL;
509 if (!BN_copy(&(to->Ni), &(from->Ni)))
510 return NULL;
511 to->ri = from->ri;
512 to->n0[0] = from->n0[0];
513 to->n0[1] = from->n0[1];
514 return (to);
515 }
516
517 BN_MONT_CTX *
BN_MONT_CTX_set_locked(BN_MONT_CTX ** pmont,int lock,const BIGNUM * mod,BN_CTX * ctx)518 BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, const BIGNUM *mod,
519 BN_CTX *ctx)
520 {
521 int got_write_lock = 0;
522 BN_MONT_CTX *ret;
523
524 CRYPTO_r_lock(lock);
525 if (!*pmont) {
526 CRYPTO_r_unlock(lock);
527 CRYPTO_w_lock(lock);
528 got_write_lock = 1;
529
530 if (!*pmont) {
531 ret = BN_MONT_CTX_new();
532 if (ret && !BN_MONT_CTX_set(ret, mod, ctx))
533 BN_MONT_CTX_free(ret);
534 else
535 *pmont = ret;
536 }
537 }
538
539 ret = *pmont;
540
541 if (got_write_lock)
542 CRYPTO_w_unlock(lock);
543 else
544 CRYPTO_r_unlock(lock);
545
546 return ret;
547 }
548