1 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
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)"
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
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.]
57 /* ====================================================================
58 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
60 * Redistribution and use in source and binary forms, with or without
61 * modification, are permitted provided that the following conditions
64 * 1. Redistributions of source code must retain the above copyright
65 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
86 * 6. Redistributions of any form whatsoever must retain the following
88 * "This product includes software developed by the OpenSSL Project
89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
112 * Details about Montgomery multiplication algorithms can be found at
113 * http://security.ece.orst.edu/publications.html, e.g.
114 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
115 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
118 #include "internal/cryptlib.h"
121 #define MONT_WORD /* use the faster word-based algorithm */
124 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
127 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
128 BN_MONT_CTX *mont, BN_CTX *ctx)
132 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
133 int num = mont->N.top;
135 if (num > 1 && a->top == num && b->top == num) {
136 if (bn_wexpand(r, num) == NULL)
138 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
139 r->neg = a->neg ^ b->neg;
148 tmp = BN_CTX_get(ctx);
154 if (!BN_sqr(tmp, a, ctx))
157 if (!BN_mul(tmp, a, b, ctx))
160 /* reduce from aRR to aR */
162 if (!BN_from_montgomery_word(r, tmp, mont))
165 if (!BN_from_montgomery(r, tmp, mont, ctx))
176 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
179 BN_ULONG *ap, *np, *rp, n0, v, carry;
189 max = (2 * nl); /* carry is stored separately */
190 if (bn_wexpand(r, max) == NULL)
197 /* clear the top words of T */
200 memset(&rp[r->top], 0, sizeof(*rp) * i);
205 for (carry = 0, i = 0; i < nl; i++, rp++) {
206 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
207 v = (v + carry + rp[nl]) & BN_MASK2;
208 carry |= (v != rp[nl]);
209 carry &= (v <= rp[nl]);
213 if (bn_wexpand(ret, nl) == NULL)
221 # define BRANCH_FREE 1
227 v = bn_sub_words(rp, ap, np, nl) - carry;
229 * if subtraction result is real, then trick unconditional memcpy
230 * below to perform in-place "refresh" instead of actual copy.
234 (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
236 for (i = 0, nl -= 4; i < nl; i += 4) {
237 BN_ULONG t1, t2, t3, t4;
252 for (nl += 4; i < nl; i++)
253 rp[i] = nrp[i], ap[i] = 0;
256 if (bn_sub_words(rp, ap, np, nl) - carry)
257 memcpy(rp, ap, nl * sizeof(BN_ULONG));
265 #endif /* MONT_WORD */
267 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
275 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
276 retn = BN_from_montgomery_word(ret, t, mont);
278 #else /* !MONT_WORD */
282 t1 = BN_CTX_get(ctx);
283 t2 = BN_CTX_get(ctx);
284 if (t1 == NULL || t2 == NULL)
289 BN_mask_bits(t1, mont->ri);
291 if (!BN_mul(t2, t1, &mont->Ni, ctx))
293 BN_mask_bits(t2, mont->ri);
295 if (!BN_mul(t1, t2, &mont->N, ctx))
297 if (!BN_add(t2, a, t1))
299 if (!BN_rshift(ret, t2, mont->ri))
302 if (BN_ucmp(ret, &(mont->N)) >= 0) {
303 if (!BN_usub(ret, ret, &(mont->N)))
310 #endif /* MONT_WORD */
314 BN_MONT_CTX *BN_MONT_CTX_new(void)
318 if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL)
321 BN_MONT_CTX_init(ret);
322 ret->flags = BN_FLG_MALLOCED;
326 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
332 ctx->n0[0] = ctx->n0[1] = 0;
336 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
341 BN_clear_free(&(mont->RR));
342 BN_clear_free(&(mont->N));
343 BN_clear_free(&(mont->Ni));
344 if (mont->flags & BN_FLG_MALLOCED)
348 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
357 if ((Ri = BN_CTX_get(ctx)) == NULL)
359 R = &(mont->RR); /* grab RR as a temp */
360 if (!BN_copy(&(mont->N), mod))
361 goto err; /* Set N */
374 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
376 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
378 * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
379 * and we could use the #else case (with a shorter R value) for the
380 * others. However, currently only the assembler files do know which
385 if (!(BN_set_bit(R, 2 * BN_BITS2)))
389 if ((buf[0] = mod->d[0]))
391 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
394 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
396 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
398 if (!BN_is_zero(Ri)) {
399 if (!BN_sub_word(Ri, 1))
401 } else { /* if N mod word size == 1 */
403 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
405 /* Ri-- (mod double word size) */
411 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
414 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
416 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
417 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
420 if (!(BN_set_bit(R, BN_BITS2)))
423 buf[0] = mod->d[0]; /* tmod = N mod word size */
425 tmod.top = buf[0] != 0 ? 1 : 0;
426 /* Ri = R^-1 mod N */
427 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
429 if (!BN_lshift(Ri, Ri, BN_BITS2))
431 if (!BN_is_zero(Ri)) {
432 if (!BN_sub_word(Ri, 1))
434 } else { /* if N mod word size == 1 */
436 if (!BN_set_word(Ri, BN_MASK2))
437 goto err; /* Ri-- (mod word size) */
439 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
442 * Ni = (R*Ri-1)/N, keep only least significant word:
444 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
448 #else /* !MONT_WORD */
449 { /* bignum version */
450 mont->ri = BN_num_bits(&mont->N);
452 if (!BN_set_bit(R, mont->ri))
453 goto err; /* R = 2^ri */
454 /* Ri = R^-1 mod N */
455 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
457 if (!BN_lshift(Ri, Ri, mont->ri))
459 if (!BN_sub_word(Ri, 1))
464 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
469 /* setup RR for conversions */
470 BN_zero(&(mont->RR));
471 if (!BN_set_bit(&(mont->RR), mont->ri * 2))
473 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
482 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
487 if (!BN_copy(&(to->RR), &(from->RR)))
489 if (!BN_copy(&(to->N), &(from->N)))
491 if (!BN_copy(&(to->Ni), &(from->Ni)))
494 to->n0[0] = from->n0[0];
495 to->n0[1] = from->n0[1];
499 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
500 const BIGNUM *mod, BN_CTX *ctx)
506 CRYPTO_r_unlock(lock);
511 * We don't want to serialise globally while doing our lazy-init math in
512 * BN_MONT_CTX_set. That punishes threads that are doing independent
513 * things. Instead, punish the case where more than one thread tries to
514 * lazy-init the same 'pmont', by having each do the lazy-init math work
515 * independently and only use the one from the thread that wins the race
516 * (the losers throw away the work they've done).
518 ret = BN_MONT_CTX_new();
521 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
522 BN_MONT_CTX_free(ret);
526 /* The locked compare-and-set, after the local work is done. */
529 BN_MONT_CTX_free(ret);
533 CRYPTO_w_unlock(lock);