1 /* crypto/bn/bn_mont.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
58 /* ====================================================================
59 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
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
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/)"
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.
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.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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 * ====================================================================
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).
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
120 #include "cryptlib.h"
123 #define MONT_WORD /* use the faster word-based algorithm */
126 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
129 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
130 BN_MONT_CTX *mont, BN_CTX *ctx)
134 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
135 int num = mont->N.top;
137 if (num > 1 && a->top == num && b->top == num) {
138 if (bn_wexpand(r, num) == NULL)
140 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {
141 r->neg = a->neg ^ b->neg;
150 tmp = BN_CTX_get(ctx);
156 if (!BN_sqr(tmp, a, ctx))
159 if (!BN_mul(tmp, a, b, ctx))
162 /* reduce from aRR to aR */
164 if (!BN_from_montgomery_word(r, tmp, mont))
167 if (!BN_from_montgomery(r, tmp, mont, ctx))
178 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
181 BN_ULONG *ap, *np, *rp, n0, v, carry;
191 max = (2 * nl); /* carry is stored separately */
192 if (bn_wexpand(r, max) == NULL)
199 /* clear the top words of T */
201 for (i = r->top; i < max; i++) /* memset? XXX */
204 memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
211 fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);
213 for (carry = 0, i = 0; i < nl; i++, rp++) {
219 t1 = rp[0] * (n0 & 0177777);
222 t3 = rp[0] & 0177777;
223 t2 = (t3 * t2) & BN_MASK2;
225 v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
228 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
230 v = (v + carry + rp[nl]) & BN_MASK2;
231 carry |= (v != rp[nl]);
232 carry &= (v <= rp[nl]);
236 if (bn_wexpand(ret, nl) == NULL)
244 # define BRANCH_FREE 1
250 v = bn_sub_words(rp, ap, np, nl) - carry;
252 * if subtraction result is real, then trick unconditional memcpy
253 * below to perform in-place "refresh" instead of actual copy.
257 (BN_ULONG *)(((PTR_SIZE_INT) rp & ~m) | ((PTR_SIZE_INT) ap & m));
259 for (i = 0, nl -= 4; i < nl; i += 4) {
260 BN_ULONG t1, t2, t3, t4;
275 for (nl += 4; i < nl; i++)
276 rp[i] = nrp[i], ap[i] = 0;
279 if (bn_sub_words(rp, ap, np, nl) - carry)
280 memcpy(rp, ap, nl * sizeof(BN_ULONG));
288 #endif /* MONT_WORD */
290 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
298 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
299 retn = BN_from_montgomery_word(ret, t, mont);
301 #else /* !MONT_WORD */
305 t1 = BN_CTX_get(ctx);
306 t2 = BN_CTX_get(ctx);
307 if (t1 == NULL || t2 == NULL)
312 BN_mask_bits(t1, mont->ri);
314 if (!BN_mul(t2, t1, &mont->Ni, ctx))
316 BN_mask_bits(t2, mont->ri);
318 if (!BN_mul(t1, t2, &mont->N, ctx))
320 if (!BN_add(t2, a, t1))
322 if (!BN_rshift(ret, t2, mont->ri))
325 if (BN_ucmp(ret, &(mont->N)) >= 0) {
326 if (!BN_usub(ret, ret, &(mont->N)))
333 #endif /* MONT_WORD */
337 BN_MONT_CTX *BN_MONT_CTX_new(void)
341 if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
344 BN_MONT_CTX_init(ret);
345 ret->flags = BN_FLG_MALLOCED;
349 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
355 ctx->n0[0] = ctx->n0[1] = 0;
359 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
364 BN_clear_free(&(mont->RR));
365 BN_clear_free(&(mont->N));
366 BN_clear_free(&(mont->Ni));
367 if (mont->flags & BN_FLG_MALLOCED)
371 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
380 if ((Ri = BN_CTX_get(ctx)) == NULL)
382 R = &(mont->RR); /* grab RR as a temp */
383 if (!BN_copy(&(mont->N), mod))
384 goto err; /* Set N */
397 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
399 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
401 * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
402 * and we could use the #else case (with a shorter R value) for the
403 * others. However, currently only the assembler files do know which
408 if (!(BN_set_bit(R, 2 * BN_BITS2)))
412 if ((buf[0] = mod->d[0]))
414 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
417 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
419 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
421 if (!BN_is_zero(Ri)) {
422 if (!BN_sub_word(Ri, 1))
424 } else { /* if N mod word size == 1 */
426 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
428 /* Ri-- (mod double word size) */
434 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
437 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
439 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
440 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
443 if (!(BN_set_bit(R, BN_BITS2)))
446 buf[0] = mod->d[0]; /* tmod = N mod word size */
448 tmod.top = buf[0] != 0 ? 1 : 0;
449 /* Ri = R^-1 mod N */
450 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
452 if (!BN_lshift(Ri, Ri, BN_BITS2))
454 if (!BN_is_zero(Ri)) {
455 if (!BN_sub_word(Ri, 1))
457 } else { /* if N mod word size == 1 */
459 if (!BN_set_word(Ri, BN_MASK2))
460 goto err; /* Ri-- (mod word size) */
462 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
465 * Ni = (R*Ri-1)/N, keep only least significant word:
467 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
471 #else /* !MONT_WORD */
472 { /* bignum version */
473 mont->ri = BN_num_bits(&mont->N);
475 if (!BN_set_bit(R, mont->ri))
476 goto err; /* R = 2^ri */
477 /* Ri = R^-1 mod N */
478 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
480 if (!BN_lshift(Ri, Ri, mont->ri))
482 if (!BN_sub_word(Ri, 1))
487 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
492 /* setup RR for conversions */
493 BN_zero(&(mont->RR));
494 if (!BN_set_bit(&(mont->RR), mont->ri * 2))
496 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
505 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
510 if (!BN_copy(&(to->RR), &(from->RR)))
512 if (!BN_copy(&(to->N), &(from->N)))
514 if (!BN_copy(&(to->Ni), &(from->Ni)))
517 to->n0[0] = from->n0[0];
518 to->n0[1] = from->n0[1];
522 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
523 const BIGNUM *mod, BN_CTX *ctx)
529 CRYPTO_r_unlock(lock);
534 * We don't want to serialise globally while doing our lazy-init math in
535 * BN_MONT_CTX_set. That punishes threads that are doing independent
536 * things. Instead, punish the case where more than one thread tries to
537 * lazy-init the same 'pmont', by having each do the lazy-init math work
538 * independently and only use the one from the thread that wins the race
539 * (the losers throw away the work they've done).
541 ret = BN_MONT_CTX_new();
544 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
545 BN_MONT_CTX_free(ret);
549 /* The locked compare-and-set, after the local work is done. */
552 BN_MONT_CTX_free(ret);
556 CRYPTO_w_unlock(lock);