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 */
125 #if defined(MONT_WORD) && defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
127 * This condition means we have a specific non-default build: In the 0.9.8
128 * branch, OPENSSL_BN_ASM_MONT is normally not set for any BN_BITS2<=32
129 * platform; an explicit "enable-montasm" is required. I.e., if we are here,
130 * the user intentionally deviates from the normal stable build to get better
131 * Montgomery performance from the 0.9.9-dev backport. In this case only, we
132 * also enable BN_from_montgomery_word() (another non-stable feature from
135 # define MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
138 #ifdef MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
139 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
142 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
143 BN_MONT_CTX *mont, BN_CTX *ctx)
147 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
148 int num = mont->N.top;
150 if (num > 1 && a->top == num && b->top == num) {
151 if (bn_wexpand(r, num) == NULL)
153 # if 0 /* for OpenSSL 0.9.9 mont->n0 */
154 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num))
156 if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, &mont->n0, num))
159 r->neg = a->neg ^ b->neg;
168 tmp = BN_CTX_get(ctx);
174 if (!BN_sqr(tmp, a, ctx))
177 if (!BN_mul(tmp, a, b, ctx))
180 /* reduce from aRR to aR */
181 #ifdef MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
182 if (!BN_from_montgomery_word(r, tmp, mont))
185 if (!BN_from_montgomery(r, tmp, mont, ctx))
195 #ifdef MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
196 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
199 BN_ULONG *ap, *np, *rp, n0, v, *nrp;
200 int al, nl, max, i, x, ri;
204 * mont->ri is the size of mont->N in bits (rounded up to the word size)
206 al = ri = mont->ri / BN_BITS2;
209 if ((al == 0) || (nl == 0)) {
214 max = (nl + al + 1); /* allow for overflow (no?) XXX */
215 if (bn_wexpand(r, max) == NULL)
223 /* clear the top words of T */
224 for (i = r->top; i < max; i++) /* memset? XXX */
228 # if 0 /* for OpenSSL 0.9.9 mont->n0 */
235 fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);
237 for (i = 0; i < nl; i++) {
243 t1 = rp[0] * (n0 & 0177777);
246 t3 = rp[0] & 0177777;
247 t2 = (t3 * t2) & BN_MASK2;
249 v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
252 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
256 if (((nrp[-1] += v) & BN_MASK2) >= v)
259 if (((++nrp[0]) & BN_MASK2) != 0)
261 if (((++nrp[1]) & BN_MASK2) != 0)
263 for (x = 2; (((++nrp[x]) & BN_MASK2) == 0); x++) ;
269 * mont->ri will be a multiple of the word size and below code is kind of
270 * BN_rshift(ret,r,mont->ri) equivalent
278 if (bn_wexpand(ret, ri) == NULL)
280 x = 0 - (((al - ri) >> (sizeof(al) * 8 - 1)) & 1);
281 ret->top = x = (ri & ~x) | (al & x); /* min(ri,al) */
290 v = bn_sub_words(rp, ap, np, ri);
292 * this ----------------^^ works even in al<ri case thanks to zealous
293 * zeroing of top of the vector in the beginning.
296 /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
298 * in other words if subtraction result is real, then trick
299 * unconditional memcpy below to perform in-place "refresh" instead
302 m1 = 0 - (size_t)(((al - ri) >> (sizeof(al) * 8 - 1)) & 1); /* al<ri */
303 m2 = 0 - (size_t)(((ri - al) >> (sizeof(al) * 8 - 1)) & 1); /* al>ri */
304 m1 |= m2; /* (al!=ri) */
305 m1 |= (0 - (size_t)v); /* (al!=ri || v) */
306 m1 &= ~m2; /* (al!=ri || v) && !al>ri */
307 nrp = (BN_ULONG *)(((size_t)rp & ~m1) | ((size_t)ap & m1));
311 * 'i<ri' is chosen to eliminate dependency on input data, even though it
312 * results in redundant copy in al<ri case.
314 for (i = 0, ri -= 4; i < ri; i += 4) {
315 BN_ULONG t1, t2, t3, t4;
330 for (ri += 4; i < ri; i++)
331 rp[i] = nrp[i], ap[i] = 0;
339 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
346 if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
347 retn = BN_from_montgomery_word(ret, t, mont);
352 #else /* !MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD */
354 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
361 BN_ULONG *ap, *np, *rp, n0, v, *nrp;
362 int al, nl, max, i, x, ri;
365 if ((r = BN_CTX_get(ctx)) == NULL)
374 * mont->ri is the size of mont->N in bits (rounded up to the word size)
376 al = ri = mont->ri / BN_BITS2;
379 if ((al == 0) || (nl == 0)) {
384 max = (nl + al + 1); /* allow for overflow (no?) XXX */
385 if (bn_wexpand(r, max) == NULL)
388 r->neg = a->neg ^ n->neg;
393 /* clear the top words of T */
395 for (i = r->top; i < max; i++) /* memset? XXX */
398 memset(&(r->d[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
405 fprintf(stderr, "word BN_from_montgomery %d * %d\n", nl, nl);
407 for (i = 0; i < nl; i++) {
413 t1 = rp[0] * (n0 & 0177777);
416 t3 = rp[0] & 0177777;
417 t2 = (t3 * t2) & BN_MASK2;
419 v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
422 v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
426 if (((nrp[-1] += v) & BN_MASK2) >= v)
429 if (((++nrp[0]) & BN_MASK2) != 0)
431 if (((++nrp[1]) & BN_MASK2) != 0)
433 for (x = 2; (((++nrp[x]) & BN_MASK2) == 0); x++) ;
439 * mont->ri will be a multiple of the word size and below code is kind of
440 * BN_rshift(ret,r,mont->ri) equivalent
449 # define BRANCH_FREE 1
451 if (bn_wexpand(ret, ri) == NULL)
453 x = 0 - (((al - ri) >> (sizeof(al) * 8 - 1)) & 1);
454 ret->top = x = (ri & ~x) | (al & x); /* min(ri,al) */
463 v = bn_sub_words(rp, ap, np, ri);
465 * this ----------------^^ works even in al<ri case thanks to zealous
466 * zeroing of top of the vector in the beginning.
469 /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
471 * in other words if subtraction result is real, then trick
472 * unconditional memcpy below to perform in-place "refresh" instead
475 m1 = 0 - (size_t)(((al - ri) >> (sizeof(al) * 8 - 1)) & 1); /* al<ri */
476 m2 = 0 - (size_t)(((ri - al) >> (sizeof(al) * 8 - 1)) & 1); /* al>ri */
477 m1 |= m2; /* (al!=ri) */
478 m1 |= (0 - (size_t)v); /* (al!=ri || v) */
479 m1 &= ~m2; /* (al!=ri || v) && !al>ri */
480 nrp = (BN_ULONG *)(((size_t)rp & ~m1) | ((size_t)ap & m1));
484 * 'i<ri' is chosen to eliminate dependency on input data, even though it
485 * results in redundant copy in al<ri case.
487 for (i = 0, ri -= 4; i < ri; i += 4) {
488 BN_ULONG t1, t2, t3, t4;
503 for (ri += 4; i < ri; i++)
504 rp[i] = nrp[i], ap[i] = 0;
508 if (bn_wexpand(ret, al) == NULL)
516 for (i = 0; i < al; i += 4) {
517 BN_ULONG t1, t2, t3, t4;
532 # else /* !MONT_WORD */
536 t1 = BN_CTX_get(ctx);
537 t2 = BN_CTX_get(ctx);
538 if (t1 == NULL || t2 == NULL)
543 BN_mask_bits(t1, mont->ri);
545 if (!BN_mul(t2, t1, &mont->Ni, ctx))
547 BN_mask_bits(t2, mont->ri);
549 if (!BN_mul(t1, t2, &mont->N, ctx))
551 if (!BN_add(t2, a, t1))
553 if (!BN_rshift(ret, t2, mont->ri))
555 # endif /* MONT_WORD */
557 # if !defined(BRANCH_FREE) || BRANCH_FREE==0
558 if (BN_ucmp(ret, &(mont->N)) >= 0) {
559 if (!BN_usub(ret, ret, &(mont->N)))
569 #endif /* MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD */
571 BN_MONT_CTX *BN_MONT_CTX_new(void)
575 if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
578 BN_MONT_CTX_init(ret);
579 ret->flags = BN_FLG_MALLOCED;
583 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
589 #if 0 /* for OpenSSL 0.9.9 mont->n0 */
590 ctx->n0[0] = ctx->n0[1] = 0;
597 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
602 BN_free(&(mont->RR));
604 BN_free(&(mont->Ni));
605 if (mont->flags & BN_FLG_MALLOCED)
609 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
615 if ((Ri = BN_CTX_get(ctx)) == NULL)
617 R = &(mont->RR); /* grab RR as a temp */
618 if (!BN_copy(&(mont->N), mod))
619 goto err; /* Set N */
627 mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
629 # if 0 /* for OpenSSL 0.9.9 mont->n0, would be "#if
630 * defined(OPENSSL_BN_ASM_MONT) &&
631 * (BN_BITS2<=32)", only certain BN_BITS2<=32
632 * platforms actually need this */
633 if (!(BN_set_bit(R, 2 * BN_BITS2)))
636 if (!(BN_set_bit(R, BN_BITS2)))
640 buf[0] = mod->d[0]; /* tmod = N mod word size */
645 tmod.top = buf[0] != 0 ? 1 : 0;
649 # if 0 /* for OpenSSL 0.9.9 mont->n0, would be "#if
650 * defined(OPENSSL_BN_ASM_MONT) &&
651 * (BN_BITS2<=32)"; only certain BN_BITS2<=32
652 * platforms actually need this */
654 if ((buf[0] = mod->d[0]))
656 if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
659 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
661 if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
663 if (!BN_is_zero(Ri)) {
664 if (!BN_sub_word(Ri, 1))
666 } else { /* if N mod word size == 1 */
668 if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
670 /* Ri-- (mod double word size) */
676 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
679 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
681 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
682 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
684 /* Ri = R^-1 mod N */
685 if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
687 if (!BN_lshift(Ri, Ri, BN_BITS2))
689 if (!BN_is_zero(Ri)) {
690 if (!BN_sub_word(Ri, 1))
692 } else { /* if N mod word size == 1 */
694 if (!BN_set_word(Ri, BN_MASK2))
695 goto err; /* Ri-- (mod word size) */
697 if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
700 * Ni = (R*Ri-1)/N, keep only least significant word:
702 # if 0 /* for OpenSSL 0.9.9 mont->n0 */
703 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
706 mont->n0 = (Ri->top > 0) ? Ri->d[0] : 0;
710 #else /* !MONT_WORD */
711 { /* bignum version */
712 mont->ri = BN_num_bits(&mont->N);
714 if (!BN_set_bit(R, mont->ri))
715 goto err; /* R = 2^ri */
716 /* Ri = R^-1 mod N */
717 if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
719 if (!BN_lshift(Ri, Ri, mont->ri))
721 if (!BN_sub_word(Ri, 1))
726 if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
731 /* setup RR for conversions */
732 BN_zero(&(mont->RR));
733 if (!BN_set_bit(&(mont->RR), mont->ri * 2))
735 if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
744 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
749 if (!BN_copy(&(to->RR), &(from->RR)))
751 if (!BN_copy(&(to->N), &(from->N)))
753 if (!BN_copy(&(to->Ni), &(from->Ni)))
756 #if 0 /* for OpenSSL 0.9.9 mont->n0 */
757 to->n0[0] = from->n0[0];
758 to->n0[1] = from->n0[1];
765 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
766 const BIGNUM *mod, BN_CTX *ctx)
772 CRYPTO_r_unlock(lock);
777 * We don't want to serialise globally while doing our lazy-init math in
778 * BN_MONT_CTX_set. That punishes threads that are doing independent
779 * things. Instead, punish the case where more than one thread tries to
780 * lazy-init the same 'pmont', by having each do the lazy-init math work
781 * independently and only use the one from the thread that wins the race
782 * (the losers throw away the work they've done).
784 ret = BN_MONT_CTX_new();
787 if (!BN_MONT_CTX_set(ret, mod, ctx)) {
788 BN_MONT_CTX_free(ret);
792 /* The locked compare-and-set, after the local work is done. */
795 BN_MONT_CTX_free(ret);
799 CRYPTO_w_unlock(lock);