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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
);