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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 */
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_free(&(mont
->RR
));
366 BN_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
)
377 if ((Ri
= BN_CTX_get(ctx
)) == NULL
)
379 R
= &(mont
->RR
); /* grab RR as a temp */
380 if (!BN_copy(&(mont
->N
), mod
))
381 goto err
; /* Set N */
394 mont
->ri
= (BN_num_bits(mod
) + (BN_BITS2
- 1)) / BN_BITS2
* BN_BITS2
;
396 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
398 * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
399 * and we could use the #else case (with a shorter R value) for the
400 * others. However, currently only the assembler files do know which
405 if (!(BN_set_bit(R
, 2 * BN_BITS2
)))
409 if ((buf
[0] = mod
->d
[0]))
411 if ((buf
[1] = mod
->top
> 1 ? mod
->d
[1] : 0))
414 if ((BN_mod_inverse(Ri
, R
, &tmod
, ctx
)) == NULL
)
416 if (!BN_lshift(Ri
, Ri
, 2 * BN_BITS2
))
418 if (!BN_is_zero(Ri
)) {
419 if (!BN_sub_word(Ri
, 1))
421 } else { /* if N mod word size == 1 */
423 if (bn_expand(Ri
, (int)sizeof(BN_ULONG
) * 2) == NULL
)
425 /* Ri-- (mod double word size) */
431 if (!BN_div(Ri
, NULL
, Ri
, &tmod
, ctx
))
434 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
436 mont
->n0
[0] = (Ri
->top
> 0) ? Ri
->d
[0] : 0;
437 mont
->n0
[1] = (Ri
->top
> 1) ? Ri
->d
[1] : 0;
440 if (!(BN_set_bit(R
, BN_BITS2
)))
443 buf
[0] = mod
->d
[0]; /* tmod = N mod word size */
445 tmod
.top
= buf
[0] != 0 ? 1 : 0;
446 /* Ri = R^-1 mod N */
447 if ((BN_mod_inverse(Ri
, R
, &tmod
, ctx
)) == NULL
)
449 if (!BN_lshift(Ri
, Ri
, BN_BITS2
))
451 if (!BN_is_zero(Ri
)) {
452 if (!BN_sub_word(Ri
, 1))
454 } else { /* if N mod word size == 1 */
456 if (!BN_set_word(Ri
, BN_MASK2
))
457 goto err
; /* Ri-- (mod word size) */
459 if (!BN_div(Ri
, NULL
, Ri
, &tmod
, ctx
))
462 * Ni = (R*Ri-1)/N, keep only least significant word:
464 mont
->n0
[0] = (Ri
->top
> 0) ? Ri
->d
[0] : 0;
468 #else /* !MONT_WORD */
469 { /* bignum version */
470 mont
->ri
= BN_num_bits(&mont
->N
);
472 if (!BN_set_bit(R
, mont
->ri
))
473 goto err
; /* R = 2^ri */
474 /* Ri = R^-1 mod N */
475 if ((BN_mod_inverse(Ri
, R
, &mont
->N
, ctx
)) == NULL
)
477 if (!BN_lshift(Ri
, Ri
, mont
->ri
))
479 if (!BN_sub_word(Ri
, 1))
484 if (!BN_div(&(mont
->Ni
), NULL
, Ri
, &mont
->N
, ctx
))
489 /* setup RR for conversions */
490 BN_zero(&(mont
->RR
));
491 if (!BN_set_bit(&(mont
->RR
), mont
->ri
* 2))
493 if (!BN_mod(&(mont
->RR
), &(mont
->RR
), &(mont
->N
), ctx
))
502 BN_MONT_CTX
*BN_MONT_CTX_copy(BN_MONT_CTX
*to
, BN_MONT_CTX
*from
)
507 if (!BN_copy(&(to
->RR
), &(from
->RR
)))
509 if (!BN_copy(&(to
->N
), &(from
->N
)))
511 if (!BN_copy(&(to
->Ni
), &(from
->Ni
)))
514 to
->n0
[0] = from
->n0
[0];
515 to
->n0
[1] = from
->n0
[1];
519 BN_MONT_CTX
*BN_MONT_CTX_set_locked(BN_MONT_CTX
**pmont
, int lock
,
520 const BIGNUM
*mod
, BN_CTX
*ctx
)
526 CRYPTO_r_unlock(lock
);
531 * We don't want to serialise globally while doing our lazy-init math in
532 * BN_MONT_CTX_set. That punishes threads that are doing independent
533 * things. Instead, punish the case where more than one thread tries to
534 * lazy-init the same 'pmont', by having each do the lazy-init math work
535 * independently and only use the one from the thread that wins the race
536 * (the losers throw away the work they've done).
538 ret
= BN_MONT_CTX_new();
541 if (!BN_MONT_CTX_set(ret
, mod
, ctx
)) {
542 BN_MONT_CTX_free(ret
);
546 /* The locked compare-and-set, after the local work is done. */
549 BN_MONT_CTX_free(ret
);
553 CRYPTO_w_unlock(lock
);