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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
119 #include "cryptlib.h"
122 #define MONT_WORD /* use the faster word-based algorithm */
125 static int BN_from_montgomery_word(BIGNUM
*ret
, BIGNUM
*r
, BN_MONT_CTX
*mont
);
128 int BN_mod_mul_montgomery(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
,
129 BN_MONT_CTX
*mont
, BN_CTX
*ctx
)
133 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
134 int num
= mont
->N
.top
;
136 if (num
> 1 && a
->top
== num
&& b
->top
== num
) {
137 if (bn_wexpand(r
, num
) == NULL
)
139 if (bn_mul_mont(r
->d
, a
->d
, b
->d
, mont
->N
.d
, mont
->n0
, num
)) {
140 r
->neg
= a
->neg
^ b
->neg
;
149 tmp
= BN_CTX_get(ctx
);
155 if (!BN_sqr(tmp
, a
, ctx
))
158 if (!BN_mul(tmp
, a
, b
, ctx
))
161 /* reduce from aRR to aR */
163 if (!BN_from_montgomery_word(r
, tmp
, mont
))
166 if (!BN_from_montgomery(r
, tmp
, mont
, ctx
))
177 static int BN_from_montgomery_word(BIGNUM
*ret
, BIGNUM
*r
, BN_MONT_CTX
*mont
)
180 BN_ULONG
*ap
, *np
, *rp
, n0
, v
, carry
;
190 max
= (2 * nl
); /* carry is stored separately */
191 if (bn_wexpand(r
, max
) == NULL
)
198 /* clear the top words of T */
199 memset(&(rp
[r
->top
]), 0, (max
- r
->top
) * sizeof(BN_ULONG
));
204 for (carry
= 0, i
= 0; i
< nl
; i
++, rp
++) {
205 v
= bn_mul_add_words(rp
, np
, nl
, (rp
[0] * n0
) & BN_MASK2
);
206 v
= (v
+ carry
+ rp
[nl
]) & BN_MASK2
;
207 carry
|= (v
!= rp
[nl
]);
208 carry
&= (v
<= rp
[nl
]);
212 if (bn_wexpand(ret
, nl
) == NULL
)
220 # define BRANCH_FREE 1
226 v
= bn_sub_words(rp
, ap
, np
, nl
) - carry
;
228 * if subtraction result is real, then trick unconditional memcpy
229 * below to perform in-place "refresh" instead of actual copy.
233 (BN_ULONG
*)(((PTR_SIZE_INT
) rp
& ~m
) | ((PTR_SIZE_INT
) ap
& m
));
235 for (i
= 0, nl
-= 4; i
< nl
; i
+= 4) {
236 BN_ULONG t1
, t2
, t3
, t4
;
251 for (nl
+= 4; i
< nl
; i
++)
252 rp
[i
] = nrp
[i
], ap
[i
] = 0;
255 if (bn_sub_words(rp
, ap
, np
, nl
) - carry
)
256 memcpy(rp
, ap
, nl
* sizeof(BN_ULONG
));
264 #endif /* MONT_WORD */
266 int BN_from_montgomery(BIGNUM
*ret
, const BIGNUM
*a
, BN_MONT_CTX
*mont
,
274 if ((t
= BN_CTX_get(ctx
)) && BN_copy(t
, a
))
275 retn
= BN_from_montgomery_word(ret
, t
, mont
);
277 #else /* !MONT_WORD */
281 t1
= BN_CTX_get(ctx
);
282 t2
= BN_CTX_get(ctx
);
283 if (t1
== NULL
|| t2
== NULL
)
288 BN_mask_bits(t1
, mont
->ri
);
290 if (!BN_mul(t2
, t1
, &mont
->Ni
, ctx
))
292 BN_mask_bits(t2
, mont
->ri
);
294 if (!BN_mul(t1
, t2
, &mont
->N
, ctx
))
296 if (!BN_add(t2
, a
, t1
))
298 if (!BN_rshift(ret
, t2
, mont
->ri
))
301 if (BN_ucmp(ret
, &(mont
->N
)) >= 0) {
302 if (!BN_usub(ret
, ret
, &(mont
->N
)))
309 #endif /* MONT_WORD */
313 BN_MONT_CTX
*BN_MONT_CTX_new(void)
317 if ((ret
= OPENSSL_malloc(sizeof(*ret
))) == NULL
)
320 BN_MONT_CTX_init(ret
);
321 ret
->flags
= BN_FLG_MALLOCED
;
325 void BN_MONT_CTX_init(BN_MONT_CTX
*ctx
)
331 ctx
->n0
[0] = ctx
->n0
[1] = 0;
335 void BN_MONT_CTX_free(BN_MONT_CTX
*mont
)
340 BN_free(&(mont
->RR
));
342 BN_free(&(mont
->Ni
));
343 if (mont
->flags
& BN_FLG_MALLOCED
)
347 int BN_MONT_CTX_set(BN_MONT_CTX
*mont
, const BIGNUM
*mod
, BN_CTX
*ctx
)
353 if ((Ri
= BN_CTX_get(ctx
)) == NULL
)
355 R
= &(mont
->RR
); /* grab RR as a temp */
356 if (!BN_copy(&(mont
->N
), mod
))
357 goto err
; /* Set N */
370 mont
->ri
= (BN_num_bits(mod
) + (BN_BITS2
- 1)) / BN_BITS2
* BN_BITS2
;
372 # if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
374 * Only certain BN_BITS2<=32 platforms actually make use of n0[1],
375 * and we could use the #else case (with a shorter R value) for the
376 * others. However, currently only the assembler files do know which
381 if (!(BN_set_bit(R
, 2 * BN_BITS2
)))
385 if ((buf
[0] = mod
->d
[0]))
387 if ((buf
[1] = mod
->top
> 1 ? mod
->d
[1] : 0))
390 if ((BN_mod_inverse(Ri
, R
, &tmod
, ctx
)) == NULL
)
392 if (!BN_lshift(Ri
, Ri
, 2 * BN_BITS2
))
394 if (!BN_is_zero(Ri
)) {
395 if (!BN_sub_word(Ri
, 1))
397 } else { /* if N mod word size == 1 */
399 if (bn_expand(Ri
, (int)sizeof(BN_ULONG
) * 2) == NULL
)
401 /* Ri-- (mod double word size) */
407 if (!BN_div(Ri
, NULL
, Ri
, &tmod
, ctx
))
410 * Ni = (R*Ri-1)/N, keep only couple of least significant words:
412 mont
->n0
[0] = (Ri
->top
> 0) ? Ri
->d
[0] : 0;
413 mont
->n0
[1] = (Ri
->top
> 1) ? Ri
->d
[1] : 0;
416 if (!(BN_set_bit(R
, BN_BITS2
)))
419 buf
[0] = mod
->d
[0]; /* tmod = N mod word size */
421 tmod
.top
= buf
[0] != 0 ? 1 : 0;
422 /* Ri = R^-1 mod N */
423 if ((BN_mod_inverse(Ri
, R
, &tmod
, ctx
)) == NULL
)
425 if (!BN_lshift(Ri
, Ri
, BN_BITS2
))
427 if (!BN_is_zero(Ri
)) {
428 if (!BN_sub_word(Ri
, 1))
430 } else { /* if N mod word size == 1 */
432 if (!BN_set_word(Ri
, BN_MASK2
))
433 goto err
; /* Ri-- (mod word size) */
435 if (!BN_div(Ri
, NULL
, Ri
, &tmod
, ctx
))
438 * Ni = (R*Ri-1)/N, keep only least significant word:
440 mont
->n0
[0] = (Ri
->top
> 0) ? Ri
->d
[0] : 0;
444 #else /* !MONT_WORD */
445 { /* bignum version */
446 mont
->ri
= BN_num_bits(&mont
->N
);
448 if (!BN_set_bit(R
, mont
->ri
))
449 goto err
; /* R = 2^ri */
450 /* Ri = R^-1 mod N */
451 if ((BN_mod_inverse(Ri
, R
, &mont
->N
, ctx
)) == NULL
)
453 if (!BN_lshift(Ri
, Ri
, mont
->ri
))
455 if (!BN_sub_word(Ri
, 1))
460 if (!BN_div(&(mont
->Ni
), NULL
, Ri
, &mont
->N
, ctx
))
465 /* setup RR for conversions */
466 BN_zero(&(mont
->RR
));
467 if (!BN_set_bit(&(mont
->RR
), mont
->ri
* 2))
469 if (!BN_mod(&(mont
->RR
), &(mont
->RR
), &(mont
->N
), ctx
))
478 BN_MONT_CTX
*BN_MONT_CTX_copy(BN_MONT_CTX
*to
, BN_MONT_CTX
*from
)
483 if (!BN_copy(&(to
->RR
), &(from
->RR
)))
485 if (!BN_copy(&(to
->N
), &(from
->N
)))
487 if (!BN_copy(&(to
->Ni
), &(from
->Ni
)))
490 to
->n0
[0] = from
->n0
[0];
491 to
->n0
[1] = from
->n0
[1];
495 BN_MONT_CTX
*BN_MONT_CTX_set_locked(BN_MONT_CTX
**pmont
, int lock
,
496 const BIGNUM
*mod
, BN_CTX
*ctx
)
502 CRYPTO_r_unlock(lock
);
507 * We don't want to serialise globally while doing our lazy-init math in
508 * BN_MONT_CTX_set. That punishes threads that are doing independent
509 * things. Instead, punish the case where more than one thread tries to
510 * lazy-init the same 'pmont', by having each do the lazy-init math work
511 * independently and only use the one from the thread that wins the race
512 * (the losers throw away the work they've done).
514 ret
= BN_MONT_CTX_new();
517 if (!BN_MONT_CTX_set(ret
, mod
, ctx
)) {
518 BN_MONT_CTX_free(ret
);
522 /* The locked compare-and-set, after the local work is done. */
525 BN_MONT_CTX_free(ret
);
529 CRYPTO_w_unlock(lock
);