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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
)
139 if (bn_wexpand(r
,num
) == NULL
) return(0);
140 if (bn_mul_mont(r
->d
,a
->d
,b
->d
,mont
->N
.d
,mont
->n0
,num
))
142 r
->neg
= a
->neg
^b
->neg
;
151 tmp
= BN_CTX_get(ctx
);
152 if (tmp
== NULL
) goto err
;
157 if (!BN_sqr(tmp
,a
,ctx
)) goto err
;
161 if (!BN_mul(tmp
,a
,b
,ctx
)) goto err
;
163 /* reduce from aRR to aR */
165 if (!BN_from_montgomery_word(r
,tmp
,mont
)) goto err
;
167 if (!BN_from_montgomery(r
,tmp
,mont
,ctx
)) goto err
;
177 static int BN_from_montgomery_word(BIGNUM
*ret
, BIGNUM
*r
, BN_MONT_CTX
*mont
)
180 BN_ULONG
*ap
,*np
,*rp
,n0
,v
,*nrp
;
181 int al
,nl
,max
,i
,x
,ri
;
184 /* mont->ri is the size of mont->N in bits (rounded up
186 al
=ri
=mont
->ri
/BN_BITS2
;
189 if ((al
== 0) || (nl
== 0)) { ret
->top
=0; return(1); }
191 max
=(nl
+al
+1); /* allow for overflow (no?) XXX */
192 if (bn_wexpand(r
,max
) == NULL
) return(0);
199 /* clear the top words of T */
201 for (i
=r
->top
; i
<max
; i
++) /* memset? XXX */
204 memset(&(r
->d
[r
->top
]),0,(max
-r
->top
)*sizeof(BN_ULONG
));
211 fprintf(stderr
,"word BN_from_montgomery_word %d * %d\n",nl
,nl
);
220 t1
= rp
[0] * (n0
& 0177777);
223 t3
= rp
[0] & 0177777;
224 t2
= (t3
* t2
) & BN_MASK2
;
226 v
=bn_mul_add_words(rp
,np
,nl
,(BN_ULONG
) t1
);
229 v
=bn_mul_add_words(rp
,np
,nl
,(rp
[0]*n0
)&BN_MASK2
);
233 if (((nrp
[-1]+=v
)&BN_MASK2
) >= v
)
237 if (((++nrp
[0])&BN_MASK2
) != 0) continue;
238 if (((++nrp
[1])&BN_MASK2
) != 0) continue;
239 for (x
=2; (((++nrp
[x
])&BN_MASK2
) == 0); x
++) ;
244 /* mont->ri will be a multiple of the word size and below code
245 * is kind of BN_rshift(ret,r,mont->ri) equivalent */
253 #define BRANCH_FREE 1
255 if (bn_wexpand(ret
,ri
) == NULL
) return(0);
256 x
=0-(((al
-ri
)>>(sizeof(al
)*8-1))&1);
257 ret
->top
=x
=(ri
&~x
)|(al
&x
); /* min(ri,al) */
266 v
=bn_sub_words(rp
,ap
,np
,ri
);
267 /* this ----------------^^ works even in al<ri case
268 * thanks to zealous zeroing of top of the vector in the
271 /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
272 /* in other words if subtraction result is real, then
273 * trick unconditional memcpy below to perform in-place
274 * "refresh" instead of actual copy. */
275 m1
=0-(size_t)(((al
-ri
)>>(sizeof(al
)*8-1))&1); /* al<ri */
276 m2
=0-(size_t)(((ri
-al
)>>(sizeof(al
)*8-1))&1); /* al>ri */
277 m1
|=m2
; /* (al!=ri) */
278 m1
|=(0-(size_t)v
); /* (al!=ri || v) */
279 m1
&=~m2
; /* (al!=ri || v) && !al>ri */
280 nrp
=(BN_ULONG
*)(((size_t)rp
&~m1
)|((size_t)ap
&m1
));
283 /* 'i<ri' is chosen to eliminate dependency on input data, even
284 * though it results in redundant copy in al<ri case. */
285 for (i
=0,ri
-=4; i
<ri
; i
+=4)
287 BN_ULONG t1
,t2
,t3
,t4
;
291 t3
=nrp
[i
+2]; ap
[i
+0]=0;
292 t4
=nrp
[i
+3]; ap
[i
+1]=0;
293 rp
[i
+0]=t1
; ap
[i
+2]=0;
294 rp
[i
+1]=t2
; ap
[i
+3]=0;
298 for (ri
+=4; i
<ri
; i
++)
299 rp
[i
]=nrp
[i
], ap
[i
]=0;
303 if (bn_wexpand(ret
,al
) == NULL
) return(0);
310 for (i
=0; i
<al
; i
+=4)
312 BN_ULONG t1
,t2
,t3
,t4
;
327 if (BN_ucmp(ret
, &(mont
->N
)) >= 0)
329 if (!BN_usub(ret
,ret
,&(mont
->N
))) return(0);
336 #endif /* MONT_WORD */
338 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
);
349 #else /* !MONT_WORD */
353 t1
= BN_CTX_get(ctx
);
354 t2
= BN_CTX_get(ctx
);
355 if (t1
== NULL
|| t2
== NULL
) goto err
;
357 if (!BN_copy(t1
,a
)) goto err
;
358 BN_mask_bits(t1
,mont
->ri
);
360 if (!BN_mul(t2
,t1
,&mont
->Ni
,ctx
)) goto err
;
361 BN_mask_bits(t2
,mont
->ri
);
363 if (!BN_mul(t1
,t2
,&mont
->N
,ctx
)) goto err
;
364 if (!BN_add(t2
,a
,t1
)) goto err
;
365 if (!BN_rshift(ret
,t2
,mont
->ri
)) goto err
;
367 if (BN_ucmp(ret
, &(mont
->N
)) >= 0)
369 if (!BN_usub(ret
,ret
,&(mont
->N
))) goto err
;
375 #endif /* MONT_WORD */
379 BN_MONT_CTX
*BN_MONT_CTX_new(void)
383 if ((ret
=(BN_MONT_CTX
*)OPENSSL_malloc(sizeof(BN_MONT_CTX
))) == NULL
)
386 BN_MONT_CTX_init(ret
);
387 ret
->flags
=BN_FLG_MALLOCED
;
391 void BN_MONT_CTX_init(BN_MONT_CTX
*ctx
)
397 ctx
->n0
[0] = ctx
->n0
[1] = 0;
401 void BN_MONT_CTX_free(BN_MONT_CTX
*mont
)
406 BN_free(&(mont
->RR
));
408 BN_free(&(mont
->Ni
));
409 if (mont
->flags
& BN_FLG_MALLOCED
)
413 int BN_MONT_CTX_set(BN_MONT_CTX
*mont
, const BIGNUM
*mod
, BN_CTX
*ctx
)
419 if((Ri
= BN_CTX_get(ctx
)) == NULL
) goto err
;
420 R
= &(mont
->RR
); /* grab RR as a temp */
421 if (!BN_copy(&(mont
->N
),mod
)) goto err
; /* Set N */
434 mont
->ri
=(BN_num_bits(mod
)+(BN_BITS2
-1))/BN_BITS2
*BN_BITS2
;
436 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
437 /* Only certain BN_BITS2<=32 platforms actually make use of
438 * n0[1], and we could use the #else case (with a shorter R
439 * value) for the others. However, currently only the assembler
440 * files do know which is which. */
443 if (!(BN_set_bit(R
,2*BN_BITS2
))) goto err
;
446 if ((buf
[0] = mod
->d
[0])) tmod
.top
=1;
447 if ((buf
[1] = mod
->top
>1 ? mod
->d
[1] : 0)) tmod
.top
=2;
449 if ((BN_mod_inverse(Ri
,R
,&tmod
,ctx
)) == NULL
)
451 if (!BN_lshift(Ri
,Ri
,2*BN_BITS2
)) goto err
; /* R*Ri */
454 if (!BN_sub_word(Ri
,1)) goto err
;
456 else /* if N mod word size == 1 */
458 if (bn_expand(Ri
,(int)sizeof(BN_ULONG
)*2) == NULL
)
460 /* Ri-- (mod double word size) */
466 if (!BN_div(Ri
,NULL
,Ri
,&tmod
,ctx
)) goto err
;
468 * keep only couple of least significant words: */
469 mont
->n0
[0] = (Ri
->top
> 0) ? Ri
->d
[0] : 0;
470 mont
->n0
[1] = (Ri
->top
> 1) ? Ri
->d
[1] : 0;
473 if (!(BN_set_bit(R
,BN_BITS2
))) goto err
; /* R */
475 buf
[0]=mod
->d
[0]; /* tmod = N mod word size */
477 tmod
.top
= buf
[0] != 0 ? 1 : 0;
479 if ((BN_mod_inverse(Ri
,R
,&tmod
,ctx
)) == NULL
)
481 if (!BN_lshift(Ri
,Ri
,BN_BITS2
)) goto err
; /* R*Ri */
484 if (!BN_sub_word(Ri
,1)) goto err
;
486 else /* if N mod word size == 1 */
488 if (!BN_set_word(Ri
,BN_MASK2
)) goto err
; /* Ri-- (mod word size) */
490 if (!BN_div(Ri
,NULL
,Ri
,&tmod
,ctx
)) goto err
;
492 * keep only least significant word: */
493 mont
->n0
[0] = (Ri
->top
> 0) ? Ri
->d
[0] : 0;
497 #else /* !MONT_WORD */
498 { /* bignum version */
499 mont
->ri
=BN_num_bits(&mont
->N
);
501 if (!BN_set_bit(R
,mont
->ri
)) goto err
; /* R = 2^ri */
503 if ((BN_mod_inverse(Ri
,R
,&mont
->N
,ctx
)) == NULL
)
505 if (!BN_lshift(Ri
,Ri
,mont
->ri
)) goto err
; /* R*Ri */
506 if (!BN_sub_word(Ri
,1)) goto err
;
507 /* Ni = (R*Ri-1) / N */
508 if (!BN_div(&(mont
->Ni
),NULL
,Ri
,&mont
->N
,ctx
)) goto err
;
512 /* setup RR for conversions */
513 BN_zero(&(mont
->RR
));
514 if (!BN_set_bit(&(mont
->RR
),mont
->ri
*2)) goto err
;
515 if (!BN_mod(&(mont
->RR
),&(mont
->RR
),&(mont
->N
),ctx
)) goto err
;
523 BN_MONT_CTX
*BN_MONT_CTX_copy(BN_MONT_CTX
*to
, BN_MONT_CTX
*from
)
525 if (to
== from
) return(to
);
527 if (!BN_copy(&(to
->RR
),&(from
->RR
))) return NULL
;
528 if (!BN_copy(&(to
->N
),&(from
->N
))) return NULL
;
529 if (!BN_copy(&(to
->Ni
),&(from
->Ni
))) return NULL
;
531 to
->n0
[0]=from
->n0
[0];
532 to
->n0
[1]=from
->n0
[1];
536 BN_MONT_CTX
*BN_MONT_CTX_set_locked(BN_MONT_CTX
**pmont
, int lock
,
537 const BIGNUM
*mod
, BN_CTX
*ctx
)
539 int got_write_lock
= 0;
545 CRYPTO_r_unlock(lock
);
551 ret
= BN_MONT_CTX_new();
552 if (ret
&& !BN_MONT_CTX_set(ret
, mod
, ctx
))
553 BN_MONT_CTX_free(ret
);
562 CRYPTO_w_unlock(lock
);
564 CRYPTO_r_unlock(lock
);