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 *)(((PTR_SIZE_INT)rp&~m1)|((PTR_SIZE_INT)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);