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.]
60 * Details about Montgomery multiplication algorithms can be found at
61 * http://security.ece.orst.edu/publications.html, e.g.
62 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
63 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
70 #define MONT_WORD /* use the faster word-based algorithm */
73 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
76 int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
77 BN_MONT_CTX *mont, BN_CTX *ctx)
81 #if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
82 int num = mont->N.top;
84 if (num>1 && a->top==num && b->top==num)
86 if (bn_wexpand(r,num) == NULL) return(0);
87 if (bn_mul_mont(r->d,a->d,b->d,mont->N.d,mont->n0,num))
89 r->neg = a->neg^b->neg;
98 tmp = BN_CTX_get(ctx);
99 if (tmp == NULL) goto err;
104 if (!BN_sqr(tmp,a,ctx)) goto err;
108 if (!BN_mul(tmp,a,b,ctx)) goto err;
110 /* reduce from aRR to aR */
112 if (!BN_from_montgomery_word(r,tmp,mont)) goto err;
114 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
124 static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
127 BN_ULONG *ap,*np,*rp,n0,v,*nrp;
128 int al,nl,max,i,x,ri;
131 /* mont->ri is the size of mont->N in bits (rounded up
133 al=ri=mont->ri/BN_BITS2;
136 if ((al == 0) || (nl == 0)) { ret->top=0; return(1); }
138 max=(nl+al+1); /* allow for overflow (no?) XXX */
139 if (bn_wexpand(r,max) == NULL) return(0);
146 /* clear the top words of T */
148 for (i=r->top; i<max; i++) /* memset? XXX */
151 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
158 fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl);
167 t1 = rp[0] * (n0 & 0177777);
170 t3 = rp[0] & 0177777;
171 t2 = (t3 * t2) & BN_MASK2;
173 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
176 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
180 if (((nrp[-1]+=v)&BN_MASK2) >= v)
184 if (((++nrp[0])&BN_MASK2) != 0) continue;
185 if (((++nrp[1])&BN_MASK2) != 0) continue;
186 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
191 /* mont->ri will be a multiple of the word size */
193 BN_rshift(ret,r,mont->ri);
201 if (bn_wexpand(ret,al) == NULL) return(0);
208 for (i=0; i<al; i+=4)
210 BN_ULONG t1,t2,t3,t4;
226 if (BN_ucmp(ret, &(mont->N)) >= 0)
228 if (!BN_usub(ret,ret,&(mont->N))) return(0);
234 #endif /* MONT_WORD */
236 int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
244 if ((t = BN_CTX_get(ctx)) && BN_copy(t,a))
245 retn = BN_from_montgomery_word(ret,t,mont);
247 #else /* !MONT_WORD */
251 t1 = BN_CTX_get(ctx);
252 t2 = BN_CTX_get(ctx);
253 if (t1 == NULL || t2 == NULL) goto err;
255 if (!BN_copy(t1,a)) goto err;
256 BN_mask_bits(t1,mont->ri);
258 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
259 BN_mask_bits(t2,mont->ri);
261 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
262 if (!BN_add(t2,a,t1)) goto err;
263 if (!BN_rshift(ret,t2,mont->ri)) goto err;
265 if (BN_ucmp(ret, &(mont->N)) >= 0)
267 if (!BN_usub(ret,ret,&(mont->N))) goto err;
273 #endif /* MONT_WORD */
277 BN_MONT_CTX *BN_MONT_CTX_new(void)
281 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
284 BN_MONT_CTX_init(ret);
285 ret->flags=BN_FLG_MALLOCED;
289 void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
298 void BN_MONT_CTX_free(BN_MONT_CTX *mont)
303 BN_free(&(mont->RR));
305 BN_free(&(mont->Ni));
306 if (mont->flags & BN_FLG_MALLOCED)
310 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
316 if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
317 R= &(mont->RR); /* grab RR as a temp */
318 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
330 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
332 #if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
334 if (!(BN_set_bit(R,2*BN_BITS2))) goto err;
337 if ((buf[0] = mod->d[0])) tmod.top=1;
338 if ((buf[1] = mod->top>1 ? mod->d[1] : 0)) tmod.top=2;
340 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
342 if (!BN_lshift(Ri,Ri,2*BN_BITS2)) goto err; /* R*Ri */
345 if (!BN_sub_word(Ri,1)) goto err;
347 else /* if N mod word size == 1 */
349 if (bn_expand(Ri,(int)sizeof(BN_ULONG)*2) == NULL)
351 /* Ri-- (mod double word size) */
357 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
359 * keep only couple of least significant words: */
360 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
361 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
364 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
366 buf[0]=mod->d[0]; /* tmod = N mod word size */
368 tmod.top = buf[0] != 0 ? 1 : 0;
370 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
372 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
375 if (!BN_sub_word(Ri,1)) goto err;
377 else /* if N mod word size == 1 */
379 if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
381 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
383 * keep only least significant word: */
384 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
388 #else /* !MONT_WORD */
389 { /* bignum version */
390 mont->ri=BN_num_bits(&mont->N);
392 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
394 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)
396 if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
397 if (!BN_sub_word(Ri,1)) goto err;
398 /* Ni = (R*Ri-1) / N */
399 if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
403 /* setup RR for conversions */
404 BN_zero(&(mont->RR));
405 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
406 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
414 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
416 if (to == from) return(to);
418 if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
419 if (!BN_copy(&(to->N),&(from->N))) return NULL;
420 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
422 to->n0[0]=from->n0[0];
423 to->n0[1]=from->n0[1];
427 BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
428 const BIGNUM *mod, BN_CTX *ctx)
436 mtmp = BN_MONT_CTX_new();
437 if (mtmp && !BN_MONT_CTX_set(mtmp, mod, ctx))
438 BN_MONT_CTX_free(mtmp);
442 CRYPTO_w_unlock(lock);