bn_mont.c revision 279264
1/* crypto/bn/bn_mont.c */ 2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) 3 * All rights reserved. 4 * 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. 8 * 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). 15 * 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. 22 * 23 * Redistribution and use in source and binary forms, with or without 24 * modification, are permitted provided that the following conditions 25 * are met: 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)" 40 * 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 51 * SUCH DAMAGE. 52 * 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.] 57 */ 58/* ==================================================================== 59 * Copyright (c) 1998-2006 The OpenSSL Project. All rights reserved. 60 * 61 * Redistribution and use in source and binary forms, with or without 62 * modification, are permitted provided that the following conditions 63 * are met: 64 * 65 * 1. Redistributions of source code must retain the above copyright 66 * notice, this list of conditions and the following disclaimer. 67 * 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 71 * distribution. 72 * 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/)" 77 * 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. 82 * 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. 86 * 87 * 6. Redistributions of any form whatsoever must retain the following 88 * acknowledgment: 89 * "This product includes software developed by the OpenSSL Project 90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)" 91 * 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 * ==================================================================== 105 * 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). 109 * 110 */ 111 112/* 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 117 */ 118 119#include <stdio.h> 120#include "cryptlib.h" 121#include "bn_lcl.h" 122 123#define MONT_WORD /* use the faster word-based algorithm */ 124 125#ifdef MONT_WORD 126static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont); 127#endif 128 129int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 130 BN_MONT_CTX *mont, BN_CTX *ctx) 131 { 132 BIGNUM *tmp; 133 int ret=0; 134#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD) 135 int num = mont->N.top; 136 137 if (num>1 && a->top==num && b->top==num) 138 { 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)) 141 { 142 r->neg = a->neg^b->neg; 143 r->top = num; 144 bn_correct_top(r); 145 return(1); 146 } 147 } 148#endif 149 150 BN_CTX_start(ctx); 151 tmp = BN_CTX_get(ctx); 152 if (tmp == NULL) goto err; 153 154 bn_check_top(tmp); 155 if (a == b) 156 { 157 if (!BN_sqr(tmp,a,ctx)) goto err; 158 } 159 else 160 { 161 if (!BN_mul(tmp,a,b,ctx)) goto err; 162 } 163 /* reduce from aRR to aR */ 164#ifdef MONT_WORD 165 if (!BN_from_montgomery_word(r,tmp,mont)) goto err; 166#else 167 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err; 168#endif 169 bn_check_top(r); 170 ret=1; 171err: 172 BN_CTX_end(ctx); 173 return(ret); 174 } 175 176#ifdef MONT_WORD 177static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont) 178 { 179 BIGNUM *n; 180 BN_ULONG *ap,*np,*rp,n0,v,carry; 181 int nl,max,i; 182 183 n= &(mont->N); 184 nl=n->top; 185 if (nl == 0) { ret->top=0; return(1); } 186 187 max=(2*nl); /* carry is stored separately */ 188 if (bn_wexpand(r,max) == NULL) return(0); 189 190 r->neg^=n->neg; 191 np=n->d; 192 rp=r->d; 193 194 /* clear the top words of T */ 195#if 1 196 for (i=r->top; i<max; i++) /* memset? XXX */ 197 rp[i]=0; 198#else 199 memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); 200#endif 201 202 r->top=max; 203 n0=mont->n0[0]; 204 205#ifdef BN_COUNT 206 fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl); 207#endif 208 for (carry=0, i=0; i<nl; i++, rp++) 209 { 210#ifdef __TANDEM 211 { 212 long long t1; 213 long long t2; 214 long long t3; 215 t1 = rp[0] * (n0 & 0177777); 216 t2 = 037777600000l; 217 t2 = n0 & t2; 218 t3 = rp[0] & 0177777; 219 t2 = (t3 * t2) & BN_MASK2; 220 t1 = t1 + t2; 221 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1); 222 } 223#else 224 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); 225#endif 226 v = (v+carry+rp[nl])&BN_MASK2; 227 carry |= (v != rp[nl]); 228 carry &= (v <= rp[nl]); 229 rp[nl]=v; 230 } 231 232 if (bn_wexpand(ret,nl) == NULL) return(0); 233 ret->top=nl; 234 ret->neg=r->neg; 235 236 rp=ret->d; 237 ap=&(r->d[nl]); 238 239#define BRANCH_FREE 1 240#if BRANCH_FREE 241 { 242 BN_ULONG *nrp; 243 size_t m; 244 245 v=bn_sub_words(rp,ap,np,nl)-carry; 246 /* if subtraction result is real, then 247 * trick unconditional memcpy below to perform in-place 248 * "refresh" instead of actual copy. */ 249 m=(0-(size_t)v); 250 nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m)); 251 252 for (i=0,nl-=4; i<nl; i+=4) 253 { 254 BN_ULONG t1,t2,t3,t4; 255 256 t1=nrp[i+0]; 257 t2=nrp[i+1]; 258 t3=nrp[i+2]; ap[i+0]=0; 259 t4=nrp[i+3]; ap[i+1]=0; 260 rp[i+0]=t1; ap[i+2]=0; 261 rp[i+1]=t2; ap[i+3]=0; 262 rp[i+2]=t3; 263 rp[i+3]=t4; 264 } 265 for (nl+=4; i<nl; i++) 266 rp[i]=nrp[i], ap[i]=0; 267 } 268#else 269 if (bn_sub_words (rp,ap,np,nl)-carry) 270 memcpy(rp,ap,nl*sizeof(BN_ULONG)); 271#endif 272 bn_correct_top(r); 273 bn_correct_top(ret); 274 bn_check_top(ret); 275 276 return(1); 277 } 278#endif /* MONT_WORD */ 279 280int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, 281 BN_CTX *ctx) 282 { 283 int retn=0; 284#ifdef MONT_WORD 285 BIGNUM *t; 286 287 BN_CTX_start(ctx); 288 if ((t = BN_CTX_get(ctx)) && BN_copy(t,a)) 289 retn = BN_from_montgomery_word(ret,t,mont); 290 BN_CTX_end(ctx); 291#else /* !MONT_WORD */ 292 BIGNUM *t1,*t2; 293 294 BN_CTX_start(ctx); 295 t1 = BN_CTX_get(ctx); 296 t2 = BN_CTX_get(ctx); 297 if (t1 == NULL || t2 == NULL) goto err; 298 299 if (!BN_copy(t1,a)) goto err; 300 BN_mask_bits(t1,mont->ri); 301 302 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err; 303 BN_mask_bits(t2,mont->ri); 304 305 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err; 306 if (!BN_add(t2,a,t1)) goto err; 307 if (!BN_rshift(ret,t2,mont->ri)) goto err; 308 309 if (BN_ucmp(ret, &(mont->N)) >= 0) 310 { 311 if (!BN_usub(ret,ret,&(mont->N))) goto err; 312 } 313 retn=1; 314 bn_check_top(ret); 315 err: 316 BN_CTX_end(ctx); 317#endif /* MONT_WORD */ 318 return(retn); 319 } 320 321BN_MONT_CTX *BN_MONT_CTX_new(void) 322 { 323 BN_MONT_CTX *ret; 324 325 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) 326 return(NULL); 327 328 BN_MONT_CTX_init(ret); 329 ret->flags=BN_FLG_MALLOCED; 330 return(ret); 331 } 332 333void BN_MONT_CTX_init(BN_MONT_CTX *ctx) 334 { 335 ctx->ri=0; 336 BN_init(&(ctx->RR)); 337 BN_init(&(ctx->N)); 338 BN_init(&(ctx->Ni)); 339 ctx->n0[0] = ctx->n0[1] = 0; 340 ctx->flags=0; 341 } 342 343void BN_MONT_CTX_free(BN_MONT_CTX *mont) 344 { 345 if(mont == NULL) 346 return; 347 348 BN_free(&(mont->RR)); 349 BN_free(&(mont->N)); 350 BN_free(&(mont->Ni)); 351 if (mont->flags & BN_FLG_MALLOCED) 352 OPENSSL_free(mont); 353 } 354 355int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) 356 { 357 int ret = 0; 358 BIGNUM *Ri,*R; 359 360 BN_CTX_start(ctx); 361 if((Ri = BN_CTX_get(ctx)) == NULL) goto err; 362 R= &(mont->RR); /* grab RR as a temp */ 363 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */ 364 mont->N.neg = 0; 365 366#ifdef MONT_WORD 367 { 368 BIGNUM tmod; 369 BN_ULONG buf[2]; 370 371 BN_init(&tmod); 372 tmod.d=buf; 373 tmod.dmax=2; 374 tmod.neg=0; 375 376 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2; 377 378#if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32) 379 /* Only certain BN_BITS2<=32 platforms actually make use of 380 * n0[1], and we could use the #else case (with a shorter R 381 * value) for the others. However, currently only the assembler 382 * files do know which is which. */ 383 384 BN_zero(R); 385 if (!(BN_set_bit(R,2*BN_BITS2))) goto err; 386 387 tmod.top=0; 388 if ((buf[0] = mod->d[0])) tmod.top=1; 389 if ((buf[1] = mod->top>1 ? mod->d[1] : 0)) tmod.top=2; 390 391 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL) 392 goto err; 393 if (!BN_lshift(Ri,Ri,2*BN_BITS2)) goto err; /* R*Ri */ 394 if (!BN_is_zero(Ri)) 395 { 396 if (!BN_sub_word(Ri,1)) goto err; 397 } 398 else /* if N mod word size == 1 */ 399 { 400 if (bn_expand(Ri,(int)sizeof(BN_ULONG)*2) == NULL) 401 goto err; 402 /* Ri-- (mod double word size) */ 403 Ri->neg=0; 404 Ri->d[0]=BN_MASK2; 405 Ri->d[1]=BN_MASK2; 406 Ri->top=2; 407 } 408 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err; 409 /* Ni = (R*Ri-1)/N, 410 * keep only couple of least significant words: */ 411 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 412 mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0; 413#else 414 BN_zero(R); 415 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */ 416 417 buf[0]=mod->d[0]; /* tmod = N mod word size */ 418 buf[1]=0; 419 tmod.top = buf[0] != 0 ? 1 : 0; 420 /* Ri = R^-1 mod N*/ 421 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL) 422 goto err; 423 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */ 424 if (!BN_is_zero(Ri)) 425 { 426 if (!BN_sub_word(Ri,1)) goto err; 427 } 428 else /* if N mod word size == 1 */ 429 { 430 if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */ 431 } 432 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err; 433 /* Ni = (R*Ri-1)/N, 434 * keep only least significant word: */ 435 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 436 mont->n0[1] = 0; 437#endif 438 } 439#else /* !MONT_WORD */ 440 { /* bignum version */ 441 mont->ri=BN_num_bits(&mont->N); 442 BN_zero(R); 443 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */ 444 /* Ri = R^-1 mod N*/ 445 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL) 446 goto err; 447 if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */ 448 if (!BN_sub_word(Ri,1)) goto err; 449 /* Ni = (R*Ri-1) / N */ 450 if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err; 451 } 452#endif 453 454 /* setup RR for conversions */ 455 BN_zero(&(mont->RR)); 456 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err; 457 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err; 458 459 ret = 1; 460err: 461 BN_CTX_end(ctx); 462 return ret; 463 } 464 465BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) 466 { 467 if (to == from) return(to); 468 469 if (!BN_copy(&(to->RR),&(from->RR))) return NULL; 470 if (!BN_copy(&(to->N),&(from->N))) return NULL; 471 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL; 472 to->ri=from->ri; 473 to->n0[0]=from->n0[0]; 474 to->n0[1]=from->n0[1]; 475 return(to); 476 } 477 478BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, 479 const BIGNUM *mod, BN_CTX *ctx) 480 { 481 BN_MONT_CTX *ret; 482 483 CRYPTO_r_lock(lock); 484 ret = *pmont; 485 CRYPTO_r_unlock(lock); 486 if (ret) 487 return ret; 488 489 /* We don't want to serialise globally while doing our lazy-init math in 490 * BN_MONT_CTX_set. That punishes threads that are doing independent 491 * things. Instead, punish the case where more than one thread tries to 492 * lazy-init the same 'pmont', by having each do the lazy-init math work 493 * independently and only use the one from the thread that wins the race 494 * (the losers throw away the work they've done). */ 495 ret = BN_MONT_CTX_new(); 496 if (!ret) 497 return NULL; 498 if (!BN_MONT_CTX_set(ret, mod, ctx)) 499 { 500 BN_MONT_CTX_free(ret); 501 return NULL; 502 } 503 504 /* The locked compare-and-set, after the local work is done. */ 505 CRYPTO_w_lock(lock); 506 if (*pmont) 507 { 508 BN_MONT_CTX_free(ret); 509 ret = *pmont; 510 } 511 else 512 *pmont = ret; 513 CRYPTO_w_unlock(lock); 514 return ret; 515 } 516