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,*nrp; 181 int al,nl,max,i,x,ri; 182 183 n= &(mont->N); 184 /* mont->ri is the size of mont->N in bits (rounded up 185 to the word size) */ 186 al=ri=mont->ri/BN_BITS2; 187 188 nl=n->top; 189 if ((al == 0) || (nl == 0)) { ret->top=0; return(1); } 190 191 max=(nl+al+1); /* allow for overflow (no?) XXX */ 192 if (bn_wexpand(r,max) == NULL) return(0); 193 194 r->neg^=n->neg; 195 np=n->d; 196 rp=r->d; 197 nrp= &(r->d[nl]); 198 199 /* clear the top words of T */ 200#if 1 201 for (i=r->top; i<max; i++) /* memset? XXX */ 202 r->d[i]=0; 203#else 204 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); 205#endif 206 207 r->top=max; 208 n0=mont->n0[0]; 209 210#ifdef BN_COUNT 211 fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl); 212#endif 213 for (i=0; i<nl; i++) 214 { 215#ifdef __TANDEM 216 { 217 long long t1; 218 long long t2; 219 long long t3; 220 t1 = rp[0] * (n0 & 0177777); 221 t2 = 037777600000l; 222 t2 = n0 & t2; 223 t3 = rp[0] & 0177777; 224 t2 = (t3 * t2) & BN_MASK2; 225 t1 = t1 + t2; 226 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1); 227 } 228#else 229 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); 230#endif 231 nrp++; 232 rp++; 233 if (((nrp[-1]+=v)&BN_MASK2) >= v) 234 continue; 235 else 236 { 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++) ; 240 } 241 } 242 bn_correct_top(r); 243 244 /* mont->ri will be a multiple of the word size and below code 245 * is kind of BN_rshift(ret,r,mont->ri) equivalent */ 246 if (r->top <= ri) 247 { 248 ret->top=0; 249 return(1); 250 } 251 al=r->top-ri; 252 253#define BRANCH_FREE 1 254#if BRANCH_FREE 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) */ 258 ret->neg=r->neg; 259 260 rp=ret->d; 261 ap=&(r->d[ri]); 262 263 { 264 size_t m1,m2; 265 266 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 269 * beginning. */ 270 271 /* 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)); 281 } 282 283 /* '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) 286 { 287 BN_ULONG t1,t2,t3,t4; 288 289 t1=nrp[i+0]; 290 t2=nrp[i+1]; 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; 295 rp[i+2]=t3; 296 rp[i+3]=t4; 297 } 298 for (ri+=4; i<ri; i++) 299 rp[i]=nrp[i], ap[i]=0; 300 bn_correct_top(r); 301 bn_correct_top(ret); 302#else 303 if (bn_wexpand(ret,al) == NULL) return(0); 304 ret->top=al; 305 ret->neg=r->neg; 306 307 rp=ret->d; 308 ap=&(r->d[ri]); 309 al-=4; 310 for (i=0; i<al; i+=4) 311 { 312 BN_ULONG t1,t2,t3,t4; 313 314 t1=ap[i+0]; 315 t2=ap[i+1]; 316 t3=ap[i+2]; 317 t4=ap[i+3]; 318 rp[i+0]=t1; 319 rp[i+1]=t2; 320 rp[i+2]=t3; 321 rp[i+3]=t4; 322 } 323 al+=4; 324 for (; i<al; i++) 325 rp[i]=ap[i]; 326 327 if (BN_ucmp(ret, &(mont->N)) >= 0) 328 { 329 if (!BN_usub(ret,ret,&(mont->N))) return(0); 330 } 331#endif 332 bn_check_top(ret); 333 334 return(1); 335 } 336#endif /* MONT_WORD */ 337 338int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, 339 BN_CTX *ctx) 340 { 341 int retn=0; 342#ifdef MONT_WORD 343 BIGNUM *t; 344 345 BN_CTX_start(ctx); 346 if ((t = BN_CTX_get(ctx)) && BN_copy(t,a)) 347 retn = BN_from_montgomery_word(ret,t,mont); 348 BN_CTX_end(ctx); 349#else /* !MONT_WORD */ 350 BIGNUM *t1,*t2; 351 352 BN_CTX_start(ctx); 353 t1 = BN_CTX_get(ctx); 354 t2 = BN_CTX_get(ctx); 355 if (t1 == NULL || t2 == NULL) goto err; 356 357 if (!BN_copy(t1,a)) goto err; 358 BN_mask_bits(t1,mont->ri); 359 360 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err; 361 BN_mask_bits(t2,mont->ri); 362 363 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; 366 367 if (BN_ucmp(ret, &(mont->N)) >= 0) 368 { 369 if (!BN_usub(ret,ret,&(mont->N))) goto err; 370 } 371 retn=1; 372 bn_check_top(ret); 373 err: 374 BN_CTX_end(ctx); 375#endif /* MONT_WORD */ 376 return(retn); 377 } 378 379BN_MONT_CTX *BN_MONT_CTX_new(void) 380 { 381 BN_MONT_CTX *ret; 382 383 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) 384 return(NULL); 385 386 BN_MONT_CTX_init(ret); 387 ret->flags=BN_FLG_MALLOCED; 388 return(ret); 389 } 390 391void BN_MONT_CTX_init(BN_MONT_CTX *ctx) 392 { 393 ctx->ri=0; 394 BN_init(&(ctx->RR)); 395 BN_init(&(ctx->N)); 396 BN_init(&(ctx->Ni)); 397 ctx->n0[0] = ctx->n0[1] = 0; 398 ctx->flags=0; 399 } 400 401void BN_MONT_CTX_free(BN_MONT_CTX *mont) 402 { 403 if(mont == NULL) 404 return; 405 406 BN_free(&(mont->RR)); 407 BN_free(&(mont->N)); 408 BN_free(&(mont->Ni)); 409 if (mont->flags & BN_FLG_MALLOCED) 410 OPENSSL_free(mont); 411 } 412 413int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) 414 { 415 int ret = 0; 416 BIGNUM *Ri,*R; 417 418 BN_CTX_start(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 */ 422 mont->N.neg = 0; 423 424#ifdef MONT_WORD 425 { 426 BIGNUM tmod; 427 BN_ULONG buf[2]; 428 429 BN_init(&tmod); 430 tmod.d=buf; 431 tmod.dmax=2; 432 tmod.neg=0; 433 434 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2; 435 436#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. */ 441 442 BN_zero(R); 443 if (!(BN_set_bit(R,2*BN_BITS2))) goto err; 444 445 tmod.top=0; 446 if ((buf[0] = mod->d[0])) tmod.top=1; 447 if ((buf[1] = mod->top>1 ? mod->d[1] : 0)) tmod.top=2; 448 449 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL) 450 goto err; 451 if (!BN_lshift(Ri,Ri,2*BN_BITS2)) goto err; /* R*Ri */ 452 if (!BN_is_zero(Ri)) 453 { 454 if (!BN_sub_word(Ri,1)) goto err; 455 } 456 else /* if N mod word size == 1 */ 457 { 458 if (bn_expand(Ri,(int)sizeof(BN_ULONG)*2) == NULL) 459 goto err; 460 /* Ri-- (mod double word size) */ 461 Ri->neg=0; 462 Ri->d[0]=BN_MASK2; 463 Ri->d[1]=BN_MASK2; 464 Ri->top=2; 465 } 466 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err; 467 /* Ni = (R*Ri-1)/N, 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; 471#else 472 BN_zero(R); 473 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */ 474 475 buf[0]=mod->d[0]; /* tmod = N mod word size */ 476 buf[1]=0; 477 tmod.top = buf[0] != 0 ? 1 : 0; 478 /* Ri = R^-1 mod N*/ 479 if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL) 480 goto err; 481 if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */ 482 if (!BN_is_zero(Ri)) 483 { 484 if (!BN_sub_word(Ri,1)) goto err; 485 } 486 else /* if N mod word size == 1 */ 487 { 488 if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */ 489 } 490 if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err; 491 /* Ni = (R*Ri-1)/N, 492 * keep only least significant word: */ 493 mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0; 494 mont->n0[1] = 0; 495#endif 496 } 497#else /* !MONT_WORD */ 498 { /* bignum version */ 499 mont->ri=BN_num_bits(&mont->N); 500 BN_zero(R); 501 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */ 502 /* Ri = R^-1 mod N*/ 503 if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL) 504 goto err; 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; 509 } 510#endif 511 512 /* 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; 516 517 ret = 1; 518err: 519 BN_CTX_end(ctx); 520 return ret; 521 } 522 523BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) 524 { 525 if (to == from) return(to); 526 527 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; 530 to->ri=from->ri; 531 to->n0[0]=from->n0[0]; 532 to->n0[1]=from->n0[1]; 533 return(to); 534 } 535 536BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, 537 const BIGNUM *mod, BN_CTX *ctx) 538 { 539 BN_MONT_CTX *ret; 540 541 CRYPTO_r_lock(lock); 542 ret = *pmont; 543 CRYPTO_r_unlock(lock); 544 if (ret) 545 return ret; 546 547 /* We don't want to serialise globally while doing our lazy-init math in 548 * BN_MONT_CTX_set. That punishes threads that are doing independent 549 * things. Instead, punish the case where more than one thread tries to 550 * lazy-init the same 'pmont', by having each do the lazy-init math work 551 * independently and only use the one from the thread that wins the race 552 * (the losers throw away the work they've done). */ 553 ret = BN_MONT_CTX_new(); 554 if (!ret) 555 return NULL; 556 if (!BN_MONT_CTX_set(ret, mod, ctx)) 557 { 558 BN_MONT_CTX_free(ret); 559 return NULL; 560 } 561 562 /* The locked compare-and-set, after the local work is done. */ 563 CRYPTO_w_lock(lock); 564 if (*pmont) 565 { 566 BN_MONT_CTX_free(ret); 567 ret = *pmont; 568 } 569 else 570 *pmont = ret; 571 CRYPTO_w_unlock(lock); 572 return ret; 573 } 574