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/* 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 64 */ 65 66#include <stdio.h> 67#include "cryptlib.h" 68#include "bn_lcl.h" 69 70#define MONT_WORD /* use the faster word-based algorithm */ 71 72int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, 73 BN_MONT_CTX *mont, BN_CTX *ctx) 74 { 75 BIGNUM *tmp; 76 int ret=0; 77 78 BN_CTX_start(ctx); 79 tmp = BN_CTX_get(ctx); 80 if (tmp == NULL) goto err; 81 82 bn_check_top(tmp); 83 if (a == b) 84 { 85 if (!BN_sqr(tmp,a,ctx)) goto err; 86 } 87 else 88 { 89 if (!BN_mul(tmp,a,b,ctx)) goto err; 90 } 91 /* reduce from aRR to aR */ 92 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err; 93 ret=1; 94err: 95 BN_CTX_end(ctx); 96 return(ret); 97 } 98 99int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, 100 BN_CTX *ctx) 101 { 102 int retn=0; 103 104#ifdef MONT_WORD 105 BIGNUM *n,*r; 106 BN_ULONG *ap,*np,*rp,n0,v,*nrp; 107 int al,nl,max,i,x,ri; 108 109 BN_CTX_start(ctx); 110 if ((r = BN_CTX_get(ctx)) == NULL) goto err; 111 112 if (!BN_copy(r,a)) goto err; 113 n= &(mont->N); 114 115 ap=a->d; 116 /* mont->ri is the size of mont->N in bits (rounded up 117 to the word size) */ 118 al=ri=mont->ri/BN_BITS2; 119 120 nl=n->top; 121 if ((al == 0) || (nl == 0)) { r->top=0; return(1); } 122 123 max=(nl+al+1); /* allow for overflow (no?) XXX */ 124 if (bn_wexpand(r,max) == NULL) goto err; 125 if (bn_wexpand(ret,max) == NULL) goto err; 126 127 r->neg=a->neg^n->neg; 128 np=n->d; 129 rp=r->d; 130 nrp= &(r->d[nl]); 131 132 /* clear the top words of T */ 133#if 1 134 for (i=r->top; i<max; i++) /* memset? XXX */ 135 r->d[i]=0; 136#else 137 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); 138#endif 139 140 r->top=max; 141 n0=mont->n0; 142 143#ifdef BN_COUNT 144 fprintf(stderr,"word BN_from_montgomery %d * %d\n",nl,nl); 145#endif 146 for (i=0; i<nl; i++) 147 { 148#ifdef __TANDEM 149 { 150 long long t1; 151 long long t2; 152 long long t3; 153 t1 = rp[0] * (n0 & 0177777); 154 t2 = 037777600000l; 155 t2 = n0 & t2; 156 t3 = rp[0] & 0177777; 157 t2 = (t3 * t2) & BN_MASK2; 158 t1 = t1 + t2; 159 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1); 160 } 161#else 162 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); 163#endif 164 nrp++; 165 rp++; 166 if (((nrp[-1]+=v)&BN_MASK2) >= v) 167 continue; 168 else 169 { 170 if (((++nrp[0])&BN_MASK2) != 0) continue; 171 if (((++nrp[1])&BN_MASK2) != 0) continue; 172 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ; 173 } 174 } 175 bn_fix_top(r); 176 177 /* mont->ri will be a multiple of the word size */ 178#if 0 179 BN_rshift(ret,r,mont->ri); 180#else 181 ret->neg = r->neg; 182 x=ri; 183 rp=ret->d; 184 ap= &(r->d[x]); 185 if (r->top < x) 186 al=0; 187 else 188 al=r->top-x; 189 ret->top=al; 190 al-=4; 191 for (i=0; i<al; i+=4) 192 { 193 BN_ULONG t1,t2,t3,t4; 194 195 t1=ap[i+0]; 196 t2=ap[i+1]; 197 t3=ap[i+2]; 198 t4=ap[i+3]; 199 rp[i+0]=t1; 200 rp[i+1]=t2; 201 rp[i+2]=t3; 202 rp[i+3]=t4; 203 } 204 al+=4; 205 for (; i<al; i++) 206 rp[i]=ap[i]; 207#endif 208#else /* !MONT_WORD */ 209 BIGNUM *t1,*t2; 210 211 BN_CTX_start(ctx); 212 t1 = BN_CTX_get(ctx); 213 t2 = BN_CTX_get(ctx); 214 if (t1 == NULL || t2 == NULL) goto err; 215 216 if (!BN_copy(t1,a)) goto err; 217 BN_mask_bits(t1,mont->ri); 218 219 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err; 220 BN_mask_bits(t2,mont->ri); 221 222 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err; 223 if (!BN_add(t2,a,t1)) goto err; 224 if (!BN_rshift(ret,t2,mont->ri)) goto err; 225#endif /* MONT_WORD */ 226 227 if (BN_ucmp(ret, &(mont->N)) >= 0) 228 { 229 if (!BN_usub(ret,ret,&(mont->N))) goto err; 230 } 231 retn=1; 232 err: 233 BN_CTX_end(ctx); 234 return(retn); 235 } 236 237BN_MONT_CTX *BN_MONT_CTX_new(void) 238 { 239 BN_MONT_CTX *ret; 240 241 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) 242 return(NULL); 243 244 BN_MONT_CTX_init(ret); 245 ret->flags=BN_FLG_MALLOCED; 246 return(ret); 247 } 248 249void BN_MONT_CTX_init(BN_MONT_CTX *ctx) 250 { 251 ctx->ri=0; 252 BN_init(&(ctx->RR)); 253 BN_init(&(ctx->N)); 254 BN_init(&(ctx->Ni)); 255 ctx->flags=0; 256 } 257 258void BN_MONT_CTX_free(BN_MONT_CTX *mont) 259 { 260 if(mont == NULL) 261 return; 262 263 BN_free(&(mont->RR)); 264 BN_free(&(mont->N)); 265 BN_free(&(mont->Ni)); 266 if (mont->flags & BN_FLG_MALLOCED) 267 OPENSSL_free(mont); 268 } 269 270int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) 271 { 272 BIGNUM Ri,*R; 273 274 BN_init(&Ri); 275 R= &(mont->RR); /* grab RR as a temp */ 276 if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */ 277 mont->N.neg = 0; 278 279#ifdef MONT_WORD 280 { 281 BIGNUM tmod; 282 BN_ULONG buf[2]; 283 284 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2; 285 if (!(BN_zero(R))) goto err; 286 if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */ 287 288 buf[0]=mod->d[0]; /* tmod = N mod word size */ 289 buf[1]=0; 290 tmod.d=buf; 291 tmod.top=1; 292 tmod.dmax=2; 293 tmod.neg=0; 294 /* Ri = R^-1 mod N*/ 295 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL) 296 goto err; 297 if (!BN_lshift(&Ri,&Ri,BN_BITS2)) goto err; /* R*Ri */ 298 if (!BN_is_zero(&Ri)) 299 { 300 if (!BN_sub_word(&Ri,1)) goto err; 301 } 302 else /* if N mod word size == 1 */ 303 { 304 if (!BN_set_word(&Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */ 305 } 306 if (!BN_div(&Ri,NULL,&Ri,&tmod,ctx)) goto err; 307 /* Ni = (R*Ri-1)/N, 308 * keep only least significant word: */ 309 mont->n0 = (Ri.top > 0) ? Ri.d[0] : 0; 310 BN_free(&Ri); 311 } 312#else /* !MONT_WORD */ 313 { /* bignum version */ 314 mont->ri=BN_num_bits(&mont->N); 315 if (!BN_zero(R)) goto err; 316 if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */ 317 /* Ri = R^-1 mod N*/ 318 if ((BN_mod_inverse(&Ri,R,&mont->N,ctx)) == NULL) 319 goto err; 320 if (!BN_lshift(&Ri,&Ri,mont->ri)) goto err; /* R*Ri */ 321 if (!BN_sub_word(&Ri,1)) goto err; 322 /* Ni = (R*Ri-1) / N */ 323 if (!BN_div(&(mont->Ni),NULL,&Ri,&mont->N,ctx)) goto err; 324 BN_free(&Ri); 325 } 326#endif 327 328 /* setup RR for conversions */ 329 if (!BN_zero(&(mont->RR))) goto err; 330 if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err; 331 if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err; 332 333 return(1); 334err: 335 return(0); 336 } 337 338BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) 339 { 340 if (to == from) return(to); 341 342 if (!BN_copy(&(to->RR),&(from->RR))) return NULL; 343 if (!BN_copy(&(to->N),&(from->N))) return NULL; 344 if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL; 345 to->ri=from->ri; 346 to->n0=from->n0; 347 return(to); 348 } 349 350