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 72 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b, 73 BN_MONT_CTX *mont, BN_CTX *ctx) 74 { 75 BIGNUM *tmp,*tmp2; 76 int ret=0; 77 78 BN_CTX_start(ctx); 79 tmp = BN_CTX_get(ctx); 80 tmp2 = BN_CTX_get(ctx); 81 if (tmp == NULL || tmp2 == NULL) goto err; 82 83 bn_check_top(tmp); 84 bn_check_top(tmp2); 85 86 if (a == b) 87 { 88 if (!BN_sqr(tmp,a,ctx)) goto err; 89 } 90 else 91 { 92 if (!BN_mul(tmp,a,b,ctx)) goto err; 93 } 94 /* reduce from aRR to aR */ 95 if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err; 96 ret=1; 97 err: 98 BN_CTX_end(ctx); 99 return(ret); 100 } 101 102 int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont, 103 BN_CTX *ctx) 104 { 105 int retn=0; 106 107 #ifdef MONT_WORD 108 BIGNUM *n,*r; 109 BN_ULONG *ap,*np,*rp,n0,v,*nrp; 110 int al,nl,max,i,x,ri; 111 112 BN_CTX_start(ctx); 113 if ((r = BN_CTX_get(ctx)) == NULL) goto err; 114 115 if (!BN_copy(r,a)) goto err; 116 n= &(mont->N); 117 118 ap=a->d; 119 /* mont->ri is the size of mont->N in bits (rounded up 120 to the word size) */ 121 al=ri=mont->ri/BN_BITS2; 122 123 nl=n->top; 124 if ((al == 0) || (nl == 0)) { r->top=0; return(1); } 125 126 max=(nl+al+1); /* allow for overflow (no?) XXX */ 127 if (bn_wexpand(r,max) == NULL) goto err; 128 if (bn_wexpand(ret,max) == NULL) goto err; 129 130 r->neg=a->neg^n->neg; 131 np=n->d; 132 rp=r->d; 133 nrp= &(r->d[nl]); 134 135 /* clear the top words of T */ 136 #if 1 137 for (i=r->top; i<max; i++) /* memset? XXX */ 138 r->d[i]=0; 139 #else 140 memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); 141 #endif 142 143 r->top=max; 144 n0=mont->n0; 145 146 #ifdef BN_COUNT 147 printf("word BN_from_montgomery %d * %d\n",nl,nl); 148 #endif 149 for (i=0; i<nl; i++) 150 { 151 #ifdef __TANDEM 152 { 153 long long t1; 154 long long t2; 155 long long t3; 156 t1 = rp[0] * (n0 & 0177777); 157 t2 = 037777600000l; 158 t2 = n0 & t2; 159 t3 = rp[0] & 0177777; 160 t2 = (t3 * t2) & BN_MASK2; 161 t1 = t1 + t2; 162 v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1); 163 } 164 #else 165 v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2); 166 #endif 167 nrp++; 168 rp++; 169 if (((nrp[-1]+=v)&BN_MASK2) >= v) 170 continue; 171 else 172 { 173 if (((++nrp[0])&BN_MASK2) != 0) continue; 174 if (((++nrp[1])&BN_MASK2) != 0) continue; 175 for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ; 176 } 177 } 178 bn_fix_top(r); 179 180 /* mont->ri will be a multiple of the word size */ 181 #if 0 182 BN_rshift(ret,r,mont->ri); 183 #else 184 ret->neg = r->neg; 185 x=ri; 186 rp=ret->d; 187 ap= &(r->d[x]); 188 if (r->top < x) 189 al=0; 190 else 191 al=r->top-x; 192 ret->top=al; 193 al-=4; 194 for (i=0; i<al; i+=4) 195 { 196 BN_ULONG t1,t2,t3,t4; 197 198 t1=ap[i+0]; 199 t2=ap[i+1]; 200 t3=ap[i+2]; 201 t4=ap[i+3]; 202 rp[i+0]=t1; 203 rp[i+1]=t2; 204 rp[i+2]=t3; 205 rp[i+3]=t4; 206 } 207 al+=4; 208 for (; i<al; i++) 209 rp[i]=ap[i]; 210 #endif 211 #else /* !MONT_WORD */ 212 BIGNUM *t1,*t2; 213 214 BN_CTX_start(ctx); 215 t1 = BN_CTX_get(ctx); 216 t2 = BN_CTX_get(ctx); 217 if (t1 == NULL || t2 == NULL) goto err; 218 219 if (!BN_copy(t1,a)) goto err; 220 BN_mask_bits(t1,mont->ri); 221 222 if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err; 223 BN_mask_bits(t2,mont->ri); 224 225 if (!BN_mul(t1,t2,&mont->N,ctx)) goto err; 226 if (!BN_add(t2,a,t1)) goto err; 227 BN_rshift(ret,t2,mont->ri); 228 #endif /* MONT_WORD */ 229 230 if (BN_ucmp(ret, &(mont->N)) >= 0) 231 { 232 BN_usub(ret,ret,&(mont->N)); 233 } 234 retn=1; 235 err: 236 BN_CTX_end(ctx); 237 return(retn); 238 } 239 240 BN_MONT_CTX *BN_MONT_CTX_new(void) 241 { 242 BN_MONT_CTX *ret; 243 244 if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL) 245 return(NULL); 246 247 BN_MONT_CTX_init(ret); 248 ret->flags=BN_FLG_MALLOCED; 249 return(ret); 250 } 251 252 void BN_MONT_CTX_init(BN_MONT_CTX *ctx) 253 { 254 ctx->ri=0; 255 BN_init(&(ctx->RR)); 256 BN_init(&(ctx->N)); 257 BN_init(&(ctx->Ni)); 258 ctx->flags=0; 259 } 260 261 void BN_MONT_CTX_free(BN_MONT_CTX *mont) 262 { 263 if(mont == NULL) 264 return; 265 266 BN_free(&(mont->RR)); 267 BN_free(&(mont->N)); 268 BN_free(&(mont->Ni)); 269 if (mont->flags & BN_FLG_MALLOCED) 270 OPENSSL_free(mont); 271 } 272 273 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx) 274 { 275 BIGNUM Ri,*R; 276 277 BN_init(&Ri); 278 R= &(mont->RR); /* grab RR as a temp */ 279 BN_copy(&(mont->N),mod); /* Set N */ 280 281 #ifdef MONT_WORD 282 { 283 BIGNUM tmod; 284 BN_ULONG buf[2]; 285 286 mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2; 287 BN_zero(R); 288 BN_set_bit(R,BN_BITS2); /* R */ 289 290 buf[0]=mod->d[0]; /* tmod = N mod word size */ 291 buf[1]=0; 292 tmod.d=buf; 293 tmod.top=1; 294 tmod.dmax=2; 295 tmod.neg=mod->neg; 296 /* Ri = R^-1 mod N*/ 297 if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL) 298 goto err; 299 BN_lshift(&Ri,&Ri,BN_BITS2); /* R*Ri */ 300 if (!BN_is_zero(&Ri)) 301 BN_sub_word(&Ri,1); 302 else /* if N mod word size == 1 */ 303 BN_set_word(&Ri,BN_MASK2); /* Ri-- (mod word size) */ 304 BN_div(&Ri,NULL,&Ri,&tmod,ctx); /* Ni = (R*Ri-1)/N, 305 * keep only least significant word: */ 306 mont->n0=Ri.d[0]; 307 BN_free(&Ri); 308 } 309 #else /* !MONT_WORD */ 310 { /* bignum version */ 311 mont->ri=BN_num_bits(mod); 312 BN_zero(R); 313 BN_set_bit(R,mont->ri); /* R = 2^ri */ 314 /* Ri = R^-1 mod N*/ 315 if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL) 316 goto err; 317 BN_lshift(&Ri,&Ri,mont->ri); /* R*Ri */ 318 BN_sub_word(&Ri,1); 319 /* Ni = (R*Ri-1) / N */ 320 BN_div(&(mont->Ni),NULL,&Ri,mod,ctx); 321 BN_free(&Ri); 322 } 323 #endif 324 325 /* setup RR for conversions */ 326 BN_zero(&(mont->RR)); 327 BN_set_bit(&(mont->RR),mont->ri*2); 328 BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx); 329 330 return(1); 331 err: 332 return(0); 333 } 334 335 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from) 336 { 337 if (to == from) return(to); 338 339 BN_copy(&(to->RR),&(from->RR)); 340 BN_copy(&(to->N),&(from->N)); 341 BN_copy(&(to->Ni),&(from->Ni)); 342 to->ri=from->ri; 343 to->n0=from->n0; 344 return(to); 345 } 346 347