1/* crypto/bn/bn_exp.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) 1998-2000 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#include <stdio.h> 114#include "bn_lcl.h" 115 116#define TABLE_SIZE 32 117 118/* slow but works */ 119int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx) 120 { 121 BIGNUM *t; 122 int r=0; 123 124 bn_check_top(a); 125 bn_check_top(b); 126 bn_check_top(m); 127 128 BN_CTX_start(ctx); 129 if ((t = BN_CTX_get(ctx)) == NULL) goto err; 130 if (a == b) 131 { if (!BN_sqr(t,a,ctx)) goto err; } 132 else 133 { if (!BN_mul(t,a,b,ctx)) goto err; } 134 if (!BN_mod(ret,t,m,ctx)) goto err; 135 r=1; 136err: 137 BN_CTX_end(ctx); 138 return(r); 139 } 140 141int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m, 142 BN_CTX *ctx) 143 { 144 int ret; 145 146 bn_check_top(a); 147 bn_check_top(p); 148 bn_check_top(m); 149 150#ifdef MONT_MUL_MOD 151 /* I have finally been able to take out this pre-condition of 152 * the top bit being set. It was caused by an error in BN_div 153 * with negatives. There was also another problem when for a^b%m 154 * a >= m. eay 07-May-97 */ 155/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ 156 157 if (BN_is_odd(m)) 158 { 159 if (a->top == 1) 160 { 161 BN_ULONG A = a->d[0]; 162 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL); 163 } 164 else 165 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); 166 } 167 else 168#endif 169#ifdef RECP_MUL_MOD 170 { ret=BN_mod_exp_recp(r,a,p,m,ctx); } 171#else 172 { ret=BN_mod_exp_simple(r,a,p,m,ctx); } 173#endif 174 175 return(ret); 176 } 177 178 179#ifdef RECP_MUL_MOD 180int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 181 const BIGNUM *m, BN_CTX *ctx) 182 { 183 int i,j,bits,ret=0,wstart,wend,window,wvalue; 184 int start=1,ts=0; 185 BIGNUM *aa; 186 BIGNUM val[TABLE_SIZE]; 187 BN_RECP_CTX recp; 188 189 bits=BN_num_bits(p); 190 191 if (bits == 0) 192 { 193 BN_one(r); 194 return(1); 195 } 196 197 BN_CTX_start(ctx); 198 if ((aa = BN_CTX_get(ctx)) == NULL) goto err; 199 200 BN_RECP_CTX_init(&recp); 201 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err; 202 203 BN_init(&(val[0])); 204 ts=1; 205 206 if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */ 207 208 window = BN_window_bits_for_exponent_size(bits); 209 if (window > 1) 210 { 211 if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx)) 212 goto err; /* 2 */ 213 j=1<<(window-1); 214 for (i=1; i<j; i++) 215 { 216 BN_init(&val[i]); 217 if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx)) 218 goto err; 219 } 220 ts=i; 221 } 222 223 start=1; /* This is used to avoid multiplication etc 224 * when there is only the value '1' in the 225 * buffer. */ 226 wvalue=0; /* The 'value' of the window */ 227 wstart=bits-1; /* The top bit of the window */ 228 wend=0; /* The bottom bit of the window */ 229 230 if (!BN_one(r)) goto err; 231 232 for (;;) 233 { 234 if (BN_is_bit_set(p,wstart) == 0) 235 { 236 if (!start) 237 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 238 goto err; 239 if (wstart == 0) break; 240 wstart--; 241 continue; 242 } 243 /* We now have wstart on a 'set' bit, we now need to work out 244 * how bit a window to do. To do this we need to scan 245 * forward until the last set bit before the end of the 246 * window */ 247 j=wstart; 248 wvalue=1; 249 wend=0; 250 for (i=1; i<window; i++) 251 { 252 if (wstart-i < 0) break; 253 if (BN_is_bit_set(p,wstart-i)) 254 { 255 wvalue<<=(i-wend); 256 wvalue|=1; 257 wend=i; 258 } 259 } 260 261 /* wend is the size of the current window */ 262 j=wend+1; 263 /* add the 'bytes above' */ 264 if (!start) 265 for (i=0; i<j; i++) 266 { 267 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) 268 goto err; 269 } 270 271 /* wvalue will be an odd number < 2^window */ 272 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx)) 273 goto err; 274 275 /* move the 'window' down further */ 276 wstart-=wend+1; 277 wvalue=0; 278 start=0; 279 if (wstart < 0) break; 280 } 281 ret=1; 282err: 283 BN_CTX_end(ctx); 284 for (i=0; i<ts; i++) 285 BN_clear_free(&(val[i])); 286 BN_RECP_CTX_free(&recp); 287 return(ret); 288 } 289#else 290 291/* The old fallback, simple version :-) */ 292int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, 293 const BIGNUM *m, BN_CTX *ctx) 294 { 295 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0; 296 int start=1; 297 BIGNUM *d; 298 BIGNUM val[TABLE_SIZE]; 299 300 bits=BN_num_bits(p); 301 302 if (bits == 0) 303 { 304 BN_one(r); 305 return(1); 306 } 307 308 BN_CTX_start(ctx); 309 if ((d = BN_CTX_get(ctx)) == NULL) goto err; 310 311 BN_init(&(val[0])); 312 ts=1; 313 if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */ 314 315 window = BN_window_bits_for_exponent_size(bits); 316 if (window > 1) 317 { 318 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx)) 319 goto err; /* 2 */ 320 j=1<<(window-1); 321 for (i=1; i<j; i++) 322 { 323 BN_init(&(val[i])); 324 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx)) 325 goto err; 326 } 327 ts=i; 328 } 329 330 start=1; /* This is used to avoid multiplication etc 331 * when there is only the value '1' in the 332 * buffer. */ 333 wvalue=0; /* The 'value' of the window */ 334 wstart=bits-1; /* The top bit of the window */ 335 wend=0; /* The bottom bit of the window */ 336 337 if (!BN_one(r)) goto err; 338 339 for (;;) 340 { 341 if (BN_is_bit_set(p,wstart) == 0) 342 { 343 if (!start) 344 if (!BN_mod_mul(r,r,r,m,ctx)) 345 goto err; 346 if (wstart == 0) break; 347 wstart--; 348 continue; 349 } 350 /* We now have wstart on a 'set' bit, we now need to work out 351 * how bit a window to do. To do this we need to scan 352 * forward until the last set bit before the end of the 353 * window */ 354 j=wstart; 355 wvalue=1; 356 wend=0; 357 for (i=1; i<window; i++) 358 { 359 if (wstart-i < 0) break; 360 if (BN_is_bit_set(p,wstart-i)) 361 { 362 wvalue<<=(i-wend); 363 wvalue|=1; 364 wend=i; 365 } 366 } 367 368 /* wend is the size of the current window */ 369 j=wend+1; 370 /* add the 'bytes above' */ 371 if (!start) 372 for (i=0; i<j; i++) 373 { 374 if (!BN_mod_mul(r,r,r,m,ctx)) 375 goto err; 376 } 377 378 /* wvalue will be an odd number < 2^window */ 379 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx)) 380 goto err; 381 382 /* move the 'window' down further */ 383 wstart-=wend+1; 384 wvalue=0; 385 start=0; 386 if (wstart < 0) break; 387 } 388 ret=1; 389err: 390 BN_CTX_end(ctx); 391 for (i=0; i<ts; i++) 392 BN_clear_free(&(val[i])); 393 return(ret); 394 } 395#endif 396