| 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 */ |
| 119 | int 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; |
| 136 | err: |
| 137 | BN_CTX_end(ctx); |
| 138 | return(r); |
| 139 | } |
| 140 | |
| 141 | int 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 |
| 180 | int 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; |
| 282 | err: |
| 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 :-) */ |
| 292 | int 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; |
| 389 | err: |
| 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 | |
