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| 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) 1998-2005 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 "cryptlib.h" | |
| 114 #include "bn_lcl.h" | |
| 115 | |
| 116 #include <stdlib.h> | |
| 117 #ifdef _WIN32 | |
| 118 # include <malloc.h> | |
| 119 # ifndef alloca | |
| 120 # define alloca _alloca | |
| 121 # endif | |
| 122 #elif defined(__GNUC__) | |
| 123 # ifndef alloca | |
| 124 # define alloca(s) __builtin_alloca((s)) | |
| 125 # endif | |
| 126 #endif | |
| 127 | |
| 128 /* maximum precomputation table size for *variable* sliding windows */ | |
| 129 #define TABLE_SIZE 32 | |
| 130 | |
| 131 /* this one works - simple but works */ | |
| 132 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) | |
| 133 { | |
| 134 int i,bits,ret=0; | |
| 135 BIGNUM *v,*rr; | |
| 136 | |
| 137 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) | |
| 138 { | |
| 139 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
| 140 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
| 141 return -1; | |
| 142 } | |
| 143 | |
| 144 BN_CTX_start(ctx); | |
| 145 if ((r == a) || (r == p)) | |
| 146 rr = BN_CTX_get(ctx); | |
| 147 else | |
| 148 rr = r; | |
| 149 v = BN_CTX_get(ctx); | |
| 150 if (rr == NULL || v == NULL) goto err; | |
| 151 | |
| 152 if (BN_copy(v,a) == NULL) goto err; | |
| 153 bits=BN_num_bits(p); | |
| 154 | |
| 155 if (BN_is_odd(p)) | |
| 156 { if (BN_copy(rr,a) == NULL) goto err; } | |
| 157 else { if (!BN_one(rr)) goto err; } | |
| 158 | |
| 159 for (i=1; i<bits; i++) | |
| 160 { | |
| 161 if (!BN_sqr(v,v,ctx)) goto err; | |
| 162 if (BN_is_bit_set(p,i)) | |
| 163 { | |
| 164 if (!BN_mul(rr,rr,v,ctx)) goto err; | |
| 165 } | |
| 166 } | |
| 167 ret=1; | |
| 168 err: | |
| 169 if (r != rr) BN_copy(r,rr); | |
| 170 BN_CTX_end(ctx); | |
| 171 bn_check_top(r); | |
| 172 return(ret); | |
| 173 } | |
| 174 | |
| 175 | |
| 176 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, | |
| 177 BN_CTX *ctx) | |
| 178 { | |
| 179 int ret; | |
| 180 | |
| 181 bn_check_top(a); | |
| 182 bn_check_top(p); | |
| 183 bn_check_top(m); | |
| 184 | |
| 185 /* For even modulus m = 2^k*m_odd, it might make sense to compute | |
| 186 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery | |
| 187 * exponentiation for the odd part), using appropriate exponent | |
| 188 * reductions, and combine the results using the CRT. | |
| 189 * | |
| 190 * For now, we use Montgomery only if the modulus is odd; otherwise, | |
| 191 * exponentiation using the reciprocal-based quick remaindering | |
| 192 * algorithm is used. | |
| 193 * | |
| 194 * (Timing obtained with expspeed.c [computations a^p mod m | |
| 195 * where a, p, m are of the same length: 256, 512, 1024, 2048, | |
| 196 * 4096, 8192 bits], compared to the running time of the | |
| 197 * standard algorithm: | |
| 198 * | |
| 199 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration
] | |
| 200 * 55 .. 77 % [UltraSparc processor, but | |
| 201 * debug-solaris-sparcv8-gcc conf.] | |
| 202 * | |
| 203 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration
] | |
| 204 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gc
c] | |
| 205 * | |
| 206 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont | |
| 207 * at 2048 and more bits, but at 512 and 1024 bits, it was | |
| 208 * slower even than the standard algorithm! | |
| 209 * | |
| 210 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] | |
| 211 * should be obtained when the new Montgomery reduction code | |
| 212 * has been integrated into OpenSSL.) | |
| 213 */ | |
| 214 | |
| 215 #define MONT_MUL_MOD | |
| 216 #define MONT_EXP_WORD | |
| 217 #define RECP_MUL_MOD | |
| 218 | |
| 219 #ifdef MONT_MUL_MOD | |
| 220 /* I have finally been able to take out this pre-condition of | |
| 221 * the top bit being set. It was caused by an error in BN_div | |
| 222 * with negatives. There was also another problem when for a^b%m | |
| 223 * a >= m. eay 07-May-97 */ | |
| 224 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ | |
| 225 | |
| 226 if (BN_is_odd(m)) | |
| 227 { | |
| 228 # ifdef MONT_EXP_WORD | |
| 229 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME)
== 0)) | |
| 230 { | |
| 231 BN_ULONG A = a->d[0]; | |
| 232 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL); | |
| 233 } | |
| 234 else | |
| 235 # endif | |
| 236 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); | |
| 237 } | |
| 238 else | |
| 239 #endif | |
| 240 #ifdef RECP_MUL_MOD | |
| 241 { ret=BN_mod_exp_recp(r,a,p,m,ctx); } | |
| 242 #else | |
| 243 { ret=BN_mod_exp_simple(r,a,p,m,ctx); } | |
| 244 #endif | |
| 245 | |
| 246 bn_check_top(r); | |
| 247 return(ret); | |
| 248 } | |
| 249 | |
| 250 | |
| 251 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, | |
| 252 const BIGNUM *m, BN_CTX *ctx) | |
| 253 { | |
| 254 int i,j,bits,ret=0,wstart,wend,window,wvalue; | |
| 255 int start=1; | |
| 256 BIGNUM *aa; | |
| 257 /* Table of variables obtained from 'ctx' */ | |
| 258 BIGNUM *val[TABLE_SIZE]; | |
| 259 BN_RECP_CTX recp; | |
| 260 | |
| 261 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) | |
| 262 { | |
| 263 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
| 264 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
| 265 return -1; | |
| 266 } | |
| 267 | |
| 268 bits=BN_num_bits(p); | |
| 269 | |
| 270 if (bits == 0) | |
| 271 { | |
| 272 ret = BN_one(r); | |
| 273 return ret; | |
| 274 } | |
| 275 | |
| 276 BN_CTX_start(ctx); | |
| 277 aa = BN_CTX_get(ctx); | |
| 278 val[0] = BN_CTX_get(ctx); | |
| 279 if(!aa || !val[0]) goto err; | |
| 280 | |
| 281 BN_RECP_CTX_init(&recp); | |
| 282 if (m->neg) | |
| 283 { | |
| 284 /* ignore sign of 'm' */ | |
| 285 if (!BN_copy(aa, m)) goto err; | |
| 286 aa->neg = 0; | |
| 287 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err; | |
| 288 } | |
| 289 else | |
| 290 { | |
| 291 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err; | |
| 292 } | |
| 293 | |
| 294 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ | |
| 295 if (BN_is_zero(val[0])) | |
| 296 { | |
| 297 BN_zero(r); | |
| 298 ret = 1; | |
| 299 goto err; | |
| 300 } | |
| 301 | |
| 302 window = BN_window_bits_for_exponent_size(bits); | |
| 303 if (window > 1) | |
| 304 { | |
| 305 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx)) | |
| 306 goto err; /* 2 */ | |
| 307 j=1<<(window-1); | |
| 308 for (i=1; i<j; i++) | |
| 309 { | |
| 310 if(((val[i] = BN_CTX_get(ctx)) == NULL) || | |
| 311 !BN_mod_mul_reciprocal(val[i],val[i-1], | |
| 312 aa,&recp,ctx)) | |
| 313 goto err; | |
| 314 } | |
| 315 } | |
| 316 | |
| 317 start=1; /* This is used to avoid multiplication etc | |
| 318 * when there is only the value '1' in the | |
| 319 * buffer. */ | |
| 320 wvalue=0; /* The 'value' of the window */ | |
| 321 wstart=bits-1; /* The top bit of the window */ | |
| 322 wend=0; /* The bottom bit of the window */ | |
| 323 | |
| 324 if (!BN_one(r)) goto err; | |
| 325 | |
| 326 for (;;) | |
| 327 { | |
| 328 if (BN_is_bit_set(p,wstart) == 0) | |
| 329 { | |
| 330 if (!start) | |
| 331 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) | |
| 332 goto err; | |
| 333 if (wstart == 0) break; | |
| 334 wstart--; | |
| 335 continue; | |
| 336 } | |
| 337 /* We now have wstart on a 'set' bit, we now need to work out | |
| 338 * how bit a window to do. To do this we need to scan | |
| 339 * forward until the last set bit before the end of the | |
| 340 * window */ | |
| 341 j=wstart; | |
| 342 wvalue=1; | |
| 343 wend=0; | |
| 344 for (i=1; i<window; i++) | |
| 345 { | |
| 346 if (wstart-i < 0) break; | |
| 347 if (BN_is_bit_set(p,wstart-i)) | |
| 348 { | |
| 349 wvalue<<=(i-wend); | |
| 350 wvalue|=1; | |
| 351 wend=i; | |
| 352 } | |
| 353 } | |
| 354 | |
| 355 /* wend is the size of the current window */ | |
| 356 j=wend+1; | |
| 357 /* add the 'bytes above' */ | |
| 358 if (!start) | |
| 359 for (i=0; i<j; i++) | |
| 360 { | |
| 361 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) | |
| 362 goto err; | |
| 363 } | |
| 364 | |
| 365 /* wvalue will be an odd number < 2^window */ | |
| 366 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx)) | |
| 367 goto err; | |
| 368 | |
| 369 /* move the 'window' down further */ | |
| 370 wstart-=wend+1; | |
| 371 wvalue=0; | |
| 372 start=0; | |
| 373 if (wstart < 0) break; | |
| 374 } | |
| 375 ret=1; | |
| 376 err: | |
| 377 BN_CTX_end(ctx); | |
| 378 BN_RECP_CTX_free(&recp); | |
| 379 bn_check_top(r); | |
| 380 return(ret); | |
| 381 } | |
| 382 | |
| 383 | |
| 384 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, | |
| 385 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) | |
| 386 { | |
| 387 int i,j,bits,ret=0,wstart,wend,window,wvalue; | |
| 388 int start=1; | |
| 389 BIGNUM *d,*r; | |
| 390 const BIGNUM *aa; | |
| 391 /* Table of variables obtained from 'ctx' */ | |
| 392 BIGNUM *val[TABLE_SIZE]; | |
| 393 BN_MONT_CTX *mont=NULL; | |
| 394 | |
| 395 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) | |
| 396 { | |
| 397 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); | |
| 398 } | |
| 399 | |
| 400 bn_check_top(a); | |
| 401 bn_check_top(p); | |
| 402 bn_check_top(m); | |
| 403 | |
| 404 if (!BN_is_odd(m)) | |
| 405 { | |
| 406 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS); | |
| 407 return(0); | |
| 408 } | |
| 409 bits=BN_num_bits(p); | |
| 410 if (bits == 0) | |
| 411 { | |
| 412 ret = BN_one(rr); | |
| 413 return ret; | |
| 414 } | |
| 415 | |
| 416 BN_CTX_start(ctx); | |
| 417 d = BN_CTX_get(ctx); | |
| 418 r = BN_CTX_get(ctx); | |
| 419 val[0] = BN_CTX_get(ctx); | |
| 420 if (!d || !r || !val[0]) goto err; | |
| 421 | |
| 422 /* If this is not done, things will break in the montgomery | |
| 423 * part */ | |
| 424 | |
| 425 if (in_mont != NULL) | |
| 426 mont=in_mont; | |
| 427 else | |
| 428 { | |
| 429 if ((mont=BN_MONT_CTX_new()) == NULL) goto err; | |
| 430 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; | |
| 431 } | |
| 432 | |
| 433 if (a->neg || BN_ucmp(a,m) >= 0) | |
| 434 { | |
| 435 if (!BN_nnmod(val[0],a,m,ctx)) | |
| 436 goto err; | |
| 437 aa= val[0]; | |
| 438 } | |
| 439 else | |
| 440 aa=a; | |
| 441 if (BN_is_zero(aa)) | |
| 442 { | |
| 443 BN_zero(rr); | |
| 444 ret = 1; | |
| 445 goto err; | |
| 446 } | |
| 447 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */ | |
| 448 | |
| 449 window = BN_window_bits_for_exponent_size(bits); | |
| 450 if (window > 1) | |
| 451 { | |
| 452 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err;
/* 2 */ | |
| 453 j=1<<(window-1); | |
| 454 for (i=1; i<j; i++) | |
| 455 { | |
| 456 if(((val[i] = BN_CTX_get(ctx)) == NULL) || | |
| 457 !BN_mod_mul_montgomery(val[i],val[i-1], | |
| 458 d,mont,ctx)) | |
| 459 goto err; | |
| 460 } | |
| 461 } | |
| 462 | |
| 463 start=1; /* This is used to avoid multiplication etc | |
| 464 * when there is only the value '1' in the | |
| 465 * buffer. */ | |
| 466 wvalue=0; /* The 'value' of the window */ | |
| 467 wstart=bits-1; /* The top bit of the window */ | |
| 468 wend=0; /* The bottom bit of the window */ | |
| 469 | |
| 470 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err; | |
| 471 for (;;) | |
| 472 { | |
| 473 if (BN_is_bit_set(p,wstart) == 0) | |
| 474 { | |
| 475 if (!start) | |
| 476 { | |
| 477 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) | |
| 478 goto err; | |
| 479 } | |
| 480 if (wstart == 0) break; | |
| 481 wstart--; | |
| 482 continue; | |
| 483 } | |
| 484 /* We now have wstart on a 'set' bit, we now need to work out | |
| 485 * how bit a window to do. To do this we need to scan | |
| 486 * forward until the last set bit before the end of the | |
| 487 * window */ | |
| 488 j=wstart; | |
| 489 wvalue=1; | |
| 490 wend=0; | |
| 491 for (i=1; i<window; i++) | |
| 492 { | |
| 493 if (wstart-i < 0) break; | |
| 494 if (BN_is_bit_set(p,wstart-i)) | |
| 495 { | |
| 496 wvalue<<=(i-wend); | |
| 497 wvalue|=1; | |
| 498 wend=i; | |
| 499 } | |
| 500 } | |
| 501 | |
| 502 /* wend is the size of the current window */ | |
| 503 j=wend+1; | |
| 504 /* add the 'bytes above' */ | |
| 505 if (!start) | |
| 506 for (i=0; i<j; i++) | |
| 507 { | |
| 508 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) | |
| 509 goto err; | |
| 510 } | |
| 511 | |
| 512 /* wvalue will be an odd number < 2^window */ | |
| 513 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx)) | |
| 514 goto err; | |
| 515 | |
| 516 /* move the 'window' down further */ | |
| 517 wstart-=wend+1; | |
| 518 wvalue=0; | |
| 519 start=0; | |
| 520 if (wstart < 0) break; | |
| 521 } | |
| 522 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err; | |
| 523 ret=1; | |
| 524 err: | |
| 525 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); | |
| 526 BN_CTX_end(ctx); | |
| 527 bn_check_top(rr); | |
| 528 return(ret); | |
| 529 } | |
| 530 | |
| 531 | |
| 532 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layou
t | |
| 533 * so that accessing any of these table values shows the same access pattern as
far | |
| 534 * as cache lines are concerned. The following functions are used to transfer a
BIGNUM | |
| 535 * from/to that table. */ | |
| 536 | |
| 537 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char
*buf, int idx, int width) | |
| 538 { | |
| 539 size_t i, j; | |
| 540 | |
| 541 if (top > b->top) | |
| 542 top = b->top; /* this works because 'buf' is explicitly zeroed *
/ | |
| 543 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) | |
| 544 { | |
| 545 buf[j] = ((unsigned char*)b->d)[i]; | |
| 546 } | |
| 547 | |
| 548 return 1; | |
| 549 } | |
| 550 | |
| 551 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf
, int idx, int width) | |
| 552 { | |
| 553 size_t i, j; | |
| 554 | |
| 555 if (bn_wexpand(b, top) == NULL) | |
| 556 return 0; | |
| 557 | |
| 558 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) | |
| 559 { | |
| 560 ((unsigned char*)b->d)[i] = buf[j]; | |
| 561 } | |
| 562 | |
| 563 b->top = top; | |
| 564 bn_correct_top(b); | |
| 565 return 1; | |
| 566 } | |
| 567 | |
| 568 /* Given a pointer value, compute the next address that is a cache line multiple
. */ | |
| 569 #define MOD_EXP_CTIME_ALIGN(x_) \ | |
| 570 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)
(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) | |
| 571 | |
| 572 /* This variant of BN_mod_exp_mont() uses fixed windows and the special | |
| 573 * precomputation memory layout to limit data-dependency to a minimum | |
| 574 * to protect secret exponents (cf. the hyper-threading timing attacks | |
| 575 * pointed out by Colin Percival, | |
| 576 * http://www.daemonology.net/hyperthreading-considered-harmful/) | |
| 577 */ | |
| 578 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, | |
| 579 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) | |
| 580 { | |
| 581 int i,bits,ret=0,window,wvalue; | |
| 582 int top; | |
| 583 BN_MONT_CTX *mont=NULL; | |
| 584 | |
| 585 int numPowers; | |
| 586 unsigned char *powerbufFree=NULL; | |
| 587 int powerbufLen = 0; | |
| 588 unsigned char *powerbuf=NULL; | |
| 589 BIGNUM tmp, am; | |
| 590 | |
| 591 bn_check_top(a); | |
| 592 bn_check_top(p); | |
| 593 bn_check_top(m); | |
| 594 | |
| 595 top = m->top; | |
| 596 | |
| 597 if (!(m->d[0] & 1)) | |
| 598 { | |
| 599 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODUL
US); | |
| 600 return(0); | |
| 601 } | |
| 602 bits=BN_num_bits(p); | |
| 603 if (bits == 0) | |
| 604 { | |
| 605 ret = BN_one(rr); | |
| 606 return ret; | |
| 607 } | |
| 608 | |
| 609 BN_CTX_start(ctx); | |
| 610 | |
| 611 /* Allocate a montgomery context if it was not supplied by the caller. | |
| 612 * If this is not done, things will break in the montgomery part. | |
| 613 */ | |
| 614 if (in_mont != NULL) | |
| 615 mont=in_mont; | |
| 616 else | |
| 617 { | |
| 618 if ((mont=BN_MONT_CTX_new()) == NULL) goto err; | |
| 619 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; | |
| 620 } | |
| 621 | |
| 622 /* Get the window size to use with size of p. */ | |
| 623 window = BN_window_bits_for_ctime_exponent_size(bits); | |
| 624 #if defined(OPENSSL_BN_ASM_MONT5) | |
| 625 if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit R
SA sign */ | |
| 626 #endif | |
| 627 | |
| 628 /* Allocate a buffer large enough to hold all of the pre-computed | |
| 629 * powers of am, am itself and tmp. | |
| 630 */ | |
| 631 numPowers = 1 << window; | |
| 632 powerbufLen = sizeof(m->d[0])*(top*numPowers + | |
| 633 ((2*top)>numPowers?(2*top):numPowers)); | |
| 634 #ifdef alloca | |
| 635 if (powerbufLen < 3072) | |
| 636 powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_W
IDTH); | |
| 637 else | |
| 638 #endif | |
| 639 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTI
ME_MIN_CACHE_LINE_WIDTH)) == NULL) | |
| 640 goto err; | |
| 641 | |
| 642 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); | |
| 643 memset(powerbuf, 0, powerbufLen); | |
| 644 | |
| 645 #ifdef alloca | |
| 646 if (powerbufLen < 3072) | |
| 647 powerbufFree = NULL; | |
| 648 #endif | |
| 649 | |
| 650 /* lay down tmp and am right after powers table */ | |
| 651 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers); | |
| 652 am.d = tmp.d + top; | |
| 653 tmp.top = am.top = 0; | |
| 654 tmp.dmax = am.dmax = top; | |
| 655 tmp.neg = am.neg = 0; | |
| 656 tmp.flags = am.flags = BN_FLG_STATIC_DATA; | |
| 657 | |
| 658 /* prepare a^0 in Montgomery domain */ | |
| 659 #if 1 | |
| 660 if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err; | |
| 661 #else | |
| 662 tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */ | |
| 663 for (i=1;i<top;i++) | |
| 664 tmp.d[i] = (~m->d[i])&BN_MASK2; | |
| 665 tmp.top = top; | |
| 666 #endif | |
| 667 | |
| 668 /* prepare a^1 in Montgomery domain */ | |
| 669 if (a->neg || BN_ucmp(a,m) >= 0) | |
| 670 { | |
| 671 if (!BN_mod(&am,a,m,ctx)) goto err; | |
| 672 if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err; | |
| 673 } | |
| 674 else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err; | |
| 675 | |
| 676 #if defined(OPENSSL_BN_ASM_MONT5) | |
| 677 /* This optimization uses ideas from http://eprint.iacr.org/2011/239, | |
| 678 * specifically optimization of cache-timing attack countermeasures | |
| 679 * and pre-computation optimization. */ | |
| 680 | |
| 681 /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as | |
| 682 * 512-bit RSA is hardly relevant, we omit it to spare size... */ | |
| 683 if (window==5) | |
| 684 { | |
| 685 void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap, | |
| 686 const void *table,const BN_ULONG *np, | |
| 687 const BN_ULONG *n0,int num,int power); | |
| 688 void bn_scatter5(const BN_ULONG *inp,size_t num, | |
| 689 void *table,size_t power); | |
| 690 void bn_gather5(BN_ULONG *out,size_t num, | |
| 691 void *table,size_t power); | |
| 692 | |
| 693 BN_ULONG *np=mont->N.d, *n0=mont->n0; | |
| 694 | |
| 695 /* BN_to_montgomery can contaminate words above .top | |
| 696 * [in BN_DEBUG[_DEBUG] build]... */ | |
| 697 for (i=am.top; i<top; i++) am.d[i]=0; | |
| 698 for (i=tmp.top; i<top; i++) tmp.d[i]=0; | |
| 699 | |
| 700 bn_scatter5(tmp.d,top,powerbuf,0); | |
| 701 bn_scatter5(am.d,am.top,powerbuf,1); | |
| 702 bn_mul_mont(tmp.d,am.d,am.d,np,n0,top); | |
| 703 bn_scatter5(tmp.d,top,powerbuf,2); | |
| 704 | |
| 705 #if 0 | |
| 706 for (i=3; i<32; i++) | |
| 707 { | |
| 708 /* Calculate a^i = a^(i-1) * a */ | |
| 709 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); | |
| 710 bn_scatter5(tmp.d,top,powerbuf,i); | |
| 711 } | |
| 712 #else | |
| 713 /* same as above, but uses squaring for 1/2 of operations */ | |
| 714 for (i=4; i<32; i*=2) | |
| 715 { | |
| 716 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 717 bn_scatter5(tmp.d,top,powerbuf,i); | |
| 718 } | |
| 719 for (i=3; i<8; i+=2) | |
| 720 { | |
| 721 int j; | |
| 722 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); | |
| 723 bn_scatter5(tmp.d,top,powerbuf,i); | |
| 724 for (j=2*i; j<32; j*=2) | |
| 725 { | |
| 726 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 727 bn_scatter5(tmp.d,top,powerbuf,j); | |
| 728 } | |
| 729 } | |
| 730 for (; i<16; i+=2) | |
| 731 { | |
| 732 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); | |
| 733 bn_scatter5(tmp.d,top,powerbuf,i); | |
| 734 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 735 bn_scatter5(tmp.d,top,powerbuf,2*i); | |
| 736 } | |
| 737 for (; i<32; i+=2) | |
| 738 { | |
| 739 bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1); | |
| 740 bn_scatter5(tmp.d,top,powerbuf,i); | |
| 741 } | |
| 742 #endif | |
| 743 bits--; | |
| 744 for (wvalue=0, i=bits%5; i>=0; i--,bits--) | |
| 745 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); | |
| 746 bn_gather5(tmp.d,top,powerbuf,wvalue); | |
| 747 | |
| 748 /* Scan the exponent one window at a time starting from the most | |
| 749 * significant bits. | |
| 750 */ | |
| 751 while (bits >= 0) | |
| 752 { | |
| 753 for (wvalue=0, i=0; i<5; i++,bits--) | |
| 754 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); | |
| 755 | |
| 756 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 757 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 758 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 759 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 760 bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top); | |
| 761 bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue); | |
| 762 } | |
| 763 | |
| 764 tmp.top=top; | |
| 765 bn_correct_top(&tmp); | |
| 766 } | |
| 767 else | |
| 768 #endif | |
| 769 { | |
| 770 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) go
to err; | |
| 771 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) go
to err; | |
| 772 | |
| 773 /* If the window size is greater than 1, then calculate | |
| 774 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) | |
| 775 * (even powers could instead be computed as (a^(i/2))^2 | |
| 776 * to use the slight performance advantage of sqr over mul). | |
| 777 */ | |
| 778 if (window > 1) | |
| 779 { | |
| 780 if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err
; | |
| 781 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPow
ers)) goto err; | |
| 782 for (i=3; i<numPowers; i++) | |
| 783 { | |
| 784 /* Calculate a^i = a^(i-1) * a */ | |
| 785 if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx)) | |
| 786 goto err; | |
| 787 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i
, numPowers)) goto err; | |
| 788 } | |
| 789 } | |
| 790 | |
| 791 bits--; | |
| 792 for (wvalue=0, i=bits%window; i>=0; i--,bits--) | |
| 793 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); | |
| 794 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers))
goto err; | |
| 795 | |
| 796 /* Scan the exponent one window at a time starting from the most | |
| 797 * significant bits. | |
| 798 */ | |
| 799 while (bits >= 0) | |
| 800 { | |
| 801 wvalue=0; /* The 'value' of the window */ | |
| 802 | |
| 803 /* Scan the window, squaring the result as we go */ | |
| 804 for (i=0; i<window; i++,bits--) | |
| 805 { | |
| 806 if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx))
goto err; | |
| 807 wvalue = (wvalue<<1)+BN_is_bit_set(p,bits); | |
| 808 } | |
| 809 | |
| 810 /* Fetch the appropriate pre-computed value from the pre-buf */ | |
| 811 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
numPowers)) goto err; | |
| 812 | |
| 813 /* Multiply the result into the intermediate result */ | |
| 814 if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err; | |
| 815 } | |
| 816 } | |
| 817 | |
| 818 /* Convert the final result from montgomery to standard format */ | |
| 819 if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err; | |
| 820 ret=1; | |
| 821 err: | |
| 822 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); | |
| 823 if (powerbuf!=NULL) | |
| 824 { | |
| 825 OPENSSL_cleanse(powerbuf,powerbufLen); | |
| 826 if (powerbufFree) OPENSSL_free(powerbufFree); | |
| 827 } | |
| 828 BN_CTX_end(ctx); | |
| 829 return(ret); | |
| 830 } | |
| 831 | |
| 832 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, | |
| 833 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) | |
| 834 { | |
| 835 BN_MONT_CTX *mont = NULL; | |
| 836 int b, bits, ret=0; | |
| 837 int r_is_one; | |
| 838 BN_ULONG w, next_w; | |
| 839 BIGNUM *d, *r, *t; | |
| 840 BIGNUM *swap_tmp; | |
| 841 #define BN_MOD_MUL_WORD(r, w, m) \ | |
| 842 (BN_mul_word(r, (w)) && \ | |
| 843 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ | |
| 844 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_
tmp, 1)))) | |
| 845 /* BN_MOD_MUL_WORD is only used with 'w' large, | |
| 846 * so the BN_ucmp test is probably more overhead | |
| 847 * than always using BN_mod (which uses BN_copy if | |
| 848 * a similar test returns true). */ | |
| 849 /* We can use BN_mod and do not need BN_nnmod because our | |
| 850 * accumulator is never negative (the result of BN_mod does | |
| 851 * not depend on the sign of the modulus). | |
| 852 */ | |
| 853 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ | |
| 854 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) | |
| 855 | |
| 856 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) | |
| 857 { | |
| 858 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
| 859 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLE
D); | |
| 860 return -1; | |
| 861 } | |
| 862 | |
| 863 bn_check_top(p); | |
| 864 bn_check_top(m); | |
| 865 | |
| 866 if (!BN_is_odd(m)) | |
| 867 { | |
| 868 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS); | |
| 869 return(0); | |
| 870 } | |
| 871 if (m->top == 1) | |
| 872 a %= m->d[0]; /* make sure that 'a' is reduced */ | |
| 873 | |
| 874 bits = BN_num_bits(p); | |
| 875 if (bits == 0) | |
| 876 { | |
| 877 ret = BN_one(rr); | |
| 878 return ret; | |
| 879 } | |
| 880 if (a == 0) | |
| 881 { | |
| 882 BN_zero(rr); | |
| 883 ret = 1; | |
| 884 return ret; | |
| 885 } | |
| 886 | |
| 887 BN_CTX_start(ctx); | |
| 888 d = BN_CTX_get(ctx); | |
| 889 r = BN_CTX_get(ctx); | |
| 890 t = BN_CTX_get(ctx); | |
| 891 if (d == NULL || r == NULL || t == NULL) goto err; | |
| 892 | |
| 893 if (in_mont != NULL) | |
| 894 mont=in_mont; | |
| 895 else | |
| 896 { | |
| 897 if ((mont = BN_MONT_CTX_new()) == NULL) goto err; | |
| 898 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; | |
| 899 } | |
| 900 | |
| 901 r_is_one = 1; /* except for Montgomery factor */ | |
| 902 | |
| 903 /* bits-1 >= 0 */ | |
| 904 | |
| 905 /* The result is accumulated in the product r*w. */ | |
| 906 w = a; /* bit 'bits-1' of 'p' is always set */ | |
| 907 for (b = bits-2; b >= 0; b--) | |
| 908 { | |
| 909 /* First, square r*w. */ | |
| 910 next_w = w*w; | |
| 911 if ((next_w/w) != w) /* overflow */ | |
| 912 { | |
| 913 if (r_is_one) | |
| 914 { | |
| 915 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err
; | |
| 916 r_is_one = 0; | |
| 917 } | |
| 918 else | |
| 919 { | |
| 920 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; | |
| 921 } | |
| 922 next_w = 1; | |
| 923 } | |
| 924 w = next_w; | |
| 925 if (!r_is_one) | |
| 926 { | |
| 927 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err
; | |
| 928 } | |
| 929 | |
| 930 /* Second, multiply r*w by 'a' if exponent bit is set. */ | |
| 931 if (BN_is_bit_set(p, b)) | |
| 932 { | |
| 933 next_w = w*a; | |
| 934 if ((next_w/a) != w) /* overflow */ | |
| 935 { | |
| 936 if (r_is_one) | |
| 937 { | |
| 938 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
goto err; | |
| 939 r_is_one = 0; | |
| 940 } | |
| 941 else | |
| 942 { | |
| 943 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; | |
| 944 } | |
| 945 next_w = a; | |
| 946 } | |
| 947 w = next_w; | |
| 948 } | |
| 949 } | |
| 950 | |
| 951 /* Finally, set r:=r*w. */ | |
| 952 if (w != 1) | |
| 953 { | |
| 954 if (r_is_one) | |
| 955 { | |
| 956 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; | |
| 957 r_is_one = 0; | |
| 958 } | |
| 959 else | |
| 960 { | |
| 961 if (!BN_MOD_MUL_WORD(r, w, m)) goto err; | |
| 962 } | |
| 963 } | |
| 964 | |
| 965 if (r_is_one) /* can happen only if a == 1*/ | |
| 966 { | |
| 967 if (!BN_one(rr)) goto err; | |
| 968 } | |
| 969 else | |
| 970 { | |
| 971 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; | |
| 972 } | |
| 973 ret = 1; | |
| 974 err: | |
| 975 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); | |
| 976 BN_CTX_end(ctx); | |
| 977 bn_check_top(rr); | |
| 978 return(ret); | |
| 979 } | |
| 980 | |
| 981 | |
| 982 /* The old fallback, simple version :-) */ | |
| 983 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, | |
| 984 const BIGNUM *m, BN_CTX *ctx) | |
| 985 { | |
| 986 int i,j,bits,ret=0,wstart,wend,window,wvalue; | |
| 987 int start=1; | |
| 988 BIGNUM *d; | |
| 989 /* Table of variables obtained from 'ctx' */ | |
| 990 BIGNUM *val[TABLE_SIZE]; | |
| 991 | |
| 992 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) | |
| 993 { | |
| 994 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ | |
| 995 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); | |
| 996 return -1; | |
| 997 } | |
| 998 | |
| 999 bits=BN_num_bits(p); | |
| 1000 | |
| 1001 if (bits == 0) | |
| 1002 { | |
| 1003 ret = BN_one(r); | |
| 1004 return ret; | |
| 1005 } | |
| 1006 | |
| 1007 BN_CTX_start(ctx); | |
| 1008 d = BN_CTX_get(ctx); | |
| 1009 val[0] = BN_CTX_get(ctx); | |
| 1010 if(!d || !val[0]) goto err; | |
| 1011 | |
| 1012 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ | |
| 1013 if (BN_is_zero(val[0])) | |
| 1014 { | |
| 1015 BN_zero(r); | |
| 1016 ret = 1; | |
| 1017 goto err; | |
| 1018 } | |
| 1019 | |
| 1020 window = BN_window_bits_for_exponent_size(bits); | |
| 1021 if (window > 1) | |
| 1022 { | |
| 1023 if (!BN_mod_mul(d,val[0],val[0],m,ctx)) | |
| 1024 goto err; /* 2 */ | |
| 1025 j=1<<(window-1); | |
| 1026 for (i=1; i<j; i++) | |
| 1027 { | |
| 1028 if(((val[i] = BN_CTX_get(ctx)) == NULL) || | |
| 1029 !BN_mod_mul(val[i],val[i-1],d,m,ctx)) | |
| 1030 goto err; | |
| 1031 } | |
| 1032 } | |
| 1033 | |
| 1034 start=1; /* This is used to avoid multiplication etc | |
| 1035 * when there is only the value '1' in the | |
| 1036 * buffer. */ | |
| 1037 wvalue=0; /* The 'value' of the window */ | |
| 1038 wstart=bits-1; /* The top bit of the window */ | |
| 1039 wend=0; /* The bottom bit of the window */ | |
| 1040 | |
| 1041 if (!BN_one(r)) goto err; | |
| 1042 | |
| 1043 for (;;) | |
| 1044 { | |
| 1045 if (BN_is_bit_set(p,wstart) == 0) | |
| 1046 { | |
| 1047 if (!start) | |
| 1048 if (!BN_mod_mul(r,r,r,m,ctx)) | |
| 1049 goto err; | |
| 1050 if (wstart == 0) break; | |
| 1051 wstart--; | |
| 1052 continue; | |
| 1053 } | |
| 1054 /* We now have wstart on a 'set' bit, we now need to work out | |
| 1055 * how bit a window to do. To do this we need to scan | |
| 1056 * forward until the last set bit before the end of the | |
| 1057 * window */ | |
| 1058 j=wstart; | |
| 1059 wvalue=1; | |
| 1060 wend=0; | |
| 1061 for (i=1; i<window; i++) | |
| 1062 { | |
| 1063 if (wstart-i < 0) break; | |
| 1064 if (BN_is_bit_set(p,wstart-i)) | |
| 1065 { | |
| 1066 wvalue<<=(i-wend); | |
| 1067 wvalue|=1; | |
| 1068 wend=i; | |
| 1069 } | |
| 1070 } | |
| 1071 | |
| 1072 /* wend is the size of the current window */ | |
| 1073 j=wend+1; | |
| 1074 /* add the 'bytes above' */ | |
| 1075 if (!start) | |
| 1076 for (i=0; i<j; i++) | |
| 1077 { | |
| 1078 if (!BN_mod_mul(r,r,r,m,ctx)) | |
| 1079 goto err; | |
| 1080 } | |
| 1081 | |
| 1082 /* wvalue will be an odd number < 2^window */ | |
| 1083 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx)) | |
| 1084 goto err; | |
| 1085 | |
| 1086 /* move the 'window' down further */ | |
| 1087 wstart-=wend+1; | |
| 1088 wvalue=0; | |
| 1089 start=0; | |
| 1090 if (wstart < 0) break; | |
| 1091 } | |
| 1092 ret=1; | |
| 1093 err: | |
| 1094 BN_CTX_end(ctx); | |
| 1095 bn_check_top(r); | |
| 1096 return(ret); | |
| 1097 } | |
| OLD | NEW |
|---|
Chromium Code Reviews
Issue 2072073002:
Delete bundled copy of OpenSSL and replace with README. (Closed)
Base URL: https://chromium.googlesource.com/chromium/deps/openssl@master