Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 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 | |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 116 | /* maximum precomputation table size for *variable* sliding windows */ |
| 117 | #define TABLE_SIZE 32 |
| 118 | |
| 119 | /* this one works - simple but works */ |
| 120 | int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
| 121 | { |
| 122 | int i,bits,ret=0; |
| 123 | BIGNUM *v,*rr; |
| 124 | |
| 125 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) |
| 126 | { |
| 127 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
| 128 | BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| 129 | return -1; |
| 130 | } |
| 131 | |
| 132 | BN_CTX_start(ctx); |
| 133 | if ((r == a) || (r == p)) |
| 134 | rr = BN_CTX_get(ctx); |
| 135 | else |
| 136 | rr = r; |
| 137 | v = BN_CTX_get(ctx); |
| 138 | if (rr == NULL || v == NULL) goto err; |
| 139 | |
| 140 | if (BN_copy(v,a) == NULL) goto err; |
| 141 | bits=BN_num_bits(p); |
| 142 | |
| 143 | if (BN_is_odd(p)) |
| 144 | { if (BN_copy(rr,a) == NULL) goto err; } |
| 145 | else { if (!BN_one(rr)) goto err; } |
| 146 | |
| 147 | for (i=1; i<bits; i++) |
| 148 | { |
| 149 | if (!BN_sqr(v,v,ctx)) goto err; |
| 150 | if (BN_is_bit_set(p,i)) |
| 151 | { |
| 152 | if (!BN_mul(rr,rr,v,ctx)) goto err; |
| 153 | } |
| 154 | } |
| 155 | ret=1; |
| 156 | err: |
| 157 | if (r != rr) BN_copy(r,rr); |
| 158 | BN_CTX_end(ctx); |
| 159 | bn_check_top(r); |
| 160 | return(ret); |
| 161 | } |
| 162 | |
| 163 | |
| 164 | int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m, |
| 165 | BN_CTX *ctx) |
| 166 | { |
| 167 | int ret; |
| 168 | |
| 169 | bn_check_top(a); |
| 170 | bn_check_top(p); |
| 171 | bn_check_top(m); |
| 172 | |
| 173 | /* For even modulus m = 2^k*m_odd, it might make sense to compute |
| 174 | * a^p mod m_odd and a^p mod 2^k separately (with Montgomery |
| 175 | * exponentiation for the odd part), using appropriate exponent |
| 176 | * reductions, and combine the results using the CRT. |
| 177 | * |
| 178 | * For now, we use Montgomery only if the modulus is odd; otherwise, |
| 179 | * exponentiation using the reciprocal-based quick remaindering |
| 180 | * algorithm is used. |
| 181 | * |
| 182 | * (Timing obtained with expspeed.c [computations a^p mod m |
| 183 | * where a, p, m are of the same length: 256, 512, 1024, 2048, |
| 184 | * 4096, 8192 bits], compared to the running time of the |
| 185 | * standard algorithm: |
| 186 | * |
| 187 | * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration] |
| 188 | * 55 .. 77 % [UltraSparc processor, but |
| 189 | * debug-solaris-sparcv8-gcc conf.] |
| 190 | * |
| 191 | * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration] |
| 192 | * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc] |
| 193 | * |
| 194 | * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont |
| 195 | * at 2048 and more bits, but at 512 and 1024 bits, it was |
| 196 | * slower even than the standard algorithm! |
| 197 | * |
| 198 | * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations] |
| 199 | * should be obtained when the new Montgomery reduction code |
| 200 | * has been integrated into OpenSSL.) |
| 201 | */ |
| 202 | |
| 203 | #define MONT_MUL_MOD |
| 204 | #define MONT_EXP_WORD |
| 205 | #define RECP_MUL_MOD |
| 206 | |
| 207 | #ifdef MONT_MUL_MOD |
| 208 | /* I have finally been able to take out this pre-condition of |
| 209 | * the top bit being set. It was caused by an error in BN_div |
| 210 | * with negatives. There was also another problem when for a^b%m |
| 211 | * a >= m. eay 07-May-97 */ |
| 212 | /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */ |
| 213 | |
| 214 | if (BN_is_odd(m)) |
| 215 | { |
| 216 | # ifdef MONT_EXP_WORD |
| 217 | if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) |
| 218 | { |
| 219 | BN_ULONG A = a->d[0]; |
| 220 | ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL); |
| 221 | } |
| 222 | else |
| 223 | # endif |
| 224 | ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); |
| 225 | } |
| 226 | else |
| 227 | #endif |
| 228 | #ifdef RECP_MUL_MOD |
| 229 | { ret=BN_mod_exp_recp(r,a,p,m,ctx); } |
| 230 | #else |
| 231 | { ret=BN_mod_exp_simple(r,a,p,m,ctx); } |
| 232 | #endif |
| 233 | |
| 234 | bn_check_top(r); |
| 235 | return(ret); |
| 236 | } |
| 237 | |
| 238 | |
| 239 | int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
| 240 | const BIGNUM *m, BN_CTX *ctx) |
| 241 | { |
| 242 | int i,j,bits,ret=0,wstart,wend,window,wvalue; |
| 243 | int start=1; |
| 244 | BIGNUM *aa; |
| 245 | /* Table of variables obtained from 'ctx' */ |
| 246 | BIGNUM *val[TABLE_SIZE]; |
| 247 | BN_RECP_CTX recp; |
| 248 | |
| 249 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) |
| 250 | { |
| 251 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
| 252 | BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| 253 | return -1; |
| 254 | } |
| 255 | |
| 256 | bits=BN_num_bits(p); |
| 257 | |
| 258 | if (bits == 0) |
| 259 | { |
| 260 | ret = BN_one(r); |
| 261 | return ret; |
| 262 | } |
| 263 | |
| 264 | BN_CTX_start(ctx); |
| 265 | aa = BN_CTX_get(ctx); |
| 266 | val[0] = BN_CTX_get(ctx); |
| 267 | if(!aa || !val[0]) goto err; |
| 268 | |
| 269 | BN_RECP_CTX_init(&recp); |
| 270 | if (m->neg) |
| 271 | { |
| 272 | /* ignore sign of 'm' */ |
| 273 | if (!BN_copy(aa, m)) goto err; |
| 274 | aa->neg = 0; |
| 275 | if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err; |
| 276 | } |
| 277 | else |
| 278 | { |
| 279 | if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err; |
| 280 | } |
| 281 | |
| 282 | if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ |
| 283 | if (BN_is_zero(val[0])) |
| 284 | { |
| 285 | BN_zero(r); |
| 286 | ret = 1; |
| 287 | goto err; |
| 288 | } |
| 289 | |
| 290 | window = BN_window_bits_for_exponent_size(bits); |
| 291 | if (window > 1) |
| 292 | { |
| 293 | if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx)) |
| 294 | goto err; /* 2 */ |
| 295 | j=1<<(window-1); |
| 296 | for (i=1; i<j; i++) |
| 297 | { |
| 298 | if(((val[i] = BN_CTX_get(ctx)) == NULL) || |
| 299 | !BN_mod_mul_reciprocal(val[i],val[i-1], |
| 300 | aa,&recp,ctx)) |
| 301 | goto err; |
| 302 | } |
| 303 | } |
| 304 | |
| 305 | start=1; /* This is used to avoid multiplication etc |
| 306 | * when there is only the value '1' in the |
| 307 | * buffer. */ |
| 308 | wvalue=0; /* The 'value' of the window */ |
| 309 | wstart=bits-1; /* The top bit of the window */ |
| 310 | wend=0; /* The bottom bit of the window */ |
| 311 | |
| 312 | if (!BN_one(r)) goto err; |
| 313 | |
| 314 | for (;;) |
| 315 | { |
| 316 | if (BN_is_bit_set(p,wstart) == 0) |
| 317 | { |
| 318 | if (!start) |
| 319 | if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) |
| 320 | goto err; |
| 321 | if (wstart == 0) break; |
| 322 | wstart--; |
| 323 | continue; |
| 324 | } |
| 325 | /* We now have wstart on a 'set' bit, we now need to work out |
| 326 | * how bit a window to do. To do this we need to scan |
| 327 | * forward until the last set bit before the end of the |
| 328 | * window */ |
| 329 | j=wstart; |
| 330 | wvalue=1; |
| 331 | wend=0; |
| 332 | for (i=1; i<window; i++) |
| 333 | { |
| 334 | if (wstart-i < 0) break; |
| 335 | if (BN_is_bit_set(p,wstart-i)) |
| 336 | { |
| 337 | wvalue<<=(i-wend); |
| 338 | wvalue|=1; |
| 339 | wend=i; |
| 340 | } |
| 341 | } |
| 342 | |
| 343 | /* wend is the size of the current window */ |
| 344 | j=wend+1; |
| 345 | /* add the 'bytes above' */ |
| 346 | if (!start) |
| 347 | for (i=0; i<j; i++) |
| 348 | { |
| 349 | if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx)) |
| 350 | goto err; |
| 351 | } |
| 352 | |
| 353 | /* wvalue will be an odd number < 2^window */ |
| 354 | if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx)) |
| 355 | goto err; |
| 356 | |
| 357 | /* move the 'window' down further */ |
| 358 | wstart-=wend+1; |
| 359 | wvalue=0; |
| 360 | start=0; |
| 361 | if (wstart < 0) break; |
| 362 | } |
| 363 | ret=1; |
| 364 | err: |
| 365 | BN_CTX_end(ctx); |
| 366 | BN_RECP_CTX_free(&recp); |
| 367 | bn_check_top(r); |
| 368 | return(ret); |
| 369 | } |
| 370 | |
| 371 | |
| 372 | int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, |
| 373 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) |
| 374 | { |
| 375 | int i,j,bits,ret=0,wstart,wend,window,wvalue; |
| 376 | int start=1; |
| 377 | BIGNUM *d,*r; |
| 378 | const BIGNUM *aa; |
| 379 | /* Table of variables obtained from 'ctx' */ |
| 380 | BIGNUM *val[TABLE_SIZE]; |
| 381 | BN_MONT_CTX *mont=NULL; |
| 382 | |
| 383 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) |
| 384 | { |
| 385 | return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont); |
| 386 | } |
| 387 | |
| 388 | bn_check_top(a); |
| 389 | bn_check_top(p); |
| 390 | bn_check_top(m); |
| 391 | |
| 392 | if (!BN_is_odd(m)) |
| 393 | { |
| 394 | BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS); |
| 395 | return(0); |
| 396 | } |
| 397 | bits=BN_num_bits(p); |
| 398 | if (bits == 0) |
| 399 | { |
| 400 | ret = BN_one(rr); |
| 401 | return ret; |
| 402 | } |
| 403 | |
| 404 | BN_CTX_start(ctx); |
| 405 | d = BN_CTX_get(ctx); |
| 406 | r = BN_CTX_get(ctx); |
| 407 | val[0] = BN_CTX_get(ctx); |
| 408 | if (!d || !r || !val[0]) goto err; |
| 409 | |
| 410 | /* If this is not done, things will break in the montgomery |
| 411 | * part */ |
| 412 | |
| 413 | if (in_mont != NULL) |
| 414 | mont=in_mont; |
| 415 | else |
| 416 | { |
| 417 | if ((mont=BN_MONT_CTX_new()) == NULL) goto err; |
| 418 | if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; |
| 419 | } |
| 420 | |
| 421 | if (a->neg || BN_ucmp(a,m) >= 0) |
| 422 | { |
| 423 | if (!BN_nnmod(val[0],a,m,ctx)) |
| 424 | goto err; |
| 425 | aa= val[0]; |
| 426 | } |
| 427 | else |
| 428 | aa=a; |
| 429 | if (BN_is_zero(aa)) |
| 430 | { |
| 431 | BN_zero(rr); |
| 432 | ret = 1; |
| 433 | goto err; |
| 434 | } |
| 435 | if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */ |
| 436 | |
| 437 | window = BN_window_bits_for_exponent_size(bits); |
| 438 | if (window > 1) |
| 439 | { |
| 440 | if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */ |
| 441 | j=1<<(window-1); |
| 442 | for (i=1; i<j; i++) |
| 443 | { |
| 444 | if(((val[i] = BN_CTX_get(ctx)) == NULL) || |
| 445 | !BN_mod_mul_montgomery(val[i],val[i-1], |
| 446 | d,mont,ctx)) |
| 447 | goto err; |
| 448 | } |
| 449 | } |
| 450 | |
| 451 | start=1; /* This is used to avoid multiplication etc |
| 452 | * when there is only the value '1' in the |
| 453 | * buffer. */ |
| 454 | wvalue=0; /* The 'value' of the window */ |
| 455 | wstart=bits-1; /* The top bit of the window */ |
| 456 | wend=0; /* The bottom bit of the window */ |
| 457 | |
| 458 | if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err; |
| 459 | for (;;) |
| 460 | { |
| 461 | if (BN_is_bit_set(p,wstart) == 0) |
| 462 | { |
| 463 | if (!start) |
| 464 | { |
| 465 | if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) |
| 466 | goto err; |
| 467 | } |
| 468 | if (wstart == 0) break; |
| 469 | wstart--; |
| 470 | continue; |
| 471 | } |
| 472 | /* We now have wstart on a 'set' bit, we now need to work out |
| 473 | * how bit a window to do. To do this we need to scan |
| 474 | * forward until the last set bit before the end of the |
| 475 | * window */ |
| 476 | j=wstart; |
| 477 | wvalue=1; |
| 478 | wend=0; |
| 479 | for (i=1; i<window; i++) |
| 480 | { |
| 481 | if (wstart-i < 0) break; |
| 482 | if (BN_is_bit_set(p,wstart-i)) |
| 483 | { |
| 484 | wvalue<<=(i-wend); |
| 485 | wvalue|=1; |
| 486 | wend=i; |
| 487 | } |
| 488 | } |
| 489 | |
| 490 | /* wend is the size of the current window */ |
| 491 | j=wend+1; |
| 492 | /* add the 'bytes above' */ |
| 493 | if (!start) |
| 494 | for (i=0; i<j; i++) |
| 495 | { |
| 496 | if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) |
| 497 | goto err; |
| 498 | } |
| 499 | |
| 500 | /* wvalue will be an odd number < 2^window */ |
| 501 | if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx)) |
| 502 | goto err; |
| 503 | |
| 504 | /* move the 'window' down further */ |
| 505 | wstart-=wend+1; |
| 506 | wvalue=0; |
| 507 | start=0; |
| 508 | if (wstart < 0) break; |
| 509 | } |
| 510 | if (!BN_from_montgomery(rr,r,mont,ctx)) goto err; |
| 511 | ret=1; |
| 512 | err: |
| 513 | if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); |
| 514 | BN_CTX_end(ctx); |
| 515 | bn_check_top(rr); |
| 516 | return(ret); |
| 517 | } |
| 518 | |
| 519 | |
| 520 | /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout |
| 521 | * so that accessing any of these table values shows the same access pattern as far |
| 522 | * as cache lines are concerned. The following functions are used to transfer a BIGNUM |
| 523 | * from/to that table. */ |
| 524 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 525 | static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 526 | { |
| 527 | size_t i, j; |
| 528 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 529 | if (bn_wexpand(b, top) == NULL) |
| 530 | return 0; |
| 531 | while (b->top < top) |
| 532 | { |
| 533 | b->d[b->top++] = 0; |
| 534 | } |
| 535 | |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 536 | for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) |
| 537 | { |
| 538 | buf[j] = ((unsigned char*)b->d)[i]; |
| 539 | } |
| 540 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 541 | bn_correct_top(b); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 542 | return 1; |
| 543 | } |
| 544 | |
| 545 | static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width) |
| 546 | { |
| 547 | size_t i, j; |
| 548 | |
| 549 | if (bn_wexpand(b, top) == NULL) |
| 550 | return 0; |
| 551 | |
| 552 | for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width) |
| 553 | { |
| 554 | ((unsigned char*)b->d)[i] = buf[j]; |
| 555 | } |
| 556 | |
| 557 | b->top = top; |
| 558 | bn_correct_top(b); |
| 559 | return 1; |
| 560 | } |
| 561 | |
| 562 | /* Given a pointer value, compute the next address that is a cache line multiple. */ |
| 563 | #define MOD_EXP_CTIME_ALIGN(x_) \ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 564 | ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK)))) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 565 | |
| 566 | /* This variant of BN_mod_exp_mont() uses fixed windows and the special |
| 567 | * precomputation memory layout to limit data-dependency to a minimum |
| 568 | * to protect secret exponents (cf. the hyper-threading timing attacks |
| 569 | * pointed out by Colin Percival, |
| 570 | * http://www.daemonology.net/hyperthreading-considered-harmful/) |
| 571 | */ |
| 572 | int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, |
| 573 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) |
| 574 | { |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 575 | int i,bits,ret=0,idx,window,wvalue; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 576 | int top; |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 577 | BIGNUM *r; |
| 578 | const BIGNUM *aa; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 579 | BN_MONT_CTX *mont=NULL; |
| 580 | |
| 581 | int numPowers; |
| 582 | unsigned char *powerbufFree=NULL; |
| 583 | int powerbufLen = 0; |
| 584 | unsigned char *powerbuf=NULL; |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 585 | BIGNUM *computeTemp=NULL, *am=NULL; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 586 | |
| 587 | bn_check_top(a); |
| 588 | bn_check_top(p); |
| 589 | bn_check_top(m); |
| 590 | |
| 591 | top = m->top; |
| 592 | |
| 593 | if (!(m->d[0] & 1)) |
| 594 | { |
| 595 | BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS); |
| 596 | return(0); |
| 597 | } |
| 598 | bits=BN_num_bits(p); |
| 599 | if (bits == 0) |
| 600 | { |
| 601 | ret = BN_one(rr); |
| 602 | return ret; |
| 603 | } |
| 604 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 605 | /* Initialize BIGNUM context and allocate intermediate result */ |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 606 | BN_CTX_start(ctx); |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 607 | r = BN_CTX_get(ctx); |
| 608 | if (r == NULL) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 609 | |
| 610 | /* Allocate a montgomery context if it was not supplied by the caller. |
| 611 | * If this is not done, things will break in the montgomery part. |
| 612 | */ |
| 613 | if (in_mont != NULL) |
| 614 | mont=in_mont; |
| 615 | else |
| 616 | { |
| 617 | if ((mont=BN_MONT_CTX_new()) == NULL) goto err; |
| 618 | if (!BN_MONT_CTX_set(mont,m,ctx)) goto err; |
| 619 | } |
| 620 | |
| 621 | /* Get the window size to use with size of p. */ |
| 622 | window = BN_window_bits_for_ctime_exponent_size(bits); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 623 | |
| 624 | /* Allocate a buffer large enough to hold all of the pre-computed |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 625 | * powers of a. |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 626 | */ |
| 627 | numPowers = 1 << window; |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 628 | powerbufLen = sizeof(m->d[0])*top*numPowers; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 629 | if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL) |
| 630 | goto err; |
| 631 | |
| 632 | powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree); |
| 633 | memset(powerbuf, 0, powerbufLen); |
| 634 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 635 | /* Initialize the intermediate result. Do this early to save double conversion, |
| 636 | * once each for a^0 and intermediate result. |
| 637 | */ |
| 638 | if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err; |
| 639 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 640 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 641 | /* Initialize computeTemp as a^1 with montgomery precalcs */ |
| 642 | computeTemp = BN_CTX_get(ctx); |
| 643 | am = BN_CTX_get(ctx); |
| 644 | if (computeTemp==NULL || am==NULL) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 645 | |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 646 | if (a->neg || BN_ucmp(a,m) >= 0) |
| 647 | { |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 648 | if (!BN_mod(am,a,m,ctx)) |
| 649 | goto err; |
| 650 | aa= am; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 651 | } |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 652 | else |
| 653 | aa=a; |
| 654 | if (!BN_to_montgomery(am,aa,mont,ctx)) goto err; |
| 655 | if (!BN_copy(computeTemp, am)) goto err; |
| 656 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 657 | |
| 658 | /* If the window size is greater than 1, then calculate |
| 659 | * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) |
| 660 | * (even powers could instead be computed as (a^(i/2))^2 |
| 661 | * to use the slight performance advantage of sqr over mul). |
| 662 | */ |
| 663 | if (window > 1) |
| 664 | { |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 665 | for (i=2; i<numPowers; i++) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 666 | { |
| 667 | /* Calculate a^i = a^(i-1) * a */ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 668 | if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx)) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 669 | goto err; |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 670 | if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 671 | } |
| 672 | } |
| 673 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 674 | /* Adjust the number of bits up to a multiple of the window size. |
| 675 | * If the exponent length is not a multiple of the window size, then |
| 676 | * this pads the most significant bits with zeros to normalize the |
| 677 | * scanning loop to there's no special cases. |
| 678 | * |
| 679 | * * NOTE: Making the window size a power of two less than the native |
| 680 | * * word size ensures that the padded bits won't go past the last |
| 681 | * * word in the internal BIGNUM structure. Going past the end will |
| 682 | * * still produce the correct result, but causes a different branch |
| 683 | * * to be taken in the BN_is_bit_set function. |
| 684 | */ |
| 685 | bits = ((bits+window-1)/window)*window; |
| 686 | idx=bits-1; /* The top bit of the window */ |
| 687 | |
| 688 | /* Scan the exponent one window at a time starting from the most |
| 689 | * significant bits. |
| 690 | */ |
| 691 | while (idx >= 0) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 692 | { |
| 693 | wvalue=0; /* The 'value' of the window */ |
| 694 | |
| 695 | /* Scan the window, squaring the result as we go */ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 696 | for (i=0; i<window; i++,idx--) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 697 | { |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 698 | if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err; |
| 699 | wvalue = (wvalue<<1)+BN_is_bit_set(p,idx); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 700 | } |
| 701 | |
| 702 | /* Fetch the appropriate pre-computed value from the pre-buf */ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 703 | if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 704 | |
| 705 | /* Multiply the result into the intermediate result */ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 706 | if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 707 | } |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 708 | |
| 709 | /* Convert the final result from montgomery to standard format */ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 710 | if (!BN_from_montgomery(rr,r,mont,ctx)) goto err; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 711 | ret=1; |
| 712 | err: |
| 713 | if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); |
| 714 | if (powerbuf!=NULL) |
| 715 | { |
| 716 | OPENSSL_cleanse(powerbuf,powerbufLen); |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 717 | OPENSSL_free(powerbufFree); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 718 | } |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 719 | if (am!=NULL) BN_clear(am); |
| 720 | if (computeTemp!=NULL) BN_clear(computeTemp); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 721 | BN_CTX_end(ctx); |
| 722 | return(ret); |
| 723 | } |
| 724 | |
| 725 | int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p, |
| 726 | const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont) |
| 727 | { |
| 728 | BN_MONT_CTX *mont = NULL; |
| 729 | int b, bits, ret=0; |
| 730 | int r_is_one; |
| 731 | BN_ULONG w, next_w; |
| 732 | BIGNUM *d, *r, *t; |
| 733 | BIGNUM *swap_tmp; |
| 734 | #define BN_MOD_MUL_WORD(r, w, m) \ |
| 735 | (BN_mul_word(r, (w)) && \ |
| 736 | (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \ |
| 737 | (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1)))) |
| 738 | /* BN_MOD_MUL_WORD is only used with 'w' large, |
| 739 | * so the BN_ucmp test is probably more overhead |
| 740 | * than always using BN_mod (which uses BN_copy if |
| 741 | * a similar test returns true). */ |
| 742 | /* We can use BN_mod and do not need BN_nnmod because our |
| 743 | * accumulator is never negative (the result of BN_mod does |
| 744 | * not depend on the sign of the modulus). |
| 745 | */ |
| 746 | #define BN_TO_MONTGOMERY_WORD(r, w, mont) \ |
| 747 | (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx)) |
| 748 | |
| 749 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) |
| 750 | { |
| 751 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
| 752 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| 753 | return -1; |
| 754 | } |
| 755 | |
| 756 | bn_check_top(p); |
| 757 | bn_check_top(m); |
| 758 | |
| 759 | if (!BN_is_odd(m)) |
| 760 | { |
| 761 | BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS); |
| 762 | return(0); |
| 763 | } |
| 764 | if (m->top == 1) |
| 765 | a %= m->d[0]; /* make sure that 'a' is reduced */ |
| 766 | |
| 767 | bits = BN_num_bits(p); |
| 768 | if (bits == 0) |
| 769 | { |
| 770 | ret = BN_one(rr); |
| 771 | return ret; |
| 772 | } |
| 773 | if (a == 0) |
| 774 | { |
| 775 | BN_zero(rr); |
| 776 | ret = 1; |
| 777 | return ret; |
| 778 | } |
| 779 | |
| 780 | BN_CTX_start(ctx); |
| 781 | d = BN_CTX_get(ctx); |
| 782 | r = BN_CTX_get(ctx); |
| 783 | t = BN_CTX_get(ctx); |
| 784 | if (d == NULL || r == NULL || t == NULL) goto err; |
| 785 | |
| 786 | if (in_mont != NULL) |
| 787 | mont=in_mont; |
| 788 | else |
| 789 | { |
| 790 | if ((mont = BN_MONT_CTX_new()) == NULL) goto err; |
| 791 | if (!BN_MONT_CTX_set(mont, m, ctx)) goto err; |
| 792 | } |
| 793 | |
| 794 | r_is_one = 1; /* except for Montgomery factor */ |
| 795 | |
| 796 | /* bits-1 >= 0 */ |
| 797 | |
| 798 | /* The result is accumulated in the product r*w. */ |
| 799 | w = a; /* bit 'bits-1' of 'p' is always set */ |
| 800 | for (b = bits-2; b >= 0; b--) |
| 801 | { |
| 802 | /* First, square r*w. */ |
| 803 | next_w = w*w; |
| 804 | if ((next_w/w) != w) /* overflow */ |
| 805 | { |
| 806 | if (r_is_one) |
| 807 | { |
| 808 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; |
| 809 | r_is_one = 0; |
| 810 | } |
| 811 | else |
| 812 | { |
| 813 | if (!BN_MOD_MUL_WORD(r, w, m)) goto err; |
| 814 | } |
| 815 | next_w = 1; |
| 816 | } |
| 817 | w = next_w; |
| 818 | if (!r_is_one) |
| 819 | { |
| 820 | if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err; |
| 821 | } |
| 822 | |
| 823 | /* Second, multiply r*w by 'a' if exponent bit is set. */ |
| 824 | if (BN_is_bit_set(p, b)) |
| 825 | { |
| 826 | next_w = w*a; |
| 827 | if ((next_w/a) != w) /* overflow */ |
| 828 | { |
| 829 | if (r_is_one) |
| 830 | { |
| 831 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; |
| 832 | r_is_one = 0; |
| 833 | } |
| 834 | else |
| 835 | { |
| 836 | if (!BN_MOD_MUL_WORD(r, w, m)) goto err; |
| 837 | } |
| 838 | next_w = a; |
| 839 | } |
| 840 | w = next_w; |
| 841 | } |
| 842 | } |
| 843 | |
| 844 | /* Finally, set r:=r*w. */ |
| 845 | if (w != 1) |
| 846 | { |
| 847 | if (r_is_one) |
| 848 | { |
| 849 | if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err; |
| 850 | r_is_one = 0; |
| 851 | } |
| 852 | else |
| 853 | { |
| 854 | if (!BN_MOD_MUL_WORD(r, w, m)) goto err; |
| 855 | } |
| 856 | } |
| 857 | |
| 858 | if (r_is_one) /* can happen only if a == 1*/ |
| 859 | { |
| 860 | if (!BN_one(rr)) goto err; |
| 861 | } |
| 862 | else |
| 863 | { |
| 864 | if (!BN_from_montgomery(rr, r, mont, ctx)) goto err; |
| 865 | } |
| 866 | ret = 1; |
| 867 | err: |
| 868 | if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont); |
| 869 | BN_CTX_end(ctx); |
| 870 | bn_check_top(rr); |
| 871 | return(ret); |
| 872 | } |
| 873 | |
| 874 | |
| 875 | /* The old fallback, simple version :-) */ |
| 876 | int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, |
| 877 | const BIGNUM *m, BN_CTX *ctx) |
| 878 | { |
| 879 | int i,j,bits,ret=0,wstart,wend,window,wvalue; |
| 880 | int start=1; |
| 881 | BIGNUM *d; |
| 882 | /* Table of variables obtained from 'ctx' */ |
| 883 | BIGNUM *val[TABLE_SIZE]; |
| 884 | |
| 885 | if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) |
| 886 | { |
| 887 | /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */ |
| 888 | BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); |
| 889 | return -1; |
| 890 | } |
| 891 | |
| 892 | bits=BN_num_bits(p); |
| 893 | |
| 894 | if (bits == 0) |
| 895 | { |
| 896 | ret = BN_one(r); |
| 897 | return ret; |
| 898 | } |
| 899 | |
| 900 | BN_CTX_start(ctx); |
| 901 | d = BN_CTX_get(ctx); |
| 902 | val[0] = BN_CTX_get(ctx); |
| 903 | if(!d || !val[0]) goto err; |
| 904 | |
| 905 | if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */ |
| 906 | if (BN_is_zero(val[0])) |
| 907 | { |
| 908 | BN_zero(r); |
| 909 | ret = 1; |
| 910 | goto err; |
| 911 | } |
| 912 | |
| 913 | window = BN_window_bits_for_exponent_size(bits); |
| 914 | if (window > 1) |
| 915 | { |
| 916 | if (!BN_mod_mul(d,val[0],val[0],m,ctx)) |
| 917 | goto err; /* 2 */ |
| 918 | j=1<<(window-1); |
| 919 | for (i=1; i<j; i++) |
| 920 | { |
| 921 | if(((val[i] = BN_CTX_get(ctx)) == NULL) || |
| 922 | !BN_mod_mul(val[i],val[i-1],d,m,ctx)) |
| 923 | goto err; |
| 924 | } |
| 925 | } |
| 926 | |
| 927 | start=1; /* This is used to avoid multiplication etc |
| 928 | * when there is only the value '1' in the |
| 929 | * buffer. */ |
| 930 | wvalue=0; /* The 'value' of the window */ |
| 931 | wstart=bits-1; /* The top bit of the window */ |
| 932 | wend=0; /* The bottom bit of the window */ |
| 933 | |
| 934 | if (!BN_one(r)) goto err; |
| 935 | |
| 936 | for (;;) |
| 937 | { |
| 938 | if (BN_is_bit_set(p,wstart) == 0) |
| 939 | { |
| 940 | if (!start) |
| 941 | if (!BN_mod_mul(r,r,r,m,ctx)) |
| 942 | goto err; |
| 943 | if (wstart == 0) break; |
| 944 | wstart--; |
| 945 | continue; |
| 946 | } |
| 947 | /* We now have wstart on a 'set' bit, we now need to work out |
| 948 | * how bit a window to do. To do this we need to scan |
| 949 | * forward until the last set bit before the end of the |
| 950 | * window */ |
| 951 | j=wstart; |
| 952 | wvalue=1; |
| 953 | wend=0; |
| 954 | for (i=1; i<window; i++) |
| 955 | { |
| 956 | if (wstart-i < 0) break; |
| 957 | if (BN_is_bit_set(p,wstart-i)) |
| 958 | { |
| 959 | wvalue<<=(i-wend); |
| 960 | wvalue|=1; |
| 961 | wend=i; |
| 962 | } |
| 963 | } |
| 964 | |
| 965 | /* wend is the size of the current window */ |
| 966 | j=wend+1; |
| 967 | /* add the 'bytes above' */ |
| 968 | if (!start) |
| 969 | for (i=0; i<j; i++) |
| 970 | { |
| 971 | if (!BN_mod_mul(r,r,r,m,ctx)) |
| 972 | goto err; |
| 973 | } |
| 974 | |
| 975 | /* wvalue will be an odd number < 2^window */ |
| 976 | if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx)) |
| 977 | goto err; |
| 978 | |
| 979 | /* move the 'window' down further */ |
| 980 | wstart-=wend+1; |
| 981 | wvalue=0; |
| 982 | start=0; |
| 983 | if (wstart < 0) break; |
| 984 | } |
| 985 | ret=1; |
| 986 | err: |
| 987 | BN_CTX_end(ctx); |
| 988 | bn_check_top(r); |
| 989 | return(ret); |
| 990 | } |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 991 | |