Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 1 | /* crypto/ec/ec_mult.c */ |
| 2 | /* |
| 3 | * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project. |
| 4 | */ |
| 5 | /* ==================================================================== |
| 6 | * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved. |
| 7 | * |
| 8 | * Redistribution and use in source and binary forms, with or without |
| 9 | * modification, are permitted provided that the following conditions |
| 10 | * are met: |
| 11 | * |
| 12 | * 1. Redistributions of source code must retain the above copyright |
| 13 | * notice, this list of conditions and the following disclaimer. |
| 14 | * |
| 15 | * 2. Redistributions in binary form must reproduce the above copyright |
| 16 | * notice, this list of conditions and the following disclaimer in |
| 17 | * the documentation and/or other materials provided with the |
| 18 | * distribution. |
| 19 | * |
| 20 | * 3. All advertising materials mentioning features or use of this |
| 21 | * software must display the following acknowledgment: |
| 22 | * "This product includes software developed by the OpenSSL Project |
| 23 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| 24 | * |
| 25 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| 26 | * endorse or promote products derived from this software without |
| 27 | * prior written permission. For written permission, please contact |
| 28 | * openssl-core@openssl.org. |
| 29 | * |
| 30 | * 5. Products derived from this software may not be called "OpenSSL" |
| 31 | * nor may "OpenSSL" appear in their names without prior written |
| 32 | * permission of the OpenSSL Project. |
| 33 | * |
| 34 | * 6. Redistributions of any form whatsoever must retain the following |
| 35 | * acknowledgment: |
| 36 | * "This product includes software developed by the OpenSSL Project |
| 37 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| 38 | * |
| 39 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| 40 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 41 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 42 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| 43 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 44 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| 45 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 46 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 47 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 48 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 49 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| 50 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
| 51 | * ==================================================================== |
| 52 | * |
| 53 | * This product includes cryptographic software written by Eric Young |
| 54 | * (eay@cryptsoft.com). This product includes software written by Tim |
| 55 | * Hudson (tjh@cryptsoft.com). |
| 56 | * |
| 57 | */ |
| 58 | /* ==================================================================== |
| 59 | * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. |
| 60 | * Portions of this software developed by SUN MICROSYSTEMS, INC., |
| 61 | * and contributed to the OpenSSL project. |
| 62 | */ |
| 63 | |
| 64 | #include <string.h> |
| 65 | |
| 66 | #include <openssl/err.h> |
| 67 | |
| 68 | #include "ec_lcl.h" |
| 69 | |
| 70 | |
| 71 | /* |
| 72 | * This file implements the wNAF-based interleaving multi-exponentation method |
| 73 | * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>); |
| 74 | * for multiplication with precomputation, we use wNAF splitting |
| 75 | * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>). |
| 76 | */ |
| 77 | |
| 78 | |
| 79 | |
| 80 | |
| 81 | /* structure for precomputed multiples of the generator */ |
| 82 | typedef struct ec_pre_comp_st { |
| 83 | const EC_GROUP *group; /* parent EC_GROUP object */ |
| 84 | size_t blocksize; /* block size for wNAF splitting */ |
| 85 | size_t numblocks; /* max. number of blocks for which we have precomputation */ |
| 86 | size_t w; /* window size */ |
| 87 | EC_POINT **points; /* array with pre-calculated multiples of generator: |
| 88 | * 'num' pointers to EC_POINT objects followed by a NULL */ |
| 89 | size_t num; /* numblocks * 2^(w-1) */ |
| 90 | int references; |
| 91 | } EC_PRE_COMP; |
| 92 | |
| 93 | /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ |
| 94 | static void *ec_pre_comp_dup(void *); |
| 95 | static void ec_pre_comp_free(void *); |
| 96 | static void ec_pre_comp_clear_free(void *); |
| 97 | |
| 98 | static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) |
| 99 | { |
| 100 | EC_PRE_COMP *ret = NULL; |
| 101 | |
| 102 | if (!group) |
| 103 | return NULL; |
| 104 | |
| 105 | ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP)); |
| 106 | if (!ret) |
| 107 | { |
| 108 | ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); |
| 109 | return ret; |
| 110 | } |
| 111 | ret->group = group; |
| 112 | ret->blocksize = 8; /* default */ |
| 113 | ret->numblocks = 0; |
| 114 | ret->w = 4; /* default */ |
| 115 | ret->points = NULL; |
| 116 | ret->num = 0; |
| 117 | ret->references = 1; |
| 118 | return ret; |
| 119 | } |
| 120 | |
| 121 | static void *ec_pre_comp_dup(void *src_) |
| 122 | { |
| 123 | EC_PRE_COMP *src = src_; |
| 124 | |
| 125 | /* no need to actually copy, these objects never change! */ |
| 126 | |
| 127 | CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); |
| 128 | |
| 129 | return src_; |
| 130 | } |
| 131 | |
| 132 | static void ec_pre_comp_free(void *pre_) |
| 133 | { |
| 134 | int i; |
| 135 | EC_PRE_COMP *pre = pre_; |
| 136 | |
| 137 | if (!pre) |
| 138 | return; |
| 139 | |
| 140 | i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); |
| 141 | if (i > 0) |
| 142 | return; |
| 143 | |
| 144 | if (pre->points) |
| 145 | { |
| 146 | EC_POINT **p; |
| 147 | |
| 148 | for (p = pre->points; *p != NULL; p++) |
| 149 | EC_POINT_free(*p); |
| 150 | OPENSSL_free(pre->points); |
| 151 | } |
| 152 | OPENSSL_free(pre); |
| 153 | } |
| 154 | |
| 155 | static void ec_pre_comp_clear_free(void *pre_) |
| 156 | { |
| 157 | int i; |
| 158 | EC_PRE_COMP *pre = pre_; |
| 159 | |
| 160 | if (!pre) |
| 161 | return; |
| 162 | |
| 163 | i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); |
| 164 | if (i > 0) |
| 165 | return; |
| 166 | |
| 167 | if (pre->points) |
| 168 | { |
| 169 | EC_POINT **p; |
| 170 | |
| 171 | for (p = pre->points; *p != NULL; p++) |
| 172 | { |
| 173 | EC_POINT_clear_free(*p); |
| 174 | OPENSSL_cleanse(p, sizeof *p); |
| 175 | } |
| 176 | OPENSSL_free(pre->points); |
| 177 | } |
| 178 | OPENSSL_cleanse(pre, sizeof *pre); |
| 179 | OPENSSL_free(pre); |
| 180 | } |
| 181 | |
| 182 | |
| 183 | |
| 184 | |
| 185 | /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'. |
| 186 | * This is an array r[] of values that are either zero or odd with an |
| 187 | * absolute value less than 2^w satisfying |
| 188 | * scalar = \sum_j r[j]*2^j |
| 189 | * where at most one of any w+1 consecutive digits is non-zero |
| 190 | * with the exception that the most significant digit may be only |
| 191 | * w-1 zeros away from that next non-zero digit. |
| 192 | */ |
| 193 | static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) |
| 194 | { |
| 195 | int window_val; |
| 196 | int ok = 0; |
| 197 | signed char *r = NULL; |
| 198 | int sign = 1; |
| 199 | int bit, next_bit, mask; |
| 200 | size_t len = 0, j; |
| 201 | |
| 202 | if (BN_is_zero(scalar)) |
| 203 | { |
| 204 | r = OPENSSL_malloc(1); |
| 205 | if (!r) |
| 206 | { |
| 207 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); |
| 208 | goto err; |
| 209 | } |
| 210 | r[0] = 0; |
| 211 | *ret_len = 1; |
| 212 | return r; |
| 213 | } |
| 214 | |
| 215 | if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */ |
| 216 | { |
| 217 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
| 218 | goto err; |
| 219 | } |
| 220 | bit = 1 << w; /* at most 128 */ |
| 221 | next_bit = bit << 1; /* at most 256 */ |
| 222 | mask = next_bit - 1; /* at most 255 */ |
| 223 | |
| 224 | if (BN_is_negative(scalar)) |
| 225 | { |
| 226 | sign = -1; |
| 227 | } |
| 228 | |
| 229 | if (scalar->d == NULL || scalar->top == 0) |
| 230 | { |
| 231 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
| 232 | goto err; |
| 233 | } |
| 234 | |
| 235 | len = BN_num_bits(scalar); |
| 236 | r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation |
| 237 | * (*ret_len will be set to the actual length, i.e. at most |
| 238 | * BN_num_bits(scalar) + 1) */ |
| 239 | if (r == NULL) |
| 240 | { |
| 241 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); |
| 242 | goto err; |
| 243 | } |
| 244 | window_val = scalar->d[0] & mask; |
| 245 | j = 0; |
| 246 | while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */ |
| 247 | { |
| 248 | int digit = 0; |
| 249 | |
| 250 | /* 0 <= window_val <= 2^(w+1) */ |
| 251 | |
| 252 | if (window_val & 1) |
| 253 | { |
| 254 | /* 0 < window_val < 2^(w+1) */ |
| 255 | |
| 256 | if (window_val & bit) |
| 257 | { |
| 258 | digit = window_val - next_bit; /* -2^w < digit < 0 */ |
| 259 | |
| 260 | #if 1 /* modified wNAF */ |
| 261 | if (j + w + 1 >= len) |
| 262 | { |
| 263 | /* special case for generating modified wNAFs: |
| 264 | * no new bits will be added into window_val, |
| 265 | * so using a positive digit here will decrease |
| 266 | * the total length of the representation */ |
| 267 | |
| 268 | digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ |
| 269 | } |
| 270 | #endif |
| 271 | } |
| 272 | else |
| 273 | { |
| 274 | digit = window_val; /* 0 < digit < 2^w */ |
| 275 | } |
| 276 | |
| 277 | if (digit <= -bit || digit >= bit || !(digit & 1)) |
| 278 | { |
| 279 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
| 280 | goto err; |
| 281 | } |
| 282 | |
| 283 | window_val -= digit; |
| 284 | |
| 285 | /* now window_val is 0 or 2^(w+1) in standard wNAF generation; |
| 286 | * for modified window NAFs, it may also be 2^w |
| 287 | */ |
| 288 | if (window_val != 0 && window_val != next_bit && window_val != bit) |
| 289 | { |
| 290 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
| 291 | goto err; |
| 292 | } |
| 293 | } |
| 294 | |
| 295 | r[j++] = sign * digit; |
| 296 | |
| 297 | window_val >>= 1; |
| 298 | window_val += bit * BN_is_bit_set(scalar, j + w); |
| 299 | |
| 300 | if (window_val > next_bit) |
| 301 | { |
| 302 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
| 303 | goto err; |
| 304 | } |
| 305 | } |
| 306 | |
| 307 | if (j > len + 1) |
| 308 | { |
| 309 | ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); |
| 310 | goto err; |
| 311 | } |
| 312 | len = j; |
| 313 | ok = 1; |
| 314 | |
| 315 | err: |
| 316 | if (!ok) |
| 317 | { |
| 318 | OPENSSL_free(r); |
| 319 | r = NULL; |
| 320 | } |
| 321 | if (ok) |
| 322 | *ret_len = len; |
| 323 | return r; |
| 324 | } |
| 325 | |
| 326 | |
| 327 | /* TODO: table should be optimised for the wNAF-based implementation, |
| 328 | * sometimes smaller windows will give better performance |
| 329 | * (thus the boundaries should be increased) |
| 330 | */ |
| 331 | #define EC_window_bits_for_scalar_size(b) \ |
| 332 | ((size_t) \ |
| 333 | ((b) >= 2000 ? 6 : \ |
| 334 | (b) >= 800 ? 5 : \ |
| 335 | (b) >= 300 ? 4 : \ |
| 336 | (b) >= 70 ? 3 : \ |
| 337 | (b) >= 20 ? 2 : \ |
| 338 | 1)) |
| 339 | |
| 340 | /* Compute |
| 341 | * \sum scalars[i]*points[i], |
| 342 | * also including |
| 343 | * scalar*generator |
| 344 | * in the addition if scalar != NULL |
| 345 | */ |
| 346 | int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, |
| 347 | size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) |
| 348 | { |
| 349 | BN_CTX *new_ctx = NULL; |
| 350 | const EC_POINT *generator = NULL; |
| 351 | EC_POINT *tmp = NULL; |
| 352 | size_t totalnum; |
| 353 | size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ |
| 354 | size_t pre_points_per_block = 0; |
| 355 | size_t i, j; |
| 356 | int k; |
| 357 | int r_is_inverted = 0; |
| 358 | int r_is_at_infinity = 1; |
| 359 | size_t *wsize = NULL; /* individual window sizes */ |
| 360 | signed char **wNAF = NULL; /* individual wNAFs */ |
| 361 | size_t *wNAF_len = NULL; |
| 362 | size_t max_len = 0; |
| 363 | size_t num_val; |
| 364 | EC_POINT **val = NULL; /* precomputation */ |
| 365 | EC_POINT **v; |
| 366 | EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */ |
| 367 | const EC_PRE_COMP *pre_comp = NULL; |
| 368 | int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars, |
| 369 | * i.e. precomputation is not available */ |
| 370 | int ret = 0; |
| 371 | |
| 372 | if (group->meth != r->meth) |
| 373 | { |
| 374 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
| 375 | return 0; |
| 376 | } |
| 377 | |
| 378 | if ((scalar == NULL) && (num == 0)) |
| 379 | { |
| 380 | return EC_POINT_set_to_infinity(group, r); |
| 381 | } |
| 382 | |
| 383 | for (i = 0; i < num; i++) |
| 384 | { |
| 385 | if (group->meth != points[i]->meth) |
| 386 | { |
| 387 | ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
| 388 | return 0; |
| 389 | } |
| 390 | } |
| 391 | |
| 392 | if (ctx == NULL) |
| 393 | { |
| 394 | ctx = new_ctx = BN_CTX_new(); |
| 395 | if (ctx == NULL) |
| 396 | goto err; |
| 397 | } |
| 398 | |
| 399 | if (scalar != NULL) |
| 400 | { |
| 401 | generator = EC_GROUP_get0_generator(group); |
| 402 | if (generator == NULL) |
| 403 | { |
| 404 | ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); |
| 405 | goto err; |
| 406 | } |
| 407 | |
| 408 | /* look if we can use precomputed multiples of generator */ |
| 409 | |
| 410 | pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); |
| 411 | |
| 412 | if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) |
| 413 | { |
| 414 | blocksize = pre_comp->blocksize; |
| 415 | |
| 416 | /* determine maximum number of blocks that wNAF splitting may yield |
| 417 | * (NB: maximum wNAF length is bit length plus one) */ |
| 418 | numblocks = (BN_num_bits(scalar) / blocksize) + 1; |
| 419 | |
| 420 | /* we cannot use more blocks than we have precomputation for */ |
| 421 | if (numblocks > pre_comp->numblocks) |
| 422 | numblocks = pre_comp->numblocks; |
| 423 | |
| 424 | pre_points_per_block = (size_t)1 << (pre_comp->w - 1); |
| 425 | |
| 426 | /* check that pre_comp looks sane */ |
| 427 | if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) |
| 428 | { |
| 429 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
| 430 | goto err; |
| 431 | } |
| 432 | } |
| 433 | else |
| 434 | { |
| 435 | /* can't use precomputation */ |
| 436 | pre_comp = NULL; |
| 437 | numblocks = 1; |
| 438 | num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */ |
| 439 | } |
| 440 | } |
| 441 | |
| 442 | totalnum = num + numblocks; |
| 443 | |
| 444 | wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); |
| 445 | wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); |
| 446 | wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */ |
| 447 | val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); |
| 448 | |
| 449 | if (!wsize || !wNAF_len || !wNAF || !val_sub) |
| 450 | { |
| 451 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
| 452 | goto err; |
| 453 | } |
| 454 | |
| 455 | wNAF[0] = NULL; /* preliminary pivot */ |
| 456 | |
| 457 | /* num_val will be the total number of temporarily precomputed points */ |
| 458 | num_val = 0; |
| 459 | |
| 460 | for (i = 0; i < num + num_scalar; i++) |
| 461 | { |
| 462 | size_t bits; |
| 463 | |
| 464 | bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); |
| 465 | wsize[i] = EC_window_bits_for_scalar_size(bits); |
| 466 | num_val += (size_t)1 << (wsize[i] - 1); |
| 467 | wNAF[i + 1] = NULL; /* make sure we always have a pivot */ |
| 468 | wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]); |
| 469 | if (wNAF[i] == NULL) |
| 470 | goto err; |
| 471 | if (wNAF_len[i] > max_len) |
| 472 | max_len = wNAF_len[i]; |
| 473 | } |
| 474 | |
| 475 | if (numblocks) |
| 476 | { |
| 477 | /* we go here iff scalar != NULL */ |
| 478 | |
| 479 | if (pre_comp == NULL) |
| 480 | { |
| 481 | if (num_scalar != 1) |
| 482 | { |
| 483 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
| 484 | goto err; |
| 485 | } |
| 486 | /* we have already generated a wNAF for 'scalar' */ |
| 487 | } |
| 488 | else |
| 489 | { |
| 490 | signed char *tmp_wNAF = NULL; |
| 491 | size_t tmp_len = 0; |
| 492 | |
| 493 | if (num_scalar != 0) |
| 494 | { |
| 495 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
| 496 | goto err; |
| 497 | } |
| 498 | |
| 499 | /* use the window size for which we have precomputation */ |
| 500 | wsize[num] = pre_comp->w; |
| 501 | tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len); |
| 502 | if (!tmp_wNAF) |
| 503 | goto err; |
| 504 | |
| 505 | if (tmp_len <= max_len) |
| 506 | { |
| 507 | /* One of the other wNAFs is at least as long |
| 508 | * as the wNAF belonging to the generator, |
| 509 | * so wNAF splitting will not buy us anything. */ |
| 510 | |
| 511 | numblocks = 1; |
| 512 | totalnum = num + 1; /* don't use wNAF splitting */ |
| 513 | wNAF[num] = tmp_wNAF; |
| 514 | wNAF[num + 1] = NULL; |
| 515 | wNAF_len[num] = tmp_len; |
| 516 | if (tmp_len > max_len) |
| 517 | max_len = tmp_len; |
| 518 | /* pre_comp->points starts with the points that we need here: */ |
| 519 | val_sub[num] = pre_comp->points; |
| 520 | } |
| 521 | else |
| 522 | { |
| 523 | /* don't include tmp_wNAF directly into wNAF array |
| 524 | * - use wNAF splitting and include the blocks */ |
| 525 | |
| 526 | signed char *pp; |
| 527 | EC_POINT **tmp_points; |
| 528 | |
| 529 | if (tmp_len < numblocks * blocksize) |
| 530 | { |
| 531 | /* possibly we can do with fewer blocks than estimated */ |
| 532 | numblocks = (tmp_len + blocksize - 1) / blocksize; |
| 533 | if (numblocks > pre_comp->numblocks) |
| 534 | { |
| 535 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
| 536 | goto err; |
| 537 | } |
| 538 | totalnum = num + numblocks; |
| 539 | } |
| 540 | |
| 541 | /* split wNAF in 'numblocks' parts */ |
| 542 | pp = tmp_wNAF; |
| 543 | tmp_points = pre_comp->points; |
| 544 | |
| 545 | for (i = num; i < totalnum; i++) |
| 546 | { |
| 547 | if (i < totalnum - 1) |
| 548 | { |
| 549 | wNAF_len[i] = blocksize; |
| 550 | if (tmp_len < blocksize) |
| 551 | { |
| 552 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
| 553 | goto err; |
| 554 | } |
| 555 | tmp_len -= blocksize; |
| 556 | } |
| 557 | else |
| 558 | /* last block gets whatever is left |
| 559 | * (this could be more or less than 'blocksize'!) */ |
| 560 | wNAF_len[i] = tmp_len; |
| 561 | |
| 562 | wNAF[i + 1] = NULL; |
| 563 | wNAF[i] = OPENSSL_malloc(wNAF_len[i]); |
| 564 | if (wNAF[i] == NULL) |
| 565 | { |
| 566 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
| 567 | OPENSSL_free(tmp_wNAF); |
| 568 | goto err; |
| 569 | } |
| 570 | memcpy(wNAF[i], pp, wNAF_len[i]); |
| 571 | if (wNAF_len[i] > max_len) |
| 572 | max_len = wNAF_len[i]; |
| 573 | |
| 574 | if (*tmp_points == NULL) |
| 575 | { |
| 576 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
| 577 | OPENSSL_free(tmp_wNAF); |
| 578 | goto err; |
| 579 | } |
| 580 | val_sub[i] = tmp_points; |
| 581 | tmp_points += pre_points_per_block; |
| 582 | pp += blocksize; |
| 583 | } |
| 584 | OPENSSL_free(tmp_wNAF); |
| 585 | } |
| 586 | } |
| 587 | } |
| 588 | |
| 589 | /* All points we precompute now go into a single array 'val'. |
| 590 | * 'val_sub[i]' is a pointer to the subarray for the i-th point, |
| 591 | * or to a subarray of 'pre_comp->points' if we already have precomputation. */ |
| 592 | val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); |
| 593 | if (val == NULL) |
| 594 | { |
| 595 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); |
| 596 | goto err; |
| 597 | } |
| 598 | val[num_val] = NULL; /* pivot element */ |
| 599 | |
| 600 | /* allocate points for precomputation */ |
| 601 | v = val; |
| 602 | for (i = 0; i < num + num_scalar; i++) |
| 603 | { |
| 604 | val_sub[i] = v; |
| 605 | for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) |
| 606 | { |
| 607 | *v = EC_POINT_new(group); |
| 608 | if (*v == NULL) goto err; |
| 609 | v++; |
| 610 | } |
| 611 | } |
| 612 | if (!(v == val + num_val)) |
| 613 | { |
| 614 | ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); |
| 615 | goto err; |
| 616 | } |
| 617 | |
| 618 | if (!(tmp = EC_POINT_new(group))) |
| 619 | goto err; |
| 620 | |
| 621 | /* prepare precomputed values: |
| 622 | * val_sub[i][0] := points[i] |
| 623 | * val_sub[i][1] := 3 * points[i] |
| 624 | * val_sub[i][2] := 5 * points[i] |
| 625 | * ... |
| 626 | */ |
| 627 | for (i = 0; i < num + num_scalar; i++) |
| 628 | { |
| 629 | if (i < num) |
| 630 | { |
| 631 | if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; |
| 632 | } |
| 633 | else |
| 634 | { |
| 635 | if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; |
| 636 | } |
| 637 | |
| 638 | if (wsize[i] > 1) |
| 639 | { |
| 640 | if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; |
| 641 | for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) |
| 642 | { |
| 643 | if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; |
| 644 | } |
| 645 | } |
| 646 | } |
| 647 | |
| 648 | #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ |
| 649 | if (!EC_POINTs_make_affine(group, num_val, val, ctx)) |
| 650 | goto err; |
| 651 | #endif |
| 652 | |
| 653 | r_is_at_infinity = 1; |
| 654 | |
| 655 | for (k = max_len - 1; k >= 0; k--) |
| 656 | { |
| 657 | if (!r_is_at_infinity) |
| 658 | { |
| 659 | if (!EC_POINT_dbl(group, r, r, ctx)) goto err; |
| 660 | } |
| 661 | |
| 662 | for (i = 0; i < totalnum; i++) |
| 663 | { |
| 664 | if (wNAF_len[i] > (size_t)k) |
| 665 | { |
| 666 | int digit = wNAF[i][k]; |
| 667 | int is_neg; |
| 668 | |
| 669 | if (digit) |
| 670 | { |
| 671 | is_neg = digit < 0; |
| 672 | |
| 673 | if (is_neg) |
| 674 | digit = -digit; |
| 675 | |
| 676 | if (is_neg != r_is_inverted) |
| 677 | { |
| 678 | if (!r_is_at_infinity) |
| 679 | { |
| 680 | if (!EC_POINT_invert(group, r, ctx)) goto err; |
| 681 | } |
| 682 | r_is_inverted = !r_is_inverted; |
| 683 | } |
| 684 | |
| 685 | /* digit > 0 */ |
| 686 | |
| 687 | if (r_is_at_infinity) |
| 688 | { |
| 689 | if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; |
| 690 | r_is_at_infinity = 0; |
| 691 | } |
| 692 | else |
| 693 | { |
| 694 | if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; |
| 695 | } |
| 696 | } |
| 697 | } |
| 698 | } |
| 699 | } |
| 700 | |
| 701 | if (r_is_at_infinity) |
| 702 | { |
| 703 | if (!EC_POINT_set_to_infinity(group, r)) goto err; |
| 704 | } |
| 705 | else |
| 706 | { |
| 707 | if (r_is_inverted) |
| 708 | if (!EC_POINT_invert(group, r, ctx)) goto err; |
| 709 | } |
| 710 | |
| 711 | ret = 1; |
| 712 | |
| 713 | err: |
| 714 | if (new_ctx != NULL) |
| 715 | BN_CTX_free(new_ctx); |
| 716 | if (tmp != NULL) |
| 717 | EC_POINT_free(tmp); |
| 718 | if (wsize != NULL) |
| 719 | OPENSSL_free(wsize); |
| 720 | if (wNAF_len != NULL) |
| 721 | OPENSSL_free(wNAF_len); |
| 722 | if (wNAF != NULL) |
| 723 | { |
| 724 | signed char **w; |
| 725 | |
| 726 | for (w = wNAF; *w != NULL; w++) |
| 727 | OPENSSL_free(*w); |
| 728 | |
| 729 | OPENSSL_free(wNAF); |
| 730 | } |
| 731 | if (val != NULL) |
| 732 | { |
| 733 | for (v = val; *v != NULL; v++) |
| 734 | EC_POINT_clear_free(*v); |
| 735 | |
| 736 | OPENSSL_free(val); |
| 737 | } |
| 738 | if (val_sub != NULL) |
| 739 | { |
| 740 | OPENSSL_free(val_sub); |
| 741 | } |
| 742 | return ret; |
| 743 | } |
| 744 | |
| 745 | |
| 746 | /* ec_wNAF_precompute_mult() |
| 747 | * creates an EC_PRE_COMP object with preprecomputed multiples of the generator |
| 748 | * for use with wNAF splitting as implemented in ec_wNAF_mul(). |
| 749 | * |
| 750 | * 'pre_comp->points' is an array of multiples of the generator |
| 751 | * of the following form: |
| 752 | * points[0] = generator; |
| 753 | * points[1] = 3 * generator; |
| 754 | * ... |
| 755 | * points[2^(w-1)-1] = (2^(w-1)-1) * generator; |
| 756 | * points[2^(w-1)] = 2^blocksize * generator; |
| 757 | * points[2^(w-1)+1] = 3 * 2^blocksize * generator; |
| 758 | * ... |
| 759 | * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator |
| 760 | * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator |
| 761 | * ... |
| 762 | * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator |
| 763 | * points[2^(w-1)*numblocks] = NULL |
| 764 | */ |
| 765 | int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) |
| 766 | { |
| 767 | const EC_POINT *generator; |
| 768 | EC_POINT *tmp_point = NULL, *base = NULL, **var; |
| 769 | BN_CTX *new_ctx = NULL; |
| 770 | BIGNUM *order; |
| 771 | size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; |
| 772 | EC_POINT **points = NULL; |
| 773 | EC_PRE_COMP *pre_comp; |
| 774 | int ret = 0; |
| 775 | |
| 776 | /* if there is an old EC_PRE_COMP object, throw it away */ |
| 777 | EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); |
| 778 | |
| 779 | if ((pre_comp = ec_pre_comp_new(group)) == NULL) |
| 780 | return 0; |
| 781 | |
| 782 | generator = EC_GROUP_get0_generator(group); |
| 783 | if (generator == NULL) |
| 784 | { |
| 785 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); |
| 786 | goto err; |
| 787 | } |
| 788 | |
| 789 | if (ctx == NULL) |
| 790 | { |
| 791 | ctx = new_ctx = BN_CTX_new(); |
| 792 | if (ctx == NULL) |
| 793 | goto err; |
| 794 | } |
| 795 | |
| 796 | BN_CTX_start(ctx); |
| 797 | order = BN_CTX_get(ctx); |
| 798 | if (order == NULL) goto err; |
| 799 | |
| 800 | if (!EC_GROUP_get_order(group, order, ctx)) goto err; |
| 801 | if (BN_is_zero(order)) |
| 802 | { |
| 803 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); |
| 804 | goto err; |
| 805 | } |
| 806 | |
| 807 | bits = BN_num_bits(order); |
| 808 | /* The following parameters mean we precompute (approximately) |
| 809 | * one point per bit. |
| 810 | * |
| 811 | * TBD: The combination 8, 4 is perfect for 160 bits; for other |
| 812 | * bit lengths, other parameter combinations might provide better |
| 813 | * efficiency. |
| 814 | */ |
| 815 | blocksize = 8; |
| 816 | w = 4; |
| 817 | if (EC_window_bits_for_scalar_size(bits) > w) |
| 818 | { |
| 819 | /* let's not make the window too small ... */ |
| 820 | w = EC_window_bits_for_scalar_size(bits); |
| 821 | } |
| 822 | |
| 823 | numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */ |
| 824 | |
| 825 | pre_points_per_block = (size_t)1 << (w - 1); |
| 826 | num = pre_points_per_block * numblocks; /* number of points to compute and store */ |
| 827 | |
| 828 | points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1)); |
| 829 | if (!points) |
| 830 | { |
| 831 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
| 832 | goto err; |
| 833 | } |
| 834 | |
| 835 | var = points; |
| 836 | var[num] = NULL; /* pivot */ |
| 837 | for (i = 0; i < num; i++) |
| 838 | { |
| 839 | if ((var[i] = EC_POINT_new(group)) == NULL) |
| 840 | { |
| 841 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
| 842 | goto err; |
| 843 | } |
| 844 | } |
| 845 | |
| 846 | if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) |
| 847 | { |
| 848 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); |
| 849 | goto err; |
| 850 | } |
| 851 | |
| 852 | if (!EC_POINT_copy(base, generator)) |
| 853 | goto err; |
| 854 | |
| 855 | /* do the precomputation */ |
| 856 | for (i = 0; i < numblocks; i++) |
| 857 | { |
| 858 | size_t j; |
| 859 | |
| 860 | if (!EC_POINT_dbl(group, tmp_point, base, ctx)) |
| 861 | goto err; |
| 862 | |
| 863 | if (!EC_POINT_copy(*var++, base)) |
| 864 | goto err; |
| 865 | |
| 866 | for (j = 1; j < pre_points_per_block; j++, var++) |
| 867 | { |
| 868 | /* calculate odd multiples of the current base point */ |
| 869 | if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) |
| 870 | goto err; |
| 871 | } |
| 872 | |
| 873 | if (i < numblocks - 1) |
| 874 | { |
| 875 | /* get the next base (multiply current one by 2^blocksize) */ |
| 876 | size_t k; |
| 877 | |
| 878 | if (blocksize <= 2) |
| 879 | { |
| 880 | ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); |
| 881 | goto err; |
| 882 | } |
| 883 | |
| 884 | if (!EC_POINT_dbl(group, base, tmp_point, ctx)) |
| 885 | goto err; |
| 886 | for (k = 2; k < blocksize; k++) |
| 887 | { |
| 888 | if (!EC_POINT_dbl(group,base,base,ctx)) |
| 889 | goto err; |
| 890 | } |
| 891 | } |
| 892 | } |
| 893 | |
| 894 | if (!EC_POINTs_make_affine(group, num, points, ctx)) |
| 895 | goto err; |
| 896 | |
| 897 | pre_comp->group = group; |
| 898 | pre_comp->blocksize = blocksize; |
| 899 | pre_comp->numblocks = numblocks; |
| 900 | pre_comp->w = w; |
| 901 | pre_comp->points = points; |
| 902 | points = NULL; |
| 903 | pre_comp->num = num; |
| 904 | |
| 905 | if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp, |
| 906 | ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free)) |
| 907 | goto err; |
| 908 | pre_comp = NULL; |
| 909 | |
| 910 | ret = 1; |
| 911 | err: |
| 912 | if (ctx != NULL) |
| 913 | BN_CTX_end(ctx); |
| 914 | if (new_ctx != NULL) |
| 915 | BN_CTX_free(new_ctx); |
| 916 | if (pre_comp) |
| 917 | ec_pre_comp_free(pre_comp); |
| 918 | if (points) |
| 919 | { |
| 920 | EC_POINT **p; |
| 921 | |
| 922 | for (p = points; *p != NULL; p++) |
| 923 | EC_POINT_free(*p); |
| 924 | OPENSSL_free(points); |
| 925 | } |
| 926 | if (tmp_point) |
| 927 | EC_POINT_free(tmp_point); |
| 928 | if (base) |
| 929 | EC_POINT_free(base); |
| 930 | return ret; |
| 931 | } |
| 932 | |
| 933 | |
| 934 | int ec_wNAF_have_precompute_mult(const EC_GROUP *group) |
| 935 | { |
| 936 | if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL) |
| 937 | return 1; |
| 938 | else |
| 939 | return 0; |
| 940 | } |