ec_mult.c revision 296465
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 * This file implements the wNAF-based interleaving multi-exponentation method 72 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>); 73 * for multiplication with precomputation, we use wNAF splitting 74 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>). 75 */ 76 77/* structure for precomputed multiples of the generator */ 78typedef struct ec_pre_comp_st { 79 const EC_GROUP *group; /* parent EC_GROUP object */ 80 size_t blocksize; /* block size for wNAF splitting */ 81 size_t numblocks; /* max. number of blocks for which we have 82 * precomputation */ 83 size_t w; /* window size */ 84 EC_POINT **points; /* array with pre-calculated multiples of 85 * generator: 'num' pointers to EC_POINT 86 * objects followed by a NULL */ 87 size_t num; /* numblocks * 2^(w-1) */ 88 int references; 89} EC_PRE_COMP; 90 91/* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ 92static void *ec_pre_comp_dup(void *); 93static void ec_pre_comp_free(void *); 94static void ec_pre_comp_clear_free(void *); 95 96static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) 97{ 98 EC_PRE_COMP *ret = NULL; 99 100 if (!group) 101 return NULL; 102 103 ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP)); 104 if (!ret) { 105 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); 106 return ret; 107 } 108 ret->group = group; 109 ret->blocksize = 8; /* default */ 110 ret->numblocks = 0; 111 ret->w = 4; /* default */ 112 ret->points = NULL; 113 ret->num = 0; 114 ret->references = 1; 115 return ret; 116} 117 118static void *ec_pre_comp_dup(void *src_) 119{ 120 EC_PRE_COMP *src = src_; 121 122 /* no need to actually copy, these objects never change! */ 123 124 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); 125 126 return src_; 127} 128 129static void ec_pre_comp_free(void *pre_) 130{ 131 int i; 132 EC_PRE_COMP *pre = pre_; 133 134 if (!pre) 135 return; 136 137 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 138 if (i > 0) 139 return; 140 141 if (pre->points) { 142 EC_POINT **p; 143 144 for (p = pre->points; *p != NULL; p++) 145 EC_POINT_free(*p); 146 OPENSSL_free(pre->points); 147 } 148 OPENSSL_free(pre); 149} 150 151static void ec_pre_comp_clear_free(void *pre_) 152{ 153 int i; 154 EC_PRE_COMP *pre = pre_; 155 156 if (!pre) 157 return; 158 159 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 160 if (i > 0) 161 return; 162 163 if (pre->points) { 164 EC_POINT **p; 165 166 for (p = pre->points; *p != NULL; p++) { 167 EC_POINT_clear_free(*p); 168 OPENSSL_cleanse(p, sizeof *p); 169 } 170 OPENSSL_free(pre->points); 171 } 172 OPENSSL_cleanse(pre, sizeof *pre); 173 OPENSSL_free(pre); 174} 175 176/*- 177 * Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'. 178 * This is an array r[] of values that are either zero or odd with an 179 * absolute value less than 2^w satisfying 180 * scalar = \sum_j r[j]*2^j 181 * where at most one of any w+1 consecutive digits is non-zero 182 * with the exception that the most significant digit may be only 183 * w-1 zeros away from that next non-zero digit. 184 */ 185static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) 186{ 187 int window_val; 188 int ok = 0; 189 signed char *r = NULL; 190 int sign = 1; 191 int bit, next_bit, mask; 192 size_t len = 0, j; 193 194 if (BN_is_zero(scalar)) { 195 r = OPENSSL_malloc(1); 196 if (!r) { 197 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); 198 goto err; 199 } 200 r[0] = 0; 201 *ret_len = 1; 202 return r; 203 } 204 205 if (w <= 0 || w > 7) { /* 'signed char' can represent integers with 206 * absolute values less than 2^7 */ 207 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 208 goto err; 209 } 210 bit = 1 << w; /* at most 128 */ 211 next_bit = bit << 1; /* at most 256 */ 212 mask = next_bit - 1; /* at most 255 */ 213 214 if (BN_is_negative(scalar)) { 215 sign = -1; 216 } 217 218 len = BN_num_bits(scalar); 219 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer 220 * than binary representation (*ret_len will 221 * be set to the actual length, i.e. at most 222 * BN_num_bits(scalar) + 1) */ 223 if (r == NULL) { 224 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); 225 goto err; 226 } 227 228 if (scalar->d == NULL || scalar->top == 0) { 229 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 230 goto err; 231 } 232 window_val = scalar->d[0] & mask; 233 j = 0; 234 while ((window_val != 0) || (j + w + 1 < len)) { /* if j+w+1 >= len, 235 * window_val will not 236 * increase */ 237 int digit = 0; 238 239 /* 0 <= window_val <= 2^(w+1) */ 240 241 if (window_val & 1) { 242 /* 0 < window_val < 2^(w+1) */ 243 244 if (window_val & bit) { 245 digit = window_val - next_bit; /* -2^w < digit < 0 */ 246 247#if 1 /* modified wNAF */ 248 if (j + w + 1 >= len) { 249 /* 250 * special case for generating modified wNAFs: no new 251 * bits will be added into window_val, so using a 252 * positive digit here will decrease the total length of 253 * the representation 254 */ 255 256 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ 257 } 258#endif 259 } else { 260 digit = window_val; /* 0 < digit < 2^w */ 261 } 262 263 if (digit <= -bit || digit >= bit || !(digit & 1)) { 264 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 265 goto err; 266 } 267 268 window_val -= digit; 269 270 /* 271 * now window_val is 0 or 2^(w+1) in standard wNAF generation; 272 * for modified window NAFs, it may also be 2^w 273 */ 274 if (window_val != 0 && window_val != next_bit 275 && window_val != bit) { 276 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 277 goto err; 278 } 279 } 280 281 r[j++] = sign * digit; 282 283 window_val >>= 1; 284 window_val += bit * BN_is_bit_set(scalar, j + w); 285 286 if (window_val > next_bit) { 287 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 288 goto err; 289 } 290 } 291 292 if (j > len + 1) { 293 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); 294 goto err; 295 } 296 len = j; 297 ok = 1; 298 299 err: 300 if (!ok) { 301 OPENSSL_free(r); 302 r = NULL; 303 } 304 if (ok) 305 *ret_len = len; 306 return r; 307} 308 309/* 310 * TODO: table should be optimised for the wNAF-based implementation, 311 * sometimes smaller windows will give better performance (thus the 312 * boundaries should be increased) 313 */ 314#define EC_window_bits_for_scalar_size(b) \ 315 ((size_t) \ 316 ((b) >= 2000 ? 6 : \ 317 (b) >= 800 ? 5 : \ 318 (b) >= 300 ? 4 : \ 319 (b) >= 70 ? 3 : \ 320 (b) >= 20 ? 2 : \ 321 1)) 322 323/*- 324 * Compute 325 * \sum scalars[i]*points[i], 326 * also including 327 * scalar*generator 328 * in the addition if scalar != NULL 329 */ 330int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, 331 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], 332 BN_CTX *ctx) 333{ 334 BN_CTX *new_ctx = NULL; 335 const EC_POINT *generator = NULL; 336 EC_POINT *tmp = NULL; 337 size_t totalnum; 338 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ 339 size_t pre_points_per_block = 0; 340 size_t i, j; 341 int k; 342 int r_is_inverted = 0; 343 int r_is_at_infinity = 1; 344 size_t *wsize = NULL; /* individual window sizes */ 345 signed char **wNAF = NULL; /* individual wNAFs */ 346 size_t *wNAF_len = NULL; 347 size_t max_len = 0; 348 size_t num_val; 349 EC_POINT **val = NULL; /* precomputation */ 350 EC_POINT **v; 351 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 352 * 'pre_comp->points' */ 353 const EC_PRE_COMP *pre_comp = NULL; 354 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be 355 * treated like other scalars, i.e. 356 * precomputation is not available */ 357 int ret = 0; 358 359 if (group->meth != r->meth) { 360 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); 361 return 0; 362 } 363 364 if ((scalar == NULL) && (num == 0)) { 365 return EC_POINT_set_to_infinity(group, r); 366 } 367 368 for (i = 0; i < num; i++) { 369 if (group->meth != points[i]->meth) { 370 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); 371 return 0; 372 } 373 } 374 375 if (ctx == NULL) { 376 ctx = new_ctx = BN_CTX_new(); 377 if (ctx == NULL) 378 goto err; 379 } 380 381 if (scalar != NULL) { 382 generator = EC_GROUP_get0_generator(group); 383 if (generator == NULL) { 384 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); 385 goto err; 386 } 387 388 /* look if we can use precomputed multiples of generator */ 389 390 pre_comp = 391 EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, 392 ec_pre_comp_free, ec_pre_comp_clear_free); 393 394 if (pre_comp && pre_comp->numblocks 395 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 396 0)) { 397 blocksize = pre_comp->blocksize; 398 399 /* 400 * determine maximum number of blocks that wNAF splitting may 401 * yield (NB: maximum wNAF length is bit length plus one) 402 */ 403 numblocks = (BN_num_bits(scalar) / blocksize) + 1; 404 405 /* 406 * we cannot use more blocks than we have precomputation for 407 */ 408 if (numblocks > pre_comp->numblocks) 409 numblocks = pre_comp->numblocks; 410 411 pre_points_per_block = 1u << (pre_comp->w - 1); 412 413 /* check that pre_comp looks sane */ 414 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { 415 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); 416 goto err; 417 } 418 } else { 419 /* can't use precomputation */ 420 pre_comp = NULL; 421 numblocks = 1; 422 num_scalar = 1; /* treat 'scalar' like 'num'-th element of 423 * 'scalars' */ 424 } 425 } 426 427 totalnum = num + numblocks; 428 429 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); 430 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); 431 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space 432 * for pivot */ 433 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); 434 435 if (!wsize || !wNAF_len || !wNAF || !val_sub) { 436 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); 437 goto err; 438 } 439 440 wNAF[0] = NULL; /* preliminary pivot */ 441 442 /* 443 * num_val will be the total number of temporarily precomputed points 444 */ 445 num_val = 0; 446 447 for (i = 0; i < num + num_scalar; i++) { 448 size_t bits; 449 450 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); 451 wsize[i] = EC_window_bits_for_scalar_size(bits); 452 num_val += 1u << (wsize[i] - 1); 453 wNAF[i + 1] = NULL; /* make sure we always have a pivot */ 454 wNAF[i] = 455 compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], 456 &wNAF_len[i]); 457 if (wNAF[i] == NULL) 458 goto err; 459 if (wNAF_len[i] > max_len) 460 max_len = wNAF_len[i]; 461 } 462 463 if (numblocks) { 464 /* we go here iff scalar != NULL */ 465 466 if (pre_comp == NULL) { 467 if (num_scalar != 1) { 468 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); 469 goto err; 470 } 471 /* we have already generated a wNAF for 'scalar' */ 472 } else { 473 signed char *tmp_wNAF = NULL; 474 size_t tmp_len = 0; 475 476 if (num_scalar != 0) { 477 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); 478 goto err; 479 } 480 481 /* 482 * use the window size for which we have precomputation 483 */ 484 wsize[num] = pre_comp->w; 485 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len); 486 if (!tmp_wNAF) 487 goto err; 488 489 if (tmp_len <= max_len) { 490 /* 491 * One of the other wNAFs is at least as long as the wNAF 492 * belonging to the generator, so wNAF splitting will not buy 493 * us anything. 494 */ 495 496 numblocks = 1; 497 totalnum = num + 1; /* don't use wNAF splitting */ 498 wNAF[num] = tmp_wNAF; 499 wNAF[num + 1] = NULL; 500 wNAF_len[num] = tmp_len; 501 if (tmp_len > max_len) 502 max_len = tmp_len; 503 /* 504 * pre_comp->points starts with the points that we need here: 505 */ 506 val_sub[num] = pre_comp->points; 507 } else { 508 /* 509 * don't include tmp_wNAF directly into wNAF array - use wNAF 510 * splitting and include the blocks 511 */ 512 513 signed char *pp; 514 EC_POINT **tmp_points; 515 516 if (tmp_len < numblocks * blocksize) { 517 /* 518 * possibly we can do with fewer blocks than estimated 519 */ 520 numblocks = (tmp_len + blocksize - 1) / blocksize; 521 if (numblocks > pre_comp->numblocks) { 522 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); 523 goto err; 524 } 525 totalnum = num + numblocks; 526 } 527 528 /* split wNAF in 'numblocks' parts */ 529 pp = tmp_wNAF; 530 tmp_points = pre_comp->points; 531 532 for (i = num; i < totalnum; i++) { 533 if (i < totalnum - 1) { 534 wNAF_len[i] = blocksize; 535 if (tmp_len < blocksize) { 536 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); 537 goto err; 538 } 539 tmp_len -= blocksize; 540 } else 541 /* 542 * last block gets whatever is left (this could be 543 * more or less than 'blocksize'!) 544 */ 545 wNAF_len[i] = tmp_len; 546 547 wNAF[i + 1] = NULL; 548 wNAF[i] = OPENSSL_malloc(wNAF_len[i]); 549 if (wNAF[i] == NULL) { 550 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); 551 OPENSSL_free(tmp_wNAF); 552 goto err; 553 } 554 memcpy(wNAF[i], pp, wNAF_len[i]); 555 if (wNAF_len[i] > max_len) 556 max_len = wNAF_len[i]; 557 558 if (*tmp_points == NULL) { 559 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); 560 OPENSSL_free(tmp_wNAF); 561 goto err; 562 } 563 val_sub[i] = tmp_points; 564 tmp_points += pre_points_per_block; 565 pp += blocksize; 566 } 567 OPENSSL_free(tmp_wNAF); 568 } 569 } 570 } 571 572 /* 573 * All points we precompute now go into a single array 'val'. 574 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a 575 * subarray of 'pre_comp->points' if we already have precomputation. 576 */ 577 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); 578 if (val == NULL) { 579 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); 580 goto err; 581 } 582 val[num_val] = NULL; /* pivot element */ 583 584 /* allocate points for precomputation */ 585 v = val; 586 for (i = 0; i < num + num_scalar; i++) { 587 val_sub[i] = v; 588 for (j = 0; j < (1u << (wsize[i] - 1)); j++) { 589 *v = EC_POINT_new(group); 590 if (*v == NULL) 591 goto err; 592 v++; 593 } 594 } 595 if (!(v == val + num_val)) { 596 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); 597 goto err; 598 } 599 600 if (!(tmp = EC_POINT_new(group))) 601 goto err; 602 603 /*- 604 * prepare precomputed values: 605 * val_sub[i][0] := points[i] 606 * val_sub[i][1] := 3 * points[i] 607 * val_sub[i][2] := 5 * points[i] 608 * ... 609 */ 610 for (i = 0; i < num + num_scalar; i++) { 611 if (i < num) { 612 if (!EC_POINT_copy(val_sub[i][0], points[i])) 613 goto err; 614 } else { 615 if (!EC_POINT_copy(val_sub[i][0], generator)) 616 goto err; 617 } 618 619 if (wsize[i] > 1) { 620 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) 621 goto err; 622 for (j = 1; j < (1u << (wsize[i] - 1)); j++) { 623 if (!EC_POINT_add 624 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) 625 goto err; 626 } 627 } 628 } 629 630#if 1 /* optional; EC_window_bits_for_scalar_size 631 * assumes we do this step */ 632 if (!EC_POINTs_make_affine(group, num_val, val, ctx)) 633 goto err; 634#endif 635 636 r_is_at_infinity = 1; 637 638 for (k = max_len - 1; k >= 0; k--) { 639 if (!r_is_at_infinity) { 640 if (!EC_POINT_dbl(group, r, r, ctx)) 641 goto err; 642 } 643 644 for (i = 0; i < totalnum; i++) { 645 if (wNAF_len[i] > (size_t)k) { 646 int digit = wNAF[i][k]; 647 int is_neg; 648 649 if (digit) { 650 is_neg = digit < 0; 651 652 if (is_neg) 653 digit = -digit; 654 655 if (is_neg != r_is_inverted) { 656 if (!r_is_at_infinity) { 657 if (!EC_POINT_invert(group, r, ctx)) 658 goto err; 659 } 660 r_is_inverted = !r_is_inverted; 661 } 662 663 /* digit > 0 */ 664 665 if (r_is_at_infinity) { 666 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) 667 goto err; 668 r_is_at_infinity = 0; 669 } else { 670 if (!EC_POINT_add 671 (group, r, r, val_sub[i][digit >> 1], ctx)) 672 goto err; 673 } 674 } 675 } 676 } 677 } 678 679 if (r_is_at_infinity) { 680 if (!EC_POINT_set_to_infinity(group, r)) 681 goto err; 682 } else { 683 if (r_is_inverted) 684 if (!EC_POINT_invert(group, r, ctx)) 685 goto err; 686 } 687 688 ret = 1; 689 690 err: 691 if (new_ctx != NULL) 692 BN_CTX_free(new_ctx); 693 if (tmp != NULL) 694 EC_POINT_free(tmp); 695 if (wsize != NULL) 696 OPENSSL_free(wsize); 697 if (wNAF_len != NULL) 698 OPENSSL_free(wNAF_len); 699 if (wNAF != NULL) { 700 signed char **w; 701 702 for (w = wNAF; *w != NULL; w++) 703 OPENSSL_free(*w); 704 705 OPENSSL_free(wNAF); 706 } 707 if (val != NULL) { 708 for (v = val; *v != NULL; v++) 709 EC_POINT_clear_free(*v); 710 711 OPENSSL_free(val); 712 } 713 if (val_sub != NULL) { 714 OPENSSL_free(val_sub); 715 } 716 return ret; 717} 718 719/*- 720 * ec_wNAF_precompute_mult() 721 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator 722 * for use with wNAF splitting as implemented in ec_wNAF_mul(). 723 * 724 * 'pre_comp->points' is an array of multiples of the generator 725 * of the following form: 726 * points[0] = generator; 727 * points[1] = 3 * generator; 728 * ... 729 * points[2^(w-1)-1] = (2^(w-1)-1) * generator; 730 * points[2^(w-1)] = 2^blocksize * generator; 731 * points[2^(w-1)+1] = 3 * 2^blocksize * generator; 732 * ... 733 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator 734 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator 735 * ... 736 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator 737 * points[2^(w-1)*numblocks] = NULL 738 */ 739int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) 740{ 741 const EC_POINT *generator; 742 EC_POINT *tmp_point = NULL, *base = NULL, **var; 743 BN_CTX *new_ctx = NULL; 744 BIGNUM *order; 745 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; 746 EC_POINT **points = NULL; 747 EC_PRE_COMP *pre_comp; 748 int ret = 0; 749 750 /* if there is an old EC_PRE_COMP object, throw it away */ 751 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, 752 ec_pre_comp_free, ec_pre_comp_clear_free); 753 754 if ((pre_comp = ec_pre_comp_new(group)) == NULL) 755 return 0; 756 757 generator = EC_GROUP_get0_generator(group); 758 if (generator == NULL) { 759 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); 760 goto err; 761 } 762 763 if (ctx == NULL) { 764 ctx = new_ctx = BN_CTX_new(); 765 if (ctx == NULL) 766 goto err; 767 } 768 769 BN_CTX_start(ctx); 770 order = BN_CTX_get(ctx); 771 if (order == NULL) 772 goto err; 773 774 if (!EC_GROUP_get_order(group, order, ctx)) 775 goto err; 776 if (BN_is_zero(order)) { 777 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); 778 goto err; 779 } 780 781 bits = BN_num_bits(order); 782 /* 783 * The following parameters mean we precompute (approximately) one point 784 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other 785 * bit lengths, other parameter combinations might provide better 786 * efficiency. 787 */ 788 blocksize = 8; 789 w = 4; 790 if (EC_window_bits_for_scalar_size(bits) > w) { 791 /* let's not make the window too small ... */ 792 w = EC_window_bits_for_scalar_size(bits); 793 } 794 795 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks 796 * to use for wNAF 797 * splitting */ 798 799 pre_points_per_block = 1u << (w - 1); 800 num = pre_points_per_block * numblocks; /* number of points to compute 801 * and store */ 802 803 points = OPENSSL_malloc(sizeof(EC_POINT *) * (num + 1)); 804 if (!points) { 805 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); 806 goto err; 807 } 808 809 var = points; 810 var[num] = NULL; /* pivot */ 811 for (i = 0; i < num; i++) { 812 if ((var[i] = EC_POINT_new(group)) == NULL) { 813 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); 814 goto err; 815 } 816 } 817 818 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) { 819 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); 820 goto err; 821 } 822 823 if (!EC_POINT_copy(base, generator)) 824 goto err; 825 826 /* do the precomputation */ 827 for (i = 0; i < numblocks; i++) { 828 size_t j; 829 830 if (!EC_POINT_dbl(group, tmp_point, base, ctx)) 831 goto err; 832 833 if (!EC_POINT_copy(*var++, base)) 834 goto err; 835 836 for (j = 1; j < pre_points_per_block; j++, var++) { 837 /* 838 * calculate odd multiples of the current base point 839 */ 840 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) 841 goto err; 842 } 843 844 if (i < numblocks - 1) { 845 /* 846 * get the next base (multiply current one by 2^blocksize) 847 */ 848 size_t k; 849 850 if (blocksize <= 2) { 851 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); 852 goto err; 853 } 854 855 if (!EC_POINT_dbl(group, base, tmp_point, ctx)) 856 goto err; 857 for (k = 2; k < blocksize; k++) { 858 if (!EC_POINT_dbl(group, base, base, ctx)) 859 goto err; 860 } 861 } 862 } 863 864 if (!EC_POINTs_make_affine(group, num, points, ctx)) 865 goto err; 866 867 pre_comp->group = group; 868 pre_comp->blocksize = blocksize; 869 pre_comp->numblocks = numblocks; 870 pre_comp->w = w; 871 pre_comp->points = points; 872 points = NULL; 873 pre_comp->num = num; 874 875 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp, 876 ec_pre_comp_dup, ec_pre_comp_free, 877 ec_pre_comp_clear_free)) 878 goto err; 879 pre_comp = NULL; 880 881 ret = 1; 882 err: 883 if (ctx != NULL) 884 BN_CTX_end(ctx); 885 if (new_ctx != NULL) 886 BN_CTX_free(new_ctx); 887 if (pre_comp) 888 ec_pre_comp_free(pre_comp); 889 if (points) { 890 EC_POINT **p; 891 892 for (p = points; *p != NULL; p++) 893 EC_POINT_free(*p); 894 OPENSSL_free(points); 895 } 896 if (tmp_point) 897 EC_POINT_free(tmp_point); 898 if (base) 899 EC_POINT_free(base); 900 return ret; 901} 902 903int ec_wNAF_have_precompute_mult(const EC_GROUP *group) 904{ 905 if (EC_EX_DATA_get_data 906 (group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, 907 ec_pre_comp_clear_free) != NULL) 908 return 1; 909 else 910 return 0; 911} 912