1 /* $OpenBSD: ec_mult.c,v 1.24 2018/07/15 16:27:39 tb Exp $ */ 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 86 * precomputation */ 87 size_t w; /* window size */ 88 EC_POINT **points; /* array with pre-calculated multiples of 89 * generator: 'num' pointers to EC_POINT 90 * objects followed by a NULL */ 91 size_t num; /* numblocks * 2^(w-1) */ 92 int references; 93 } EC_PRE_COMP; 94 95 /* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */ 96 static void *ec_pre_comp_dup(void *); 97 static void ec_pre_comp_free(void *); 98 static void ec_pre_comp_clear_free(void *); 99 100 static EC_PRE_COMP * 101 ec_pre_comp_new(const EC_GROUP * group) 102 { 103 EC_PRE_COMP *ret = NULL; 104 105 if (!group) 106 return NULL; 107 108 ret = malloc(sizeof(EC_PRE_COMP)); 109 if (!ret) { 110 ECerror(ERR_R_MALLOC_FAILURE); 111 return ret; 112 } 113 ret->group = group; 114 ret->blocksize = 8; /* default */ 115 ret->numblocks = 0; 116 ret->w = 4; /* default */ 117 ret->points = NULL; 118 ret->num = 0; 119 ret->references = 1; 120 return ret; 121 } 122 123 static void * 124 ec_pre_comp_dup(void *src_) 125 { 126 EC_PRE_COMP *src = src_; 127 128 /* no need to actually copy, these objects never change! */ 129 130 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); 131 132 return src_; 133 } 134 135 static void 136 ec_pre_comp_free(void *pre_) 137 { 138 int i; 139 EC_PRE_COMP *pre = pre_; 140 141 if (!pre) 142 return; 143 144 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 145 if (i > 0) 146 return; 147 148 if (pre->points) { 149 EC_POINT **p; 150 151 for (p = pre->points; *p != NULL; p++) 152 EC_POINT_free(*p); 153 free(pre->points); 154 } 155 free(pre); 156 } 157 158 static void 159 ec_pre_comp_clear_free(void *pre_) 160 { 161 int i; 162 EC_PRE_COMP *pre = pre_; 163 164 if (!pre) 165 return; 166 167 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); 168 if (i > 0) 169 return; 170 171 if (pre->points) { 172 EC_POINT **p; 173 174 for (p = pre->points; *p != NULL; p++) { 175 EC_POINT_clear_free(*p); 176 explicit_bzero(p, sizeof *p); 177 } 178 free(pre->points); 179 } 180 freezero(pre, sizeof *pre); 181 } 182 183 184 185 186 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'. 187 * This is an array r[] of values that are either zero or odd with an 188 * absolute value less than 2^w satisfying 189 * scalar = \sum_j r[j]*2^j 190 * where at most one of any w+1 consecutive digits is non-zero 191 * with the exception that the most significant digit may be only 192 * w-1 zeros away from that next non-zero digit. 193 */ 194 static signed char * 195 compute_wNAF(const BIGNUM * scalar, int w, size_t * ret_len) 196 { 197 int window_val; 198 int ok = 0; 199 signed char *r = NULL; 200 int sign = 1; 201 int bit, next_bit, mask; 202 size_t len = 0, j; 203 204 if (BN_is_zero(scalar)) { 205 r = malloc(1); 206 if (!r) { 207 ECerror(ERR_R_MALLOC_FAILURE); 208 goto err; 209 } 210 r[0] = 0; 211 *ret_len = 1; 212 return r; 213 } 214 if (w <= 0 || w > 7) { 215 /* 'signed char' can represent integers with 216 * absolute values less than 2^7 */ 217 ECerror(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 sign = -1; 226 } 227 if (scalar->d == NULL || scalar->top == 0) { 228 ECerror(ERR_R_INTERNAL_ERROR); 229 goto err; 230 } 231 len = BN_num_bits(scalar); 232 r = malloc(len + 1); /* modified wNAF may be one digit longer than 233 * binary representation (*ret_len will be 234 * set to the actual length, i.e. at most 235 * BN_num_bits(scalar) + 1) */ 236 if (r == NULL) { 237 ECerror(ERR_R_MALLOC_FAILURE); 238 goto err; 239 } 240 window_val = scalar->d[0] & mask; 241 j = 0; 242 while ((window_val != 0) || (j + w + 1 < len)) { 243 /* if j+w+1 >= len, window_val will not increase */ 244 int digit = 0; 245 246 /* 0 <= window_val <= 2^(w+1) */ 247 if (window_val & 1) { 248 /* 0 < window_val < 2^(w+1) */ 249 if (window_val & bit) { 250 digit = window_val - next_bit; /* -2^w < digit < 0 */ 251 252 #if 1 /* modified wNAF */ 253 if (j + w + 1 >= len) { 254 /* 255 * special case for generating 256 * modified wNAFs: no new bits will 257 * be added into window_val, so using 258 * a positive digit here will 259 * decrease the total length of the 260 * representation 261 */ 262 263 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */ 264 } 265 #endif 266 } else { 267 digit = window_val; /* 0 < digit < 2^w */ 268 } 269 270 if (digit <= -bit || digit >= bit || !(digit & 1)) { 271 ECerror(ERR_R_INTERNAL_ERROR); 272 goto err; 273 } 274 window_val -= digit; 275 276 /* 277 * now window_val is 0 or 2^(w+1) in standard wNAF 278 * generation; for modified window NAFs, it may also 279 * be 2^w 280 */ 281 if (window_val != 0 && window_val != next_bit && window_val != bit) { 282 ECerror(ERR_R_INTERNAL_ERROR); 283 goto err; 284 } 285 } 286 r[j++] = sign * digit; 287 288 window_val >>= 1; 289 window_val += bit * BN_is_bit_set(scalar, j + w); 290 291 if (window_val > next_bit) { 292 ECerror(ERR_R_INTERNAL_ERROR); 293 goto err; 294 } 295 } 296 297 if (j > len + 1) { 298 ECerror(ERR_R_INTERNAL_ERROR); 299 goto err; 300 } 301 len = j; 302 ok = 1; 303 304 err: 305 if (!ok) { 306 free(r); 307 r = NULL; 308 } 309 if (ok) 310 *ret_len = len; 311 return r; 312 } 313 314 315 /* TODO: table should be optimised for the wNAF-based implementation, 316 * sometimes smaller windows will give better performance 317 * (thus the boundaries should be increased) 318 */ 319 #define EC_window_bits_for_scalar_size(b) \ 320 ((size_t) \ 321 ((b) >= 2000 ? 6 : \ 322 (b) >= 800 ? 5 : \ 323 (b) >= 300 ? 4 : \ 324 (b) >= 70 ? 3 : \ 325 (b) >= 20 ? 2 : \ 326 1)) 327 328 /* Compute 329 * \sum scalars[i]*points[i], 330 * also including 331 * scalar*generator 332 * in the addition if scalar != NULL 333 */ 334 int 335 ec_wNAF_mul(const EC_GROUP * group, EC_POINT * r, const BIGNUM * scalar, 336 size_t num, const EC_POINT * points[], const BIGNUM * scalars[], BN_CTX * ctx) 337 { 338 BN_CTX *new_ctx = NULL; 339 const EC_POINT *generator = NULL; 340 EC_POINT *tmp = NULL; 341 size_t totalnum; 342 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ 343 size_t pre_points_per_block = 0; 344 size_t i, j; 345 int k; 346 int r_is_inverted = 0; 347 int r_is_at_infinity = 1; 348 size_t *wsize = NULL; /* individual window sizes */ 349 signed char **wNAF = NULL; /* individual wNAFs */ 350 signed char *tmp_wNAF = NULL; 351 size_t *wNAF_len = NULL; 352 size_t max_len = 0; 353 size_t num_val; 354 EC_POINT **val = NULL; /* precomputation */ 355 EC_POINT **v; 356 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 357 * 'pre_comp->points' */ 358 const EC_PRE_COMP *pre_comp = NULL; 359 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be 360 * treated like other scalars, i.e. 361 * precomputation is not available */ 362 int ret = 0; 363 364 if (group->meth != r->meth) { 365 ECerror(EC_R_INCOMPATIBLE_OBJECTS); 366 return 0; 367 } 368 if ((scalar == NULL) && (num == 0)) { 369 return EC_POINT_set_to_infinity(group, r); 370 } 371 for (i = 0; i < num; i++) { 372 if (group->meth != points[i]->meth) { 373 ECerror(EC_R_INCOMPATIBLE_OBJECTS); 374 return 0; 375 } 376 } 377 378 if (ctx == NULL) { 379 ctx = new_ctx = BN_CTX_new(); 380 if (ctx == NULL) 381 goto err; 382 } 383 if (scalar != NULL) { 384 generator = EC_GROUP_get0_generator(group); 385 if (generator == NULL) { 386 ECerror(EC_R_UNDEFINED_GENERATOR); 387 goto err; 388 } 389 /* look if we can use precomputed multiples of generator */ 390 391 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); 392 393 if (pre_comp && pre_comp->numblocks && 394 (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0)) { 395 blocksize = pre_comp->blocksize; 396 397 /* 398 * determine maximum number of blocks that wNAF 399 * splitting may yield (NB: maximum wNAF length is 400 * bit length plus one) 401 */ 402 numblocks = (BN_num_bits(scalar) / blocksize) + 1; 403 404 /* 405 * we cannot use more blocks than we have 406 * precomputation for 407 */ 408 if (numblocks > pre_comp->numblocks) 409 numblocks = pre_comp->numblocks; 410 411 pre_points_per_block = (size_t) 1 << (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 ECerror(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 423 * element of 'scalars' */ 424 } 425 } 426 totalnum = num + numblocks; 427 428 /* includes space for pivot */ 429 wNAF = reallocarray(NULL, (totalnum + 1), sizeof wNAF[0]); 430 if (wNAF == NULL) { 431 ECerror(ERR_R_MALLOC_FAILURE); 432 goto err; 433 } 434 435 wNAF[0] = NULL; /* preliminary pivot */ 436 437 wsize = reallocarray(NULL, totalnum, sizeof wsize[0]); 438 wNAF_len = reallocarray(NULL, totalnum, sizeof wNAF_len[0]); 439 val_sub = reallocarray(NULL, totalnum, sizeof val_sub[0]); 440 441 if (wsize == NULL || wNAF_len == NULL || val_sub == NULL) { 442 ECerror(ERR_R_MALLOC_FAILURE); 443 goto err; 444 } 445 446 /* num_val will be the total number of temporarily precomputed points */ 447 num_val = 0; 448 449 for (i = 0; i < num + num_scalar; i++) { 450 size_t bits; 451 452 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); 453 wsize[i] = EC_window_bits_for_scalar_size(bits); 454 num_val += (size_t) 1 << (wsize[i] - 1); 455 wNAF[i + 1] = NULL; /* make sure we always have a pivot */ 456 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &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 ECerror(ERR_R_INTERNAL_ERROR); 469 goto err; 470 } 471 /* we have already generated a wNAF for 'scalar' */ 472 } else { 473 size_t tmp_len = 0; 474 475 if (num_scalar != 0) { 476 ECerror(ERR_R_INTERNAL_ERROR); 477 goto err; 478 } 479 /* 480 * use the window size for which we have 481 * precomputation 482 */ 483 wsize[num] = pre_comp->w; 484 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len); 485 if (tmp_wNAF == NULL) 486 goto err; 487 488 if (tmp_len <= max_len) { 489 /* 490 * One of the other wNAFs is at least as long 491 * as the wNAF belonging to the generator, so 492 * wNAF splitting will not buy us anything. 493 */ 494 495 numblocks = 1; 496 totalnum = num + 1; /* don't use wNAF 497 * splitting */ 498 wNAF[num] = tmp_wNAF; 499 tmp_wNAF = NULL; 500 wNAF[num + 1] = NULL; 501 wNAF_len[num] = tmp_len; 502 if (tmp_len > max_len) 503 max_len = tmp_len; 504 /* 505 * pre_comp->points starts with the points 506 * that we need here: 507 */ 508 val_sub[num] = pre_comp->points; 509 } else { 510 /* 511 * don't include tmp_wNAF directly into wNAF 512 * array - use wNAF splitting and include the 513 * blocks 514 */ 515 516 signed char *pp; 517 EC_POINT **tmp_points; 518 519 if (tmp_len < numblocks * blocksize) { 520 /* 521 * possibly we can do with fewer 522 * blocks than estimated 523 */ 524 numblocks = (tmp_len + blocksize - 1) / blocksize; 525 if (numblocks > pre_comp->numblocks) { 526 ECerror(ERR_R_INTERNAL_ERROR); 527 goto err; 528 } 529 totalnum = num + numblocks; 530 } 531 /* split wNAF in 'numblocks' parts */ 532 pp = tmp_wNAF; 533 tmp_points = pre_comp->points; 534 535 for (i = num; i < totalnum; i++) { 536 if (i < totalnum - 1) { 537 wNAF_len[i] = blocksize; 538 if (tmp_len < blocksize) { 539 ECerror(ERR_R_INTERNAL_ERROR); 540 goto err; 541 } 542 tmp_len -= blocksize; 543 } else 544 /* 545 * last block gets whatever 546 * is left (this could be 547 * more or less than 548 * 'blocksize'!) 549 */ 550 wNAF_len[i] = tmp_len; 551 552 wNAF[i + 1] = NULL; 553 wNAF[i] = malloc(wNAF_len[i]); 554 if (wNAF[i] == NULL) { 555 ECerror(ERR_R_MALLOC_FAILURE); 556 goto err; 557 } 558 memcpy(wNAF[i], pp, wNAF_len[i]); 559 if (wNAF_len[i] > max_len) 560 max_len = wNAF_len[i]; 561 562 if (*tmp_points == NULL) { 563 ECerror(ERR_R_INTERNAL_ERROR); 564 goto err; 565 } 566 val_sub[i] = tmp_points; 567 tmp_points += pre_points_per_block; 568 pp += blocksize; 569 } 570 } 571 } 572 } 573 /* 574 * All points we precompute now go into a single array 'val'. 575 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or 576 * to a subarray of 'pre_comp->points' if we already have 577 * precomputation. 578 */ 579 val = reallocarray(NULL, (num_val + 1), sizeof val[0]); 580 if (val == NULL) { 581 ECerror(ERR_R_MALLOC_FAILURE); 582 goto err; 583 } 584 val[num_val] = NULL; /* pivot element */ 585 586 /* allocate points for precomputation */ 587 v = val; 588 for (i = 0; i < num + num_scalar; i++) { 589 val_sub[i] = v; 590 for (j = 0; j < ((size_t) 1 << (wsize[i] - 1)); j++) { 591 *v = EC_POINT_new(group); 592 if (*v == NULL) 593 goto err; 594 v++; 595 } 596 } 597 if (!(v == val + num_val)) { 598 ECerror(ERR_R_INTERNAL_ERROR); 599 goto err; 600 } 601 if (!(tmp = EC_POINT_new(group))) 602 goto err; 603 604 /* 605 * prepare precomputed values: val_sub[i][0] := points[i] 606 * val_sub[i][1] := 3 * points[i] val_sub[i][2] := 5 * points[i] ... 607 */ 608 for (i = 0; i < num + num_scalar; i++) { 609 if (i < num) { 610 if (!EC_POINT_copy(val_sub[i][0], points[i])) 611 goto err; 612 } else { 613 if (!EC_POINT_copy(val_sub[i][0], generator)) 614 goto err; 615 } 616 617 if (wsize[i] > 1) { 618 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) 619 goto err; 620 for (j = 1; j < ((size_t) 1 << (wsize[i] - 1)); j++) { 621 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) 622 goto err; 623 } 624 } 625 } 626 627 if (!EC_POINTs_make_affine(group, num_val, val, ctx)) 628 goto err; 629 630 r_is_at_infinity = 1; 631 632 for (k = max_len - 1; k >= 0; k--) { 633 if (!r_is_at_infinity) { 634 if (!EC_POINT_dbl(group, r, r, ctx)) 635 goto err; 636 } 637 for (i = 0; i < totalnum; i++) { 638 if (wNAF_len[i] > (size_t) k) { 639 int digit = wNAF[i][k]; 640 int is_neg; 641 642 if (digit) { 643 is_neg = digit < 0; 644 645 if (is_neg) 646 digit = -digit; 647 648 if (is_neg != r_is_inverted) { 649 if (!r_is_at_infinity) { 650 if (!EC_POINT_invert(group, r, ctx)) 651 goto err; 652 } 653 r_is_inverted = !r_is_inverted; 654 } 655 /* digit > 0 */ 656 657 if (r_is_at_infinity) { 658 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) 659 goto err; 660 r_is_at_infinity = 0; 661 } else { 662 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) 663 goto err; 664 } 665 } 666 } 667 } 668 } 669 670 if (r_is_at_infinity) { 671 if (!EC_POINT_set_to_infinity(group, r)) 672 goto err; 673 } else { 674 if (r_is_inverted) 675 if (!EC_POINT_invert(group, r, ctx)) 676 goto err; 677 } 678 679 ret = 1; 680 681 err: 682 BN_CTX_free(new_ctx); 683 EC_POINT_free(tmp); 684 free(wsize); 685 free(wNAF_len); 686 free(tmp_wNAF); 687 if (wNAF != NULL) { 688 signed char **w; 689 690 for (w = wNAF; *w != NULL; w++) 691 free(*w); 692 693 free(wNAF); 694 } 695 if (val != NULL) { 696 for (v = val; *v != NULL; v++) 697 EC_POINT_clear_free(*v); 698 free(val); 699 } 700 free(val_sub); 701 return ret; 702 } 703 704 705 /* ec_wNAF_precompute_mult() 706 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator 707 * for use with wNAF splitting as implemented in ec_wNAF_mul(). 708 * 709 * 'pre_comp->points' is an array of multiples of the generator 710 * of the following form: 711 * points[0] = generator; 712 * points[1] = 3 * generator; 713 * ... 714 * points[2^(w-1)-1] = (2^(w-1)-1) * generator; 715 * points[2^(w-1)] = 2^blocksize * generator; 716 * points[2^(w-1)+1] = 3 * 2^blocksize * generator; 717 * ... 718 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator 719 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator 720 * ... 721 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator 722 * points[2^(w-1)*numblocks] = NULL 723 */ 724 int 725 ec_wNAF_precompute_mult(EC_GROUP * group, BN_CTX * ctx) 726 { 727 const EC_POINT *generator; 728 EC_POINT *tmp_point = NULL, *base = NULL, **var; 729 BN_CTX *new_ctx = NULL; 730 BIGNUM *order; 731 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, 732 num; 733 EC_POINT **points = NULL; 734 EC_PRE_COMP *pre_comp; 735 int ret = 0; 736 737 /* if there is an old EC_PRE_COMP object, throw it away */ 738 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free); 739 740 if ((pre_comp = ec_pre_comp_new(group)) == NULL) 741 return 0; 742 743 generator = EC_GROUP_get0_generator(group); 744 if (generator == NULL) { 745 ECerror(EC_R_UNDEFINED_GENERATOR); 746 goto err; 747 } 748 if (ctx == NULL) { 749 ctx = new_ctx = BN_CTX_new(); 750 if (ctx == NULL) 751 goto err; 752 } 753 BN_CTX_start(ctx); 754 if ((order = BN_CTX_get(ctx)) == NULL) 755 goto err; 756 757 if (!EC_GROUP_get_order(group, order, ctx)) 758 goto err; 759 if (BN_is_zero(order)) { 760 ECerror(EC_R_UNKNOWN_ORDER); 761 goto err; 762 } 763 bits = BN_num_bits(order); 764 /* 765 * The following parameters mean we precompute (approximately) one 766 * point per bit. 767 * 768 * TBD: The combination 8, 4 is perfect for 160 bits; for other bit 769 * lengths, other parameter combinations might provide better 770 * efficiency. 771 */ 772 blocksize = 8; 773 w = 4; 774 if (EC_window_bits_for_scalar_size(bits) > w) { 775 /* let's not make the window too small ... */ 776 w = EC_window_bits_for_scalar_size(bits); 777 } 778 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks 779 * to use for wNAF 780 * splitting */ 781 782 pre_points_per_block = (size_t) 1 << (w - 1); 783 num = pre_points_per_block * numblocks; /* number of points to 784 * compute and store */ 785 786 points = reallocarray(NULL, (num + 1), sizeof(EC_POINT *)); 787 if (!points) { 788 ECerror(ERR_R_MALLOC_FAILURE); 789 goto err; 790 } 791 var = points; 792 var[num] = NULL; /* pivot */ 793 for (i = 0; i < num; i++) { 794 if ((var[i] = EC_POINT_new(group)) == NULL) { 795 ECerror(ERR_R_MALLOC_FAILURE); 796 goto err; 797 } 798 } 799 800 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group))) { 801 ECerror(ERR_R_MALLOC_FAILURE); 802 goto err; 803 } 804 if (!EC_POINT_copy(base, generator)) 805 goto err; 806 807 /* do the precomputation */ 808 for (i = 0; i < numblocks; i++) { 809 size_t j; 810 811 if (!EC_POINT_dbl(group, tmp_point, base, ctx)) 812 goto err; 813 814 if (!EC_POINT_copy(*var++, base)) 815 goto err; 816 817 for (j = 1; j < pre_points_per_block; j++, var++) { 818 /* calculate odd multiples of the current base point */ 819 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) 820 goto err; 821 } 822 823 if (i < numblocks - 1) { 824 /* 825 * get the next base (multiply current one by 826 * 2^blocksize) 827 */ 828 size_t k; 829 830 if (blocksize <= 2) { 831 ECerror(ERR_R_INTERNAL_ERROR); 832 goto err; 833 } 834 if (!EC_POINT_dbl(group, base, tmp_point, ctx)) 835 goto err; 836 for (k = 2; k < blocksize; k++) { 837 if (!EC_POINT_dbl(group, base, base, ctx)) 838 goto err; 839 } 840 } 841 } 842 843 if (!EC_POINTs_make_affine(group, num, points, ctx)) 844 goto err; 845 846 pre_comp->group = group; 847 pre_comp->blocksize = blocksize; 848 pre_comp->numblocks = numblocks; 849 pre_comp->w = w; 850 pre_comp->points = points; 851 points = NULL; 852 pre_comp->num = num; 853 854 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp, 855 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free)) 856 goto err; 857 pre_comp = NULL; 858 859 ret = 1; 860 err: 861 if (ctx != NULL) 862 BN_CTX_end(ctx); 863 BN_CTX_free(new_ctx); 864 ec_pre_comp_free(pre_comp); 865 if (points) { 866 EC_POINT **p; 867 868 for (p = points; *p != NULL; p++) 869 EC_POINT_free(*p); 870 free(points); 871 } 872 EC_POINT_free(tmp_point); 873 EC_POINT_free(base); 874 return ret; 875 } 876 877 878 int 879 ec_wNAF_have_precompute_mult(const EC_GROUP * group) 880 { 881 if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL) 882 return 1; 883 else 884 return 0; 885 } 886