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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 */
82typedef 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 */
94static void *ec_pre_comp_dup(void *);
95static void ec_pre_comp_free(void *);
96static void ec_pre_comp_clear_free(void *);
97
98static 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
121static 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
132static 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
155static 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 EC_POINT_clear_free(*p);
173 OPENSSL_cleanse(pre->points, sizeof pre->points);
174 OPENSSL_free(pre->points);
175 }
176 OPENSSL_cleanse(pre, sizeof pre);
177 OPENSSL_free(pre);
178 }
179
180
181
182
183/* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
184 * This is an array r[] of values that are either zero or odd with an
185 * absolute value less than 2^w satisfying
186 * scalar = \sum_j r[j]*2^j
187 * where at most one of any w+1 consecutive digits is non-zero
188 * with the exception that the most significant digit may be only
189 * w-1 zeros away from that next non-zero digit.
190 */
191static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
192 {
193 int window_val;
194 int ok = 0;
195 signed char *r = NULL;
196 int sign = 1;
197 int bit, next_bit, mask;
198 size_t len = 0, j;
199
200 if (BN_is_zero(scalar))
201 {
202 r = OPENSSL_malloc(1);
203 if (!r)
204 {
205 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
206 goto err;
207 }
208 r[0] = 0;
209 *ret_len = 1;
210 return r;
211 }
212
213 if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
214 {
215 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
216 goto err;
217 }
218 bit = 1 << w; /* at most 128 */
219 next_bit = bit << 1; /* at most 256 */
220 mask = next_bit - 1; /* at most 255 */
221
222 if (BN_is_negative(scalar))
223 {
224 sign = -1;
225 }
226
227 len = BN_num_bits(scalar);
228 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
229 * (*ret_len will be set to the actual length, i.e. at most
230 * BN_num_bits(scalar) + 1) */
231 if (r == NULL)
232 {
233 ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
234 goto err;
235 }
236
237 if (scalar->d == NULL || scalar->top == 0)
238 {
239 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
240 goto err;
241 }
242 window_val = scalar->d[0] & mask;
243 j = 0;
244 while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
245 {
246 int digit = 0;
247
248 /* 0 <= window_val <= 2^(w+1) */
249
250 if (window_val & 1)
251 {
252 /* 0 < window_val < 2^(w+1) */
253
254 if (window_val & bit)
255 {
256 digit = window_val - next_bit; /* -2^w < digit < 0 */
257
258#if 1 /* modified wNAF */
259 if (j + w + 1 >= len)
260 {
261 /* special case for generating modified wNAFs:
262 * no new bits will be added into window_val,
263 * so using a positive digit here will decrease
264 * the total length of the representation */
265
266 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
267 }
268#endif
269 }
270 else
271 {
272 digit = window_val; /* 0 < digit < 2^w */
273 }
274
275 if (digit <= -bit || digit >= bit || !(digit & 1))
276 {
277 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
278 goto err;
279 }
280
281 window_val -= digit;
282
283 /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
284 * for modified window NAFs, it may also be 2^w
285 */
286 if (window_val != 0 && window_val != next_bit && window_val != bit)
287 {
288 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
289 goto err;
290 }
291 }
292
293 r[j++] = sign * digit;
294
295 window_val >>= 1;
296 window_val += bit * BN_is_bit_set(scalar, j + w);
297
298 if (window_val > next_bit)
299 {
300 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
301 goto err;
302 }
303 }
304
305 if (j > len + 1)
306 {
307 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
308 goto err;
309 }
310 len = j;
311 ok = 1;
312
313 err:
314 if (!ok)
315 {
316 OPENSSL_free(r);
317 r = NULL;
318 }
319 if (ok)
320 *ret_len = len;
321 return r;
322 }
323
324
325/* TODO: table should be optimised for the wNAF-based implementation,
326 * sometimes smaller windows will give better performance
327 * (thus the boundaries should be increased)
328 */
329#define EC_window_bits_for_scalar_size(b) \
330 ((size_t) \
331 ((b) >= 2000 ? 6 : \
332 (b) >= 800 ? 5 : \
333 (b) >= 300 ? 4 : \
334 (b) >= 70 ? 3 : \
335 (b) >= 20 ? 2 : \
336 1))
337
338/* Compute
339 * \sum scalars[i]*points[i],
340 * also including
341 * scalar*generator
342 * in the addition if scalar != NULL
343 */
344int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
345 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
346 {
347 BN_CTX *new_ctx = NULL;
348 const EC_POINT *generator = NULL;
349 EC_POINT *tmp = NULL;
350 size_t totalnum;
351 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
352 size_t pre_points_per_block = 0;
353 size_t i, j;
354 int k;
355 int r_is_inverted = 0;
356 int r_is_at_infinity = 1;
357 size_t *wsize = NULL; /* individual window sizes */
358 signed char **wNAF = NULL; /* individual wNAFs */
359 size_t *wNAF_len = NULL;
360 size_t max_len = 0;
361 size_t num_val;
362 EC_POINT **val = NULL; /* precomputation */
363 EC_POINT **v;
364 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
365 const EC_PRE_COMP *pre_comp = NULL;
366 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
367 * i.e. precomputation is not available */
368 int ret = 0;
369
370 if (group->meth != r->meth)
371 {
372 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
373 return 0;
374 }
375
376 if ((scalar == NULL) && (num == 0))
377 {
378 return EC_POINT_set_to_infinity(group, r);
379 }
380
381 for (i = 0; i < num; i++)
382 {
383 if (group->meth != points[i]->meth)
384 {
385 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
386 return 0;
387 }
388 }
389
390 if (ctx == NULL)
391 {
392 ctx = new_ctx = BN_CTX_new();
393 if (ctx == NULL)
394 goto err;
395 }
396
397 if (scalar != NULL)
398 {
399 generator = EC_GROUP_get0_generator(group);
400 if (generator == NULL)
401 {
402 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
403 goto err;
404 }
405
406 /* look if we can use precomputed multiples of generator */
407
408 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
409
410 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
411 {
412 blocksize = pre_comp->blocksize;
413
414 /* determine maximum number of blocks that wNAF splitting may yield
415 * (NB: maximum wNAF length is bit length plus one) */
416 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
417
418 /* we cannot use more blocks than we have precomputation for */
419 if (numblocks > pre_comp->numblocks)
420 numblocks = pre_comp->numblocks;
421
422 pre_points_per_block = 1u << (pre_comp->w - 1);
423
424 /* check that pre_comp looks sane */
425 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
426 {
427 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
428 goto err;
429 }
430 }
431 else
432 {
433 /* can't use precomputation */
434 pre_comp = NULL;
435 numblocks = 1;
436 num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
437 }
438 }
439
440 totalnum = num + numblocks;
441
442 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
443 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
444 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
445 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
446
447 if (!wsize || !wNAF_len || !wNAF || !val_sub)
448 {
449 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
450 goto err;
451 }
452
453 wNAF[0] = NULL; /* preliminary pivot */
454
455 /* num_val will be the total number of temporarily precomputed points */
456 num_val = 0;
457
458 for (i = 0; i < num + num_scalar; i++)
459 {
460 size_t bits;
461
462 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
463 wsize[i] = EC_window_bits_for_scalar_size(bits);
464 num_val += 1u << (wsize[i] - 1);
465 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
466 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
467 if (wNAF[i] == NULL)
468 goto err;
469 if (wNAF_len[i] > max_len)
470 max_len = wNAF_len[i];
471 }
472
473 if (numblocks)
474 {
475 /* we go here iff scalar != NULL */
476
477 if (pre_comp == NULL)
478 {
479 if (num_scalar != 1)
480 {
481 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
482 goto err;
483 }
484 /* we have already generated a wNAF for 'scalar' */
485 }
486 else
487 {
488 signed char *tmp_wNAF = NULL;
489 size_t tmp_len = 0;
490
491 if (num_scalar != 0)
492 {
493 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
494 goto err;
495 }
496
497 /* use the window size for which we have precomputation */
498 wsize[num] = pre_comp->w;
499 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
500 if (!tmp_wNAF)
501 goto err;
502
503 if (tmp_len <= max_len)
504 {
505 /* One of the other wNAFs is at least as long
506 * as the wNAF belonging to the generator,
507 * so wNAF splitting will not buy us anything. */
508
509 numblocks = 1;
510 totalnum = num + 1; /* don't use wNAF splitting */
511 wNAF[num] = tmp_wNAF;
512 wNAF[num + 1] = NULL;
513 wNAF_len[num] = tmp_len;
514 if (tmp_len > max_len)
515 max_len = tmp_len;
516 /* pre_comp->points starts with the points that we need here: */
517 val_sub[num] = pre_comp->points;
518 }
519 else
520 {
521 /* don't include tmp_wNAF directly into wNAF array
522 * - use wNAF splitting and include the blocks */
523
524 signed char *pp;
525 EC_POINT **tmp_points;
526
527 if (tmp_len < numblocks * blocksize)
528 {
529 /* possibly we can do with fewer blocks than estimated */
530 numblocks = (tmp_len + blocksize - 1) / blocksize;
531 if (numblocks > pre_comp->numblocks)
532 {
533 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
534 goto err;
535 }
536 totalnum = num + numblocks;
537 }
538
539 /* split wNAF in 'numblocks' parts */
540 pp = tmp_wNAF;
541 tmp_points = pre_comp->points;
542
543 for (i = num; i < totalnum; i++)
544 {
545 if (i < totalnum - 1)
546 {
547 wNAF_len[i] = blocksize;
548 if (tmp_len < blocksize)
549 {
550 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
551 goto err;
552 }
553 tmp_len -= blocksize;
554 }
555 else
556 /* last block gets whatever is left
557 * (this could be more or less than 'blocksize'!) */
558 wNAF_len[i] = tmp_len;
559
560 wNAF[i + 1] = NULL;
561 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
562 if (wNAF[i] == NULL)
563 {
564 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
565 OPENSSL_free(tmp_wNAF);
566 goto err;
567 }
568 memcpy(wNAF[i], pp, wNAF_len[i]);
569 if (wNAF_len[i] > max_len)
570 max_len = wNAF_len[i];
571
572 if (*tmp_points == NULL)
573 {
574 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
575 OPENSSL_free(tmp_wNAF);
576 goto err;
577 }
578 val_sub[i] = tmp_points;
579 tmp_points += pre_points_per_block;
580 pp += blocksize;
581 }
582 OPENSSL_free(tmp_wNAF);
583 }
584 }
585 }
586
587 /* All points we precompute now go into a single array 'val'.
588 * 'val_sub[i]' is a pointer to the subarray for the i-th point,
589 * or to a subarray of 'pre_comp->points' if we already have precomputation. */
590 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
591 if (val == NULL)
592 {
593 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
594 goto err;
595 }
596 val[num_val] = NULL; /* pivot element */
597
598 /* allocate points for precomputation */
599 v = val;
600 for (i = 0; i < num + num_scalar; i++)
601 {
602 val_sub[i] = v;
603 for (j = 0; j < (1u << (wsize[i] - 1)); j++)
604 {
605 *v = EC_POINT_new(group);
606 if (*v == NULL) goto err;
607 v++;
608 }
609 }
610 if (!(v == val + num_val))
611 {
612 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
613 goto err;
614 }
615
616 if (!(tmp = EC_POINT_new(group)))
617 goto err;
618
619 /* prepare precomputed values:
620 * val_sub[i][0] := points[i]
621 * val_sub[i][1] := 3 * points[i]
622 * val_sub[i][2] := 5 * points[i]
623 * ...
624 */
625 for (i = 0; i < num + num_scalar; i++)
626 {
627 if (i < num)
628 {
629 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
630 }
631 else
632 {
633 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
634 }
635
636 if (wsize[i] > 1)
637 {
638 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
639 for (j = 1; j < (1u << (wsize[i] - 1)); j++)
640 {
641 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
642 }
643 }
644 }
645
646#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
647 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
648 goto err;
649#endif
650
651 r_is_at_infinity = 1;
652
653 for (k = max_len - 1; k >= 0; k--)
654 {
655 if (!r_is_at_infinity)
656 {
657 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
658 }
659
660 for (i = 0; i < totalnum; i++)
661 {
662 if (wNAF_len[i] > (size_t)k)
663 {
664 int digit = wNAF[i][k];
665 int is_neg;
666
667 if (digit)
668 {
669 is_neg = digit < 0;
670
671 if (is_neg)
672 digit = -digit;
673
674 if (is_neg != r_is_inverted)
675 {
676 if (!r_is_at_infinity)
677 {
678 if (!EC_POINT_invert(group, r, ctx)) goto err;
679 }
680 r_is_inverted = !r_is_inverted;
681 }
682
683 /* digit > 0 */
684
685 if (r_is_at_infinity)
686 {
687 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
688 r_is_at_infinity = 0;
689 }
690 else
691 {
692 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
693 }
694 }
695 }
696 }
697 }
698
699 if (r_is_at_infinity)
700 {
701 if (!EC_POINT_set_to_infinity(group, r)) goto err;
702 }
703 else
704 {
705 if (r_is_inverted)
706 if (!EC_POINT_invert(group, r, ctx)) goto err;
707 }
708
709 ret = 1;
710
711 err:
712 if (new_ctx != NULL)
713 BN_CTX_free(new_ctx);
714 if (tmp != NULL)
715 EC_POINT_free(tmp);
716 if (wsize != NULL)
717 OPENSSL_free(wsize);
718 if (wNAF_len != NULL)
719 OPENSSL_free(wNAF_len);
720 if (wNAF != NULL)
721 {
722 signed char **w;
723
724 for (w = wNAF; *w != NULL; w++)
725 OPENSSL_free(*w);
726
727 OPENSSL_free(wNAF);
728 }
729 if (val != NULL)
730 {
731 for (v = val; *v != NULL; v++)
732 EC_POINT_clear_free(*v);
733
734 OPENSSL_free(val);
735 }
736 if (val_sub != NULL)
737 {
738 OPENSSL_free(val_sub);
739 }
740 return ret;
741 }
742
743
744/* ec_wNAF_precompute_mult()
745 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
746 * for use with wNAF splitting as implemented in ec_wNAF_mul().
747 *
748 * 'pre_comp->points' is an array of multiples of the generator
749 * of the following form:
750 * points[0] = generator;
751 * points[1] = 3 * generator;
752 * ...
753 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
754 * points[2^(w-1)] = 2^blocksize * generator;
755 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
756 * ...
757 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
758 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
759 * ...
760 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
761 * points[2^(w-1)*numblocks] = NULL
762 */
763int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
764 {
765 const EC_POINT *generator;
766 EC_POINT *tmp_point = NULL, *base = NULL, **var;
767 BN_CTX *new_ctx = NULL;
768 BIGNUM *order;
769 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
770 EC_POINT **points = NULL;
771 EC_PRE_COMP *pre_comp;
772 int ret = 0;
773
774 /* if there is an old EC_PRE_COMP object, throw it away */
775 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
776
777 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
778 return 0;
779
780 generator = EC_GROUP_get0_generator(group);
781 if (generator == NULL)
782 {
783 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
784 goto err;
785 }
786
787 if (ctx == NULL)
788 {
789 ctx = new_ctx = BN_CTX_new();
790 if (ctx == NULL)
791 goto err;
792 }
793
794 BN_CTX_start(ctx);
795 order = BN_CTX_get(ctx);
796 if (order == NULL) goto err;
797
798 if (!EC_GROUP_get_order(group, order, ctx)) goto err;
799 if (BN_is_zero(order))
800 {
801 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
802 goto err;
803 }
804
805 bits = BN_num_bits(order);
806 /* The following parameters mean we precompute (approximately)
807 * one point per bit.
808 *
809 * TBD: The combination 8, 4 is perfect for 160 bits; for other
810 * bit lengths, other parameter combinations might provide better
811 * efficiency.
812 */
813 blocksize = 8;
814 w = 4;
815 if (EC_window_bits_for_scalar_size(bits) > w)
816 {
817 /* let's not make the window too small ... */
818 w = EC_window_bits_for_scalar_size(bits);
819 }
820
821 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
822
823 pre_points_per_block = 1u << (w - 1);
824 num = pre_points_per_block * numblocks; /* number of points to compute and store */
825
826 points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
827 if (!points)
828 {
829 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
830 goto err;
831 }
832
833 var = points;
834 var[num] = NULL; /* pivot */
835 for (i = 0; i < num; i++)
836 {
837 if ((var[i] = EC_POINT_new(group)) == NULL)
838 {
839 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
840 goto err;
841 }
842 }
843
844 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
845 {
846 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
847 goto err;
848 }
849
850 if (!EC_POINT_copy(base, generator))
851 goto err;
852
853 /* do the precomputation */
854 for (i = 0; i < numblocks; i++)
855 {
856 size_t j;
857
858 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
859 goto err;
860
861 if (!EC_POINT_copy(*var++, base))
862 goto err;
863
864 for (j = 1; j < pre_points_per_block; j++, var++)
865 {
866 /* calculate odd multiples of the current base point */
867 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
868 goto err;
869 }
870
871 if (i < numblocks - 1)
872 {
873 /* get the next base (multiply current one by 2^blocksize) */
874 size_t k;
875
876 if (blocksize <= 2)
877 {
878 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
879 goto err;
880 }
881
882 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
883 goto err;
884 for (k = 2; k < blocksize; k++)
885 {
886 if (!EC_POINT_dbl(group,base,base,ctx))
887 goto err;
888 }
889 }
890 }
891
892 if (!EC_POINTs_make_affine(group, num, points, ctx))
893 goto err;
894
895 pre_comp->group = group;
896 pre_comp->blocksize = blocksize;
897 pre_comp->numblocks = numblocks;
898 pre_comp->w = w;
899 pre_comp->points = points;
900 points = NULL;
901 pre_comp->num = num;
902
903 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
904 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
905 goto err;
906 pre_comp = NULL;
907
908 ret = 1;
909 err:
910 if (ctx != NULL)
911 BN_CTX_end(ctx);
912 if (new_ctx != NULL)
913 BN_CTX_free(new_ctx);
914 if (pre_comp)
915 ec_pre_comp_free(pre_comp);
916 if (points)
917 {
918 EC_POINT **p;
919
920 for (p = points; *p != NULL; p++)
921 EC_POINT_free(*p);
922 OPENSSL_free(points);
923 }
924 if (tmp_point)
925 EC_POINT_free(tmp_point);
926 if (base)
927 EC_POINT_free(base);
928 return ret;
929 }
930
931
932int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
933 {
934 if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
935 return 1;
936 else
937 return 0;
938 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-10-25 19:15:19 +0000