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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 {
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 */
193static 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 */
346int 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 */
765int 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
934int 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 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-03-21 07:41:19 +0000