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 *
ec_pre_comp_new(const EC_GROUP * group)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 *
ec_pre_comp_dup(void * src_)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
ec_pre_comp_free(void * pre_)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
ec_pre_comp_clear_free(void * pre_)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 *
compute_wNAF(const BIGNUM * scalar,int w,size_t * ret_len)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
ec_wNAF_mul(const EC_GROUP * group,EC_POINT * r,const BIGNUM * scalar,size_t num,const EC_POINT * points[],const BIGNUM * scalars[],BN_CTX * ctx)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
ec_wNAF_precompute_mult(EC_GROUP * group,BN_CTX * ctx)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
ec_wNAF_have_precompute_mult(const EC_GROUP * group)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