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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 */
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 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 */
94 static void *ec_pre_comp_dup(void *);
95 static void ec_pre_comp_free(void *);
96 static void ec_pre_comp_clear_free(void *);
97
98 static 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
121 static 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
132 static 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
155 static 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 */
193 static 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 */
346 int 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 /* Ensure wNAF is initialised in case we end up going to err */
450 if (wNAF) wNAF[0] = NULL; /* preliminary pivot */
451
452 if (!wsize || !wNAF_len || !wNAF || !val_sub)
453 {
454 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
455 goto err;
456 }
457
458 /* num_val will be the total number of temporarily precomputed points */
459 num_val = 0;
460
461 for (i = 0; i < num + num_scalar; i++)
462 {
463 size_t bits;
464
465 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
466 wsize[i] = EC_window_bits_for_scalar_size(bits);
467 num_val += (size_t)1 << (wsize[i] - 1);
468 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
469 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
470 if (wNAF[i] == NULL)
471 goto err;
472 if (wNAF_len[i] > max_len)
473 max_len = wNAF_len[i];
474 }
475
476 if (numblocks)
477 {
478 /* we go here iff scalar != NULL */
479
480 if (pre_comp == NULL)
481 {
482 if (num_scalar != 1)
483 {
484 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
485 goto err;
486 }
487 /* we have already generated a wNAF for 'scalar' */
488 }
489 else
490 {
491 signed char *tmp_wNAF = NULL;
492 size_t tmp_len = 0;
493
494 if (num_scalar != 0)
495 {
496 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
497 goto err;
498 }
499
500 /* use the window size for which we have precomputation */
501 wsize[num] = pre_comp->w;
502 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
503 if (!tmp_wNAF)
504 goto err;
505
506 if (tmp_len <= max_len)
507 {
508 /* One of the other wNAFs is at least as long
509 * as the wNAF belonging to the generator,
510 * so wNAF splitting will not buy us anything. */
511
512 numblocks = 1;
513 totalnum = num + 1; /* don't use wNAF splitting */
514 wNAF[num] = tmp_wNAF;
515 wNAF[num + 1] = NULL;
516 wNAF_len[num] = tmp_len;
517 if (tmp_len > max_len)
518 max_len = tmp_len;
519 /* pre_comp->points starts with the points that we need here: */
520 val_sub[num] = pre_comp->points;
521 }
522 else
523 {
524 /* don't include tmp_wNAF directly into wNAF array
525 * - use wNAF splitting and include the blocks */
526
527 signed char *pp;
528 EC_POINT **tmp_points;
529
530 if (tmp_len < numblocks * blocksize)
531 {
532 /* possibly we can do with fewer blocks than estimated */
533 numblocks = (tmp_len + blocksize - 1) / blocksize;
534 if (numblocks > pre_comp->numblocks)
535 {
536 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
537 goto err;
538 }
539 totalnum = num + numblocks;
540 }
541
542 /* split wNAF in 'numblocks' parts */
543 pp = tmp_wNAF;
544 tmp_points = pre_comp->points;
545
546 for (i = num; i < totalnum; i++)
547 {
548 if (i < totalnum - 1)
549 {
550 wNAF_len[i] = blocksize;
551 if (tmp_len < blocksize)
552 {
553 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
554 goto err;
555 }
556 tmp_len -= blocksize;
557 }
558 else
559 /* last block gets whatever is left
560 * (this could be more or less than 'blocksize'!) */
561 wNAF_len[i] = tmp_len;
562
563 wNAF[i + 1] = NULL;
564 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
565 if (wNAF[i] == NULL)
566 {
567 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
568 OPENSSL_free(tmp_wNAF);
569 goto err;
570 }
571 memcpy(wNAF[i], pp, wNAF_len[i]);
572 if (wNAF_len[i] > max_len)
573 max_len = wNAF_len[i];
574
575 if (*tmp_points == NULL)
576 {
577 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
578 OPENSSL_free(tmp_wNAF);
579 goto err;
580 }
581 val_sub[i] = tmp_points;
582 tmp_points += pre_points_per_block;
583 pp += blocksize;
584 }
585 OPENSSL_free(tmp_wNAF);
586 }
587 }
588 }
589
590 /* All points we precompute now go into a single array 'val'.
591 * 'val_sub[i]' is a pointer to the subarray for the i-th point,
592 * or to a subarray of 'pre_comp->points' if we already have precomputation. */
593 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
594 if (val == NULL)
595 {
596 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
597 goto err;
598 }
599 val[num_val] = NULL; /* pivot element */
600
601 /* allocate points for precomputation */
602 v = val;
603 for (i = 0; i < num + num_scalar; i++)
604 {
605 val_sub[i] = v;
606 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++)
607 {
608 *v = EC_POINT_new(group);
609 if (*v == NULL) goto err;
610 v++;
611 }
612 }
613 if (!(v == val + num_val))
614 {
615 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
616 goto err;
617 }
618
619 if (!(tmp = EC_POINT_new(group)))
620 goto err;
621
622 /* prepare precomputed values:
623 * val_sub[i][0] := points[i]
624 * val_sub[i][1] := 3 * points[i]
625 * val_sub[i][2] := 5 * points[i]
626 * ...
627 */
628 for (i = 0; i < num + num_scalar; i++)
629 {
630 if (i < num)
631 {
632 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
633 }
634 else
635 {
636 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
637 }
638
639 if (wsize[i] > 1)
640 {
641 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
642 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++)
643 {
644 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
645 }
646 }
647 }
648
649 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
650 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
651 goto err;
652 #endif
653
654 r_is_at_infinity = 1;
655
656 for (k = max_len - 1; k >= 0; k--)
657 {
658 if (!r_is_at_infinity)
659 {
660 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
661 }
662
663 for (i = 0; i < totalnum; i++)
664 {
665 if (wNAF_len[i] > (size_t)k)
666 {
667 int digit = wNAF[i][k];
668 int is_neg;
669
670 if (digit)
671 {
672 is_neg = digit < 0;
673
674 if (is_neg)
675 digit = -digit;
676
677 if (is_neg != r_is_inverted)
678 {
679 if (!r_is_at_infinity)
680 {
681 if (!EC_POINT_invert(group, r, ctx)) goto err;
682 }
683 r_is_inverted = !r_is_inverted;
684 }
685
686 /* digit > 0 */
687
688 if (r_is_at_infinity)
689 {
690 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
691 r_is_at_infinity = 0;
692 }
693 else
694 {
695 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
696 }
697 }
698 }
699 }
700 }
701
702 if (r_is_at_infinity)
703 {
704 if (!EC_POINT_set_to_infinity(group, r)) goto err;
705 }
706 else
707 {
708 if (r_is_inverted)
709 if (!EC_POINT_invert(group, r, ctx)) goto err;
710 }
711
712 ret = 1;
713
714 err:
715 if (new_ctx != NULL)
716 BN_CTX_free(new_ctx);
717 if (tmp != NULL)
718 EC_POINT_free(tmp);
719 if (wsize != NULL)
720 OPENSSL_free(wsize);
721 if (wNAF_len != NULL)
722 OPENSSL_free(wNAF_len);
723 if (wNAF != NULL)
724 {
725 signed char **w;
726
727 for (w = wNAF; *w != NULL; w++)
728 OPENSSL_free(*w);
729
730 OPENSSL_free(wNAF);
731 }
732 if (val != NULL)
733 {
734 for (v = val; *v != NULL; v++)
735 EC_POINT_clear_free(*v);
736
737 OPENSSL_free(val);
738 }
739 if (val_sub != NULL)
740 {
741 OPENSSL_free(val_sub);
742 }
743 return ret;
744 }
745
746
747 /* ec_wNAF_precompute_mult()
748 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
749 * for use with wNAF splitting as implemented in ec_wNAF_mul().
750 *
751 * 'pre_comp->points' is an array of multiples of the generator
752 * of the following form:
753 * points[0] = generator;
754 * points[1] = 3 * generator;
755 * ...
756 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
757 * points[2^(w-1)] = 2^blocksize * generator;
758 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
759 * ...
760 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
761 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
762 * ...
763 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
764 * points[2^(w-1)*numblocks] = NULL
765 */
766 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
767 {
768 const EC_POINT *generator;
769 EC_POINT *tmp_point = NULL, *base = NULL, **var;
770 BN_CTX *new_ctx = NULL;
771 BIGNUM *order;
772 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
773 EC_POINT **points = NULL;
774 EC_PRE_COMP *pre_comp;
775 int ret = 0;
776
777 /* if there is an old EC_PRE_COMP object, throw it away */
778 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
779
780 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
781 return 0;
782
783 generator = EC_GROUP_get0_generator(group);
784 if (generator == NULL)
785 {
786 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
787 goto err;
788 }
789
790 if (ctx == NULL)
791 {
792 ctx = new_ctx = BN_CTX_new();
793 if (ctx == NULL)
794 goto err;
795 }
796
797 BN_CTX_start(ctx);
798 order = BN_CTX_get(ctx);
799 if (order == NULL) goto err;
800
801 if (!EC_GROUP_get_order(group, order, ctx)) goto err;
802 if (BN_is_zero(order))
803 {
804 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
805 goto err;
806 }
807
808 bits = BN_num_bits(order);
809 /* The following parameters mean we precompute (approximately)
810 * one point per bit.
811 *
812 * TBD: The combination 8, 4 is perfect for 160 bits; for other
813 * bit lengths, other parameter combinations might provide better
814 * efficiency.
815 */
816 blocksize = 8;
817 w = 4;
818 if (EC_window_bits_for_scalar_size(bits) > w)
819 {
820 /* let's not make the window too small ... */
821 w = EC_window_bits_for_scalar_size(bits);
822 }
823
824 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
825
826 pre_points_per_block = (size_t)1 << (w - 1);
827 num = pre_points_per_block * numblocks; /* number of points to compute and store */
828
829 points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
830 if (!points)
831 {
832 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
833 goto err;
834 }
835
836 var = points;
837 var[num] = NULL; /* pivot */
838 for (i = 0; i < num; i++)
839 {
840 if ((var[i] = EC_POINT_new(group)) == NULL)
841 {
842 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
843 goto err;
844 }
845 }
846
847 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
848 {
849 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
850 goto err;
851 }
852
853 if (!EC_POINT_copy(base, generator))
854 goto err;
855
856 /* do the precomputation */
857 for (i = 0; i < numblocks; i++)
858 {
859 size_t j;
860
861 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
862 goto err;
863
864 if (!EC_POINT_copy(*var++, base))
865 goto err;
866
867 for (j = 1; j < pre_points_per_block; j++, var++)
868 {
869 /* calculate odd multiples of the current base point */
870 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
871 goto err;
872 }
873
874 if (i < numblocks - 1)
875 {
876 /* get the next base (multiply current one by 2^blocksize) */
877 size_t k;
878
879 if (blocksize <= 2)
880 {
881 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
882 goto err;
883 }
884
885 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
886 goto err;
887 for (k = 2; k < blocksize; k++)
888 {
889 if (!EC_POINT_dbl(group,base,base,ctx))
890 goto err;
891 }
892 }
893 }
894
895 if (!EC_POINTs_make_affine(group, num, points, ctx))
896 goto err;
897
898 pre_comp->group = group;
899 pre_comp->blocksize = blocksize;
900 pre_comp->numblocks = numblocks;
901 pre_comp->w = w;
902 pre_comp->points = points;
903 points = NULL;
904 pre_comp->num = num;
905
906 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
907 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
908 goto err;
909 pre_comp = NULL;
910
911 ret = 1;
912 err:
913 if (ctx != NULL)
914 BN_CTX_end(ctx);
915 if (new_ctx != NULL)
916 BN_CTX_free(new_ctx);
917 if (pre_comp)
918 ec_pre_comp_free(pre_comp);
919 if (points)
920 {
921 EC_POINT **p;
922
923 for (p = points; *p != NULL; p++)
924 EC_POINT_free(*p);
925 OPENSSL_free(points);
926 }
927 if (tmp_point)
928 EC_POINT_free(tmp_point);
929 if (base)
930 EC_POINT_free(base);
931 return ret;
932 }
933
934
935 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
936 {
937 if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
938 return 1;
939 else
940 return 0;
941 }
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