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[thirdparty/openssl.git] / crypto / ec / ec_mult.c
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) 1998-2003 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 return ret;
108 ret->group = group;
109 ret->blocksize = 8; /* default */
110 ret->numblocks = 0;
111 ret->w = 4; /* default */
112 ret->points = NULL;
113 ret->num = 0;
114 ret->references = 1;
115 return ret;
116 }
117
118 static void *ec_pre_comp_dup(void *src_)
119 {
120 EC_PRE_COMP *src = src_;
121
122 /* no need to actually copy, these objects never change! */
123
124 CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
125
126 return src_;
127 }
128
129 static void ec_pre_comp_free(void *pre_)
130 {
131 int i;
132 EC_PRE_COMP *pre = pre_;
133
134 if (!pre)
135 return;
136
137 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
138 if (i > 0)
139 return;
140
141 if (pre->points)
142 {
143 EC_POINT **p;
144
145 for (p = pre->points; *p != NULL; p++)
146 EC_POINT_free(*p);
147 OPENSSL_free(pre->points);
148 }
149 OPENSSL_free(pre);
150 }
151
152 static void ec_pre_comp_clear_free(void *pre_)
153 {
154 int i;
155 EC_PRE_COMP *pre = pre_;
156
157 if (!pre)
158 return;
159
160 i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
161 if (i > 0)
162 return;
163
164 if (pre->points)
165 {
166 EC_POINT **p;
167
168 for (p = pre->points; *p != NULL; p++)
169 EC_POINT_clear_free(*p);
170 OPENSSL_cleanse(pre->points, sizeof pre->points);
171 OPENSSL_free(pre->points);
172 }
173 OPENSSL_cleanse(pre, sizeof pre);
174 OPENSSL_free(pre);
175 }
176
177
178
179
180 /* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
181 * This is an array r[] of values that are either zero or odd with an
182 * absolute value less than 2^w satisfying
183 * scalar = \sum_j r[j]*2^j
184 * where at most one of any w+1 consecutive digits is non-zero
185 * with the exception that the most significant digit may be only
186 * w-1 zeros away from that next non-zero digit.
187 */
188 static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
189 {
190 int window_val;
191 int ok = 0;
192 signed char *r = NULL;
193 int sign = 1;
194 int bit, next_bit, mask;
195 size_t len = 0, j;
196
197 if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
198 {
199 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
200 goto err;
201 }
202 bit = 1 << w; /* at most 128 */
203 next_bit = bit << 1; /* at most 256 */
204 mask = next_bit - 1; /* at most 255 */
205
206 if (BN_is_negative(scalar))
207 {
208 sign = -1;
209 }
210
211 len = BN_num_bits(scalar);
212 r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
213 * (*ret_len will be set to the actual length, i.e. at most
214 * BN_num_bits(scalar) + 1) */
215 if (r == NULL) goto err;
216
217 if (scalar->d == NULL || scalar->top == 0)
218 {
219 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
220 goto err;
221 }
222 window_val = scalar->d[0] & mask;
223 j = 0;
224 while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
225 {
226 int digit = 0;
227
228 /* 0 <= window_val <= 2^(w+1) */
229
230 if (window_val & 1)
231 {
232 /* 0 < window_val < 2^(w+1) */
233
234 if (window_val & bit)
235 {
236 digit = window_val - next_bit; /* -2^w < digit < 0 */
237
238 #if 1 /* modified wNAF */
239 if (j + w + 1 >= len)
240 {
241 /* special case for generating modified wNAFs:
242 * no new bits will be added into window_val,
243 * so using a positive digit here will decrease
244 * the total length of the representation */
245
246 digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
247 }
248 #endif
249 }
250 else
251 {
252 digit = window_val; /* 0 < digit < 2^w */
253 }
254
255 if (digit <= -bit || digit >= bit || !(digit & 1))
256 {
257 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
258 goto err;
259 }
260
261 window_val -= digit;
262
263 /* now window_val is 0 or 2^(w+1) in standard wNAF generation;
264 * for modified window NAFs, it may also be 2^w
265 */
266 if (window_val != 0 && window_val != next_bit && window_val != bit)
267 {
268 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
269 goto err;
270 }
271 }
272
273 r[j++] = sign * digit;
274
275 window_val >>= 1;
276 window_val += bit * BN_is_bit_set(scalar, j + w);
277
278 if (window_val > next_bit)
279 {
280 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
281 goto err;
282 }
283 }
284
285 if (j > len + 1)
286 {
287 ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
288 goto err;
289 }
290 len = j;
291 ok = 1;
292
293 err:
294 if (!ok)
295 {
296 OPENSSL_free(r);
297 r = NULL;
298 }
299 if (ok)
300 *ret_len = len;
301 return r;
302 }
303
304
305 /* TODO: table should be optimised for the wNAF-based implementation,
306 * sometimes smaller windows will give better performance
307 * (thus the boundaries should be increased)
308 */
309 #define EC_window_bits_for_scalar_size(b) \
310 ((size_t) \
311 ((b) >= 2000 ? 6 : \
312 (b) >= 800 ? 5 : \
313 (b) >= 300 ? 4 : \
314 (b) >= 70 ? 3 : \
315 (b) >= 20 ? 2 : \
316 1))
317
318 /* Compute
319 * \sum scalars[i]*points[i],
320 * also including
321 * scalar*generator
322 * in the addition if scalar != NULL
323 */
324 int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
325 size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
326 {
327 BN_CTX *new_ctx = NULL;
328 const EC_POINT *generator = NULL;
329 EC_POINT *tmp = NULL;
330 size_t totalnum;
331 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
332 size_t pre_points_per_block = 0;
333 size_t i, j;
334 int k;
335 int r_is_inverted = 0;
336 int r_is_at_infinity = 1;
337 size_t *wsize = NULL; /* individual window sizes */
338 signed char **wNAF = NULL; /* individual wNAFs */
339 size_t *wNAF_len = NULL;
340 size_t max_len = 0;
341 size_t num_val;
342 EC_POINT **val = NULL; /* precomputation */
343 EC_POINT **v;
344 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or 'pre_comp->points' */
345 const EC_PRE_COMP *pre_comp = NULL;
346 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be treated like other scalars,
347 * i.e. precomputation is not available */
348 int ret = 0;
349
350 if (group->meth != r->meth)
351 {
352 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
353 return 0;
354 }
355
356 if ((scalar == NULL) && (num == 0))
357 {
358 return EC_POINT_set_to_infinity(group, r);
359 }
360
361 for (i = 0; i < num; i++)
362 {
363 if (group->meth != points[i]->meth)
364 {
365 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
366 return 0;
367 }
368 }
369
370 if (ctx == NULL)
371 {
372 ctx = new_ctx = BN_CTX_new();
373 if (ctx == NULL)
374 goto err;
375 }
376
377 if (scalar != NULL)
378 {
379 generator = EC_GROUP_get0_generator(group);
380 if (generator == NULL)
381 {
382 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
383 goto err;
384 }
385
386 /* look if we can use precomputed multiples of generator */
387
388 pre_comp = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
389
390 if (pre_comp && pre_comp->numblocks && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == 0))
391 {
392 blocksize = pre_comp->blocksize;
393
394 /* determine maximum number of blocks that wNAF splitting may yield
395 * (NB: maximum wNAF length is bit length plus one) */
396 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
397
398 /* we cannot use more blocks than we have precomputation for */
399 if (numblocks > pre_comp->numblocks)
400 numblocks = pre_comp->numblocks;
401
402 pre_points_per_block = 1u << (pre_comp->w - 1);
403
404 /* check that pre_comp looks sane */
405 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block))
406 {
407 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
408 goto err;
409 }
410 }
411 else
412 {
413 /* can't use precomputation */
414 pre_comp = NULL;
415 numblocks = 1;
416 num_scalar = 1; /* treat 'scalar' like 'num'-th element of 'scalars' */
417 }
418 }
419
420 totalnum = num + numblocks;
421
422 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
423 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
424 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
425 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
426
427 if (!wsize || !wNAF_len || !wNAF || !val_sub)
428 goto err;
429
430 wNAF[0] = NULL; /* preliminary pivot */
431
432 /* num_val will be the total number of temporarily precomputed points */
433 num_val = 0;
434
435 for (i = 0; i < num + num_scalar; i++)
436 {
437 size_t bits;
438
439 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
440 wsize[i] = EC_window_bits_for_scalar_size(bits);
441 num_val += 1u << (wsize[i] - 1);
442 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
443 wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
444 if (wNAF[i] == NULL)
445 goto err;
446 if (wNAF_len[i] > max_len)
447 max_len = wNAF_len[i];
448 }
449
450 if (numblocks)
451 {
452 /* we go here iff scalar != NULL */
453
454 if (pre_comp == NULL)
455 {
456 if (num_scalar != 1)
457 {
458 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
459 goto err;
460 }
461 /* we have already generated a wNAF for 'scalar' */
462 }
463 else
464 {
465 signed char *tmp_wNAF = NULL;
466 size_t tmp_len = 0;
467
468 if (num_scalar != 0)
469 {
470 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
471 goto err;
472 }
473
474 /* use the window size for which we have precomputation */
475 wsize[num] = pre_comp->w;
476 tmp_wNAF = compute_wNAF(scalar, wsize[num], &tmp_len);
477 if (!tmp_wNAF)
478 goto err;
479
480 if (tmp_len <= max_len)
481 {
482 /* One of the other wNAFs is at least as long
483 * as the wNAF belonging to the generator,
484 * so wNAF splitting will not buy us anything. */
485
486 numblocks = 1;
487 totalnum = num + 1; /* don't use wNAF splitting */
488 wNAF[num] = tmp_wNAF;
489 wNAF[num + 1] = NULL;
490 wNAF_len[num] = tmp_len;
491 if (tmp_len > max_len)
492 max_len = tmp_len;
493 /* pre_comp->points starts with the points that we need here: */
494 val_sub[num] = pre_comp->points;
495 }
496 else
497 {
498 /* don't include tmp_wNAF directly into wNAF array
499 * - use wNAF splitting and include the blocks */
500
501 signed char *pp;
502 EC_POINT **tmp_points;
503
504 if (tmp_len < numblocks * blocksize)
505 {
506 /* possibly we can do with fewer blocks than estimated */
507 numblocks = (tmp_len + blocksize - 1) / blocksize;
508 if (numblocks > pre_comp->numblocks)
509 {
510 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
511 goto err;
512 }
513 totalnum = num + numblocks;
514 }
515
516 /* split wNAF in 'numblocks' parts */
517 pp = tmp_wNAF;
518 tmp_points = pre_comp->points;
519
520 for (i = num; i < totalnum; i++)
521 {
522 if (i < totalnum - 1)
523 {
524 wNAF_len[i] = blocksize;
525 if (tmp_len < blocksize)
526 {
527 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
528 goto err;
529 }
530 tmp_len -= blocksize;
531 }
532 else
533 /* last block gets whatever is left
534 * (this could be more or less than 'blocksize'!) */
535 wNAF_len[i] = tmp_len;
536
537 wNAF[i + 1] = NULL;
538 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
539 if (wNAF[i] == NULL)
540 {
541 OPENSSL_free(tmp_wNAF);
542 goto err;
543 }
544 memcpy(wNAF[i], pp, wNAF_len[i]);
545 if (wNAF_len[i] > max_len)
546 max_len = wNAF_len[i];
547
548 if (*tmp_points == NULL)
549 {
550 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
551 OPENSSL_free(tmp_wNAF);
552 goto err;
553 }
554 val_sub[i] = tmp_points;
555 tmp_points += pre_points_per_block;
556 pp += blocksize;
557 }
558 OPENSSL_free(tmp_wNAF);
559 }
560 }
561 }
562
563 /* All points we precompute now go into a single array 'val'.
564 * 'val_sub[i]' is a pointer to the subarray for the i-th point,
565 * or to a subarray of 'pre_comp->points' if we already have precomputation. */
566 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
567 if (val == NULL) goto err;
568 val[num_val] = NULL; /* pivot element */
569
570 /* allocate points for precomputation */
571 v = val;
572 for (i = 0; i < num + num_scalar; i++)
573 {
574 val_sub[i] = v;
575 for (j = 0; j < (1u << (wsize[i] - 1)); j++)
576 {
577 *v = EC_POINT_new(group);
578 if (*v == NULL) goto err;
579 v++;
580 }
581 }
582 if (!(v == val + num_val))
583 {
584 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
585 goto err;
586 }
587
588 if (!(tmp = EC_POINT_new(group)))
589 goto err;
590
591 /* prepare precomputed values:
592 * val_sub[i][0] := points[i]
593 * val_sub[i][1] := 3 * points[i]
594 * val_sub[i][2] := 5 * points[i]
595 * ...
596 */
597 for (i = 0; i < num + num_scalar; i++)
598 {
599 if (i < num)
600 {
601 if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
602 }
603 else
604 {
605 if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
606 }
607
608 if (wsize[i] > 1)
609 {
610 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
611 for (j = 1; j < (1u << (wsize[i] - 1)); j++)
612 {
613 if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
614 }
615 }
616 }
617
618 #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
619 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
620 goto err;
621 #endif
622
623 r_is_at_infinity = 1;
624
625 for (k = max_len - 1; k >= 0; k--)
626 {
627 if (!r_is_at_infinity)
628 {
629 if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
630 }
631
632 for (i = 0; i < totalnum; i++)
633 {
634 if (wNAF_len[i] > (size_t)k)
635 {
636 int digit = wNAF[i][k];
637 int is_neg;
638
639 if (digit)
640 {
641 is_neg = digit < 0;
642
643 if (is_neg)
644 digit = -digit;
645
646 if (is_neg != r_is_inverted)
647 {
648 if (!r_is_at_infinity)
649 {
650 if (!EC_POINT_invert(group, r, ctx)) goto err;
651 }
652 r_is_inverted = !r_is_inverted;
653 }
654
655 /* digit > 0 */
656
657 if (r_is_at_infinity)
658 {
659 if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
660 r_is_at_infinity = 0;
661 }
662 else
663 {
664 if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
665 }
666 }
667 }
668 }
669 }
670
671 if (r_is_at_infinity)
672 {
673 if (!EC_POINT_set_to_infinity(group, r)) goto err;
674 }
675 else
676 {
677 if (r_is_inverted)
678 if (!EC_POINT_invert(group, r, ctx)) goto err;
679 }
680
681 ret = 1;
682
683 err:
684 if (new_ctx != NULL)
685 BN_CTX_free(new_ctx);
686 if (tmp != NULL)
687 EC_POINT_free(tmp);
688 if (wsize != NULL)
689 OPENSSL_free(wsize);
690 if (wNAF_len != NULL)
691 OPENSSL_free(wNAF_len);
692 if (wNAF != NULL)
693 {
694 signed char **w;
695
696 for (w = wNAF; *w != NULL; w++)
697 OPENSSL_free(*w);
698
699 OPENSSL_free(wNAF);
700 }
701 if (val != NULL)
702 {
703 for (v = val; *v != NULL; v++)
704 EC_POINT_clear_free(*v);
705
706 OPENSSL_free(val);
707 }
708 if (val_sub != NULL)
709 {
710 OPENSSL_free(val_sub);
711 }
712 return ret;
713 }
714
715
716 /* ec_wNAF_precompute_mult()
717 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
718 * for use with wNAF splitting as implemented in ec_wNAF_mul().
719 *
720 * 'pre_comp->points' is an array of multiples of the generator
721 * of the following form:
722 * points[0] = generator;
723 * points[1] = 3 * generator;
724 * ...
725 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
726 * points[2^(w-1)] = 2^blocksize * generator;
727 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
728 * ...
729 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
730 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
731 * ...
732 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
733 * points[2^(w-1)*numblocks] = NULL
734 */
735 int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
736 {
737 const EC_POINT *generator;
738 EC_POINT *tmp_point = NULL, *base = NULL, **var;
739 BN_CTX *new_ctx = NULL;
740 BIGNUM *order;
741 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
742 EC_POINT **points = NULL;
743 EC_PRE_COMP *pre_comp;
744 int ret = 0;
745
746 /* if there is an old EC_PRE_COMP object, throw it away */
747 EC_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
748
749 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
750 return 0;
751
752 generator = EC_GROUP_get0_generator(group);
753 if (generator == NULL)
754 {
755 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
756 goto err;
757 }
758
759 if (ctx == NULL)
760 {
761 ctx = new_ctx = BN_CTX_new();
762 if (ctx == NULL)
763 goto err;
764 }
765
766 BN_CTX_start(ctx);
767 order = BN_CTX_get(ctx);
768 if (order == NULL) goto err;
769
770 if (!EC_GROUP_get_order(group, order, ctx)) goto err;
771 if (BN_is_zero(order))
772 {
773 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
774 goto err;
775 }
776
777 bits = BN_num_bits(order);
778 /* The following parameters mean we precompute (approximately)
779 * one point per bit.
780 *
781 * TBD: The combination 8, 4 is perfect for 160 bits; for other
782 * bit lengths, other parameter combinations might provide better
783 * efficiency.
784 */
785 blocksize = 8;
786 w = 4;
787 if (EC_window_bits_for_scalar_size(bits) > w)
788 {
789 /* let's not make the window too small ... */
790 w = EC_window_bits_for_scalar_size(bits);
791 }
792
793 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */
794
795 pre_points_per_block = 1u << (w - 1);
796 num = pre_points_per_block * numblocks; /* number of points to compute and store */
797
798 points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
799 if (!points)
800 {
801 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
802 goto err;
803 }
804
805 var = points;
806 var[num] = NULL; /* pivot */
807 for (i = 0; i < num; i++)
808 {
809 if ((var[i] = EC_POINT_new(group)) == NULL)
810 {
811 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
812 goto err;
813 }
814 }
815
816 if (!(tmp_point = EC_POINT_new(group)) || !(base = EC_POINT_new(group)))
817 {
818 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
819 goto err;
820 }
821
822 if (!EC_POINT_copy(base, generator))
823 goto err;
824
825 /* do the precomputation */
826 for (i = 0; i < numblocks; i++)
827 {
828 size_t j;
829
830 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
831 goto err;
832
833 if (!EC_POINT_copy(*var++, base))
834 goto err;
835
836 for (j = 1; j < pre_points_per_block; j++, var++)
837 {
838 /* calculate odd multiples of the current base point */
839 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
840 goto err;
841 }
842
843 if (i < numblocks - 1)
844 {
845 /* get the next base (multiply current one by 2^blocksize) */
846 size_t k;
847
848 if (blocksize <= 2)
849 {
850 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
851 goto err;
852 }
853
854 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
855 goto err;
856 for (k = 2; k < blocksize; k++)
857 {
858 if (!EC_POINT_dbl(group,base,base,ctx))
859 goto err;
860 }
861 }
862 }
863
864 if (!EC_POINTs_make_affine(group, num, points, ctx))
865 goto err;
866
867 pre_comp->group = group;
868 pre_comp->blocksize = blocksize;
869 pre_comp->numblocks = numblocks;
870 pre_comp->w = w;
871 pre_comp->points = points;
872 points = NULL;
873 pre_comp->num = num;
874
875 if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
876 ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
877 goto err;
878 pre_comp = NULL;
879
880 ret = 1;
881 err:
882 BN_CTX_end(ctx);
883 if (new_ctx != NULL)
884 BN_CTX_free(new_ctx);
885 if (pre_comp)
886 ec_pre_comp_free(pre_comp);
887 if (points)
888 {
889 EC_POINT **p;
890
891 for (p = points; *p != NULL; p++)
892 EC_POINT_free(*p);
893 OPENSSL_free(points);
894 }
895 if (tmp_point)
896 EC_POINT_free(tmp_point);
897 if (base)
898 EC_POINT_free(base);
899 return ret;
900 }
901
902
903 int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
904 {
905 if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
906 return 1;
907 else
908 return 0;
909 }
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