source: EcnlProtoTool/trunk/openssl-1.1.0e/crypto/ec/ec_mult.c@ 331

Last change on this file since 331 was 331, checked in by coas-nagasima, 6 years ago

prototoolに関連するプロジェクトをnewlibからmuslを使うよう変更・更新
ntshellをnewlibの下位の実装から、muslのsyscallの実装に変更・更新
以下のOSSをアップデート
・mruby-1.3.0
・musl-1.1.18
・onigmo-6.1.3
・tcc-0.9.27
以下のOSSを追加
・openssl-1.1.0e
・curl-7.57.0
・zlib-1.2.11
以下のmrbgemsを追加
・iij/mruby-digest
・iij/mruby-env
・iij/mruby-errno
・iij/mruby-iijson
・iij/mruby-ipaddr
・iij/mruby-mock
・iij/mruby-require
・iij/mruby-tls-openssl
  • Property svn:eol-style set to native
  • Property svn:mime-type set to text/x-csrc
File size: 20.7 KB
Line 
1/*
2 * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10/* ====================================================================
11 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
12 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
13 * and contributed to the OpenSSL project.
14 */
15
16#include <string.h>
17#include <openssl/err.h>
18
19#include "internal/cryptlib.h"
20#include "internal/bn_int.h"
21#include "ec_lcl.h"
22
23/*
24 * This file implements the wNAF-based interleaving multi-exponentiation method
25 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
26 * for multiplication with precomputation, we use wNAF splitting
27 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
28 */
29
30/* structure for precomputed multiples of the generator */
31struct ec_pre_comp_st {
32 const EC_GROUP *group; /* parent EC_GROUP object */
33 size_t blocksize; /* block size for wNAF splitting */
34 size_t numblocks; /* max. number of blocks for which we have
35 * precomputation */
36 size_t w; /* window size */
37 EC_POINT **points; /* array with pre-calculated multiples of
38 * generator: 'num' pointers to EC_POINT
39 * objects followed by a NULL */
40 size_t num; /* numblocks * 2^(w-1) */
41 int references;
42 CRYPTO_RWLOCK *lock;
43};
44
45static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
46{
47 EC_PRE_COMP *ret = NULL;
48
49 if (!group)
50 return NULL;
51
52 ret = OPENSSL_zalloc(sizeof(*ret));
53 if (ret == NULL) {
54 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
55 return ret;
56 }
57
58 ret->group = group;
59 ret->blocksize = 8; /* default */
60 ret->w = 4; /* default */
61 ret->references = 1;
62
63 ret->lock = CRYPTO_THREAD_lock_new();
64 if (ret->lock == NULL) {
65 ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
66 OPENSSL_free(ret);
67 return NULL;
68 }
69 return ret;
70}
71
72EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)
73{
74 int i;
75 if (pre != NULL)
76 CRYPTO_atomic_add(&pre->references, 1, &i, pre->lock);
77 return pre;
78}
79
80void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
81{
82 int i;
83
84 if (pre == NULL)
85 return;
86
87 CRYPTO_atomic_add(&pre->references, -1, &i, pre->lock);
88 REF_PRINT_COUNT("EC_ec", pre);
89 if (i > 0)
90 return;
91 REF_ASSERT_ISNT(i < 0);
92
93 if (pre->points != NULL) {
94 EC_POINT **pts;
95
96 for (pts = pre->points; *pts != NULL; pts++)
97 EC_POINT_free(*pts);
98 OPENSSL_free(pre->points);
99 }
100 CRYPTO_THREAD_lock_free(pre->lock);
101 OPENSSL_free(pre);
102}
103
104/*
105 * TODO: table should be optimised for the wNAF-based implementation,
106 * sometimes smaller windows will give better performance (thus the
107 * boundaries should be increased)
108 */
109#define EC_window_bits_for_scalar_size(b) \
110 ((size_t) \
111 ((b) >= 2000 ? 6 : \
112 (b) >= 800 ? 5 : \
113 (b) >= 300 ? 4 : \
114 (b) >= 70 ? 3 : \
115 (b) >= 20 ? 2 : \
116 1))
117
118/*-
119 * Compute
120 * \sum scalars[i]*points[i],
121 * also including
122 * scalar*generator
123 * in the addition if scalar != NULL
124 */
125int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
126 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
127 BN_CTX *ctx)
128{
129 BN_CTX *new_ctx = NULL;
130 const EC_POINT *generator = NULL;
131 EC_POINT *tmp = NULL;
132 size_t totalnum;
133 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
134 size_t pre_points_per_block = 0;
135 size_t i, j;
136 int k;
137 int r_is_inverted = 0;
138 int r_is_at_infinity = 1;
139 size_t *wsize = NULL; /* individual window sizes */
140 signed char **wNAF = NULL; /* individual wNAFs */
141 size_t *wNAF_len = NULL;
142 size_t max_len = 0;
143 size_t num_val;
144 EC_POINT **val = NULL; /* precomputation */
145 EC_POINT **v;
146 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
147 * 'pre_comp->points' */
148 const EC_PRE_COMP *pre_comp = NULL;
149 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
150 * treated like other scalars, i.e.
151 * precomputation is not available */
152 int ret = 0;
153
154 if (group->meth != r->meth) {
155 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
156 return 0;
157 }
158
159 if ((scalar == NULL) && (num == 0)) {
160 return EC_POINT_set_to_infinity(group, r);
161 }
162
163 for (i = 0; i < num; i++) {
164 if (group->meth != points[i]->meth) {
165 ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
166 return 0;
167 }
168 }
169
170 if (ctx == NULL) {
171 ctx = new_ctx = BN_CTX_new();
172 if (ctx == NULL)
173 goto err;
174 }
175
176 if (scalar != NULL) {
177 generator = EC_GROUP_get0_generator(group);
178 if (generator == NULL) {
179 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
180 goto err;
181 }
182
183 /* look if we can use precomputed multiples of generator */
184
185 pre_comp = group->pre_comp.ec;
186 if (pre_comp && pre_comp->numblocks
187 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
188 0)) {
189 blocksize = pre_comp->blocksize;
190
191 /*
192 * determine maximum number of blocks that wNAF splitting may
193 * yield (NB: maximum wNAF length is bit length plus one)
194 */
195 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
196
197 /*
198 * we cannot use more blocks than we have precomputation for
199 */
200 if (numblocks > pre_comp->numblocks)
201 numblocks = pre_comp->numblocks;
202
203 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
204
205 /* check that pre_comp looks sane */
206 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
207 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
208 goto err;
209 }
210 } else {
211 /* can't use precomputation */
212 pre_comp = NULL;
213 numblocks = 1;
214 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
215 * 'scalars' */
216 }
217 }
218
219 totalnum = num + numblocks;
220
221 wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
222 wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
223 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space
224 * for pivot */
225 val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
226
227 /* Ensure wNAF is initialised in case we end up going to err */
228 if (wNAF != NULL)
229 wNAF[0] = NULL; /* preliminary pivot */
230
231 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
232 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
233 goto err;
234 }
235
236 /*
237 * num_val will be the total number of temporarily precomputed points
238 */
239 num_val = 0;
240
241 for (i = 0; i < num + num_scalar; i++) {
242 size_t bits;
243
244 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
245 wsize[i] = EC_window_bits_for_scalar_size(bits);
246 num_val += (size_t)1 << (wsize[i] - 1);
247 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
248 wNAF[i] =
249 bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
250 &wNAF_len[i]);
251 if (wNAF[i] == NULL)
252 goto err;
253 if (wNAF_len[i] > max_len)
254 max_len = wNAF_len[i];
255 }
256
257 if (numblocks) {
258 /* we go here iff scalar != NULL */
259
260 if (pre_comp == NULL) {
261 if (num_scalar != 1) {
262 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
263 goto err;
264 }
265 /* we have already generated a wNAF for 'scalar' */
266 } else {
267 signed char *tmp_wNAF = NULL;
268 size_t tmp_len = 0;
269
270 if (num_scalar != 0) {
271 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
272 goto err;
273 }
274
275 /*
276 * use the window size for which we have precomputation
277 */
278 wsize[num] = pre_comp->w;
279 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
280 if (!tmp_wNAF)
281 goto err;
282
283 if (tmp_len <= max_len) {
284 /*
285 * One of the other wNAFs is at least as long as the wNAF
286 * belonging to the generator, so wNAF splitting will not buy
287 * us anything.
288 */
289
290 numblocks = 1;
291 totalnum = num + 1; /* don't use wNAF splitting */
292 wNAF[num] = tmp_wNAF;
293 wNAF[num + 1] = NULL;
294 wNAF_len[num] = tmp_len;
295 /*
296 * pre_comp->points starts with the points that we need here:
297 */
298 val_sub[num] = pre_comp->points;
299 } else {
300 /*
301 * don't include tmp_wNAF directly into wNAF array - use wNAF
302 * splitting and include the blocks
303 */
304
305 signed char *pp;
306 EC_POINT **tmp_points;
307
308 if (tmp_len < numblocks * blocksize) {
309 /*
310 * possibly we can do with fewer blocks than estimated
311 */
312 numblocks = (tmp_len + blocksize - 1) / blocksize;
313 if (numblocks > pre_comp->numblocks) {
314 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
315 OPENSSL_free(tmp_wNAF);
316 goto err;
317 }
318 totalnum = num + numblocks;
319 }
320
321 /* split wNAF in 'numblocks' parts */
322 pp = tmp_wNAF;
323 tmp_points = pre_comp->points;
324
325 for (i = num; i < totalnum; i++) {
326 if (i < totalnum - 1) {
327 wNAF_len[i] = blocksize;
328 if (tmp_len < blocksize) {
329 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
330 OPENSSL_free(tmp_wNAF);
331 goto err;
332 }
333 tmp_len -= blocksize;
334 } else
335 /*
336 * last block gets whatever is left (this could be
337 * more or less than 'blocksize'!)
338 */
339 wNAF_len[i] = tmp_len;
340
341 wNAF[i + 1] = NULL;
342 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
343 if (wNAF[i] == NULL) {
344 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
345 OPENSSL_free(tmp_wNAF);
346 goto err;
347 }
348 memcpy(wNAF[i], pp, wNAF_len[i]);
349 if (wNAF_len[i] > max_len)
350 max_len = wNAF_len[i];
351
352 if (*tmp_points == NULL) {
353 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
354 OPENSSL_free(tmp_wNAF);
355 goto err;
356 }
357 val_sub[i] = tmp_points;
358 tmp_points += pre_points_per_block;
359 pp += blocksize;
360 }
361 OPENSSL_free(tmp_wNAF);
362 }
363 }
364 }
365
366 /*
367 * All points we precompute now go into a single array 'val'.
368 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
369 * subarray of 'pre_comp->points' if we already have precomputation.
370 */
371 val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
372 if (val == NULL) {
373 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
374 goto err;
375 }
376 val[num_val] = NULL; /* pivot element */
377
378 /* allocate points for precomputation */
379 v = val;
380 for (i = 0; i < num + num_scalar; i++) {
381 val_sub[i] = v;
382 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
383 *v = EC_POINT_new(group);
384 if (*v == NULL)
385 goto err;
386 v++;
387 }
388 }
389 if (!(v == val + num_val)) {
390 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
391 goto err;
392 }
393
394 if ((tmp = EC_POINT_new(group)) == NULL)
395 goto err;
396
397 /*-
398 * prepare precomputed values:
399 * val_sub[i][0] := points[i]
400 * val_sub[i][1] := 3 * points[i]
401 * val_sub[i][2] := 5 * points[i]
402 * ...
403 */
404 for (i = 0; i < num + num_scalar; i++) {
405 if (i < num) {
406 if (!EC_POINT_copy(val_sub[i][0], points[i]))
407 goto err;
408 } else {
409 if (!EC_POINT_copy(val_sub[i][0], generator))
410 goto err;
411 }
412
413 if (wsize[i] > 1) {
414 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
415 goto err;
416 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
417 if (!EC_POINT_add
418 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
419 goto err;
420 }
421 }
422 }
423
424 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
425 goto err;
426
427 r_is_at_infinity = 1;
428
429 for (k = max_len - 1; k >= 0; k--) {
430 if (!r_is_at_infinity) {
431 if (!EC_POINT_dbl(group, r, r, ctx))
432 goto err;
433 }
434
435 for (i = 0; i < totalnum; i++) {
436 if (wNAF_len[i] > (size_t)k) {
437 int digit = wNAF[i][k];
438 int is_neg;
439
440 if (digit) {
441 is_neg = digit < 0;
442
443 if (is_neg)
444 digit = -digit;
445
446 if (is_neg != r_is_inverted) {
447 if (!r_is_at_infinity) {
448 if (!EC_POINT_invert(group, r, ctx))
449 goto err;
450 }
451 r_is_inverted = !r_is_inverted;
452 }
453
454 /* digit > 0 */
455
456 if (r_is_at_infinity) {
457 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
458 goto err;
459 r_is_at_infinity = 0;
460 } else {
461 if (!EC_POINT_add
462 (group, r, r, val_sub[i][digit >> 1], ctx))
463 goto err;
464 }
465 }
466 }
467 }
468 }
469
470 if (r_is_at_infinity) {
471 if (!EC_POINT_set_to_infinity(group, r))
472 goto err;
473 } else {
474 if (r_is_inverted)
475 if (!EC_POINT_invert(group, r, ctx))
476 goto err;
477 }
478
479 ret = 1;
480
481 err:
482 BN_CTX_free(new_ctx);
483 EC_POINT_free(tmp);
484 OPENSSL_free(wsize);
485 OPENSSL_free(wNAF_len);
486 if (wNAF != NULL) {
487 signed char **w;
488
489 for (w = wNAF; *w != NULL; w++)
490 OPENSSL_free(*w);
491
492 OPENSSL_free(wNAF);
493 }
494 if (val != NULL) {
495 for (v = val; *v != NULL; v++)
496 EC_POINT_clear_free(*v);
497
498 OPENSSL_free(val);
499 }
500 OPENSSL_free(val_sub);
501 return ret;
502}
503
504/*-
505 * ec_wNAF_precompute_mult()
506 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
507 * for use with wNAF splitting as implemented in ec_wNAF_mul().
508 *
509 * 'pre_comp->points' is an array of multiples of the generator
510 * of the following form:
511 * points[0] = generator;
512 * points[1] = 3 * generator;
513 * ...
514 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
515 * points[2^(w-1)] = 2^blocksize * generator;
516 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
517 * ...
518 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
519 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
520 * ...
521 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
522 * points[2^(w-1)*numblocks] = NULL
523 */
524int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
525{
526 const EC_POINT *generator;
527 EC_POINT *tmp_point = NULL, *base = NULL, **var;
528 BN_CTX *new_ctx = NULL;
529 const BIGNUM *order;
530 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
531 EC_POINT **points = NULL;
532 EC_PRE_COMP *pre_comp;
533 int ret = 0;
534
535 /* if there is an old EC_PRE_COMP object, throw it away */
536 EC_pre_comp_free(group);
537 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
538 return 0;
539
540 generator = EC_GROUP_get0_generator(group);
541 if (generator == NULL) {
542 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
543 goto err;
544 }
545
546 if (ctx == NULL) {
547 ctx = new_ctx = BN_CTX_new();
548 if (ctx == NULL)
549 goto err;
550 }
551
552 BN_CTX_start(ctx);
553
554 order = EC_GROUP_get0_order(group);
555 if (order == NULL)
556 goto err;
557 if (BN_is_zero(order)) {
558 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
559 goto err;
560 }
561
562 bits = BN_num_bits(order);
563 /*
564 * The following parameters mean we precompute (approximately) one point
565 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
566 * bit lengths, other parameter combinations might provide better
567 * efficiency.
568 */
569 blocksize = 8;
570 w = 4;
571 if (EC_window_bits_for_scalar_size(bits) > w) {
572 /* let's not make the window too small ... */
573 w = EC_window_bits_for_scalar_size(bits);
574 }
575
576 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
577 * to use for wNAF
578 * splitting */
579
580 pre_points_per_block = (size_t)1 << (w - 1);
581 num = pre_points_per_block * numblocks; /* number of points to compute
582 * and store */
583
584 points = OPENSSL_malloc(sizeof(*points) * (num + 1));
585 if (points == NULL) {
586 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
587 goto err;
588 }
589
590 var = points;
591 var[num] = NULL; /* pivot */
592 for (i = 0; i < num; i++) {
593 if ((var[i] = EC_POINT_new(group)) == NULL) {
594 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
595 goto err;
596 }
597 }
598
599 if ((tmp_point = EC_POINT_new(group)) == NULL
600 || (base = EC_POINT_new(group)) == NULL) {
601 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
602 goto err;
603 }
604
605 if (!EC_POINT_copy(base, generator))
606 goto err;
607
608 /* do the precomputation */
609 for (i = 0; i < numblocks; i++) {
610 size_t j;
611
612 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
613 goto err;
614
615 if (!EC_POINT_copy(*var++, base))
616 goto err;
617
618 for (j = 1; j < pre_points_per_block; j++, var++) {
619 /*
620 * calculate odd multiples of the current base point
621 */
622 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
623 goto err;
624 }
625
626 if (i < numblocks - 1) {
627 /*
628 * get the next base (multiply current one by 2^blocksize)
629 */
630 size_t k;
631
632 if (blocksize <= 2) {
633 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
634 goto err;
635 }
636
637 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
638 goto err;
639 for (k = 2; k < blocksize; k++) {
640 if (!EC_POINT_dbl(group, base, base, ctx))
641 goto err;
642 }
643 }
644 }
645
646 if (!EC_POINTs_make_affine(group, num, points, ctx))
647 goto err;
648
649 pre_comp->group = group;
650 pre_comp->blocksize = blocksize;
651 pre_comp->numblocks = numblocks;
652 pre_comp->w = w;
653 pre_comp->points = points;
654 points = NULL;
655 pre_comp->num = num;
656 SETPRECOMP(group, ec, pre_comp);
657 pre_comp = NULL;
658 ret = 1;
659
660 err:
661 if (ctx != NULL)
662 BN_CTX_end(ctx);
663 BN_CTX_free(new_ctx);
664 EC_ec_pre_comp_free(pre_comp);
665 if (points) {
666 EC_POINT **p;
667
668 for (p = points; *p != NULL; p++)
669 EC_POINT_free(*p);
670 OPENSSL_free(points);
671 }
672 EC_POINT_free(tmp_point);
673 EC_POINT_free(base);
674 return ret;
675}
676
677int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
678{
679 return HAVEPRECOMP(group, ec);
680}
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