1 /*
2 * Copyright 2001-2021 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
4 *
5 * Licensed under the Apache License 2.0 (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 */
10
11 /*
12 * ECDSA low level APIs are deprecated for public use, but still ok for
13 * internal use.
14 */
15 #include "internal/deprecated.h"
16
17 #include <string.h>
18 #include <openssl/err.h>
19
20 #include "internal/cryptlib.h"
21 #include "crypto/bn.h"
22 #include "ec_local.h"
23 #include "internal/refcount.h"
24
25 /*
26 * This file implements the wNAF-based interleaving multi-exponentiation method
27 * Formerly at:
28 * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
29 * You might now find it here:
30 * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
31 * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
32 * For multiplication with precomputation, we use wNAF splitting, formerly at:
33 * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
34 */
35
36 /* structure for precomputed multiples of the generator */
37 struct ec_pre_comp_st {
38 const EC_GROUP *group; /* parent EC_GROUP object */
39 size_t blocksize; /* block size for wNAF splitting */
40 size_t numblocks; /* max. number of blocks for which we have
41 * precomputation */
42 size_t w; /* window size */
43 EC_POINT **points; /* array with pre-calculated multiples of
44 * generator: 'num' pointers to EC_POINT
45 * objects followed by a NULL */
46 size_t num; /* numblocks * 2^(w-1) */
47 CRYPTO_REF_COUNT references;
48 CRYPTO_RWLOCK *lock;
49 };
50
ec_pre_comp_new(const EC_GROUP * group)51 static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
52 {
53 EC_PRE_COMP *ret = NULL;
54
55 if (!group)
56 return NULL;
57
58 ret = OPENSSL_zalloc(sizeof(*ret));
59 if (ret == NULL) {
60 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
61 return ret;
62 }
63
64 ret->group = group;
65 ret->blocksize = 8; /* default */
66 ret->w = 4; /* default */
67 ret->references = 1;
68
69 ret->lock = CRYPTO_THREAD_lock_new();
70 if (ret->lock == NULL) {
71 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
72 OPENSSL_free(ret);
73 return NULL;
74 }
75 return ret;
76 }
77
EC_ec_pre_comp_dup(EC_PRE_COMP * pre)78 EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)
79 {
80 int i;
81 if (pre != NULL)
82 CRYPTO_UP_REF(&pre->references, &i, pre->lock);
83 return pre;
84 }
85
EC_ec_pre_comp_free(EC_PRE_COMP * pre)86 void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
87 {
88 int i;
89
90 if (pre == NULL)
91 return;
92
93 CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
94 REF_PRINT_COUNT("EC_ec", pre);
95 if (i > 0)
96 return;
97 REF_ASSERT_ISNT(i < 0);
98
99 if (pre->points != NULL) {
100 EC_POINT **pts;
101
102 for (pts = pre->points; *pts != NULL; pts++)
103 EC_POINT_free(*pts);
104 OPENSSL_free(pre->points);
105 }
106 CRYPTO_THREAD_lock_free(pre->lock);
107 OPENSSL_free(pre);
108 }
109
110 #define EC_POINT_BN_set_flags(P, flags) do { \
111 BN_set_flags((P)->X, (flags)); \
112 BN_set_flags((P)->Y, (flags)); \
113 BN_set_flags((P)->Z, (flags)); \
114 } while(0)
115
116 /*-
117 * This functions computes a single point multiplication over the EC group,
118 * using, at a high level, a Montgomery ladder with conditional swaps, with
119 * various timing attack defenses.
120 *
121 * It performs either a fixed point multiplication
122 * (scalar * generator)
123 * when point is NULL, or a variable point multiplication
124 * (scalar * point)
125 * when point is not NULL.
126 *
127 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
128 * constant time bets are off (where n is the cardinality of the EC group).
129 *
130 * This function expects `group->order` and `group->cardinality` to be well
131 * defined and non-zero: it fails with an error code otherwise.
132 *
133 * NB: This says nothing about the constant-timeness of the ladder step
134 * implementation (i.e., the default implementation is based on EC_POINT_add and
135 * EC_POINT_dbl, which of course are not constant time themselves) or the
136 * underlying multiprecision arithmetic.
137 *
138 * The product is stored in `r`.
139 *
140 * This is an internal function: callers are in charge of ensuring that the
141 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
142 *
143 * Returns 1 on success, 0 otherwise.
144 */
ossl_ec_scalar_mul_ladder(const EC_GROUP * group,EC_POINT * r,const BIGNUM * scalar,const EC_POINT * point,BN_CTX * ctx)145 int ossl_ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
146 const BIGNUM *scalar, const EC_POINT *point,
147 BN_CTX *ctx)
148 {
149 int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
150 EC_POINT *p = NULL;
151 EC_POINT *s = NULL;
152 BIGNUM *k = NULL;
153 BIGNUM *lambda = NULL;
154 BIGNUM *cardinality = NULL;
155 int ret = 0;
156
157 /* early exit if the input point is the point at infinity */
158 if (point != NULL && EC_POINT_is_at_infinity(group, point))
159 return EC_POINT_set_to_infinity(group, r);
160
161 if (BN_is_zero(group->order)) {
162 ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);
163 return 0;
164 }
165 if (BN_is_zero(group->cofactor)) {
166 ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_COFACTOR);
167 return 0;
168 }
169
170 BN_CTX_start(ctx);
171
172 if (((p = EC_POINT_new(group)) == NULL)
173 || ((s = EC_POINT_new(group)) == NULL)) {
174 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
175 goto err;
176 }
177
178 if (point == NULL) {
179 if (!EC_POINT_copy(p, group->generator)) {
180 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
181 goto err;
182 }
183 } else {
184 if (!EC_POINT_copy(p, point)) {
185 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
186 goto err;
187 }
188 }
189
190 EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME);
191 EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
192 EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
193
194 cardinality = BN_CTX_get(ctx);
195 lambda = BN_CTX_get(ctx);
196 k = BN_CTX_get(ctx);
197 if (k == NULL) {
198 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
199 goto err;
200 }
201
202 if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) {
203 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
204 goto err;
205 }
206
207 /*
208 * Group cardinalities are often on a word boundary.
209 * So when we pad the scalar, some timing diff might
210 * pop if it needs to be expanded due to carries.
211 * So expand ahead of time.
212 */
213 cardinality_bits = BN_num_bits(cardinality);
214 group_top = bn_get_top(cardinality);
215 if ((bn_wexpand(k, group_top + 2) == NULL)
216 || (bn_wexpand(lambda, group_top + 2) == NULL)) {
217 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
218 goto err;
219 }
220
221 if (!BN_copy(k, scalar)) {
222 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
223 goto err;
224 }
225
226 BN_set_flags(k, BN_FLG_CONSTTIME);
227
228 if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {
229 /*-
230 * this is an unusual input, and we don't guarantee
231 * constant-timeness
232 */
233 if (!BN_nnmod(k, k, cardinality, ctx)) {
234 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
235 goto err;
236 }
237 }
238
239 if (!BN_add(lambda, k, cardinality)) {
240 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
241 goto err;
242 }
243 BN_set_flags(lambda, BN_FLG_CONSTTIME);
244 if (!BN_add(k, lambda, cardinality)) {
245 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
246 goto err;
247 }
248 /*
249 * lambda := scalar + cardinality
250 * k := scalar + 2*cardinality
251 */
252 kbit = BN_is_bit_set(lambda, cardinality_bits);
253 BN_consttime_swap(kbit, k, lambda, group_top + 2);
254
255 group_top = bn_get_top(group->field);
256 if ((bn_wexpand(s->X, group_top) == NULL)
257 || (bn_wexpand(s->Y, group_top) == NULL)
258 || (bn_wexpand(s->Z, group_top) == NULL)
259 || (bn_wexpand(r->X, group_top) == NULL)
260 || (bn_wexpand(r->Y, group_top) == NULL)
261 || (bn_wexpand(r->Z, group_top) == NULL)
262 || (bn_wexpand(p->X, group_top) == NULL)
263 || (bn_wexpand(p->Y, group_top) == NULL)
264 || (bn_wexpand(p->Z, group_top) == NULL)) {
265 ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB);
266 goto err;
267 }
268
269 /* ensure input point is in affine coords for ladder step efficiency */
270 if (!p->Z_is_one && (group->meth->make_affine == NULL
271 || !group->meth->make_affine(group, p, ctx))) {
272 ERR_raise(ERR_LIB_EC, ERR_R_EC_LIB);
273 goto err;
274 }
275
276 /* Initialize the Montgomery ladder */
277 if (!ec_point_ladder_pre(group, r, s, p, ctx)) {
278 ERR_raise(ERR_LIB_EC, EC_R_LADDER_PRE_FAILURE);
279 goto err;
280 }
281
282 /* top bit is a 1, in a fixed pos */
283 pbit = 1;
284
285 #define EC_POINT_CSWAP(c, a, b, w, t) do { \
286 BN_consttime_swap(c, (a)->X, (b)->X, w); \
287 BN_consttime_swap(c, (a)->Y, (b)->Y, w); \
288 BN_consttime_swap(c, (a)->Z, (b)->Z, w); \
289 t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
290 (a)->Z_is_one ^= (t); \
291 (b)->Z_is_one ^= (t); \
292 } while(0)
293
294 /*-
295 * The ladder step, with branches, is
296 *
297 * k[i] == 0: S = add(R, S), R = dbl(R)
298 * k[i] == 1: R = add(S, R), S = dbl(S)
299 *
300 * Swapping R, S conditionally on k[i] leaves you with state
301 *
302 * k[i] == 0: T, U = R, S
303 * k[i] == 1: T, U = S, R
304 *
305 * Then perform the ECC ops.
306 *
307 * U = add(T, U)
308 * T = dbl(T)
309 *
310 * Which leaves you with state
311 *
312 * k[i] == 0: U = add(R, S), T = dbl(R)
313 * k[i] == 1: U = add(S, R), T = dbl(S)
314 *
315 * Swapping T, U conditionally on k[i] leaves you with state
316 *
317 * k[i] == 0: R, S = T, U
318 * k[i] == 1: R, S = U, T
319 *
320 * Which leaves you with state
321 *
322 * k[i] == 0: S = add(R, S), R = dbl(R)
323 * k[i] == 1: R = add(S, R), S = dbl(S)
324 *
325 * So we get the same logic, but instead of a branch it's a
326 * conditional swap, followed by ECC ops, then another conditional swap.
327 *
328 * Optimization: The end of iteration i and start of i-1 looks like
329 *
330 * ...
331 * CSWAP(k[i], R, S)
332 * ECC
333 * CSWAP(k[i], R, S)
334 * (next iteration)
335 * CSWAP(k[i-1], R, S)
336 * ECC
337 * CSWAP(k[i-1], R, S)
338 * ...
339 *
340 * So instead of two contiguous swaps, you can merge the condition
341 * bits and do a single swap.
342 *
343 * k[i] k[i-1] Outcome
344 * 0 0 No Swap
345 * 0 1 Swap
346 * 1 0 Swap
347 * 1 1 No Swap
348 *
349 * This is XOR. pbit tracks the previous bit of k.
350 */
351
352 for (i = cardinality_bits - 1; i >= 0; i--) {
353 kbit = BN_is_bit_set(k, i) ^ pbit;
354 EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
355
356 /* Perform a single step of the Montgomery ladder */
357 if (!ec_point_ladder_step(group, r, s, p, ctx)) {
358 ERR_raise(ERR_LIB_EC, EC_R_LADDER_STEP_FAILURE);
359 goto err;
360 }
361 /*
362 * pbit logic merges this cswap with that of the
363 * next iteration
364 */
365 pbit ^= kbit;
366 }
367 /* one final cswap to move the right value into r */
368 EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
369 #undef EC_POINT_CSWAP
370
371 /* Finalize ladder (and recover full point coordinates) */
372 if (!ec_point_ladder_post(group, r, s, p, ctx)) {
373 ERR_raise(ERR_LIB_EC, EC_R_LADDER_POST_FAILURE);
374 goto err;
375 }
376
377 ret = 1;
378
379 err:
380 EC_POINT_free(p);
381 EC_POINT_clear_free(s);
382 BN_CTX_end(ctx);
383
384 return ret;
385 }
386
387 #undef EC_POINT_BN_set_flags
388
389 /*
390 * Table could be optimised for the wNAF-based implementation,
391 * sometimes smaller windows will give better performance (thus the
392 * boundaries should be increased)
393 */
394 #define EC_window_bits_for_scalar_size(b) \
395 ((size_t) \
396 ((b) >= 2000 ? 6 : \
397 (b) >= 800 ? 5 : \
398 (b) >= 300 ? 4 : \
399 (b) >= 70 ? 3 : \
400 (b) >= 20 ? 2 : \
401 1))
402
403 /*-
404 * Compute
405 * \sum scalars[i]*points[i],
406 * also including
407 * scalar*generator
408 * in the addition if scalar != NULL
409 */
ossl_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)410 int ossl_ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
411 size_t num, const EC_POINT *points[],
412 const BIGNUM *scalars[], BN_CTX *ctx)
413 {
414 const EC_POINT *generator = NULL;
415 EC_POINT *tmp = NULL;
416 size_t totalnum;
417 size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
418 size_t pre_points_per_block = 0;
419 size_t i, j;
420 int k;
421 int r_is_inverted = 0;
422 int r_is_at_infinity = 1;
423 size_t *wsize = NULL; /* individual window sizes */
424 signed char **wNAF = NULL; /* individual wNAFs */
425 size_t *wNAF_len = NULL;
426 size_t max_len = 0;
427 size_t num_val;
428 EC_POINT **val = NULL; /* precomputation */
429 EC_POINT **v;
430 EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
431 * 'pre_comp->points' */
432 const EC_PRE_COMP *pre_comp = NULL;
433 int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
434 * treated like other scalars, i.e.
435 * precomputation is not available */
436 int ret = 0;
437
438 if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) {
439 /*-
440 * Handle the common cases where the scalar is secret, enforcing a
441 * scalar multiplication implementation based on a Montgomery ladder,
442 * with various timing attack defenses.
443 */
444 if ((scalar != group->order) && (scalar != NULL) && (num == 0)) {
445 /*-
446 * In this case we want to compute scalar * GeneratorPoint: this
447 * codepath is reached most prominently by (ephemeral) key
448 * generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
449 * ECDH keygen/first half), where the scalar is always secret. This
450 * is why we ignore if BN_FLG_CONSTTIME is actually set and we
451 * always call the ladder version.
452 */
453 return ossl_ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
454 }
455 if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) {
456 /*-
457 * In this case we want to compute scalar * VariablePoint: this
458 * codepath is reached most prominently by the second half of ECDH,
459 * where the secret scalar is multiplied by the peer's public point.
460 * To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
461 * actually set and we always call the ladder version.
462 */
463 return ossl_ec_scalar_mul_ladder(group, r, scalars[0], points[0],
464 ctx);
465 }
466 }
467
468 if (scalar != NULL) {
469 generator = EC_GROUP_get0_generator(group);
470 if (generator == NULL) {
471 ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
472 goto err;
473 }
474
475 /* look if we can use precomputed multiples of generator */
476
477 pre_comp = group->pre_comp.ec;
478 if (pre_comp && pre_comp->numblocks
479 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
480 0)) {
481 blocksize = pre_comp->blocksize;
482
483 /*
484 * determine maximum number of blocks that wNAF splitting may
485 * yield (NB: maximum wNAF length is bit length plus one)
486 */
487 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
488
489 /*
490 * we cannot use more blocks than we have precomputation for
491 */
492 if (numblocks > pre_comp->numblocks)
493 numblocks = pre_comp->numblocks;
494
495 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
496
497 /* check that pre_comp looks sane */
498 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
499 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
500 goto err;
501 }
502 } else {
503 /* can't use precomputation */
504 pre_comp = NULL;
505 numblocks = 1;
506 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
507 * 'scalars' */
508 }
509 }
510
511 totalnum = num + numblocks;
512
513 wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
514 wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
515 /* include space for pivot */
516 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
517 val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
518
519 /* Ensure wNAF is initialised in case we end up going to err */
520 if (wNAF != NULL)
521 wNAF[0] = NULL; /* preliminary pivot */
522
523 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
524 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
525 goto err;
526 }
527
528 /*
529 * num_val will be the total number of temporarily precomputed points
530 */
531 num_val = 0;
532
533 for (i = 0; i < num + num_scalar; i++) {
534 size_t bits;
535
536 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
537 wsize[i] = EC_window_bits_for_scalar_size(bits);
538 num_val += (size_t)1 << (wsize[i] - 1);
539 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
540 wNAF[i] =
541 bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
542 &wNAF_len[i]);
543 if (wNAF[i] == NULL)
544 goto err;
545 if (wNAF_len[i] > max_len)
546 max_len = wNAF_len[i];
547 }
548
549 if (numblocks) {
550 /* we go here iff scalar != NULL */
551
552 if (pre_comp == NULL) {
553 if (num_scalar != 1) {
554 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
555 goto err;
556 }
557 /* we have already generated a wNAF for 'scalar' */
558 } else {
559 signed char *tmp_wNAF = NULL;
560 size_t tmp_len = 0;
561
562 if (num_scalar != 0) {
563 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
564 goto err;
565 }
566
567 /*
568 * use the window size for which we have precomputation
569 */
570 wsize[num] = pre_comp->w;
571 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
572 if (!tmp_wNAF)
573 goto err;
574
575 if (tmp_len <= max_len) {
576 /*
577 * One of the other wNAFs is at least as long as the wNAF
578 * belonging to the generator, so wNAF splitting will not buy
579 * us anything.
580 */
581
582 numblocks = 1;
583 totalnum = num + 1; /* don't use wNAF splitting */
584 wNAF[num] = tmp_wNAF;
585 wNAF[num + 1] = NULL;
586 wNAF_len[num] = tmp_len;
587 /*
588 * pre_comp->points starts with the points that we need here:
589 */
590 val_sub[num] = pre_comp->points;
591 } else {
592 /*
593 * don't include tmp_wNAF directly into wNAF array - use wNAF
594 * splitting and include the blocks
595 */
596
597 signed char *pp;
598 EC_POINT **tmp_points;
599
600 if (tmp_len < numblocks * blocksize) {
601 /*
602 * possibly we can do with fewer blocks than estimated
603 */
604 numblocks = (tmp_len + blocksize - 1) / blocksize;
605 if (numblocks > pre_comp->numblocks) {
606 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
607 OPENSSL_free(tmp_wNAF);
608 goto err;
609 }
610 totalnum = num + numblocks;
611 }
612
613 /* split wNAF in 'numblocks' parts */
614 pp = tmp_wNAF;
615 tmp_points = pre_comp->points;
616
617 for (i = num; i < totalnum; i++) {
618 if (i < totalnum - 1) {
619 wNAF_len[i] = blocksize;
620 if (tmp_len < blocksize) {
621 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
622 OPENSSL_free(tmp_wNAF);
623 goto err;
624 }
625 tmp_len -= blocksize;
626 } else
627 /*
628 * last block gets whatever is left (this could be
629 * more or less than 'blocksize'!)
630 */
631 wNAF_len[i] = tmp_len;
632
633 wNAF[i + 1] = NULL;
634 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
635 if (wNAF[i] == NULL) {
636 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
637 OPENSSL_free(tmp_wNAF);
638 goto err;
639 }
640 memcpy(wNAF[i], pp, wNAF_len[i]);
641 if (wNAF_len[i] > max_len)
642 max_len = wNAF_len[i];
643
644 if (*tmp_points == NULL) {
645 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
646 OPENSSL_free(tmp_wNAF);
647 goto err;
648 }
649 val_sub[i] = tmp_points;
650 tmp_points += pre_points_per_block;
651 pp += blocksize;
652 }
653 OPENSSL_free(tmp_wNAF);
654 }
655 }
656 }
657
658 /*
659 * All points we precompute now go into a single array 'val'.
660 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
661 * subarray of 'pre_comp->points' if we already have precomputation.
662 */
663 val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
664 if (val == NULL) {
665 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
666 goto err;
667 }
668 val[num_val] = NULL; /* pivot element */
669
670 /* allocate points for precomputation */
671 v = val;
672 for (i = 0; i < num + num_scalar; i++) {
673 val_sub[i] = v;
674 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
675 *v = EC_POINT_new(group);
676 if (*v == NULL)
677 goto err;
678 v++;
679 }
680 }
681 if (!(v == val + num_val)) {
682 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
683 goto err;
684 }
685
686 if ((tmp = EC_POINT_new(group)) == NULL)
687 goto err;
688
689 /*-
690 * prepare precomputed values:
691 * val_sub[i][0] := points[i]
692 * val_sub[i][1] := 3 * points[i]
693 * val_sub[i][2] := 5 * points[i]
694 * ...
695 */
696 for (i = 0; i < num + num_scalar; i++) {
697 if (i < num) {
698 if (!EC_POINT_copy(val_sub[i][0], points[i]))
699 goto err;
700 } else {
701 if (!EC_POINT_copy(val_sub[i][0], generator))
702 goto err;
703 }
704
705 if (wsize[i] > 1) {
706 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
707 goto err;
708 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
709 if (!EC_POINT_add
710 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
711 goto err;
712 }
713 }
714 }
715
716 if (group->meth->points_make_affine == NULL
717 || !group->meth->points_make_affine(group, num_val, val, ctx))
718 goto err;
719
720 r_is_at_infinity = 1;
721
722 for (k = max_len - 1; k >= 0; k--) {
723 if (!r_is_at_infinity) {
724 if (!EC_POINT_dbl(group, r, r, ctx))
725 goto err;
726 }
727
728 for (i = 0; i < totalnum; i++) {
729 if (wNAF_len[i] > (size_t)k) {
730 int digit = wNAF[i][k];
731 int is_neg;
732
733 if (digit) {
734 is_neg = digit < 0;
735
736 if (is_neg)
737 digit = -digit;
738
739 if (is_neg != r_is_inverted) {
740 if (!r_is_at_infinity) {
741 if (!EC_POINT_invert(group, r, ctx))
742 goto err;
743 }
744 r_is_inverted = !r_is_inverted;
745 }
746
747 /* digit > 0 */
748
749 if (r_is_at_infinity) {
750 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
751 goto err;
752
753 /*-
754 * Apply coordinate blinding for EC_POINT.
755 *
756 * The underlying EC_METHOD can optionally implement this function:
757 * ossl_ec_point_blind_coordinates() returns 0 in case of errors or 1 on
758 * success or if coordinate blinding is not implemented for this
759 * group.
760 */
761 if (!ossl_ec_point_blind_coordinates(group, r, ctx)) {
762 ERR_raise(ERR_LIB_EC, EC_R_POINT_COORDINATES_BLIND_FAILURE);
763 goto err;
764 }
765
766 r_is_at_infinity = 0;
767 } else {
768 if (!EC_POINT_add
769 (group, r, r, val_sub[i][digit >> 1], ctx))
770 goto err;
771 }
772 }
773 }
774 }
775 }
776
777 if (r_is_at_infinity) {
778 if (!EC_POINT_set_to_infinity(group, r))
779 goto err;
780 } else {
781 if (r_is_inverted)
782 if (!EC_POINT_invert(group, r, ctx))
783 goto err;
784 }
785
786 ret = 1;
787
788 err:
789 EC_POINT_free(tmp);
790 OPENSSL_free(wsize);
791 OPENSSL_free(wNAF_len);
792 if (wNAF != NULL) {
793 signed char **w;
794
795 for (w = wNAF; *w != NULL; w++)
796 OPENSSL_free(*w);
797
798 OPENSSL_free(wNAF);
799 }
800 if (val != NULL) {
801 for (v = val; *v != NULL; v++)
802 EC_POINT_clear_free(*v);
803
804 OPENSSL_free(val);
805 }
806 OPENSSL_free(val_sub);
807 return ret;
808 }
809
810 /*-
811 * ossl_ec_wNAF_precompute_mult()
812 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
813 * for use with wNAF splitting as implemented in ossl_ec_wNAF_mul().
814 *
815 * 'pre_comp->points' is an array of multiples of the generator
816 * of the following form:
817 * points[0] = generator;
818 * points[1] = 3 * generator;
819 * ...
820 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
821 * points[2^(w-1)] = 2^blocksize * generator;
822 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
823 * ...
824 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
825 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
826 * ...
827 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
828 * points[2^(w-1)*numblocks] = NULL
829 */
ossl_ec_wNAF_precompute_mult(EC_GROUP * group,BN_CTX * ctx)830 int ossl_ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
831 {
832 const EC_POINT *generator;
833 EC_POINT *tmp_point = NULL, *base = NULL, **var;
834 const BIGNUM *order;
835 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
836 EC_POINT **points = NULL;
837 EC_PRE_COMP *pre_comp;
838 int ret = 0;
839 int used_ctx = 0;
840 #ifndef FIPS_MODULE
841 BN_CTX *new_ctx = NULL;
842 #endif
843
844 /* if there is an old EC_PRE_COMP object, throw it away */
845 EC_pre_comp_free(group);
846 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
847 return 0;
848
849 generator = EC_GROUP_get0_generator(group);
850 if (generator == NULL) {
851 ERR_raise(ERR_LIB_EC, EC_R_UNDEFINED_GENERATOR);
852 goto err;
853 }
854
855 #ifndef FIPS_MODULE
856 if (ctx == NULL)
857 ctx = new_ctx = BN_CTX_new();
858 #endif
859 if (ctx == NULL)
860 goto err;
861
862 BN_CTX_start(ctx);
863 used_ctx = 1;
864
865 order = EC_GROUP_get0_order(group);
866 if (order == NULL)
867 goto err;
868 if (BN_is_zero(order)) {
869 ERR_raise(ERR_LIB_EC, EC_R_UNKNOWN_ORDER);
870 goto err;
871 }
872
873 bits = BN_num_bits(order);
874 /*
875 * The following parameters mean we precompute (approximately) one point
876 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
877 * bit lengths, other parameter combinations might provide better
878 * efficiency.
879 */
880 blocksize = 8;
881 w = 4;
882 if (EC_window_bits_for_scalar_size(bits) > w) {
883 /* let's not make the window too small ... */
884 w = EC_window_bits_for_scalar_size(bits);
885 }
886
887 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
888 * to use for wNAF
889 * splitting */
890
891 pre_points_per_block = (size_t)1 << (w - 1);
892 num = pre_points_per_block * numblocks; /* number of points to compute
893 * and store */
894
895 points = OPENSSL_malloc(sizeof(*points) * (num + 1));
896 if (points == NULL) {
897 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
898 goto err;
899 }
900
901 var = points;
902 var[num] = NULL; /* pivot */
903 for (i = 0; i < num; i++) {
904 if ((var[i] = EC_POINT_new(group)) == NULL) {
905 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
906 goto err;
907 }
908 }
909
910 if ((tmp_point = EC_POINT_new(group)) == NULL
911 || (base = EC_POINT_new(group)) == NULL) {
912 ERR_raise(ERR_LIB_EC, ERR_R_MALLOC_FAILURE);
913 goto err;
914 }
915
916 if (!EC_POINT_copy(base, generator))
917 goto err;
918
919 /* do the precomputation */
920 for (i = 0; i < numblocks; i++) {
921 size_t j;
922
923 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
924 goto err;
925
926 if (!EC_POINT_copy(*var++, base))
927 goto err;
928
929 for (j = 1; j < pre_points_per_block; j++, var++) {
930 /*
931 * calculate odd multiples of the current base point
932 */
933 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
934 goto err;
935 }
936
937 if (i < numblocks - 1) {
938 /*
939 * get the next base (multiply current one by 2^blocksize)
940 */
941 size_t k;
942
943 if (blocksize <= 2) {
944 ERR_raise(ERR_LIB_EC, ERR_R_INTERNAL_ERROR);
945 goto err;
946 }
947
948 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
949 goto err;
950 for (k = 2; k < blocksize; k++) {
951 if (!EC_POINT_dbl(group, base, base, ctx))
952 goto err;
953 }
954 }
955 }
956
957 if (group->meth->points_make_affine == NULL
958 || !group->meth->points_make_affine(group, num, points, ctx))
959 goto err;
960
961 pre_comp->group = group;
962 pre_comp->blocksize = blocksize;
963 pre_comp->numblocks = numblocks;
964 pre_comp->w = w;
965 pre_comp->points = points;
966 points = NULL;
967 pre_comp->num = num;
968 SETPRECOMP(group, ec, pre_comp);
969 pre_comp = NULL;
970 ret = 1;
971
972 err:
973 if (used_ctx)
974 BN_CTX_end(ctx);
975 #ifndef FIPS_MODULE
976 BN_CTX_free(new_ctx);
977 #endif
978 EC_ec_pre_comp_free(pre_comp);
979 if (points) {
980 EC_POINT **p;
981
982 for (p = points; *p != NULL; p++)
983 EC_POINT_free(*p);
984 OPENSSL_free(points);
985 }
986 EC_POINT_free(tmp_point);
987 EC_POINT_free(base);
988 return ret;
989 }
990
ossl_ec_wNAF_have_precompute_mult(const EC_GROUP * group)991 int ossl_ec_wNAF_have_precompute_mult(const EC_GROUP *group)
992 {
993 return HAVEPRECOMP(group, ec);
994 }
995