1/*
2 * Copyright 2001-2018 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#include <string.h>
12#include <openssl/err.h>
13
14#include "internal/cryptlib.h"
15#include "crypto/bn.h"
16#include "ec_local.h"
17#include "internal/refcount.h"
18
19/*
20 * This file implements the wNAF-based interleaving multi-exponentiation method
21 * Formerly at:
22 * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
23 * You might now find it here:
24 * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
25 * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
26 * For multiplication with precomputation, we use wNAF splitting, formerly at:
27 * 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 CRYPTO_REF_COUNT 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_UP_REF(&pre->references, &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_DOWN_REF(&pre->references, &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#define EC_POINT_BN_set_flags(P, flags) do { \
105 BN_set_flags((P)->X, (flags)); \
106 BN_set_flags((P)->Y, (flags)); \
107 BN_set_flags((P)->Z, (flags)); \
108} while(0)
109
110/*-
111 * This functions computes a single point multiplication over the EC group,
112 * using, at a high level, a Montgomery ladder with conditional swaps, with
113 * various timing attack defenses.
114 *
115 * It performs either a fixed point multiplication
116 * (scalar * generator)
117 * when point is NULL, or a variable point multiplication
118 * (scalar * point)
119 * when point is not NULL.
120 *
121 * `scalar` cannot be NULL and should be in the range [0,n) otherwise all
122 * constant time bets are off (where n is the cardinality of the EC group).
123 *
124 * This function expects `group->order` and `group->cardinality` to be well
125 * defined and non-zero: it fails with an error code otherwise.
126 *
127 * NB: This says nothing about the constant-timeness of the ladder step
128 * implementation (i.e., the default implementation is based on EC_POINT_add and
129 * EC_POINT_dbl, which of course are not constant time themselves) or the
130 * underlying multiprecision arithmetic.
131 *
132 * The product is stored in `r`.
133 *
134 * This is an internal function: callers are in charge of ensuring that the
135 * input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
136 *
137 * Returns 1 on success, 0 otherwise.
138 */
139int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
140 const BIGNUM *scalar, const EC_POINT *point,
141 BN_CTX *ctx)
142{
143 int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
144 EC_POINT *p = NULL;
145 EC_POINT *s = NULL;
146 BIGNUM *k = NULL;
147 BIGNUM *lambda = NULL;
148 BIGNUM *cardinality = NULL;
149 int ret = 0;
150
151 /* early exit if the input point is the point at infinity */
152 if (point != NULL && EC_POINT_is_at_infinity(group, point))
153 return EC_POINT_set_to_infinity(group, r);
154
155 if (BN_is_zero(group->order)) {
156 ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER);
157 return 0;
158 }
159 if (BN_is_zero(group->cofactor)) {
160 ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR);
161 return 0;
162 }
163
164 BN_CTX_start(ctx);
165
166 if (((p = EC_POINT_new(group)) == NULL)
167 || ((s = EC_POINT_new(group)) == NULL)) {
168 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);
169 goto err;
170 }
171
172 if (point == NULL) {
173 if (!EC_POINT_copy(p, group->generator)) {
174 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);
175 goto err;
176 }
177 } else {
178 if (!EC_POINT_copy(p, point)) {
179 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);
180 goto err;
181 }
182 }
183
184 EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME);
185 EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
186 EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
187
188 cardinality = BN_CTX_get(ctx);
189 lambda = BN_CTX_get(ctx);
190 k = BN_CTX_get(ctx);
191 if (k == NULL) {
192 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);
193 goto err;
194 }
195
196 if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) {
197 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
198 goto err;
199 }
200
201 /*
202 * Group cardinalities are often on a word boundary.
203 * So when we pad the scalar, some timing diff might
204 * pop if it needs to be expanded due to carries.
205 * So expand ahead of time.
206 */
207 cardinality_bits = BN_num_bits(cardinality);
208 group_top = bn_get_top(cardinality);
209 if ((bn_wexpand(k, group_top + 2) == NULL)
210 || (bn_wexpand(lambda, group_top + 2) == NULL)) {
211 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
212 goto err;
213 }
214
215 if (!BN_copy(k, scalar)) {
216 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
217 goto err;
218 }
219
220 BN_set_flags(k, BN_FLG_CONSTTIME);
221
222 if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {
223 /*-
224 * this is an unusual input, and we don't guarantee
225 * constant-timeness
226 */
227 if (!BN_nnmod(k, k, cardinality, ctx)) {
228 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
229 goto err;
230 }
231 }
232
233 if (!BN_add(lambda, k, cardinality)) {
234 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
235 goto err;
236 }
237 BN_set_flags(lambda, BN_FLG_CONSTTIME);
238 if (!BN_add(k, lambda, cardinality)) {
239 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
240 goto err;
241 }
242 /*
243 * lambda := scalar + cardinality
244 * k := scalar + 2*cardinality
245 */
246 kbit = BN_is_bit_set(lambda, cardinality_bits);
247 BN_consttime_swap(kbit, k, lambda, group_top + 2);
248
249 group_top = bn_get_top(group->field);
250 if ((bn_wexpand(s->X, group_top) == NULL)
251 || (bn_wexpand(s->Y, group_top) == NULL)
252 || (bn_wexpand(s->Z, group_top) == NULL)
253 || (bn_wexpand(r->X, group_top) == NULL)
254 || (bn_wexpand(r->Y, group_top) == NULL)
255 || (bn_wexpand(r->Z, group_top) == NULL)
256 || (bn_wexpand(p->X, group_top) == NULL)
257 || (bn_wexpand(p->Y, group_top) == NULL)
258 || (bn_wexpand(p->Z, group_top) == NULL)) {
259 ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
260 goto err;
261 }
262
263 /*-
264 * Apply coordinate blinding for EC_POINT.
265 *
266 * The underlying EC_METHOD can optionally implement this function:
267 * ec_point_blind_coordinates() returns 0 in case of errors or 1 on
268 * success or if coordinate blinding is not implemented for this
269 * group.
270 */
271 if (!ec_point_blind_coordinates(group, p, ctx)) {
272 ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_POINT_COORDINATES_BLIND_FAILURE);
273 goto err;
274 }
275
276 /* Initialize the Montgomery ladder */
277 if (!ec_point_ladder_pre(group, r, s, p, ctx)) {
278 ECerr(EC_F_EC_SCALAR_MUL_LADDER, 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 ECerr(EC_F_EC_SCALAR_MUL_LADDER, 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 ECerr(EC_F_EC_SCALAR_MUL_LADDER, 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 * TODO: table should 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 */
410int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
411 size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
412 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 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 ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);
464 }
465 }
466
467 if (scalar != NULL) {
468 generator = EC_GROUP_get0_generator(group);
469 if (generator == NULL) {
470 ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
471 goto err;
472 }
473
474 /* look if we can use precomputed multiples of generator */
475
476 pre_comp = group->pre_comp.ec;
477 if (pre_comp && pre_comp->numblocks
478 && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
479 0)) {
480 blocksize = pre_comp->blocksize;
481
482 /*
483 * determine maximum number of blocks that wNAF splitting may
484 * yield (NB: maximum wNAF length is bit length plus one)
485 */
486 numblocks = (BN_num_bits(scalar) / blocksize) + 1;
487
488 /*
489 * we cannot use more blocks than we have precomputation for
490 */
491 if (numblocks > pre_comp->numblocks)
492 numblocks = pre_comp->numblocks;
493
494 pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
495
496 /* check that pre_comp looks sane */
497 if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
498 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
499 goto err;
500 }
501 } else {
502 /* can't use precomputation */
503 pre_comp = NULL;
504 numblocks = 1;
505 num_scalar = 1; /* treat 'scalar' like 'num'-th element of
506 * 'scalars' */
507 }
508 }
509
510 totalnum = num + numblocks;
511
512 wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
513 wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
514 /* include space for pivot */
515 wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
516 val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
517
518 /* Ensure wNAF is initialised in case we end up going to err */
519 if (wNAF != NULL)
520 wNAF[0] = NULL; /* preliminary pivot */
521
522 if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
523 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
524 goto err;
525 }
526
527 /*
528 * num_val will be the total number of temporarily precomputed points
529 */
530 num_val = 0;
531
532 for (i = 0; i < num + num_scalar; i++) {
533 size_t bits;
534
535 bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
536 wsize[i] = EC_window_bits_for_scalar_size(bits);
537 num_val += (size_t)1 << (wsize[i] - 1);
538 wNAF[i + 1] = NULL; /* make sure we always have a pivot */
539 wNAF[i] =
540 bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
541 &wNAF_len[i]);
542 if (wNAF[i] == NULL)
543 goto err;
544 if (wNAF_len[i] > max_len)
545 max_len = wNAF_len[i];
546 }
547
548 if (numblocks) {
549 /* we go here iff scalar != NULL */
550
551 if (pre_comp == NULL) {
552 if (num_scalar != 1) {
553 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
554 goto err;
555 }
556 /* we have already generated a wNAF for 'scalar' */
557 } else {
558 signed char *tmp_wNAF = NULL;
559 size_t tmp_len = 0;
560
561 if (num_scalar != 0) {
562 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
563 goto err;
564 }
565
566 /*
567 * use the window size for which we have precomputation
568 */
569 wsize[num] = pre_comp->w;
570 tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
571 if (!tmp_wNAF)
572 goto err;
573
574 if (tmp_len <= max_len) {
575 /*
576 * One of the other wNAFs is at least as long as the wNAF
577 * belonging to the generator, so wNAF splitting will not buy
578 * us anything.
579 */
580
581 numblocks = 1;
582 totalnum = num + 1; /* don't use wNAF splitting */
583 wNAF[num] = tmp_wNAF;
584 wNAF[num + 1] = NULL;
585 wNAF_len[num] = tmp_len;
586 /*
587 * pre_comp->points starts with the points that we need here:
588 */
589 val_sub[num] = pre_comp->points;
590 } else {
591 /*
592 * don't include tmp_wNAF directly into wNAF array - use wNAF
593 * splitting and include the blocks
594 */
595
596 signed char *pp;
597 EC_POINT **tmp_points;
598
599 if (tmp_len < numblocks * blocksize) {
600 /*
601 * possibly we can do with fewer blocks than estimated
602 */
603 numblocks = (tmp_len + blocksize - 1) / blocksize;
604 if (numblocks > pre_comp->numblocks) {
605 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
606 OPENSSL_free(tmp_wNAF);
607 goto err;
608 }
609 totalnum = num + numblocks;
610 }
611
612 /* split wNAF in 'numblocks' parts */
613 pp = tmp_wNAF;
614 tmp_points = pre_comp->points;
615
616 for (i = num; i < totalnum; i++) {
617 if (i < totalnum - 1) {
618 wNAF_len[i] = blocksize;
619 if (tmp_len < blocksize) {
620 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
621 OPENSSL_free(tmp_wNAF);
622 goto err;
623 }
624 tmp_len -= blocksize;
625 } else
626 /*
627 * last block gets whatever is left (this could be
628 * more or less than 'blocksize'!)
629 */
630 wNAF_len[i] = tmp_len;
631
632 wNAF[i + 1] = NULL;
633 wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
634 if (wNAF[i] == NULL) {
635 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
636 OPENSSL_free(tmp_wNAF);
637 goto err;
638 }
639 memcpy(wNAF[i], pp, wNAF_len[i]);
640 if (wNAF_len[i] > max_len)
641 max_len = wNAF_len[i];
642
643 if (*tmp_points == NULL) {
644 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
645 OPENSSL_free(tmp_wNAF);
646 goto err;
647 }
648 val_sub[i] = tmp_points;
649 tmp_points += pre_points_per_block;
650 pp += blocksize;
651 }
652 OPENSSL_free(tmp_wNAF);
653 }
654 }
655 }
656
657 /*
658 * All points we precompute now go into a single array 'val'.
659 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
660 * subarray of 'pre_comp->points' if we already have precomputation.
661 */
662 val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
663 if (val == NULL) {
664 ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
665 goto err;
666 }
667 val[num_val] = NULL; /* pivot element */
668
669 /* allocate points for precomputation */
670 v = val;
671 for (i = 0; i < num + num_scalar; i++) {
672 val_sub[i] = v;
673 for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
674 *v = EC_POINT_new(group);
675 if (*v == NULL)
676 goto err;
677 v++;
678 }
679 }
680 if (!(v == val + num_val)) {
681 ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
682 goto err;
683 }
684
685 if ((tmp = EC_POINT_new(group)) == NULL)
686 goto err;
687
688 /*-
689 * prepare precomputed values:
690 * val_sub[i][0] := points[i]
691 * val_sub[i][1] := 3 * points[i]
692 * val_sub[i][2] := 5 * points[i]
693 * ...
694 */
695 for (i = 0; i < num + num_scalar; i++) {
696 if (i < num) {
697 if (!EC_POINT_copy(val_sub[i][0], points[i]))
698 goto err;
699 } else {
700 if (!EC_POINT_copy(val_sub[i][0], generator))
701 goto err;
702 }
703
704 if (wsize[i] > 1) {
705 if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
706 goto err;
707 for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
708 if (!EC_POINT_add
709 (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
710 goto err;
711 }
712 }
713 }
714
715 if (!EC_POINTs_make_affine(group, num_val, val, ctx))
716 goto err;
717
718 r_is_at_infinity = 1;
719
720 for (k = max_len - 1; k >= 0; k--) {
721 if (!r_is_at_infinity) {
722 if (!EC_POINT_dbl(group, r, r, ctx))
723 goto err;
724 }
725
726 for (i = 0; i < totalnum; i++) {
727 if (wNAF_len[i] > (size_t)k) {
728 int digit = wNAF[i][k];
729 int is_neg;
730
731 if (digit) {
732 is_neg = digit < 0;
733
734 if (is_neg)
735 digit = -digit;
736
737 if (is_neg != r_is_inverted) {
738 if (!r_is_at_infinity) {
739 if (!EC_POINT_invert(group, r, ctx))
740 goto err;
741 }
742 r_is_inverted = !r_is_inverted;
743 }
744
745 /* digit > 0 */
746
747 if (r_is_at_infinity) {
748 if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
749 goto err;
750 r_is_at_infinity = 0;
751 } else {
752 if (!EC_POINT_add
753 (group, r, r, val_sub[i][digit >> 1], ctx))
754 goto err;
755 }
756 }
757 }
758 }
759 }
760
761 if (r_is_at_infinity) {
762 if (!EC_POINT_set_to_infinity(group, r))
763 goto err;
764 } else {
765 if (r_is_inverted)
766 if (!EC_POINT_invert(group, r, ctx))
767 goto err;
768 }
769
770 ret = 1;
771
772 err:
773 EC_POINT_free(tmp);
774 OPENSSL_free(wsize);
775 OPENSSL_free(wNAF_len);
776 if (wNAF != NULL) {
777 signed char **w;
778
779 for (w = wNAF; *w != NULL; w++)
780 OPENSSL_free(*w);
781
782 OPENSSL_free(wNAF);
783 }
784 if (val != NULL) {
785 for (v = val; *v != NULL; v++)
786 EC_POINT_clear_free(*v);
787
788 OPENSSL_free(val);
789 }
790 OPENSSL_free(val_sub);
791 return ret;
792}
793
794/*-
795 * ec_wNAF_precompute_mult()
796 * creates an EC_PRE_COMP object with preprecomputed multiples of the generator
797 * for use with wNAF splitting as implemented in ec_wNAF_mul().
798 *
799 * 'pre_comp->points' is an array of multiples of the generator
800 * of the following form:
801 * points[0] = generator;
802 * points[1] = 3 * generator;
803 * ...
804 * points[2^(w-1)-1] = (2^(w-1)-1) * generator;
805 * points[2^(w-1)] = 2^blocksize * generator;
806 * points[2^(w-1)+1] = 3 * 2^blocksize * generator;
807 * ...
808 * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
809 * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
810 * ...
811 * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
812 * points[2^(w-1)*numblocks] = NULL
813 */
814int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
815{
816 const EC_POINT *generator;
817 EC_POINT *tmp_point = NULL, *base = NULL, **var;
818 const BIGNUM *order;
819 size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
820 EC_POINT **points = NULL;
821 EC_PRE_COMP *pre_comp;
822 int ret = 0;
823#ifndef FIPS_MODE
824 BN_CTX *new_ctx = NULL;
825#endif
826
827 /* if there is an old EC_PRE_COMP object, throw it away */
828 EC_pre_comp_free(group);
829 if ((pre_comp = ec_pre_comp_new(group)) == NULL)
830 return 0;
831
832 generator = EC_GROUP_get0_generator(group);
833 if (generator == NULL) {
834 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
835 goto err;
836 }
837
838#ifndef FIPS_MODE
839 if (ctx == NULL)
840 ctx = new_ctx = BN_CTX_new();
841#endif
842 if (ctx == NULL)
843 goto err;
844
845 BN_CTX_start(ctx);
846
847 order = EC_GROUP_get0_order(group);
848 if (order == NULL)
849 goto err;
850 if (BN_is_zero(order)) {
851 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
852 goto err;
853 }
854
855 bits = BN_num_bits(order);
856 /*
857 * The following parameters mean we precompute (approximately) one point
858 * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
859 * bit lengths, other parameter combinations might provide better
860 * efficiency.
861 */
862 blocksize = 8;
863 w = 4;
864 if (EC_window_bits_for_scalar_size(bits) > w) {
865 /* let's not make the window too small ... */
866 w = EC_window_bits_for_scalar_size(bits);
867 }
868
869 numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
870 * to use for wNAF
871 * splitting */
872
873 pre_points_per_block = (size_t)1 << (w - 1);
874 num = pre_points_per_block * numblocks; /* number of points to compute
875 * and store */
876
877 points = OPENSSL_malloc(sizeof(*points) * (num + 1));
878 if (points == NULL) {
879 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
880 goto err;
881 }
882
883 var = points;
884 var[num] = NULL; /* pivot */
885 for (i = 0; i < num; i++) {
886 if ((var[i] = EC_POINT_new(group)) == NULL) {
887 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
888 goto err;
889 }
890 }
891
892 if ((tmp_point = EC_POINT_new(group)) == NULL
893 || (base = EC_POINT_new(group)) == NULL) {
894 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
895 goto err;
896 }
897
898 if (!EC_POINT_copy(base, generator))
899 goto err;
900
901 /* do the precomputation */
902 for (i = 0; i < numblocks; i++) {
903 size_t j;
904
905 if (!EC_POINT_dbl(group, tmp_point, base, ctx))
906 goto err;
907
908 if (!EC_POINT_copy(*var++, base))
909 goto err;
910
911 for (j = 1; j < pre_points_per_block; j++, var++) {
912 /*
913 * calculate odd multiples of the current base point
914 */
915 if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
916 goto err;
917 }
918
919 if (i < numblocks - 1) {
920 /*
921 * get the next base (multiply current one by 2^blocksize)
922 */
923 size_t k;
924
925 if (blocksize <= 2) {
926 ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
927 goto err;
928 }
929
930 if (!EC_POINT_dbl(group, base, tmp_point, ctx))
931 goto err;
932 for (k = 2; k < blocksize; k++) {
933 if (!EC_POINT_dbl(group, base, base, ctx))
934 goto err;
935 }
936 }
937 }
938
939 if (!EC_POINTs_make_affine(group, num, points, ctx))
940 goto err;
941
942 pre_comp->group = group;
943 pre_comp->blocksize = blocksize;
944 pre_comp->numblocks = numblocks;
945 pre_comp->w = w;
946 pre_comp->points = points;
947 points = NULL;
948 pre_comp->num = num;
949 SETPRECOMP(group, ec, pre_comp);
950 pre_comp = NULL;
951 ret = 1;
952
953 err:
954 BN_CTX_end(ctx);
955#ifndef FIPS_MODE
956 BN_CTX_free(new_ctx);
957#endif
958 EC_ec_pre_comp_free(pre_comp);
959 if (points) {
960 EC_POINT **p;
961
962 for (p = points; *p != NULL; p++)
963 EC_POINT_free(*p);
964 OPENSSL_free(points);
965 }
966 EC_POINT_free(tmp_point);
967 EC_POINT_free(base);
968 return ret;
969}
970
971int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
972{
973 return HAVEPRECOMP(group, ec);
974}
975