1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
|
/*
* Copyright 2001-2020 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
*
* Licensed under the Apache License 2.0 (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
/*
* ECDSA low level APIs are deprecated for public use, but still ok for
* internal use.
*/
#include "internal/deprecated.h"
#include <string.h>
#include <openssl/err.h>
#include "internal/cryptlib.h"
#include "crypto/bn.h"
#include "ec_local.h"
#include "internal/refcount.h"
/*
* This file implements the wNAF-based interleaving multi-exponentiation method
* Formerly at:
* http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
* You might now find it here:
* http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
* http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
* For multiplication with precomputation, we use wNAF splitting, formerly at:
* http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
*/
/* structure for precomputed multiples of the generator */
struct ec_pre_comp_st {
const EC_GROUP *group; /* parent EC_GROUP object */
size_t blocksize; /* block size for wNAF splitting */
size_t numblocks; /* max. number of blocks for which we have
* precomputation */
size_t w; /* window size */
EC_POINT **points; /* array with pre-calculated multiples of
* generator: 'num' pointers to EC_POINT
* objects followed by a NULL */
size_t num; /* numblocks * 2^(w-1) */
CRYPTO_REF_COUNT references;
CRYPTO_RWLOCK *lock;
};
static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
{
EC_PRE_COMP *ret = NULL;
if (!group)
return NULL;
ret = OPENSSL_zalloc(sizeof(*ret));
if (ret == NULL) {
ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
return ret;
}
ret->group = group;
ret->blocksize = 8; /* default */
ret->w = 4; /* default */
ret->references = 1;
ret->lock = CRYPTO_THREAD_lock_new();
if (ret->lock == NULL) {
ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
OPENSSL_free(ret);
return NULL;
}
return ret;
}
EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)
{
int i;
if (pre != NULL)
CRYPTO_UP_REF(&pre->references, &i, pre->lock);
return pre;
}
void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
{
int i;
if (pre == NULL)
return;
CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
REF_PRINT_COUNT("EC_ec", pre);
if (i > 0)
return;
REF_ASSERT_ISNT(i < 0);
if (pre->points != NULL) {
EC_POINT **pts;
for (pts = pre->points; *pts != NULL; pts++)
EC_POINT_free(*pts);
OPENSSL_free(pre->points);
}
CRYPTO_THREAD_lock_free(pre->lock);
OPENSSL_free(pre);
}
#define EC_POINT_BN_set_flags(P, flags) do { \
BN_set_flags((P)->X, (flags)); \
BN_set_flags((P)->Y, (flags)); \
BN_set_flags((P)->Z, (flags)); \
} while(0)
/*-
* This functions computes a single point multiplication over the EC group,
* using, at a high level, a Montgomery ladder with conditional swaps, with
* various timing attack defenses.
*
* It performs either a fixed point multiplication
* (scalar * generator)
* when point is NULL, or a variable point multiplication
* (scalar * point)
* when point is not NULL.
*
* `scalar` cannot be NULL and should be in the range [0,n) otherwise all
* constant time bets are off (where n is the cardinality of the EC group).
*
* This function expects `group->order` and `group->cardinality` to be well
* defined and non-zero: it fails with an error code otherwise.
*
* NB: This says nothing about the constant-timeness of the ladder step
* implementation (i.e., the default implementation is based on EC_POINT_add and
* EC_POINT_dbl, which of course are not constant time themselves) or the
* underlying multiprecision arithmetic.
*
* The product is stored in `r`.
*
* This is an internal function: callers are in charge of ensuring that the
* input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
*
* Returns 1 on success, 0 otherwise.
*/
int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
const BIGNUM *scalar, const EC_POINT *point,
BN_CTX *ctx)
{
int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
EC_POINT *p = NULL;
EC_POINT *s = NULL;
BIGNUM *k = NULL;
BIGNUM *lambda = NULL;
BIGNUM *cardinality = NULL;
int ret = 0;
/* early exit if the input point is the point at infinity */
if (point != NULL && EC_POINT_is_at_infinity(group, point))
return EC_POINT_set_to_infinity(group, r);
if (BN_is_zero(group->order)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER);
return 0;
}
if (BN_is_zero(group->cofactor)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR);
return 0;
}
BN_CTX_start(ctx);
if (((p = EC_POINT_new(group)) == NULL)
|| ((s = EC_POINT_new(group)) == NULL)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);
goto err;
}
if (point == NULL) {
if (!EC_POINT_copy(p, group->generator)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);
goto err;
}
} else {
if (!EC_POINT_copy(p, point)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);
goto err;
}
}
EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME);
EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
cardinality = BN_CTX_get(ctx);
lambda = BN_CTX_get(ctx);
k = BN_CTX_get(ctx);
if (k == NULL) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);
goto err;
}
if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
goto err;
}
/*
* Group cardinalities are often on a word boundary.
* So when we pad the scalar, some timing diff might
* pop if it needs to be expanded due to carries.
* So expand ahead of time.
*/
cardinality_bits = BN_num_bits(cardinality);
group_top = bn_get_top(cardinality);
if ((bn_wexpand(k, group_top + 2) == NULL)
|| (bn_wexpand(lambda, group_top + 2) == NULL)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
goto err;
}
if (!BN_copy(k, scalar)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
goto err;
}
BN_set_flags(k, BN_FLG_CONSTTIME);
if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {
/*-
* this is an unusual input, and we don't guarantee
* constant-timeness
*/
if (!BN_nnmod(k, k, cardinality, ctx)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
goto err;
}
}
if (!BN_add(lambda, k, cardinality)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
goto err;
}
BN_set_flags(lambda, BN_FLG_CONSTTIME);
if (!BN_add(k, lambda, cardinality)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
goto err;
}
/*
* lambda := scalar + cardinality
* k := scalar + 2*cardinality
*/
kbit = BN_is_bit_set(lambda, cardinality_bits);
BN_consttime_swap(kbit, k, lambda, group_top + 2);
group_top = bn_get_top(group->field);
if ((bn_wexpand(s->X, group_top) == NULL)
|| (bn_wexpand(s->Y, group_top) == NULL)
|| (bn_wexpand(s->Z, group_top) == NULL)
|| (bn_wexpand(r->X, group_top) == NULL)
|| (bn_wexpand(r->Y, group_top) == NULL)
|| (bn_wexpand(r->Z, group_top) == NULL)
|| (bn_wexpand(p->X, group_top) == NULL)
|| (bn_wexpand(p->Y, group_top) == NULL)
|| (bn_wexpand(p->Z, group_top) == NULL)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
goto err;
}
/* ensure input point is in affine coords for ladder step efficiency */
if (!p->Z_is_one && !EC_POINT_make_affine(group, p, ctx)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);
goto err;
}
/* Initialize the Montgomery ladder */
if (!ec_point_ladder_pre(group, r, s, p, ctx)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_PRE_FAILURE);
goto err;
}
/* top bit is a 1, in a fixed pos */
pbit = 1;
#define EC_POINT_CSWAP(c, a, b, w, t) do { \
BN_consttime_swap(c, (a)->X, (b)->X, w); \
BN_consttime_swap(c, (a)->Y, (b)->Y, w); \
BN_consttime_swap(c, (a)->Z, (b)->Z, w); \
t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
(a)->Z_is_one ^= (t); \
(b)->Z_is_one ^= (t); \
} while(0)
/*-
* The ladder step, with branches, is
*
* k[i] == 0: S = add(R, S), R = dbl(R)
* k[i] == 1: R = add(S, R), S = dbl(S)
*
* Swapping R, S conditionally on k[i] leaves you with state
*
* k[i] == 0: T, U = R, S
* k[i] == 1: T, U = S, R
*
* Then perform the ECC ops.
*
* U = add(T, U)
* T = dbl(T)
*
* Which leaves you with state
*
* k[i] == 0: U = add(R, S), T = dbl(R)
* k[i] == 1: U = add(S, R), T = dbl(S)
*
* Swapping T, U conditionally on k[i] leaves you with state
*
* k[i] == 0: R, S = T, U
* k[i] == 1: R, S = U, T
*
* Which leaves you with state
*
* k[i] == 0: S = add(R, S), R = dbl(R)
* k[i] == 1: R = add(S, R), S = dbl(S)
*
* So we get the same logic, but instead of a branch it's a
* conditional swap, followed by ECC ops, then another conditional swap.
*
* Optimization: The end of iteration i and start of i-1 looks like
*
* ...
* CSWAP(k[i], R, S)
* ECC
* CSWAP(k[i], R, S)
* (next iteration)
* CSWAP(k[i-1], R, S)
* ECC
* CSWAP(k[i-1], R, S)
* ...
*
* So instead of two contiguous swaps, you can merge the condition
* bits and do a single swap.
*
* k[i] k[i-1] Outcome
* 0 0 No Swap
* 0 1 Swap
* 1 0 Swap
* 1 1 No Swap
*
* This is XOR. pbit tracks the previous bit of k.
*/
for (i = cardinality_bits - 1; i >= 0; i--) {
kbit = BN_is_bit_set(k, i) ^ pbit;
EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
/* Perform a single step of the Montgomery ladder */
if (!ec_point_ladder_step(group, r, s, p, ctx)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_STEP_FAILURE);
goto err;
}
/*
* pbit logic merges this cswap with that of the
* next iteration
*/
pbit ^= kbit;
}
/* one final cswap to move the right value into r */
EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
#undef EC_POINT_CSWAP
/* Finalize ladder (and recover full point coordinates) */
if (!ec_point_ladder_post(group, r, s, p, ctx)) {
ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_POST_FAILURE);
goto err;
}
ret = 1;
err:
EC_POINT_free(p);
EC_POINT_clear_free(s);
BN_CTX_end(ctx);
return ret;
}
#undef EC_POINT_BN_set_flags
/*
* TODO: table should be optimised for the wNAF-based implementation,
* sometimes smaller windows will give better performance (thus the
* boundaries should be increased)
*/
#define EC_window_bits_for_scalar_size(b) \
((size_t) \
((b) >= 2000 ? 6 : \
(b) >= 800 ? 5 : \
(b) >= 300 ? 4 : \
(b) >= 70 ? 3 : \
(b) >= 20 ? 2 : \
1))
/*-
* Compute
* \sum scalars[i]*points[i],
* also including
* scalar*generator
* in the addition if scalar != NULL
*/
int 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)
{
const EC_POINT *generator = NULL;
EC_POINT *tmp = NULL;
size_t totalnum;
size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
size_t pre_points_per_block = 0;
size_t i, j;
int k;
int r_is_inverted = 0;
int r_is_at_infinity = 1;
size_t *wsize = NULL; /* individual window sizes */
signed char **wNAF = NULL; /* individual wNAFs */
size_t *wNAF_len = NULL;
size_t max_len = 0;
size_t num_val;
EC_POINT **val = NULL; /* precomputation */
EC_POINT **v;
EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
* 'pre_comp->points' */
const EC_PRE_COMP *pre_comp = NULL;
int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
* treated like other scalars, i.e.
* precomputation is not available */
int ret = 0;
if (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) {
/*-
* Handle the common cases where the scalar is secret, enforcing a
* scalar multiplication implementation based on a Montgomery ladder,
* with various timing attack defenses.
*/
if ((scalar != group->order) && (scalar != NULL) && (num == 0)) {
/*-
* In this case we want to compute scalar * GeneratorPoint: this
* codepath is reached most prominently by (ephemeral) key
* generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
* ECDH keygen/first half), where the scalar is always secret. This
* is why we ignore if BN_FLG_CONSTTIME is actually set and we
* always call the ladder version.
*/
return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
}
if ((scalar == NULL) && (num == 1) && (scalars[0] != group->order)) {
/*-
* In this case we want to compute scalar * VariablePoint: this
* codepath is reached most prominently by the second half of ECDH,
* where the secret scalar is multiplied by the peer's public point.
* To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
* actually set and we always call the ladder version.
*/
return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);
}
}
if (scalar != NULL) {
generator = EC_GROUP_get0_generator(group);
if (generator == NULL) {
ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
goto err;
}
/* look if we can use precomputed multiples of generator */
pre_comp = group->pre_comp.ec;
if (pre_comp && pre_comp->numblocks
&& (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
0)) {
blocksize = pre_comp->blocksize;
/*
* determine maximum number of blocks that wNAF splitting may
* yield (NB: maximum wNAF length is bit length plus one)
*/
numblocks = (BN_num_bits(scalar) / blocksize) + 1;
/*
* we cannot use more blocks than we have precomputation for
*/
if (numblocks > pre_comp->numblocks)
numblocks = pre_comp->numblocks;
pre_points_per_block = (size_t)1 << (pre_comp->w - 1);
/* check that pre_comp looks sane */
if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
} else {
/* can't use precomputation */
pre_comp = NULL;
numblocks = 1;
num_scalar = 1; /* treat 'scalar' like 'num'-th element of
* 'scalars' */
}
}
totalnum = num + numblocks;
wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0]));
wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0]));
/* include space for pivot */
wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
/* Ensure wNAF is initialised in case we end up going to err */
if (wNAF != NULL)
wNAF[0] = NULL; /* preliminary pivot */
if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
goto err;
}
/*
* num_val will be the total number of temporarily precomputed points
*/
num_val = 0;
for (i = 0; i < num + num_scalar; i++) {
size_t bits;
bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
wsize[i] = EC_window_bits_for_scalar_size(bits);
num_val += (size_t)1 << (wsize[i] - 1);
wNAF[i + 1] = NULL; /* make sure we always have a pivot */
wNAF[i] =
bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i],
&wNAF_len[i]);
if (wNAF[i] == NULL)
goto err;
if (wNAF_len[i] > max_len)
max_len = wNAF_len[i];
}
if (numblocks) {
/* we go here iff scalar != NULL */
if (pre_comp == NULL) {
if (num_scalar != 1) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
/* we have already generated a wNAF for 'scalar' */
} else {
signed char *tmp_wNAF = NULL;
size_t tmp_len = 0;
if (num_scalar != 0) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
/*
* use the window size for which we have precomputation
*/
wsize[num] = pre_comp->w;
tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len);
if (!tmp_wNAF)
goto err;
if (tmp_len <= max_len) {
/*
* One of the other wNAFs is at least as long as the wNAF
* belonging to the generator, so wNAF splitting will not buy
* us anything.
*/
numblocks = 1;
totalnum = num + 1; /* don't use wNAF splitting */
wNAF[num] = tmp_wNAF;
wNAF[num + 1] = NULL;
wNAF_len[num] = tmp_len;
/*
* pre_comp->points starts with the points that we need here:
*/
val_sub[num] = pre_comp->points;
} else {
/*
* don't include tmp_wNAF directly into wNAF array - use wNAF
* splitting and include the blocks
*/
signed char *pp;
EC_POINT **tmp_points;
if (tmp_len < numblocks * blocksize) {
/*
* possibly we can do with fewer blocks than estimated
*/
numblocks = (tmp_len + blocksize - 1) / blocksize;
if (numblocks > pre_comp->numblocks) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
OPENSSL_free(tmp_wNAF);
goto err;
}
totalnum = num + numblocks;
}
/* split wNAF in 'numblocks' parts */
pp = tmp_wNAF;
tmp_points = pre_comp->points;
for (i = num; i < totalnum; i++) {
if (i < totalnum - 1) {
wNAF_len[i] = blocksize;
if (tmp_len < blocksize) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
OPENSSL_free(tmp_wNAF);
goto err;
}
tmp_len -= blocksize;
} else
/*
* last block gets whatever is left (this could be
* more or less than 'blocksize'!)
*/
wNAF_len[i] = tmp_len;
wNAF[i + 1] = NULL;
wNAF[i] = OPENSSL_malloc(wNAF_len[i]);
if (wNAF[i] == NULL) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
OPENSSL_free(tmp_wNAF);
goto err;
}
memcpy(wNAF[i], pp, wNAF_len[i]);
if (wNAF_len[i] > max_len)
max_len = wNAF_len[i];
if (*tmp_points == NULL) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
OPENSSL_free(tmp_wNAF);
goto err;
}
val_sub[i] = tmp_points;
tmp_points += pre_points_per_block;
pp += blocksize;
}
OPENSSL_free(tmp_wNAF);
}
}
}
/*
* All points we precompute now go into a single array 'val'.
* 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a
* subarray of 'pre_comp->points' if we already have precomputation.
*/
val = OPENSSL_malloc((num_val + 1) * sizeof(val[0]));
if (val == NULL) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
goto err;
}
val[num_val] = NULL; /* pivot element */
/* allocate points for precomputation */
v = val;
for (i = 0; i < num + num_scalar; i++) {
val_sub[i] = v;
for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) {
*v = EC_POINT_new(group);
if (*v == NULL)
goto err;
v++;
}
}
if (!(v == val + num_val)) {
ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR);
goto err;
}
if ((tmp = EC_POINT_new(group)) == NULL)
goto err;
/*-
* prepare precomputed values:
* val_sub[i][0] := points[i]
* val_sub[i][1] := 3 * points[i]
* val_sub[i][2] := 5 * points[i]
* ...
*/
for (i = 0; i < num + num_scalar; i++) {
if (i < num) {
if (!EC_POINT_copy(val_sub[i][0], points[i]))
goto err;
} else {
if (!EC_POINT_copy(val_sub[i][0], generator))
goto err;
}
if (wsize[i] > 1) {
if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
goto err;
for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) {
if (!EC_POINT_add
(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
goto err;
}
}
}
if (!EC_POINTs_make_affine(group, num_val, val, ctx))
goto err;
r_is_at_infinity = 1;
for (k = max_len - 1; k >= 0; k--) {
if (!r_is_at_infinity) {
if (!EC_POINT_dbl(group, r, r, ctx))
goto err;
}
for (i = 0; i < totalnum; i++) {
if (wNAF_len[i] > (size_t)k) {
int digit = wNAF[i][k];
int is_neg;
if (digit) {
is_neg = digit < 0;
if (is_neg)
digit = -digit;
if (is_neg != r_is_inverted) {
if (!r_is_at_infinity) {
if (!EC_POINT_invert(group, r, ctx))
goto err;
}
r_is_inverted = !r_is_inverted;
}
/* digit > 0 */
if (r_is_at_infinity) {
if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
goto err;
/*-
* Apply coordinate blinding for EC_POINT.
*
* The underlying EC_METHOD can optionally implement this function:
* ec_point_blind_coordinates() returns 0 in case of errors or 1 on
* success or if coordinate blinding is not implemented for this
* group.
*/
if (!ec_point_blind_coordinates(group, r, ctx)) {
ECerr(EC_F_EC_WNAF_MUL, EC_R_POINT_COORDINATES_BLIND_FAILURE);
goto err;
}
r_is_at_infinity = 0;
} else {
if (!EC_POINT_add
(group, r, r, val_sub[i][digit >> 1], ctx))
goto err;
}
}
}
}
}
if (r_is_at_infinity) {
if (!EC_POINT_set_to_infinity(group, r))
goto err;
} else {
if (r_is_inverted)
if (!EC_POINT_invert(group, r, ctx))
goto err;
}
ret = 1;
err:
EC_POINT_free(tmp);
OPENSSL_free(wsize);
OPENSSL_free(wNAF_len);
if (wNAF != NULL) {
signed char **w;
for (w = wNAF; *w != NULL; w++)
OPENSSL_free(*w);
OPENSSL_free(wNAF);
}
if (val != NULL) {
for (v = val; *v != NULL; v++)
EC_POINT_clear_free(*v);
OPENSSL_free(val);
}
OPENSSL_free(val_sub);
return ret;
}
/*-
* ec_wNAF_precompute_mult()
* creates an EC_PRE_COMP object with preprecomputed multiples of the generator
* for use with wNAF splitting as implemented in ec_wNAF_mul().
*
* 'pre_comp->points' is an array of multiples of the generator
* of the following form:
* points[0] = generator;
* points[1] = 3 * generator;
* ...
* points[2^(w-1)-1] = (2^(w-1)-1) * generator;
* points[2^(w-1)] = 2^blocksize * generator;
* points[2^(w-1)+1] = 3 * 2^blocksize * generator;
* ...
* points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator
* points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator
* ...
* points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator
* points[2^(w-1)*numblocks] = NULL
*/
int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
{
const EC_POINT *generator;
EC_POINT *tmp_point = NULL, *base = NULL, **var;
const BIGNUM *order;
size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num;
EC_POINT **points = NULL;
EC_PRE_COMP *pre_comp;
int ret = 0;
#ifndef FIPS_MODE
BN_CTX *new_ctx = NULL;
#endif
/* if there is an old EC_PRE_COMP object, throw it away */
EC_pre_comp_free(group);
if ((pre_comp = ec_pre_comp_new(group)) == NULL)
return 0;
generator = EC_GROUP_get0_generator(group);
if (generator == NULL) {
ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
goto err;
}
#ifndef FIPS_MODE
if (ctx == NULL)
ctx = new_ctx = BN_CTX_new();
#endif
if (ctx == NULL)
goto err;
BN_CTX_start(ctx);
order = EC_GROUP_get0_order(group);
if (order == NULL)
goto err;
if (BN_is_zero(order)) {
ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
goto err;
}
bits = BN_num_bits(order);
/*
* The following parameters mean we precompute (approximately) one point
* per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other
* bit lengths, other parameter combinations might provide better
* efficiency.
*/
blocksize = 8;
w = 4;
if (EC_window_bits_for_scalar_size(bits) > w) {
/* let's not make the window too small ... */
w = EC_window_bits_for_scalar_size(bits);
}
numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks
* to use for wNAF
* splitting */
pre_points_per_block = (size_t)1 << (w - 1);
num = pre_points_per_block * numblocks; /* number of points to compute
* and store */
points = OPENSSL_malloc(sizeof(*points) * (num + 1));
if (points == NULL) {
ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
goto err;
}
var = points;
var[num] = NULL; /* pivot */
for (i = 0; i < num; i++) {
if ((var[i] = EC_POINT_new(group)) == NULL) {
ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
goto err;
}
}
if ((tmp_point = EC_POINT_new(group)) == NULL
|| (base = EC_POINT_new(group)) == NULL) {
ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE);
goto err;
}
if (!EC_POINT_copy(base, generator))
goto err;
/* do the precomputation */
for (i = 0; i < numblocks; i++) {
size_t j;
if (!EC_POINT_dbl(group, tmp_point, base, ctx))
goto err;
if (!EC_POINT_copy(*var++, base))
goto err;
for (j = 1; j < pre_points_per_block; j++, var++) {
/*
* calculate odd multiples of the current base point
*/
if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx))
goto err;
}
if (i < numblocks - 1) {
/*
* get the next base (multiply current one by 2^blocksize)
*/
size_t k;
if (blocksize <= 2) {
ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR);
goto err;
}
if (!EC_POINT_dbl(group, base, tmp_point, ctx))
goto err;
for (k = 2; k < blocksize; k++) {
if (!EC_POINT_dbl(group, base, base, ctx))
goto err;
}
}
}
if (!EC_POINTs_make_affine(group, num, points, ctx))
goto err;
pre_comp->group = group;
pre_comp->blocksize = blocksize;
pre_comp->numblocks = numblocks;
pre_comp->w = w;
pre_comp->points = points;
points = NULL;
pre_comp->num = num;
SETPRECOMP(group, ec, pre_comp);
pre_comp = NULL;
ret = 1;
err:
BN_CTX_end(ctx);
#ifndef FIPS_MODE
BN_CTX_free(new_ctx);
#endif
EC_ec_pre_comp_free(pre_comp);
if (points) {
EC_POINT **p;
for (p = points; *p != NULL; p++)
EC_POINT_free(*p);
OPENSSL_free(points);
}
EC_POINT_free(tmp_point);
EC_POINT_free(base);
return ret;
}
int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
{
return HAVEPRECOMP(group, ec);
}
|