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
|
/*
* Copyright 2017-2022 The OpenSSL Project Authors. All Rights Reserved.
* Copyright 2015-2016 Cryptography Research, Inc.
*
* 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
*
* Originally written by Mike Hamburg
*/
#include <openssl/crypto.h>
#include "word.h"
#include "field.h"
#include "point_448.h"
#include "ed448.h"
#include "crypto/ecx.h"
#include "curve448_local.h"
#define COFACTOR 4
#define C448_WNAF_FIXED_TABLE_BITS 5
#define C448_WNAF_VAR_TABLE_BITS 3
#define EDWARDS_D (-39081)
static const curve448_scalar_t precomputed_scalarmul_adjustment = {
{
{
SC_LIMB(0xc873d6d54a7bb0cfULL), SC_LIMB(0xe933d8d723a70aadULL),
SC_LIMB(0xbb124b65129c96fdULL), SC_LIMB(0x00000008335dc163ULL)
}
}
};
#define TWISTED_D (EDWARDS_D - 1)
#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
/* Inverse. */
static void gf_invert(gf y, const gf x, int assert_nonzero)
{
mask_t ret;
gf t1, t2;
ossl_gf_sqr(t1, x); /* o^2 */
ret = gf_isr(t2, t1); /* +-1/sqrt(o^2) = +-1/o */
(void)ret;
if (assert_nonzero)
assert(ret);
ossl_gf_sqr(t1, t2);
ossl_gf_mul(t2, t1, x); /* not direct to y in case of alias. */
gf_copy(y, t2);
}
/** identity = (0,1) */
const curve448_point_t ossl_curve448_point_identity =
{ {{{{0}}}, {{{1}}}, {{{1}}}, {{{0}}}} };
static void point_double_internal(curve448_point_t p, const curve448_point_t q,
int before_double)
{
gf a, b, c, d;
ossl_gf_sqr(c, q->x);
ossl_gf_sqr(a, q->y);
gf_add_nr(d, c, a); /* 2+e */
gf_add_nr(p->t, q->y, q->x); /* 2+e */
ossl_gf_sqr(b, p->t);
gf_subx_nr(b, b, d, 3); /* 4+e */
gf_sub_nr(p->t, a, c); /* 3+e */
ossl_gf_sqr(p->x, q->z);
gf_add_nr(p->z, p->x, p->x); /* 2+e */
gf_subx_nr(a, p->z, p->t, 4); /* 6+e */
if (GF_HEADROOM == 5)
gf_weak_reduce(a); /* or 1+e */
ossl_gf_mul(p->x, a, b);
ossl_gf_mul(p->z, p->t, a);
ossl_gf_mul(p->y, p->t, d);
if (!before_double)
ossl_gf_mul(p->t, b, d);
}
void ossl_curve448_point_double(curve448_point_t p, const curve448_point_t q)
{
point_double_internal(p, q, 0);
}
/* Operations on [p]niels */
static ossl_inline void cond_neg_niels(niels_t n, mask_t neg)
{
gf_cond_swap(n->a, n->b, neg);
gf_cond_neg(n->c, neg);
}
static void pt_to_pniels(pniels_t b, const curve448_point_t a)
{
gf_sub(b->n->a, a->y, a->x);
gf_add(b->n->b, a->x, a->y);
gf_mulw(b->n->c, a->t, 2 * TWISTED_D);
gf_add(b->z, a->z, a->z);
}
static void pniels_to_pt(curve448_point_t e, const pniels_t d)
{
gf eu;
gf_add(eu, d->n->b, d->n->a);
gf_sub(e->y, d->n->b, d->n->a);
ossl_gf_mul(e->t, e->y, eu);
ossl_gf_mul(e->x, d->z, e->y);
ossl_gf_mul(e->y, d->z, eu);
ossl_gf_sqr(e->z, d->z);
}
static void niels_to_pt(curve448_point_t e, const niels_t n)
{
gf_add(e->y, n->b, n->a);
gf_sub(e->x, n->b, n->a);
ossl_gf_mul(e->t, e->y, e->x);
gf_copy(e->z, ONE);
}
static void add_niels_to_pt(curve448_point_t d, const niels_t e,
int before_double)
{
gf a, b, c;
gf_sub_nr(b, d->y, d->x); /* 3+e */
ossl_gf_mul(a, e->a, b);
gf_add_nr(b, d->x, d->y); /* 2+e */
ossl_gf_mul(d->y, e->b, b);
ossl_gf_mul(d->x, e->c, d->t);
gf_add_nr(c, a, d->y); /* 2+e */
gf_sub_nr(b, d->y, a); /* 3+e */
gf_sub_nr(d->y, d->z, d->x); /* 3+e */
gf_add_nr(a, d->x, d->z); /* 2+e */
ossl_gf_mul(d->z, a, d->y);
ossl_gf_mul(d->x, d->y, b);
ossl_gf_mul(d->y, a, c);
if (!before_double)
ossl_gf_mul(d->t, b, c);
}
static void sub_niels_from_pt(curve448_point_t d, const niels_t e,
int before_double)
{
gf a, b, c;
gf_sub_nr(b, d->y, d->x); /* 3+e */
ossl_gf_mul(a, e->b, b);
gf_add_nr(b, d->x, d->y); /* 2+e */
ossl_gf_mul(d->y, e->a, b);
ossl_gf_mul(d->x, e->c, d->t);
gf_add_nr(c, a, d->y); /* 2+e */
gf_sub_nr(b, d->y, a); /* 3+e */
gf_add_nr(d->y, d->z, d->x); /* 2+e */
gf_sub_nr(a, d->z, d->x); /* 3+e */
ossl_gf_mul(d->z, a, d->y);
ossl_gf_mul(d->x, d->y, b);
ossl_gf_mul(d->y, a, c);
if (!before_double)
ossl_gf_mul(d->t, b, c);
}
static void add_pniels_to_pt(curve448_point_t p, const pniels_t pn,
int before_double)
{
gf L0;
ossl_gf_mul(L0, p->z, pn->z);
gf_copy(p->z, L0);
add_niels_to_pt(p, pn->n, before_double);
}
static void sub_pniels_from_pt(curve448_point_t p, const pniels_t pn,
int before_double)
{
gf L0;
ossl_gf_mul(L0, p->z, pn->z);
gf_copy(p->z, L0);
sub_niels_from_pt(p, pn->n, before_double);
}
c448_bool_t
ossl_curve448_point_eq(const curve448_point_t p,
const curve448_point_t q)
{
mask_t succ;
gf a, b;
/* equality mod 2-torsion compares x/y */
ossl_gf_mul(a, p->y, q->x);
ossl_gf_mul(b, q->y, p->x);
succ = gf_eq(a, b);
return mask_to_bool(succ);
}
c448_bool_t
ossl_curve448_point_valid(const curve448_point_t p)
{
mask_t out;
gf a, b, c;
ossl_gf_mul(a, p->x, p->y);
ossl_gf_mul(b, p->z, p->t);
out = gf_eq(a, b);
ossl_gf_sqr(a, p->x);
ossl_gf_sqr(b, p->y);
gf_sub(a, b, a);
ossl_gf_sqr(b, p->t);
gf_mulw(c, b, TWISTED_D);
ossl_gf_sqr(b, p->z);
gf_add(b, b, c);
out &= gf_eq(a, b);
out &= ~gf_eq(p->z, ZERO);
return mask_to_bool(out);
}
static ossl_inline void constant_time_lookup_niels(niels_s * RESTRICT ni,
const niels_t * table,
int nelts, int idx)
{
constant_time_lookup(ni, table, sizeof(niels_s), nelts, idx);
}
void
ossl_curve448_precomputed_scalarmul(curve448_point_t out,
const curve448_precomputed_s * table,
const curve448_scalar_t scalar)
{
unsigned int i, j, k;
const unsigned int n = COMBS_N, t = COMBS_T, s = COMBS_S;
niels_t ni;
curve448_scalar_t scalar1x;
ossl_curve448_scalar_add(scalar1x, scalar, precomputed_scalarmul_adjustment);
ossl_curve448_scalar_halve(scalar1x, scalar1x);
for (i = s; i > 0; i--) {
if (i != s)
point_double_internal(out, out, 0);
for (j = 0; j < n; j++) {
int tab = 0;
mask_t invert;
for (k = 0; k < t; k++) {
unsigned int bit = (i - 1) + s * (k + j * t);
if (bit < C448_SCALAR_BITS)
tab |=
(scalar1x->limb[bit / WBITS] >> (bit % WBITS) & 1) << k;
}
invert = (tab >> (t - 1)) - 1;
tab ^= invert;
tab &= (1 << (t - 1)) - 1;
constant_time_lookup_niels(ni, &table->table[j << (t - 1)],
1 << (t - 1), tab);
cond_neg_niels(ni, invert);
if ((i != s) || j != 0)
add_niels_to_pt(out, ni, j == n - 1 && i != 1);
else
niels_to_pt(out, ni);
}
}
OPENSSL_cleanse(ni, sizeof(ni));
OPENSSL_cleanse(scalar1x, sizeof(scalar1x));
}
void
ossl_curve448_point_mul_by_ratio_and_encode_like_eddsa(
uint8_t enc[EDDSA_448_PUBLIC_BYTES],
const curve448_point_t p)
{
gf x, y, z, t;
curve448_point_t q;
/* The point is now on the twisted curve. Move it to untwisted. */
curve448_point_copy(q, p);
{
/* 4-isogeny: 2xy/(y^+x^2), (y^2-x^2)/(2z^2-y^2+x^2) */
gf u;
ossl_gf_sqr(x, q->x);
ossl_gf_sqr(t, q->y);
gf_add(u, x, t);
gf_add(z, q->y, q->x);
ossl_gf_sqr(y, z);
gf_sub(y, y, u);
gf_sub(z, t, x);
ossl_gf_sqr(x, q->z);
gf_add(t, x, x);
gf_sub(t, t, z);
ossl_gf_mul(x, t, y);
ossl_gf_mul(y, z, u);
ossl_gf_mul(z, u, t);
OPENSSL_cleanse(u, sizeof(u));
}
/* Affinize */
gf_invert(z, z, 1);
ossl_gf_mul(t, x, z);
ossl_gf_mul(x, y, z);
/* Encode */
enc[EDDSA_448_PRIVATE_BYTES - 1] = 0;
gf_serialize(enc, x, 1);
enc[EDDSA_448_PRIVATE_BYTES - 1] |= 0x80 & gf_lobit(t);
OPENSSL_cleanse(x, sizeof(x));
OPENSSL_cleanse(y, sizeof(y));
OPENSSL_cleanse(z, sizeof(z));
OPENSSL_cleanse(t, sizeof(t));
ossl_curve448_point_destroy(q);
}
c448_error_t
ossl_curve448_point_decode_like_eddsa_and_mul_by_ratio(
curve448_point_t p,
const uint8_t enc[EDDSA_448_PUBLIC_BYTES])
{
uint8_t enc2[EDDSA_448_PUBLIC_BYTES];
mask_t low;
mask_t succ;
memcpy(enc2, enc, sizeof(enc2));
low = ~word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1] & 0x80);
enc2[EDDSA_448_PRIVATE_BYTES - 1] &= ~0x80;
succ = gf_deserialize(p->y, enc2, 1, 0);
succ &= word_is_zero(enc2[EDDSA_448_PRIVATE_BYTES - 1]);
ossl_gf_sqr(p->x, p->y);
gf_sub(p->z, ONE, p->x); /* num = 1-y^2 */
gf_mulw(p->t, p->x, EDWARDS_D); /* dy^2 */
gf_sub(p->t, ONE, p->t); /* denom = 1-dy^2 or 1-d + dy^2 */
ossl_gf_mul(p->x, p->z, p->t);
succ &= gf_isr(p->t, p->x); /* 1/sqrt(num * denom) */
ossl_gf_mul(p->x, p->t, p->z); /* sqrt(num / denom) */
gf_cond_neg(p->x, gf_lobit(p->x) ^ low);
gf_copy(p->z, ONE);
{
gf a, b, c, d;
/* 4-isogeny 2xy/(y^2-ax^2), (y^2+ax^2)/(2-y^2-ax^2) */
ossl_gf_sqr(c, p->x);
ossl_gf_sqr(a, p->y);
gf_add(d, c, a);
gf_add(p->t, p->y, p->x);
ossl_gf_sqr(b, p->t);
gf_sub(b, b, d);
gf_sub(p->t, a, c);
ossl_gf_sqr(p->x, p->z);
gf_add(p->z, p->x, p->x);
gf_sub(a, p->z, d);
ossl_gf_mul(p->x, a, b);
ossl_gf_mul(p->z, p->t, a);
ossl_gf_mul(p->y, p->t, d);
ossl_gf_mul(p->t, b, d);
OPENSSL_cleanse(a, sizeof(a));
OPENSSL_cleanse(b, sizeof(b));
OPENSSL_cleanse(c, sizeof(c));
OPENSSL_cleanse(d, sizeof(d));
}
OPENSSL_cleanse(enc2, sizeof(enc2));
assert(ossl_curve448_point_valid(p) || ~succ);
return c448_succeed_if(mask_to_bool(succ));
}
c448_error_t
ossl_x448_int(uint8_t out[X_PUBLIC_BYTES],
const uint8_t base[X_PUBLIC_BYTES],
const uint8_t scalar[X_PRIVATE_BYTES])
{
gf x1, x2, z2, x3, z3, t1, t2;
int t;
mask_t swap = 0;
mask_t nz;
(void)gf_deserialize(x1, base, 1, 0);
gf_copy(x2, ONE);
gf_copy(z2, ZERO);
gf_copy(x3, x1);
gf_copy(z3, ONE);
for (t = X_PRIVATE_BITS - 1; t >= 0; t--) {
uint8_t sb = scalar[t / 8];
mask_t k_t;
/* Scalar conditioning */
if (t / 8 == 0)
sb &= -(uint8_t)COFACTOR;
else if (t == X_PRIVATE_BITS - 1)
sb = -1;
k_t = (sb >> (t % 8)) & 1;
k_t = 0 - k_t; /* set to all 0s or all 1s */
swap ^= k_t;
gf_cond_swap(x2, x3, swap);
gf_cond_swap(z2, z3, swap);
swap = k_t;
/*
* The "_nr" below skips coefficient reduction. In the following
* comments, "2+e" is saying that the coefficients are at most 2+epsilon
* times the reduction limit.
*/
gf_add_nr(t1, x2, z2); /* A = x2 + z2 */ /* 2+e */
gf_sub_nr(t2, x2, z2); /* B = x2 - z2 */ /* 3+e */
gf_sub_nr(z2, x3, z3); /* D = x3 - z3 */ /* 3+e */
ossl_gf_mul(x2, t1, z2); /* DA */
gf_add_nr(z2, z3, x3); /* C = x3 + z3 */ /* 2+e */
ossl_gf_mul(x3, t2, z2); /* CB */
gf_sub_nr(z3, x2, x3); /* DA-CB */ /* 3+e */
ossl_gf_sqr(z2, z3); /* (DA-CB)^2 */
ossl_gf_mul(z3, x1, z2); /* z3 = x1(DA-CB)^2 */
gf_add_nr(z2, x2, x3); /* (DA+CB) */ /* 2+e */
ossl_gf_sqr(x3, z2); /* x3 = (DA+CB)^2 */
ossl_gf_sqr(z2, t1); /* AA = A^2 */
ossl_gf_sqr(t1, t2); /* BB = B^2 */
ossl_gf_mul(x2, z2, t1); /* x2 = AA*BB */
gf_sub_nr(t2, z2, t1); /* E = AA-BB */ /* 3+e */
gf_mulw(t1, t2, -EDWARDS_D); /* E*-d = a24*E */
gf_add_nr(t1, t1, z2); /* AA + a24*E */ /* 2+e */
ossl_gf_mul(z2, t2, t1); /* z2 = E(AA+a24*E) */
}
/* Finish */
gf_cond_swap(x2, x3, swap);
gf_cond_swap(z2, z3, swap);
gf_invert(z2, z2, 0);
ossl_gf_mul(x1, x2, z2);
gf_serialize(out, x1, 1);
nz = ~gf_eq(x1, ZERO);
OPENSSL_cleanse(x1, sizeof(x1));
OPENSSL_cleanse(x2, sizeof(x2));
OPENSSL_cleanse(z2, sizeof(z2));
OPENSSL_cleanse(x3, sizeof(x3));
OPENSSL_cleanse(z3, sizeof(z3));
OPENSSL_cleanse(t1, sizeof(t1));
OPENSSL_cleanse(t2, sizeof(t2));
return c448_succeed_if(mask_to_bool(nz));
}
void
ossl_curve448_point_mul_by_ratio_and_encode_like_x448(uint8_t
out[X_PUBLIC_BYTES],
const curve448_point_t p)
{
curve448_point_t q;
curve448_point_copy(q, p);
gf_invert(q->t, q->x, 0); /* 1/x */
ossl_gf_mul(q->z, q->t, q->y); /* y/x */
ossl_gf_sqr(q->y, q->z); /* (y/x)^2 */
gf_serialize(out, q->y, 1);
ossl_curve448_point_destroy(q);
}
void ossl_x448_derive_public_key(uint8_t out[X_PUBLIC_BYTES],
const uint8_t scalar[X_PRIVATE_BYTES])
{
/* Scalar conditioning */
uint8_t scalar2[X_PRIVATE_BYTES];
curve448_scalar_t the_scalar;
curve448_point_t p;
unsigned int i;
memcpy(scalar2, scalar, sizeof(scalar2));
scalar2[0] &= -(uint8_t)COFACTOR;
scalar2[X_PRIVATE_BYTES - 1] &= ~((0u - 1u) << ((X_PRIVATE_BITS + 7) % 8));
scalar2[X_PRIVATE_BYTES - 1] |= 1 << ((X_PRIVATE_BITS + 7) % 8);
ossl_curve448_scalar_decode_long(the_scalar, scalar2, sizeof(scalar2));
/* Compensate for the encoding ratio */
for (i = 1; i < X448_ENCODE_RATIO; i <<= 1)
ossl_curve448_scalar_halve(the_scalar, the_scalar);
ossl_curve448_precomputed_scalarmul(p, ossl_curve448_precomputed_base,
the_scalar);
ossl_curve448_point_mul_by_ratio_and_encode_like_x448(out, p);
ossl_curve448_point_destroy(p);
}
/* Control for variable-time scalar multiply algorithms. */
struct smvt_control {
int power, addend;
};
#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ > 3))
# define NUMTRAILINGZEROS __builtin_ctz
#else
# define NUMTRAILINGZEROS numtrailingzeros
static uint32_t numtrailingzeros(uint32_t i)
{
uint32_t tmp;
uint32_t num = 31;
if (i == 0)
return 32;
tmp = i << 16;
if (tmp != 0) {
i = tmp;
num -= 16;
}
tmp = i << 8;
if (tmp != 0) {
i = tmp;
num -= 8;
}
tmp = i << 4;
if (tmp != 0) {
i = tmp;
num -= 4;
}
tmp = i << 2;
if (tmp != 0) {
i = tmp;
num -= 2;
}
tmp = i << 1;
if (tmp != 0)
num--;
return num;
}
#endif
static int recode_wnaf(struct smvt_control *control,
/* [nbits/(table_bits + 1) + 3] */
const curve448_scalar_t scalar,
unsigned int table_bits)
{
unsigned int table_size = C448_SCALAR_BITS / (table_bits + 1) + 3;
int position = table_size - 1; /* at the end */
uint64_t current = scalar->limb[0] & 0xFFFF;
uint32_t mask = (1 << (table_bits + 1)) - 1;
unsigned int w;
const unsigned int B_OVER_16 = sizeof(scalar->limb[0]) / 2;
unsigned int n, i;
/* place the end marker */
control[position].power = -1;
control[position].addend = 0;
position--;
/*
* PERF: Could negate scalar if it's large. But then would need more cases
* in the actual code that uses it, all for an expected reduction of like
* 1/5 op. Probably not worth it.
*/
for (w = 1; w < (C448_SCALAR_BITS - 1) / 16 + 3; w++) {
if (w < (C448_SCALAR_BITS - 1) / 16 + 1) {
/* Refill the 16 high bits of current */
current += (uint32_t)((scalar->limb[w / B_OVER_16]
>> (16 * (w % B_OVER_16))) << 16);
}
while (current & 0xFFFF) {
uint32_t pos = NUMTRAILINGZEROS((uint32_t)current);
uint32_t odd = (uint32_t)current >> pos;
int32_t delta = odd & mask;
assert(position >= 0);
if (odd & (1 << (table_bits + 1)))
delta -= (1 << (table_bits + 1));
/*
* Coverity gets confused by the value of pos, thinking it might be
* 32. This would require current & 0xFFFF to be zero which isn't
* possible. Suppress this false positive, since adding a check
* isn't desirable.
*/
/* coverity[overflow_before_widen] */
current -= delta * (1 << pos);
control[position].power = pos + 16 * (w - 1);
control[position].addend = delta;
position--;
}
current >>= 16;
}
assert(current == 0);
position++;
n = table_size - position;
for (i = 0; i < n; i++)
control[i] = control[i + position];
return n - 1;
}
static void prepare_wnaf_table(pniels_t * output,
const curve448_point_t working,
unsigned int tbits)
{
curve448_point_t tmp;
int i;
pniels_t twop;
pt_to_pniels(output[0], working);
if (tbits == 0)
return;
ossl_curve448_point_double(tmp, working);
pt_to_pniels(twop, tmp);
add_pniels_to_pt(tmp, output[0], 0);
pt_to_pniels(output[1], tmp);
for (i = 2; i < 1 << tbits; i++) {
add_pniels_to_pt(tmp, twop, 0);
pt_to_pniels(output[i], tmp);
}
ossl_curve448_point_destroy(tmp);
OPENSSL_cleanse(twop, sizeof(twop));
}
void
ossl_curve448_base_double_scalarmul_non_secret(curve448_point_t combo,
const curve448_scalar_t scalar1,
const curve448_point_t base2,
const curve448_scalar_t scalar2)
{
const int table_bits_var = C448_WNAF_VAR_TABLE_BITS;
const int table_bits_pre = C448_WNAF_FIXED_TABLE_BITS;
struct smvt_control control_var[C448_SCALAR_BITS /
(C448_WNAF_VAR_TABLE_BITS + 1) + 3];
struct smvt_control control_pre[C448_SCALAR_BITS /
(C448_WNAF_FIXED_TABLE_BITS + 1) + 3];
int ncb_pre = recode_wnaf(control_pre, scalar1, table_bits_pre);
int ncb_var = recode_wnaf(control_var, scalar2, table_bits_var);
pniels_t precmp_var[1 << C448_WNAF_VAR_TABLE_BITS];
int contp = 0, contv = 0, i;
prepare_wnaf_table(precmp_var, base2, table_bits_var);
i = control_var[0].power;
if (i < 0) {
curve448_point_copy(combo, ossl_curve448_point_identity);
return;
}
if (i > control_pre[0].power) {
pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
contv++;
} else if (i == control_pre[0].power && i >= 0) {
pniels_to_pt(combo, precmp_var[control_var[0].addend >> 1]);
add_niels_to_pt(combo,
ossl_curve448_wnaf_base[control_pre[0].addend >> 1],
i);
contv++;
contp++;
} else {
i = control_pre[0].power;
niels_to_pt(combo, ossl_curve448_wnaf_base[control_pre[0].addend >> 1]);
contp++;
}
for (i--; i >= 0; i--) {
int cv = (i == control_var[contv].power);
int cp = (i == control_pre[contp].power);
point_double_internal(combo, combo, i && !(cv || cp));
if (cv) {
assert(control_var[contv].addend);
if (control_var[contv].addend > 0)
add_pniels_to_pt(combo,
precmp_var[control_var[contv].addend >> 1],
i && !cp);
else
sub_pniels_from_pt(combo,
precmp_var[(-control_var[contv].addend)
>> 1], i && !cp);
contv++;
}
if (cp) {
assert(control_pre[contp].addend);
if (control_pre[contp].addend > 0)
add_niels_to_pt(combo,
ossl_curve448_wnaf_base[control_pre[contp].addend
>> 1], i);
else
sub_niels_from_pt(combo,
ossl_curve448_wnaf_base[(-control_pre
[contp].addend) >> 1], i);
contp++;
}
}
/* This function is non-secret, but whatever this is cheap. */
OPENSSL_cleanse(control_var, sizeof(control_var));
OPENSSL_cleanse(control_pre, sizeof(control_pre));
OPENSSL_cleanse(precmp_var, sizeof(precmp_var));
assert(contv == ncb_var);
(void)ncb_var;
assert(contp == ncb_pre);
(void)ncb_pre;
}
void ossl_curve448_point_destroy(curve448_point_t point)
{
OPENSSL_cleanse(point, sizeof(curve448_point_t));
}
int ossl_x448(uint8_t out_shared_key[56], const uint8_t private_key[56],
const uint8_t peer_public_value[56])
{
return ossl_x448_int(out_shared_key, peer_public_value, private_key)
== C448_SUCCESS;
}
void ossl_x448_public_from_private(uint8_t out_public_value[56],
const uint8_t private_key[56])
{
ossl_x448_derive_public_key(out_public_value, private_key);
}
|