forked from kmackay/micro-ecc
-
Notifications
You must be signed in to change notification settings - Fork 0
/
uECC.c
1529 lines (1319 loc) · 51.8 KB
/
uECC.c
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
988
989
990
991
992
993
994
995
996
997
998
999
1000
/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */
#include "uECC.h"
#include "uECC_vli.h"
#ifndef uECC_RNG_MAX_TRIES
#define uECC_RNG_MAX_TRIES 64
#endif
#if uECC_ENABLE_VLI_API
#define uECC_VLI_API
#else
#define uECC_VLI_API static
#endif
#define CONCATX(a, ...) a ## __VA_ARGS__
#define CONCAT(a, ...) CONCATX(a, __VA_ARGS__)
#define STRX(a) #a
#define STR(a) STRX(a)
#define EVAL(...) EVAL1(EVAL1(EVAL1(EVAL1(__VA_ARGS__))))
#define EVAL1(...) EVAL2(EVAL2(EVAL2(EVAL2(__VA_ARGS__))))
#define EVAL2(...) EVAL3(EVAL3(EVAL3(EVAL3(__VA_ARGS__))))
#define EVAL3(...) EVAL4(EVAL4(EVAL4(EVAL4(__VA_ARGS__))))
#define EVAL4(...) __VA_ARGS__
#define DEC_1 0
#define DEC_2 1
#define DEC_3 2
#define DEC_4 3
#define DEC_5 4
#define DEC_6 5
#define DEC_7 6
#define DEC_8 7
#define DEC_9 8
#define DEC_10 9
#define DEC_11 10
#define DEC_12 11
#define DEC_13 12
#define DEC_14 13
#define DEC_15 14
#define DEC_16 15
#define DEC_17 16
#define DEC_18 17
#define DEC_19 18
#define DEC_20 19
#define DEC_21 20
#define DEC_22 21
#define DEC_23 22
#define DEC_24 23
#define DEC_25 24
#define DEC_26 25
#define DEC_27 26
#define DEC_28 27
#define DEC_29 28
#define DEC_30 29
#define DEC_31 30
#define DEC_32 31
#define DEC(N) CONCAT(DEC_, N)
#define SECOND_ARG(_, val, ...) val
#define SOME_CHECK_0 ~, 0
#define GET_SECOND_ARG(...) SECOND_ARG(__VA_ARGS__, SOME,)
#define SOME_OR_0(N) GET_SECOND_ARG(CONCAT(SOME_CHECK_, N))
#define EMPTY(...)
#define DEFER(...) __VA_ARGS__ EMPTY()
#define REPEAT_NAME_0() REPEAT_0
#define REPEAT_NAME_SOME() REPEAT_SOME
#define REPEAT_0(...)
#define REPEAT_SOME(N, stuff) DEFER(CONCAT(REPEAT_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), stuff) stuff
#define REPEAT(N, stuff) EVAL(REPEAT_SOME(N, stuff))
#define REPEATM_NAME_0() REPEATM_0
#define REPEATM_NAME_SOME() REPEATM_SOME
#define REPEATM_0(...)
#define REPEATM_SOME(N, macro) macro(N) \
DEFER(CONCAT(REPEATM_NAME_, SOME_OR_0(DEC(N))))()(DEC(N), macro)
#define REPEATM(N, macro) EVAL(REPEATM_SOME(N, macro))
#include "platform-specific.inc"
#if (uECC_WORD_SIZE == 1)
#if uECC_SUPPORTS_secp160r1
#define uECC_MAX_WORDS 21 /* Due to the size of curve_n. */
#endif
#if uECC_SUPPORTS_secp192r1
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 24
#endif
#if uECC_SUPPORTS_secp224r1
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 28
#endif
#if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1)
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 32
#endif
#elif (uECC_WORD_SIZE == 4)
#if uECC_SUPPORTS_secp160r1
#define uECC_MAX_WORDS 6 /* Due to the size of curve_n. */
#endif
#if uECC_SUPPORTS_secp192r1
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 6
#endif
#if uECC_SUPPORTS_secp224r1
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 7
#endif
#if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1)
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 8
#endif
#elif (uECC_WORD_SIZE == 8)
#if uECC_SUPPORTS_secp160r1
#define uECC_MAX_WORDS 3
#endif
#if uECC_SUPPORTS_secp192r1
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 3
#endif
#if uECC_SUPPORTS_secp224r1
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 4
#endif
#if (uECC_SUPPORTS_secp256r1 || uECC_SUPPORTS_secp256k1)
#undef uECC_MAX_WORDS
#define uECC_MAX_WORDS 4
#endif
#endif /* uECC_WORD_SIZE */
#define BITS_TO_WORDS(num_bits) ((num_bits + ((uECC_WORD_SIZE * 8) - 1)) / (uECC_WORD_SIZE * 8))
#define BITS_TO_BYTES(num_bits) ((num_bits + 7) / 8)
struct uECC_Curve_t {
wordcount_t num_words;
wordcount_t num_bytes;
bitcount_t num_n_bits;
uECC_word_t p[uECC_MAX_WORDS];
uECC_word_t n[uECC_MAX_WORDS];
uECC_word_t G[uECC_MAX_WORDS * 2];
uECC_word_t b[uECC_MAX_WORDS];
void (*double_jacobian)(uECC_word_t * X1,
uECC_word_t * Y1,
uECC_word_t * Z1,
uECC_Curve curve);
#if uECC_SUPPORT_COMPRESSED_POINT
void (*mod_sqrt)(uECC_word_t *a, uECC_Curve curve);
#endif
void (*x_side)(uECC_word_t *result, const uECC_word_t *x, uECC_Curve curve);
#if (uECC_OPTIMIZATION_LEVEL > 0)
void (*mmod_fast)(uECC_word_t *result, uECC_word_t *product);
#endif
};
static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words);
#if (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || \
uECC_PLATFORM == uECC_arm_thumb2)
#include "asm_arm.inc"
#endif
#if (uECC_PLATFORM == uECC_avr)
#include "asm_avr.inc"
#endif
#if default_RNG_defined
static uECC_RNG_Function g_rng_function = &default_RNG;
#else
static uECC_RNG_Function g_rng_function = 0;
#endif
void uECC_set_rng(uECC_RNG_Function rng_function) {
g_rng_function = rng_function;
}
#if !asm_clear
uECC_VLI_API void uECC_vli_clear(uECC_word_t *vli, wordcount_t num_words) {
wordcount_t i;
for (i = 0; i < num_words; ++i) {
vli[i] = 0;
}
}
#endif /* !asm_clear */
/* Constant-time comparison to zero - secure way to compare long integers */
/* Returns 1 if vli == 0, 0 otherwise. */
uECC_VLI_API uECC_word_t uECC_vli_isZero(const uECC_word_t *vli, wordcount_t num_words) {
uECC_word_t bits = 0;
wordcount_t i;
for (i = 0; i < num_words; ++i) {
bits |= vli[i];
}
return (bits == 0);
}
/* Returns nonzero if bit 'bit' of vli is set. */
uECC_VLI_API uECC_word_t uECC_vli_testBit(const uECC_word_t *vli, bitcount_t bit) {
return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK)));
}
/* Counts the number of words in vli. */
static wordcount_t vli_numDigits(const uECC_word_t *vli, const wordcount_t max_words) {
wordcount_t i;
/* Search from the end until we find a non-zero digit.
We do it in reverse because we expect that most digits will be nonzero. */
for (i = max_words - 1; i >= 0 && vli[i] == 0; --i) {
}
return (i + 1);
}
/* Counts the number of bits required to represent vli. */
uECC_VLI_API bitcount_t uECC_vli_numBits(const uECC_word_t *vli, const wordcount_t max_words) {
uECC_word_t i;
uECC_word_t digit;
wordcount_t num_digits = vli_numDigits(vli, max_words);
if (num_digits == 0) {
return 0;
}
digit = vli[num_digits - 1];
for (i = 0; digit; ++i) {
digit >>= 1;
}
return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i);
}
/* Sets dest = src. */
#if !asm_set
uECC_VLI_API void uECC_vli_set(uECC_word_t *dest, const uECC_word_t *src, wordcount_t num_words) {
wordcount_t i;
for (i = 0; i < num_words; ++i) {
dest[i] = src[i];
}
}
#endif /* !asm_set */
/* Returns sign of left - right. */
static cmpresult_t uECC_vli_cmp_unsafe(const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words) {
wordcount_t i;
for (i = num_words - 1; i >= 0; --i) {
if (left[i] > right[i]) {
return 1;
} else if (left[i] < right[i]) {
return -1;
}
}
return 0;
}
/* Constant-time comparison function - secure way to compare long integers */
/* Returns one if left == right, zero otherwise. */
uECC_VLI_API uECC_word_t uECC_vli_equal(const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words) {
uECC_word_t diff = 0;
wordcount_t i;
for (i = num_words - 1; i >= 0; --i) {
diff |= (left[i] ^ right[i]);
}
return (diff == 0);
}
uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words);
/* Returns sign of left - right, in constant time. */
uECC_VLI_API cmpresult_t uECC_vli_cmp(const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words) {
uECC_word_t tmp[uECC_MAX_WORDS];
uECC_word_t neg = !!uECC_vli_sub(tmp, left, right, num_words);
uECC_word_t equal = uECC_vli_isZero(tmp, num_words);
return (!equal - 2 * neg);
}
/* Computes vli = vli >> 1. */
#if !asm_rshift1
uECC_VLI_API void uECC_vli_rshift1(uECC_word_t *vli, wordcount_t num_words) {
uECC_word_t *end = vli;
uECC_word_t carry = 0;
vli += num_words;
while (vli-- > end) {
uECC_word_t temp = *vli;
*vli = (temp >> 1) | carry;
carry = temp << (uECC_WORD_BITS - 1);
}
}
#endif /* !asm_rshift1 */
/* Computes result = left + right, returning carry. Can modify in place. */
#if !asm_add
uECC_VLI_API uECC_word_t uECC_vli_add(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words) {
uECC_word_t carry = 0;
wordcount_t i;
for (i = 0; i < num_words; ++i) {
uECC_word_t sum = left[i] + right[i] + carry;
if (sum != left[i]) {
carry = (sum < left[i]);
}
result[i] = sum;
}
return carry;
}
#endif /* !asm_add */
/* Computes result = left - right, returning borrow. Can modify in place. */
#if !asm_sub
uECC_VLI_API uECC_word_t uECC_vli_sub(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words) {
uECC_word_t borrow = 0;
wordcount_t i;
for (i = 0; i < num_words; ++i) {
uECC_word_t diff = left[i] - right[i] - borrow;
if (diff != left[i]) {
borrow = (diff > left[i]);
}
result[i] = diff;
}
return borrow;
}
#endif /* !asm_sub */
#if !asm_mult || (uECC_SQUARE_FUNC && !asm_square) || \
(uECC_SUPPORTS_secp256k1 && (uECC_OPTIMIZATION_LEVEL > 0) && \
((uECC_WORD_SIZE == 1) || (uECC_WORD_SIZE == 8)))
static void muladd(uECC_word_t a,
uECC_word_t b,
uECC_word_t *r0,
uECC_word_t *r1,
uECC_word_t *r2) {
#if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
uint64_t a0 = a & 0xffffffffull;
uint64_t a1 = a >> 32;
uint64_t b0 = b & 0xffffffffull;
uint64_t b1 = b >> 32;
uint64_t i0 = a0 * b0;
uint64_t i1 = a0 * b1;
uint64_t i2 = a1 * b0;
uint64_t i3 = a1 * b1;
uint64_t p0, p1;
i2 += (i0 >> 32);
i2 += i1;
if (i2 < i1) { /* overflow */
i3 += 0x100000000ull;
}
p0 = (i0 & 0xffffffffull) | (i2 << 32);
p1 = i3 + (i2 >> 32);
*r0 += p0;
*r1 += (p1 + (*r0 < p0));
*r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
#else
uECC_dword_t p = (uECC_dword_t)a * b;
uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
r01 += p;
*r2 += (r01 < p);
*r1 = r01 >> uECC_WORD_BITS;
*r0 = (uECC_word_t)r01;
#endif
}
#endif /* muladd needed */
#if !asm_mult
uECC_VLI_API void uECC_vli_mult(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
wordcount_t num_words) {
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t i, k;
/* Compute each digit of result in sequence, maintaining the carries. */
for (k = 0; k < num_words; ++k) {
for (i = 0; i <= k; ++i) {
muladd(left[i], right[k - i], &r0, &r1, &r2);
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
for (k = num_words; k < num_words * 2 - 1; ++k) {
for (i = (k + 1) - num_words; i < num_words; ++i) {
muladd(left[i], right[k - i], &r0, &r1, &r2);
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[num_words * 2 - 1] = r0;
}
#endif /* !asm_mult */
#if uECC_SQUARE_FUNC
#if !asm_square
static void mul2add(uECC_word_t a,
uECC_word_t b,
uECC_word_t *r0,
uECC_word_t *r1,
uECC_word_t *r2) {
#if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
uint64_t a0 = a & 0xffffffffull;
uint64_t a1 = a >> 32;
uint64_t b0 = b & 0xffffffffull;
uint64_t b1 = b >> 32;
uint64_t i0 = a0 * b0;
uint64_t i1 = a0 * b1;
uint64_t i2 = a1 * b0;
uint64_t i3 = a1 * b1;
uint64_t p0, p1;
i2 += (i0 >> 32);
i2 += i1;
if (i2 < i1)
{ /* overflow */
i3 += 0x100000000ull;
}
p0 = (i0 & 0xffffffffull) | (i2 << 32);
p1 = i3 + (i2 >> 32);
*r2 += (p1 >> 63);
p1 = (p1 << 1) | (p0 >> 63);
p0 <<= 1;
*r0 += p0;
*r1 += (p1 + (*r0 < p0));
*r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
#else
uECC_dword_t p = (uECC_dword_t)a * b;
uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
*r2 += (p >> (uECC_WORD_BITS * 2 - 1));
p *= 2;
r01 += p;
*r2 += (r01 < p);
*r1 = r01 >> uECC_WORD_BITS;
*r0 = (uECC_word_t)r01;
#endif
}
uECC_VLI_API void uECC_vli_square(uECC_word_t *result,
const uECC_word_t *left,
wordcount_t num_words) {
uECC_word_t r0 = 0;
uECC_word_t r1 = 0;
uECC_word_t r2 = 0;
wordcount_t i, k;
for (k = 0; k < num_words * 2 - 1; ++k) {
uECC_word_t min = (k < num_words ? 0 : (k + 1) - num_words);
for (i = min; i <= k && i <= k - i; ++i) {
if (i < k-i) {
mul2add(left[i], left[k - i], &r0, &r1, &r2);
} else {
muladd(left[i], left[k - i], &r0, &r1, &r2);
}
}
result[k] = r0;
r0 = r1;
r1 = r2;
r2 = 0;
}
result[num_words * 2 - 1] = r0;
}
#endif /* !asm_square */
#else /* uECC_SQUARE_FUNC */
#if uECC_ENABLE_VLI_API
uECC_VLI_API void uECC_vli_square(uECC_word_t *result,
const uECC_word_t *left,
wordcount_t num_words) {
uECC_vli_mult(result, left, left, num_words);
}
#endif /* uECC_ENABLE_VLI_API */
#endif /* uECC_SQUARE_FUNC */
/* Computes result = (left + right) % mod.
Assumes that left < mod and right < mod, and that result does not overlap mod. */
uECC_VLI_API void uECC_vli_modAdd(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_word_t carry = uECC_vli_add(result, left, right, num_words);
if (carry || uECC_vli_cmp_unsafe(mod, result, num_words) != 1) {
/* result > mod (result = mod + remainder), so subtract mod to get remainder. */
uECC_vli_sub(result, result, mod, num_words);
}
}
/* Computes result = (left - right) % mod.
Assumes that left < mod and right < mod, and that result does not overlap mod. */
uECC_VLI_API void uECC_vli_modSub(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_word_t l_borrow = uECC_vli_sub(result, left, right, num_words);
if (l_borrow) {
/* In this case, result == -diff == (max int) - diff. Since -x % d == d - x,
we can get the correct result from result + mod (with overflow). */
uECC_vli_add(result, result, mod, num_words);
}
}
/* Computes result = product % mod, where product is 2N words long. */
/* Currently only designed to work for curve_p or curve_n. */
uECC_VLI_API void uECC_vli_mmod(uECC_word_t *result,
uECC_word_t *product,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_word_t mod_multiple[2 * uECC_MAX_WORDS];
uECC_word_t tmp[2 * uECC_MAX_WORDS];
uECC_word_t *v[2] = {tmp, product};
uECC_word_t index;
/* Shift mod so its highest set bit is at the maximum position. */
bitcount_t shift = (num_words * 2 * uECC_WORD_BITS) - uECC_vli_numBits(mod, num_words);
wordcount_t word_shift = shift / uECC_WORD_BITS;
wordcount_t bit_shift = shift % uECC_WORD_BITS;
uECC_word_t carry = 0;
uECC_vli_clear(mod_multiple, word_shift);
if (bit_shift > 0) {
for(index = 0; index < (uECC_word_t)num_words; ++index) {
mod_multiple[word_shift + index] = (mod[index] << bit_shift) | carry;
carry = mod[index] >> (uECC_WORD_BITS - bit_shift);
}
} else {
uECC_vli_set(mod_multiple + word_shift, mod, num_words);
}
for (index = 1; shift >= 0; --shift) {
uECC_word_t borrow = 0;
wordcount_t i;
for (i = 0; i < num_words * 2; ++i) {
uECC_word_t diff = v[index][i] - mod_multiple[i] - borrow;
if (diff != v[index][i]) {
borrow = (diff > v[index][i]);
}
v[1 - index][i] = diff;
}
index = !(index ^ borrow); /* Swap the index if there was no borrow */
uECC_vli_rshift1(mod_multiple, num_words);
mod_multiple[num_words - 1] |= mod_multiple[num_words] << (uECC_WORD_BITS - 1);
uECC_vli_rshift1(mod_multiple + num_words, num_words);
}
uECC_vli_set(result, v[index], num_words);
}
/* Computes result = (left * right) % mod. */
uECC_VLI_API void uECC_vli_modMult(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_word_t product[2 * uECC_MAX_WORDS];
uECC_vli_mult(product, left, right, num_words);
uECC_vli_mmod(result, product, mod, num_words);
}
uECC_VLI_API void uECC_vli_modMult_fast(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *right,
uECC_Curve curve) {
uECC_word_t product[2 * uECC_MAX_WORDS];
uECC_vli_mult(product, left, right, curve->num_words);
#if (uECC_OPTIMIZATION_LEVEL > 0)
curve->mmod_fast(result, product);
#else
uECC_vli_mmod(result, product, curve->p, curve->num_words);
#endif
}
#if uECC_SQUARE_FUNC
#if uECC_ENABLE_VLI_API
/* Computes result = left^2 % mod. */
uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_word_t product[2 * uECC_MAX_WORDS];
uECC_vli_square(product, left, num_words);
uECC_vli_mmod(result, product, mod, num_words);
}
#endif /* uECC_ENABLE_VLI_API */
uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result,
const uECC_word_t *left,
uECC_Curve curve) {
uECC_word_t product[2 * uECC_MAX_WORDS];
uECC_vli_square(product, left, curve->num_words);
#if (uECC_OPTIMIZATION_LEVEL > 0)
curve->mmod_fast(result, product);
#else
uECC_vli_mmod(result, product, curve->p, curve->num_words);
#endif
}
#else /* uECC_SQUARE_FUNC */
#if uECC_ENABLE_VLI_API
uECC_VLI_API void uECC_vli_modSquare(uECC_word_t *result,
const uECC_word_t *left,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_vli_modMult(result, left, left, mod, num_words);
}
#endif /* uECC_ENABLE_VLI_API */
uECC_VLI_API void uECC_vli_modSquare_fast(uECC_word_t *result,
const uECC_word_t *left,
uECC_Curve curve) {
uECC_vli_modMult_fast(result, left, left, curve);
}
#endif /* uECC_SQUARE_FUNC */
#define EVEN(vli) (!(vli[0] & 1))
static void vli_modInv_update(uECC_word_t *uv,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_word_t carry = 0;
if (!EVEN(uv)) {
carry = uECC_vli_add(uv, uv, mod, num_words);
}
uECC_vli_rshift1(uv, num_words);
if (carry) {
uv[num_words - 1] |= HIGH_BIT_SET;
}
}
/* Computes result = (1 / input) % mod. All VLIs are the same size.
See "From Euclid's GCD to Montgomery Multiplication to the Great Divide" */
uECC_VLI_API void uECC_vli_modInv(uECC_word_t *result,
const uECC_word_t *input,
const uECC_word_t *mod,
wordcount_t num_words) {
uECC_word_t a[uECC_MAX_WORDS], b[uECC_MAX_WORDS], u[uECC_MAX_WORDS], v[uECC_MAX_WORDS];
cmpresult_t cmpResult;
if (uECC_vli_isZero(input, num_words)) {
uECC_vli_clear(result, num_words);
return;
}
uECC_vli_set(a, input, num_words);
uECC_vli_set(b, mod, num_words);
uECC_vli_clear(u, num_words);
u[0] = 1;
uECC_vli_clear(v, num_words);
while ((cmpResult = uECC_vli_cmp_unsafe(a, b, num_words)) != 0) {
if (EVEN(a)) {
uECC_vli_rshift1(a, num_words);
vli_modInv_update(u, mod, num_words);
} else if (EVEN(b)) {
uECC_vli_rshift1(b, num_words);
vli_modInv_update(v, mod, num_words);
} else if (cmpResult > 0) {
uECC_vli_sub(a, a, b, num_words);
uECC_vli_rshift1(a, num_words);
if (uECC_vli_cmp_unsafe(u, v, num_words) < 0) {
uECC_vli_add(u, u, mod, num_words);
}
uECC_vli_sub(u, u, v, num_words);
vli_modInv_update(u, mod, num_words);
} else {
uECC_vli_sub(b, b, a, num_words);
uECC_vli_rshift1(b, num_words);
if (uECC_vli_cmp_unsafe(v, u, num_words) < 0) {
uECC_vli_add(v, v, mod, num_words);
}
uECC_vli_sub(v, v, u, num_words);
vli_modInv_update(v, mod, num_words);
}
}
uECC_vli_set(result, u, num_words);
}
/* ------ Point operations ------ */
#include "curve-specific.inc"
/* Returns 1 if 'point' is the point at infinity, 0 otherwise. */
#define EccPoint_isZero(point, curve) uECC_vli_isZero((point), (curve)->num_words * 2)
/* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates.
From http://eprint.iacr.org/2011/338.pdf
*/
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
static void apply_z(uECC_word_t * X1,
uECC_word_t * Y1,
const uECC_word_t * const Z,
uECC_Curve curve) {
uECC_word_t t1[uECC_MAX_WORDS];
uECC_vli_modSquare_fast(t1, Z, curve); /* z^2 */
uECC_vli_modMult_fast(X1, X1, t1, curve); /* x1 * z^2 */
uECC_vli_modMult_fast(t1, t1, Z, curve); /* z^3 */
uECC_vli_modMult_fast(Y1, Y1, t1, curve); /* y1 * z^3 */
}
/* P = (x1, y1) => 2P, (x2, y2) => P' */
static void XYcZ_initial_double(uECC_word_t * X1,
uECC_word_t * Y1,
uECC_word_t * X2,
uECC_word_t * Y2,
const uECC_word_t * const initial_Z,
uECC_Curve curve) {
uECC_word_t z[uECC_MAX_WORDS];
wordcount_t num_words = curve->num_words;
if (initial_Z) {
uECC_vli_set(z, initial_Z, num_words);
} else {
uECC_vli_clear(z, num_words);
z[0] = 1;
}
uECC_vli_set(X2, X1, num_words);
uECC_vli_set(Y2, Y1, num_words);
apply_z(X1, Y1, z, curve);
curve->double_jacobian(X1, Y1, z, curve);
apply_z(X2, Y2, z, curve);
}
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
or P => P', Q => P + Q
*/
static void XYcZ_add(uECC_word_t * X1,
uECC_word_t * Y1,
uECC_word_t * X2,
uECC_word_t * Y2,
uECC_Curve curve) {
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uECC_word_t t5[uECC_MAX_WORDS];
wordcount_t num_words = curve->num_words;
uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */
uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */
uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */
uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */
uECC_vli_modSquare_fast(t5, Y2, curve); /* t5 = (y2 - y1)^2 = D */
uECC_vli_modSub(t5, t5, X1, curve->p, num_words); /* t5 = D - B */
uECC_vli_modSub(t5, t5, X2, curve->p, num_words); /* t5 = D - B - C = x3 */
uECC_vli_modSub(X2, X2, X1, curve->p, num_words); /* t3 = C - B */
uECC_vli_modMult_fast(Y1, Y1, X2, curve); /* t2 = y1*(C - B) */
uECC_vli_modSub(X2, X1, t5, curve->p, num_words); /* t3 = B - x3 */
uECC_vli_modMult_fast(Y2, Y2, X2, curve); /* t4 = (y2 - y1)*(B - x3) */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y3 */
uECC_vli_set(X2, t5, num_words);
}
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
or P => P - Q, Q => P + Q
*/
static void XYcZ_addC(uECC_word_t * X1,
uECC_word_t * Y1,
uECC_word_t * X2,
uECC_word_t * Y2,
uECC_Curve curve) {
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uECC_word_t t5[uECC_MAX_WORDS];
uECC_word_t t6[uECC_MAX_WORDS];
uECC_word_t t7[uECC_MAX_WORDS];
wordcount_t num_words = curve->num_words;
uECC_vli_modSub(t5, X2, X1, curve->p, num_words); /* t5 = x2 - x1 */
uECC_vli_modSquare_fast(t5, t5, curve); /* t5 = (x2 - x1)^2 = A */
uECC_vli_modMult_fast(X1, X1, t5, curve); /* t1 = x1*A = B */
uECC_vli_modMult_fast(X2, X2, t5, curve); /* t3 = x2*A = C */
uECC_vli_modAdd(t5, Y2, Y1, curve->p, num_words); /* t5 = y2 + y1 */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = y2 - y1 */
uECC_vli_modSub(t6, X2, X1, curve->p, num_words); /* t6 = C - B */
uECC_vli_modMult_fast(Y1, Y1, t6, curve); /* t2 = y1 * (C - B) = E */
uECC_vli_modAdd(t6, X1, X2, curve->p, num_words); /* t6 = B + C */
uECC_vli_modSquare_fast(X2, Y2, curve); /* t3 = (y2 - y1)^2 = D */
uECC_vli_modSub(X2, X2, t6, curve->p, num_words); /* t3 = D - (B + C) = x3 */
uECC_vli_modSub(t7, X1, X2, curve->p, num_words); /* t7 = B - x3 */
uECC_vli_modMult_fast(Y2, Y2, t7, curve); /* t4 = (y2 - y1)*(B - x3) */
uECC_vli_modSub(Y2, Y2, Y1, curve->p, num_words); /* t4 = (y2 - y1)*(B - x3) - E = y3 */
uECC_vli_modSquare_fast(t7, t5, curve); /* t7 = (y2 + y1)^2 = F */
uECC_vli_modSub(t7, t7, t6, curve->p, num_words); /* t7 = F - (B + C) = x3' */
uECC_vli_modSub(t6, t7, X1, curve->p, num_words); /* t6 = x3' - B */
uECC_vli_modMult_fast(t6, t6, t5, curve); /* t6 = (y2+y1)*(x3' - B) */
uECC_vli_modSub(Y1, t6, Y1, curve->p, num_words); /* t2 = (y2+y1)*(x3' - B) - E = y3' */
uECC_vli_set(X1, t7, num_words);
}
/* result may overlap point. */
static void EccPoint_mult(uECC_word_t * result,
const uECC_word_t * point,
const uECC_word_t * scalar,
const uECC_word_t * initial_Z,
bitcount_t num_bits,
uECC_Curve curve) {
/* R0 and R1 */
uECC_word_t Rx[2][uECC_MAX_WORDS];
uECC_word_t Ry[2][uECC_MAX_WORDS];
uECC_word_t z[uECC_MAX_WORDS];
bitcount_t i;
uECC_word_t nb;
wordcount_t num_words = curve->num_words;
uECC_vli_set(Rx[1], point, num_words);
uECC_vli_set(Ry[1], point + num_words, num_words);
XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initial_Z, curve);
for (i = num_bits - 2; i > 0; --i) {
nb = !uECC_vli_testBit(scalar, i);
XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve);
XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve);
}
nb = !uECC_vli_testBit(scalar, 0);
XYcZ_addC(Rx[1 - nb], Ry[1 - nb], Rx[nb], Ry[nb], curve);
/* Find final 1/Z value. */
uECC_vli_modSub(z, Rx[1], Rx[0], curve->p, num_words); /* X1 - X0 */
uECC_vli_modMult_fast(z, z, Ry[1 - nb], curve); /* Yb * (X1 - X0) */
uECC_vli_modMult_fast(z, z, point, curve); /* xP * Yb * (X1 - X0) */
uECC_vli_modInv(z, z, curve->p, num_words); /* 1 / (xP * Yb * (X1 - X0)) */
/* yP / (xP * Yb * (X1 - X0)) */
uECC_vli_modMult_fast(z, z, point + num_words, curve);
uECC_vli_modMult_fast(z, z, Rx[1 - nb], curve); /* Xb * yP / (xP * Yb * (X1 - X0)) */
/* End 1/Z calculation */
XYcZ_add(Rx[nb], Ry[nb], Rx[1 - nb], Ry[1 - nb], curve);
apply_z(Rx[0], Ry[0], z, curve);
uECC_vli_set(result, Rx[0], num_words);
uECC_vli_set(result + num_words, Ry[0], num_words);
}
static uECC_word_t regularize_k(const uECC_word_t * const k,
uECC_word_t *k0,
uECC_word_t *k1,
uECC_Curve curve) {
wordcount_t num_n_words = BITS_TO_WORDS(curve->num_n_bits);
bitcount_t num_n_bits = curve->num_n_bits;
uECC_word_t carry = uECC_vli_add(k0, k, curve->n, num_n_words) ||
(num_n_bits < ((bitcount_t)num_n_words * uECC_WORD_SIZE * 8) &&
uECC_vli_testBit(k0, num_n_bits));
uECC_vli_add(k1, k0, curve->n, num_n_words);
return carry;
}
static uECC_word_t EccPoint_compute_public_key(uECC_word_t *result,
uECC_word_t *private,
uECC_Curve curve) {
uECC_word_t tmp1[uECC_MAX_WORDS];
uECC_word_t tmp2[uECC_MAX_WORDS];
uECC_word_t *p2[2] = {tmp1, tmp2};
uECC_word_t carry;
/* Regularize the bitcount for the private key so that attackers cannot use a side channel
attack to learn the number of leading zeros. */
carry = regularize_k(private, tmp1, tmp2, curve);
EccPoint_mult(result, curve->G, p2[!carry], 0, curve->num_n_bits + 1, curve);
if (EccPoint_isZero(result, curve)) {
return 0;
}
return 1;
}
#if uECC_WORD_SIZE == 1
uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes,
int num_bytes,
const uint8_t *native) {
wordcount_t i;
for (i = 0; i < num_bytes; ++i) {
bytes[i] = native[(num_bytes - 1) - i];
}
}
uECC_VLI_API void uECC_vli_bytesToNative(uint8_t *native,
const uint8_t *bytes,
int num_bytes) {
uECC_vli_nativeToBytes(native, num_bytes, bytes);
}
#else
uECC_VLI_API void uECC_vli_nativeToBytes(uint8_t *bytes,
int num_bytes,
const uECC_word_t *native) {
wordcount_t i;
for (i = 0; i < num_bytes; ++i) {
unsigned b = num_bytes - 1 - i;
bytes[i] = native[b / uECC_WORD_SIZE] >> (8 * (b % uECC_WORD_SIZE));
}
}
uECC_VLI_API void uECC_vli_bytesToNative(uECC_word_t *native,
const uint8_t *bytes,
int num_bytes) {
wordcount_t i;
uECC_vli_clear(native, (num_bytes + (uECC_WORD_SIZE - 1)) / uECC_WORD_SIZE);
for (i = 0; i < num_bytes; ++i) {
unsigned b = num_bytes - 1 - i;
native[b / uECC_WORD_SIZE] |=
(uECC_word_t)bytes[i] << (8 * (b % uECC_WORD_SIZE));
}
}
#endif /* uECC_WORD_SIZE */
/* Generates a random integer in the range 0 < random < top.
Both random and top have num_words words. */
uECC_VLI_API int uECC_generate_random_int(uECC_word_t *random,
const uECC_word_t *top,
wordcount_t num_words) {
uECC_word_t mask = (uECC_word_t)-1;
uECC_word_t tries;
bitcount_t num_bits = uECC_vli_numBits(top, num_words);
if (!g_rng_function) {
return 0;
}
for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
if (!g_rng_function((uint8_t *)random, num_words * uECC_WORD_SIZE)) {
return 0;
}
random[num_words - 1] &= mask >> ((bitcount_t)(num_words * uECC_WORD_SIZE * 8 - num_bits));
if (!uECC_vli_isZero(random, num_words) &&
uECC_vli_cmp(top, random, num_words) == 1) {
return 1;
}
}
return 0;
}
int uECC_make_key(uint8_t *public_key,
uint8_t *private_key,
uECC_Curve curve) {
uECC_word_t private[uECC_MAX_WORDS];
uECC_word_t public[uECC_MAX_WORDS * 2];
uECC_word_t tries;
for (tries = 0; tries < uECC_RNG_MAX_TRIES; ++tries) {
if (!uECC_generate_random_int(private, curve->n, BITS_TO_WORDS(curve->num_n_bits))) {
return 0;
}
if (EccPoint_compute_public_key(public, private, curve)) {
uECC_vli_nativeToBytes(private_key, BITS_TO_BYTES(curve->num_n_bits), private);
uECC_vli_nativeToBytes(public_key, curve->num_bytes, public);
uECC_vli_nativeToBytes(
public_key + curve->num_bytes, curve->num_bytes, public + curve->num_words);
return 1;
}
}