aboutsummaryrefslogtreecommitdiffstats
path: root/crypto/bn/bn_lib.c
blob: eb4a31849bef11837d273d7b7208b0e72d8caa3b (plain) (blame)
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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
/*
 * Copyright 1995-2020 The OpenSSL Project Authors. All Rights Reserved.
 *
 * Licensed under the OpenSSL license (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
 */

#include <assert.h>
#include <limits.h>
#include "internal/cryptlib.h"
#include "bn_local.h"
#include <openssl/opensslconf.h>
#include "internal/constant_time.h"

/* This stuff appears to be completely unused, so is deprecated */
#if OPENSSL_API_COMPAT < 0x00908000L
/*-
 * For a 32 bit machine
 * 2 -   4 ==  128
 * 3 -   8 ==  256
 * 4 -  16 ==  512
 * 5 -  32 == 1024
 * 6 -  64 == 2048
 * 7 - 128 == 4096
 * 8 - 256 == 8192
 */
static int bn_limit_bits = 0;
static int bn_limit_num = 8;    /* (1<<bn_limit_bits) */
static int bn_limit_bits_low = 0;
static int bn_limit_num_low = 8; /* (1<<bn_limit_bits_low) */
static int bn_limit_bits_high = 0;
static int bn_limit_num_high = 8; /* (1<<bn_limit_bits_high) */
static int bn_limit_bits_mont = 0;
static int bn_limit_num_mont = 8; /* (1<<bn_limit_bits_mont) */

void BN_set_params(int mult, int high, int low, int mont)
{
    if (mult >= 0) {
        if (mult > (int)(sizeof(int) * 8) - 1)
            mult = sizeof(int) * 8 - 1;
        bn_limit_bits = mult;
        bn_limit_num = 1 << mult;
    }
    if (high >= 0) {
        if (high > (int)(sizeof(int) * 8) - 1)
            high = sizeof(int) * 8 - 1;
        bn_limit_bits_high = high;
        bn_limit_num_high = 1 << high;
    }
    if (low >= 0) {
        if (low > (int)(sizeof(int) * 8) - 1)
            low = sizeof(int) * 8 - 1;
        bn_limit_bits_low = low;
        bn_limit_num_low = 1 << low;
    }
    if (mont >= 0) {
        if (mont > (int)(sizeof(int) * 8) - 1)
            mont = sizeof(int) * 8 - 1;
        bn_limit_bits_mont = mont;
        bn_limit_num_mont = 1 << mont;
    }
}

int BN_get_params(int which)
{
    if (which == 0)
        return bn_limit_bits;
    else if (which == 1)
        return bn_limit_bits_high;
    else if (which == 2)
        return bn_limit_bits_low;
    else if (which == 3)
        return bn_limit_bits_mont;
    else
        return 0;
}
#endif

const BIGNUM *BN_value_one(void)
{
    static const BN_ULONG data_one = 1L;
    static const BIGNUM const_one =
        { (BN_ULONG *)&data_one, 1, 1, 0, BN_FLG_STATIC_DATA };

    return &const_one;
}

/*
 * Old Visual Studio ARM compiler miscompiles BN_num_bits_word()
 * https://mta.openssl.org/pipermail/openssl-users/2018-August/008465.html
 */
#if defined(_MSC_VER) && defined(_ARM_) && defined(_WIN32_WCE) \
    && _MSC_VER>=1400 && _MSC_VER<1501
# define MS_BROKEN_BN_num_bits_word
# pragma optimize("", off)
#endif
int BN_num_bits_word(BN_ULONG l)
{
    BN_ULONG x, mask;
    int bits = (l != 0);

#if BN_BITS2 > 32
    x = l >> 32;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 32 & mask;
    l ^= (x ^ l) & mask;
#endif

    x = l >> 16;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 16 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 8;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 8 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 4;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 4 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 2;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 2 & mask;
    l ^= (x ^ l) & mask;

    x = l >> 1;
    mask = (0 - x) & BN_MASK2;
    mask = (0 - (mask >> (BN_BITS2 - 1)));
    bits += 1 & mask;

    return bits;
}
#ifdef MS_BROKEN_BN_num_bits_word
# pragma optimize("", on)
#endif

/*
 * This function still leaks `a->dmax`: it's caller's responsibility to
 * expand the input `a` in advance to a public length.
 */
static ossl_inline
int bn_num_bits_consttime(const BIGNUM *a)
{
    int j, ret;
    unsigned int mask, past_i;
    int i = a->top - 1;
    bn_check_top(a);

    for (j = 0, past_i = 0, ret = 0; j < a->dmax; j++) {
        mask = constant_time_eq_int(i, j); /* 0xff..ff if i==j, 0x0 otherwise */

        ret += BN_BITS2 & (~mask & ~past_i);
        ret += BN_num_bits_word(a->d[j]) & mask;

        past_i |= mask; /* past_i will become 0xff..ff after i==j */
    }

    /*
     * if BN_is_zero(a) => i is -1 and ret contains garbage, so we mask the
     * final result.
     */
    mask = ~(constant_time_eq_int(i, ((int)-1)));

    return ret & mask;
}

int BN_num_bits(const BIGNUM *a)
{
    int i = a->top - 1;
    bn_check_top(a);

    if (a->flags & BN_FLG_CONSTTIME) {
        /*
         * We assume that BIGNUMs flagged as CONSTTIME have also been expanded
         * so that a->dmax is not leaking secret information.
         *
         * In other words, it's the caller's responsibility to ensure `a` has
         * been preallocated in advance to a public length if we hit this
         * branch.
         *
         */
        return bn_num_bits_consttime(a);
    }

    if (BN_is_zero(a))
        return 0;

    return ((i * BN_BITS2) + BN_num_bits_word(a->d[i]));
}

static void bn_free_d(BIGNUM *a, int clear)
{
    if (BN_get_flags(a, BN_FLG_SECURE))
        OPENSSL_secure_clear_free(a->d, a->dmax * sizeof(a->d[0]));
    else if (clear != 0)
        OPENSSL_clear_free(a->d, a->dmax * sizeof(a->d[0]));
    else
        OPENSSL_free(a->d);
}


void BN_clear_free(BIGNUM *a)
{
    if (a == NULL)
        return;
    if (a->d != NULL && !BN_get_flags(a, BN_FLG_STATIC_DATA))
        bn_free_d(a, 1);
    if (BN_get_flags(a, BN_FLG_MALLOCED)) {
        OPENSSL_cleanse(a, sizeof(*a));
        OPENSSL_free(a);
    }
}

void BN_free(BIGNUM *a)
{
    if (a == NULL)
        return;
    if (!BN_get_flags(a, BN_FLG_STATIC_DATA))
        bn_free_d(a, 0);
    if (a->flags & BN_FLG_MALLOCED)
        OPENSSL_free(a);
}

void bn_init(BIGNUM *a)
{
    static BIGNUM nilbn;

    *a = nilbn;
    bn_check_top(a);
}

BIGNUM *BN_new(void)
{
    BIGNUM *ret;

    if ((ret = OPENSSL_zalloc(sizeof(*ret))) == NULL) {
        BNerr(BN_F_BN_NEW, ERR_R_MALLOC_FAILURE);
        return NULL;
    }
    ret->flags = BN_FLG_MALLOCED;
    bn_check_top(ret);
    return ret;
}

 BIGNUM *BN_secure_new(void)
 {
     BIGNUM *ret = BN_new();
     if (ret != NULL)
         ret->flags |= BN_FLG_SECURE;
     return ret;
 }

/* This is used by bn_expand2() */
/* The caller MUST check that words > b->dmax before calling this */
static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
{
    BN_ULONG *a = NULL;

    if (words > (INT_MAX / (4 * BN_BITS2))) {
        BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_BIGNUM_TOO_LONG);
        return NULL;
    }
    if (BN_get_flags(b, BN_FLG_STATIC_DATA)) {
        BNerr(BN_F_BN_EXPAND_INTERNAL, BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
        return NULL;
    }
    if (BN_get_flags(b, BN_FLG_SECURE))
        a = OPENSSL_secure_zalloc(words * sizeof(*a));
    else
        a = OPENSSL_zalloc(words * sizeof(*a));
    if (a == NULL) {
        BNerr(BN_F_BN_EXPAND_INTERNAL, ERR_R_MALLOC_FAILURE);
        return NULL;
    }

    assert(b->top <= words);
    if (b->top > 0)
        memcpy(a, b->d, sizeof(*a) * b->top);

    return a;
}

/*
 * This is an internal function that should not be used in applications. It
 * ensures that 'b' has enough room for a 'words' word number and initialises
 * any unused part of b->d with leading zeros. It is mostly used by the
 * various BIGNUM routines. If there is an error, NULL is returned. If not,
 * 'b' is returned.
 */

BIGNUM *bn_expand2(BIGNUM *b, int words)
{
    if (words > b->dmax) {
        BN_ULONG *a = bn_expand_internal(b, words);
        if (!a)
            return NULL;
        if (b->d != NULL)
            bn_free_d(b, 1);
        b->d = a;
        b->dmax = words;
    }

    return b;
}

BIGNUM *BN_dup(const BIGNUM *a)
{
    BIGNUM *t;

    if (a == NULL)
        return NULL;
    bn_check_top(a);

    t = BN_get_flags(a, BN_FLG_SECURE) ? BN_secure_new() : BN_new();
    if (t == NULL)
        return NULL;
    if (!BN_copy(t, a)) {
        BN_free(t);
        return NULL;
    }
    bn_check_top(t);
    return t;
}

BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
{
    int bn_words;

    bn_check_top(b);

    bn_words = BN_get_flags(b, BN_FLG_CONSTTIME) ? b->dmax : b->top;

    if (a == b)
        return a;
    if (bn_wexpand(a, bn_words) == NULL)
        return NULL;

    if (b->top > 0)
        memcpy(a->d, b->d, sizeof(b->d[0]) * bn_words);

    a->neg = b->neg;
    a->top = b->top;
    a->flags |= b->flags & BN_FLG_FIXED_TOP;
    bn_check_top(a);
    return a;
}

#define FLAGS_DATA(flags) ((flags) & (BN_FLG_STATIC_DATA \
                                    | BN_FLG_CONSTTIME   \
                                    | BN_FLG_SECURE      \
                                    | BN_FLG_FIXED_TOP))
#define FLAGS_STRUCT(flags) ((flags) & (BN_FLG_MALLOCED))

void BN_swap(BIGNUM *a, BIGNUM *b)
{
    int flags_old_a, flags_old_b;
    BN_ULONG *tmp_d;
    int tmp_top, tmp_dmax, tmp_neg;

    bn_check_top(a);
    bn_check_top(b);

    flags_old_a = a->flags;
    flags_old_b = b->flags;

    tmp_d = a->d;
    tmp_top = a->top;
    tmp_dmax = a->dmax;
    tmp_neg = a->neg;

    a->d = b->d;
    a->top = b->top;
    a->dmax = b->dmax;
    a->neg = b->neg;

    b->d = tmp_d;
    b->top = tmp_top;
    b->dmax = tmp_dmax;
    b->neg = tmp_neg;

    a->flags = FLAGS_STRUCT(flags_old_a) | FLAGS_DATA(flags_old_b);
    b->flags = FLAGS_STRUCT(flags_old_b) | FLAGS_DATA(flags_old_a);
    bn_check_top(a);
    bn_check_top(b);
}

void BN_clear(BIGNUM *a)
{
    if (a == NULL)
        return;
    bn_check_top(a);
    if (a->d != NULL)
        OPENSSL_cleanse(a->d, sizeof(*a->d) * a->dmax);
    a->neg = 0;
    a->top = 0;
    a->flags &= ~BN_FLG_FIXED_TOP;
}

BN_ULONG BN_get_word(const BIGNUM *a)
{
    if (a->top > 1)
        return BN_MASK2;
    else if (a->top == 1)
        return a->d[0];
    /* a->top == 0 */
    return 0;
}

int BN_set_word(BIGNUM *a, BN_ULONG w)
{
    bn_check_top(a);
    if (bn_expand(a, (int)sizeof(BN_ULONG) * 8) == NULL)
        return 0;
    a->neg = 0;
    a->d[0] = w;
    a->top = (w ? 1 : 0);
    a->flags &= ~BN_FLG_FIXED_TOP;
    bn_check_top(a);
    return 1;
}

BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
    unsigned int i, m;
    unsigned int n;
    BN_ULONG l;
    BIGNUM *bn = NULL;

    if (ret == NULL)
        ret = bn = BN_new();
    if (ret == NULL)
        return NULL;
    bn_check_top(ret);
    /* Skip leading zero's. */
    for ( ; len > 0 && *s == 0; s++, len--)
        continue;
    n = len;
    if (n == 0) {
        ret->top = 0;
        return ret;
    }
    i = ((n - 1) / BN_BYTES) + 1;
    m = ((n - 1) % (BN_BYTES));
    if (bn_wexpand(ret, (int)i) == NULL) {
        BN_free(bn);
        return NULL;
    }
    ret->top = i;
    ret->neg = 0;
    l = 0;
    while (n--) {
        l = (l << 8L) | *(s++);
        if (m-- == 0) {
            ret->d[--i] = l;
            l = 0;
            m = BN_BYTES - 1;
        }
    }
    /*
     * need to call this due to clear byte at top if avoiding having the top
     * bit set (-ve number)
     */
    bn_correct_top(ret);
    return ret;
}

typedef enum {big, little} endianess_t;

/* ignore negative */
static
int bn2binpad(const BIGNUM *a, unsigned char *to, int tolen, endianess_t endianess)
{
    int n;
    size_t i, lasti, j, atop, mask;
    BN_ULONG l;

    /*
     * In case |a| is fixed-top, BN_num_bytes can return bogus length,
     * but it's assumed that fixed-top inputs ought to be "nominated"
     * even for padded output, so it works out...
     */
    n = BN_num_bytes(a);
    if (tolen == -1) {
        tolen = n;
    } else if (tolen < n) {     /* uncommon/unlike case */
        BIGNUM temp = *a;

        bn_correct_top(&temp);
        n = BN_num_bytes(&temp);
        if (tolen < n)
            return -1;
    }

    /* Swipe through whole available data and don't give away padded zero. */
    atop = a->dmax * BN_BYTES;
    if (atop == 0) {
        OPENSSL_cleanse(to, tolen);
        return tolen;
    }

    lasti = atop - 1;
    atop = a->top * BN_BYTES;
    if (endianess == big)
        to += tolen; /* start from the end of the buffer */
    for (i = 0, j = 0; j < (size_t)tolen; j++) {
        unsigned char val;
        l = a->d[i / BN_BYTES];
        mask = 0 - ((j - atop) >> (8 * sizeof(i) - 1));
        val = (unsigned char)(l >> (8 * (i % BN_BYTES)) & mask);
        if (endianess == big)
            *--to = val;
        else
            *to++ = val;
        i += (i - lasti) >> (8 * sizeof(i) - 1); /* stay on last limb */
    }

    return tolen;
}

int BN_bn2binpad(const BIGNUM *a, unsigned char *to, int tolen)
{
    if (tolen < 0)
        return -1;
    return bn2binpad(a, to, tolen, big);
}

int BN_bn2bin(const BIGNUM *a, unsigned char *to)
{
    return bn2binpad(a, to, -1, big);
}

BIGNUM *BN_lebin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
    unsigned int i, m;
    unsigned int n;
    BN_ULONG l;
    BIGNUM *bn = NULL;

    if (ret == NULL)
        ret = bn = BN_new();
    if (ret == NULL)
        return NULL;
    bn_check_top(ret);
    s += len;
    /* Skip trailing zeroes. */
    for ( ; len > 0 && s[-1] == 0; s--, len--)
        continue;
    n = len;
    if (n == 0) {
        ret->top = 0;
        return ret;
    }
    i = ((n - 1) / BN_BYTES) + 1;
    m = ((n - 1) % (BN_BYTES));
    if (bn_wexpand(ret, (int)i) == NULL) {
        BN_free(bn);
        return NULL;
    }
    ret->top = i;
    ret->neg = 0;
    l = 0;
    while (n--) {
        s--;
        l = (l << 8L) | *s;
        if (m-- == 0) {
            ret->d[--i] = l;
            l = 0;
            m = BN_BYTES - 1;
        }
    }
    /*
     * need to call this due to clear byte at top if avoiding having the top
     * bit set (-ve number)
     */
    bn_correct_top(ret);
    return ret;
}

int BN_bn2lebinpad(const BIGNUM *a, unsigned char *to, int tolen)
{
    if (tolen < 0)
        return -1;
    return bn2binpad(a, to, tolen, little);
}

int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
{
    int i;
    BN_ULONG t1, t2, *ap, *bp;

    bn_check_top(a);
    bn_check_top(b);

    i = a->top - b->top;
    if (i != 0)
        return i;
    ap = a->d;
    bp = b->d;
    for (i = a->top - 1; i >= 0; i--) {
        t1 = ap[i];
        t2 = bp[i];
        if (t1 != t2)
            return ((t1 > t2) ? 1 : -1);
    }
    return 0;
}

int BN_cmp(const BIGNUM *a, const BIGNUM *b)
{
    int i;
    int gt, lt;
    BN_ULONG t1, t2;

    if ((a == NULL) || (b == NULL)) {
        if (a != NULL)
            return -1;
        else if (b != NULL)
            return 1;
        else
            return 0;
    }

    bn_check_top(a);
    bn_check_top(b);

    if (a->neg != b->neg) {
        if (a->neg)
            return -1;
        else
            return 1;
    }
    if (a->neg == 0) {
        gt = 1;
        lt = -1;
    } else {
        gt = -1;
        lt = 1;
    }

    if (a->top > b->top)
        return gt;
    if (a->top < b->top)
        return lt;
    for (i = a->top - 1; i >= 0; i--) {
        t1 = a->d[i];
        t2 = b->d[i];
        if (t1 > t2)
            return gt;
        if (t1 < t2)
            return lt;
    }
    return 0;
}

int BN_set_bit(BIGNUM *a, int n)
{
    int i, j, k;

    if (n < 0)
        return 0;

    i = n / BN_BITS2;
    j = n % BN_BITS2;
    if (a->top <= i) {
        if (bn_wexpand(a, i + 1) == NULL)
            return 0;
        for (k = a->top; k < i + 1; k++)
            a->d[k] = 0;
        a->top = i + 1;
        a->flags &= ~BN_FLG_FIXED_TOP;
    }

    a->d[i] |= (((BN_ULONG)1) << j);
    bn_check_top(a);
    return 1;
}

int BN_clear_bit(BIGNUM *a, int n)
{
    int i, j;

    bn_check_top(a);
    if (n < 0)
        return 0;

    i = n / BN_BITS2;
    j = n % BN_BITS2;
    if (a->top <= i)
        return 0;

    a->d[i] &= (~(((BN_ULONG)1) << j));
    bn_correct_top(a);
    return 1;
}

int BN_is_bit_set(const BIGNUM *a, int n)
{
    int i, j;

    bn_check_top(a);
    if (n < 0)
        return 0;
    i = n / BN_BITS2;
    j = n % BN_BITS2;
    if (a->top <= i)
        return 0;
    return (int)(((a->d[i]) >> j) & ((BN_ULONG)1));
}

int BN_mask_bits(BIGNUM *a, int n)
{
    int b, w;

    bn_check_top(a);
    if (n < 0)
        return 0;

    w = n / BN_BITS2;
    b = n % BN_BITS2;
    if (w >= a->top)
        return 0;
    if (b == 0)
        a->top = w;
    else {
        a->top = w + 1;
        a->d[w] &= ~(BN_MASK2 << b);
    }
    bn_correct_top(a);
    return 1;
}

void BN_set_negative(BIGNUM *a, int b)
{
    if (b && !BN_is_zero(a))
        a->neg = 1;
    else
        a->neg = 0;
}

int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
{
    int i;
    BN_ULONG aa, bb;

    if (n == 0)
        return 0;

    aa = a[n - 1];
    bb = b[n - 1];
    if (aa != bb)
        return ((aa > bb) ? 1 : -1);
    for (i = n - 2; i >= 0; i--) {
        aa = a[i];
        bb = b[i];
        if (aa != bb)
            return ((aa > bb) ? 1 : -1);
    }
    return 0;
}

/*
 * Here follows a specialised variants of bn_cmp_words().  It has the
 * capability of performing the operation on arrays of different sizes. The
 * sizes of those arrays is expressed through cl, which is the common length
 * ( basically, min(len(a),len(b)) ), and dl, which is the delta between the
 * two lengths, calculated as len(a)-len(b). All lengths are the number of
 * BN_ULONGs...
 */

int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl)
{
    int n, i;
    n = cl - 1;

    if (dl < 0) {
        for (i = dl; i < 0; i++) {
            if (b[n - i] != 0)
                return -1;      /* a < b */
        }
    }
    if (dl > 0) {
        for (i = dl; i > 0; i--) {
            if (a[n + i] != 0)
                return 1;       /* a > b */
        }
    }
    return bn_cmp_words(a, b, cl);
}

/*-
 * Constant-time conditional swap of a and b.
 * a and b are swapped if condition is not 0.
 * nwords is the number of words to swap.
 * Assumes that at least nwords are allocated in both a and b.
 * Assumes that no more than nwords are used by either a or b.
 */
void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
{
    BN_ULONG t;
    int i;

    if (a == b)
        return;

    bn_wcheck_size(a, nwords);
    bn_wcheck_size(b, nwords);

    condition = ((~condition & ((condition - 1))) >> (BN_BITS2 - 1)) - 1;

    t = (a->top ^ b->top) & condition;
    a->top ^= t;
    b->top ^= t;

    t = (a->neg ^ b->neg) & condition;
    a->neg ^= t;
    b->neg ^= t;

    /*-
     * BN_FLG_STATIC_DATA: indicates that data may not be written to. Intention
     * is actually to treat it as it's read-only data, and some (if not most)
     * of it does reside in read-only segment. In other words observation of
     * BN_FLG_STATIC_DATA in BN_consttime_swap should be treated as fatal
     * condition. It would either cause SEGV or effectively cause data
     * corruption.
     *
     * BN_FLG_MALLOCED: refers to BN structure itself, and hence must be
     * preserved.
     *
     * BN_FLG_SECURE: must be preserved, because it determines how x->d was
     * allocated and hence how to free it.
     *
     * BN_FLG_CONSTTIME: sufficient to mask and swap
     *
     * BN_FLG_FIXED_TOP: indicates that we haven't called bn_correct_top() on
     * the data, so the d array may be padded with additional 0 values (i.e.
     * top could be greater than the minimal value that it could be). We should
     * be swapping it
     */

#define BN_CONSTTIME_SWAP_FLAGS (BN_FLG_CONSTTIME | BN_FLG_FIXED_TOP)

    t = ((a->flags ^ b->flags) & BN_CONSTTIME_SWAP_FLAGS) & condition;
    a->flags ^= t;
    b->flags ^= t;

    /* conditionally swap the data */
    for (i = 0; i < nwords; i++) {
        t = (a->d[i] ^ b->d[i]) & condition;
        a->d[i] ^= t;
        b->d[i] ^= t;
    }
}

#undef BN_CONSTTIME_SWAP_FLAGS

/* Bits of security, see SP800-57 */

int BN_security_bits(int L, int N)
{
    int secbits, bits;
    if (L >= 15360)
        secbits = 256;
    else if (L >= 7680)
        secbits = 192;
    else if (L >= 3072)
        secbits = 128;
    else if (L >= 2048)
        secbits = 112;
    else if (L >= 1024)
        secbits = 80;
    else
        return 0;
    if (N == -1)
        return secbits;
    bits = N / 2;
    if (bits < 80)
        return 0;
    return bits >= secbits ? secbits : bits;
}

void BN_zero_ex(BIGNUM *a)
{
    a->neg = 0;
    a->top = 0;
    a->flags &= ~BN_FLG_FIXED_TOP;
}

int BN_abs_is_word(const BIGNUM *a, const BN_ULONG w)
{
    return ((a->top == 1) && (a->d[0] == w)) || ((w == 0) && (a->top == 0));
}

int BN_is_zero(const BIGNUM *a)
{
    return a->top == 0;
}

int BN_is_one(const BIGNUM *a)
{
    return BN_abs_is_word(a, 1) && !a->neg;
}

int BN_is_word(const BIGNUM *a, const BN_ULONG w)
{
    return BN_abs_is_word(a, w) && (!w || !a->neg);
}

int BN_is_odd(const BIGNUM *a)
{
    return (a->top > 0) && (a->d[0] & 1);
}

int BN_is_negative(const BIGNUM *a)
{
    return (a->neg != 0);
}

int BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont,
                     BN_CTX *ctx)
{
    return BN_mod_mul_montgomery(r, a, &(mont->RR), mont, ctx);
}

void BN_with_flags(BIGNUM *dest, const BIGNUM *b, int flags)
{
    dest->d = b->d;
    dest->top = b->top;
    dest->dmax = b->dmax;
    dest->neg = b->neg;
    dest->flags = ((dest->flags & BN_FLG_MALLOCED)
                   | (b->flags & ~BN_FLG_MALLOCED)
                   | BN_FLG_STATIC_DATA | flags);
}

BN_GENCB *BN_GENCB_new(void)
{
    BN_GENCB *ret;

    if ((ret = OPENSSL_malloc(sizeof(*ret))) == NULL) {
        BNerr(BN_F_BN_GENCB_NEW, ERR_R_MALLOC_FAILURE);
        return NULL;
    }

    return ret;
}

void BN_GENCB_free(BN_GENCB *cb)
{
    if (cb == NULL)
        return;
    OPENSSL_free(cb);
}

void BN_set_flags(BIGNUM *b, int n)
{
    b->flags |= n;
}

int BN_get_flags(const BIGNUM *b, int n)
{
    return b->flags & n;
}

/* Populate a BN_GENCB structure with an "old"-style callback */
void BN_GENCB_set_old(BN_GENCB *gencb, void (*callback) (int, int, void *),
                      void *cb_arg)
{
    BN_GENCB *tmp_gencb = gencb;
    tmp_gencb->ver = 1;
    tmp_gencb->arg = cb_arg;
    tmp_gencb->cb.cb_1 = callback;
}

/* Populate a BN_GENCB structure with a "new"-style callback */
void BN_GENCB_set(BN_GENCB *gencb, int (*callback) (int, int, BN_GENCB *),
                  void *cb_arg)
{
    BN_GENCB *tmp_gencb = gencb;
    tmp_gencb->ver = 2;
    tmp_gencb->arg = cb_arg;
    tmp_gencb->cb.cb_2 = callback;
}

void *BN_GENCB_get_arg(BN_GENCB *cb)
{
    return cb->arg;
}

BIGNUM *bn_wexpand(BIGNUM *a, int words)
{
    return (words <= a->dmax) ? a : bn_expand2(a, words);
}

void bn_correct_top(BIGNUM *a)
{
    BN_ULONG *ftl;
    int tmp_top = a->top;

    if (tmp_top > 0) {
        for (ftl = &(a->d[tmp_top]); tmp_top > 0; tmp_top--) {
            ftl--;
            if (*ftl != 0)
                break;
        }
        a->top = tmp_top;
    }
    if (a->top == 0)
        a->neg = 0;
    a->flags &= ~BN_FLG_FIXED_TOP;
    bn_pollute(a);
}