summaryrefslogtreecommitdiff
path: root/lib/libcrypto/bn/bn_lib.c
blob: 4ee9b2bbdec95ec08604a958a82d8a3ef948f0ed (plain)
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
/* $OpenBSD: bn_lib.c,v 1.32 2014/07/11 08:44:48 jsing Exp $ */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 *
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 *
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 *
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */

#ifndef BN_DEBUG
# undef NDEBUG /* avoid conflicting definitions */
# define NDEBUG
#endif

#include <assert.h>
#include <limits.h>
#include <stdio.h>
#include <string.h>

#include <openssl/opensslconf.h>

#include <openssl/err.h>

#include "bn_lcl.h"

/* This stuff appears to be completely unused, so is deprecated */
#ifndef OPENSSL_NO_DEPRECATED
/* 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);
}

int
BN_num_bits_word(BN_ULONG l)
{
	static const unsigned char bits[256] = {
		0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
		5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
		6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
		6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
		7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
		7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
		7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
		7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,  8, 8, 8, 8,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
		8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
	};

#ifdef _LP64
	if (l & 0xffffffff00000000L) {
		if (l & 0xffff000000000000L) {
			if (l & 0xff00000000000000L) {
				return (bits[(int)(l >> 56)] + 56);
			} else
				return (bits[(int)(l >> 48)] + 48);
		} else {
			if (l & 0x0000ff0000000000L) {
				return (bits[(int)(l >> 40)] + 40);
			} else
				return (bits[(int)(l >> 32)] + 32);
		}
	} else
#endif
	{
		if (l & 0xffff0000L) {
			if (l & 0xff000000L)
				return (bits[(int)(l >> 24L)] + 24);
			else
				return (bits[(int)(l >> 16L)] + 16);
		} else {
			if (l & 0xff00L)
				return (bits[(int)(l >> 8)] + 8);
			else
				return (bits[(int)(l)]);
		}
	}
}

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

	bn_check_top(a);

	if (BN_is_zero(a))
		return 0;
	return ((i * BN_BITS2) + BN_num_bits_word(a->d[i]));
}

void
BN_clear_free(BIGNUM *a)
{
	int i;

	if (a == NULL)
		return;
	bn_check_top(a);
	if (a->d != NULL && !(BN_get_flags(a, BN_FLG_STATIC_DATA))) {
		OPENSSL_cleanse(a->d, a->dmax * sizeof(a->d[0]));
		free(a->d);
	}
	i = BN_get_flags(a, BN_FLG_MALLOCED);
	OPENSSL_cleanse(a, sizeof(BIGNUM));
	if (i)
		free(a);
}

void
BN_free(BIGNUM *a)
{
	BN_clear_free(a);
}

void
BN_init(BIGNUM *a)
{
	memset(a, 0, sizeof(BIGNUM));
	bn_check_top(a);
}

BIGNUM *
BN_new(void)
{
	BIGNUM *ret;

	if ((ret = malloc(sizeof(BIGNUM))) == NULL) {
		BNerr(BN_F_BN_NEW, ERR_R_MALLOC_FAILURE);
		return (NULL);
	}
	ret->flags = BN_FLG_MALLOCED;
	ret->top = 0;
	ret->neg = 0;
	ret->dmax = 0;
	ret->d = NULL;
	bn_check_top(ret);
	return (ret);
}

/* This is used both by bn_expand2() and bn_dup_expand() */
/* 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, *a = NULL;
	const BN_ULONG *B;
	int i;

	bn_check_top(b);

	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);
	}
	a = A = reallocarray(NULL, words, sizeof(BN_ULONG));
	if (A == NULL) {
		BNerr(BN_F_BN_EXPAND_INTERNAL, ERR_R_MALLOC_FAILURE);
		return (NULL);
	}
#if 1
	B = b->d;
	/* Check if the previous number needs to be copied */
	if (B != NULL) {
		for (i = b->top >> 2; i > 0; i--, A += 4, B += 4) {
			/*
			 * The fact that the loop is unrolled
			 * 4-wise is a tribute to Intel. It's
			 * the one that doesn't have enough
			 * registers to accomodate more data.
			 * I'd unroll it 8-wise otherwise:-)
			 *
			 *		<appro@fy.chalmers.se>
			 */
			BN_ULONG a0, a1, a2, a3;
			a0 = B[0];
			a1 = B[1];
			a2 = B[2];
			a3 = B[3];
			A[0] = a0;
			A[1] = a1;
			A[2] = a2;
			A[3] = a3;
		}
		switch (b->top & 3) {
		case 3:
			A[2] = B[2];
		case 2:
			A[1] = B[1];
		case 1:
			A[0] = B[0];
		}
	}

#else
	memset(A, 0, sizeof(BN_ULONG) * words);
	memcpy(A, b->d, sizeof(b->d[0]) * b->top);
#endif

	return (a);
}

/* This is an internal function that can be used instead of bn_expand2()
 * when there is a need to copy BIGNUMs instead of only expanding the
 * data part, while still expanding them.
 * Especially useful when needing to expand BIGNUMs that are declared
 * 'const' and should therefore not be changed.
 * The reason to use this instead of a BN_dup() followed by a bn_expand2()
 * is memory allocation overhead.  A BN_dup() followed by a bn_expand2()
 * will allocate new memory for the BIGNUM data twice, and free it once,
 * while bn_dup_expand() makes sure allocation is made only once.
 */

#ifndef OPENSSL_NO_DEPRECATED
BIGNUM *
bn_dup_expand(const BIGNUM *b, int words)
{
	BIGNUM *r = NULL;

	bn_check_top(b);

	/* This function does not work if
	 *      words <= b->dmax && top < words
	 * because BN_dup() does not preserve 'dmax'!
	 * (But bn_dup_expand() is not used anywhere yet.)
	 */

	if (words > b->dmax) {
		BN_ULONG *a = bn_expand_internal(b, words);

		if (a) {
			r = BN_new();
			if (r) {
				r->top = b->top;
				r->dmax = words;
				r->neg = b->neg;
				r->d = a;
			} else {
				/* r == NULL, BN_new failure */
				free(a);
			}
		}
		/* If a == NULL, there was an error in allocation in
		   bn_expand_internal(), and NULL should be returned */
	} else {
		r = BN_dup(b);
	}

	bn_check_top(r);
	return r;
}
#endif

/* 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)
{
	bn_check_top(b);

	if (words > b->dmax) {
		BN_ULONG *a = bn_expand_internal(b, words);
		if (!a)
			return NULL;
		if (b->d) {
			OPENSSL_cleanse(b->d, b->dmax * sizeof(b->d[0]));
			free(b->d);
		}
		b->d = a;
		b->dmax = words;
	}

/* None of this should be necessary because of what b->top means! */
#if 0
	/* NB: bn_wexpand() calls this only if the BIGNUM really has to grow */
	if (b->top < b->dmax) {
		int i;
		BN_ULONG *A = &(b->d[b->top]);
		for (i = (b->dmax - b->top) >> 3; i > 0; i--, A += 8) {
			A[0] = 0;
			A[1] = 0;
			A[2] = 0;
			A[3] = 0;
			A[4] = 0;
			A[5] = 0;
			A[6] = 0;
			A[7] = 0;
		}
		for (i = (b->dmax - b->top)&7; i > 0; i--, A++)
			A[0] = 0;
		assert(A == &(b->d[b->dmax]));
	}
#endif
	bn_check_top(b);
	return b;
}

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

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

	t = 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 i;
	BN_ULONG *A;
	const BN_ULONG *B;

	bn_check_top(b);

	if (a == b)
		return (a);
	if (bn_wexpand(a, b->top) == NULL)
		return (NULL);

#if 1
	A = a->d;
	B = b->d;
	for (i = b->top >> 2; i > 0; i--, A += 4, B += 4) {
		BN_ULONG a0, a1, a2, a3;
		a0 = B[0];
		a1 = B[1];
		a2 = B[2];
		a3 = B[3];
		A[0] = a0;
		A[1] = a1;
		A[2] = a2;
		A[3] = a3;
	}
	switch (b->top & 3) {
	case 3:
		A[2] = B[2];
	case 2:
		A[1] = B[1];
	case 1:
		A[0] = B[0];
	}
#else
	memcpy(a->d, b->d, sizeof(b->d[0]) * b->top);
#endif

	a->top = b->top;
	a->neg = b->neg;
	bn_check_top(a);
	return (a);
}

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_old_a & BN_FLG_MALLOCED) |
	    (flags_old_b & BN_FLG_STATIC_DATA);
	b->flags = (flags_old_b & BN_FLG_MALLOCED) |
	    (flags_old_a & BN_FLG_STATIC_DATA);
	bn_check_top(a);
	bn_check_top(b);
}

void
BN_clear(BIGNUM *a)
{
	bn_check_top(a);
	if (a->d != NULL)
		memset(a->d, 0, a->dmax * sizeof(a->d[0]));
	a->top = 0;
	a->neg = 0;
}

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);
	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);
	l = 0;
	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) {
		if (bn)
			BN_free(bn);
		return NULL;
	}
	ret->top = i;
	ret->neg = 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);
}

/* ignore negative */
int
BN_bn2bin(const BIGNUM *a, unsigned char *to)
{
	int n, i;
	BN_ULONG l;

	bn_check_top(a);
	n = i=BN_num_bytes(a);
	while (i--) {
		l = a->d[i / BN_BYTES];
		*(to++) = (unsigned char)(l >> (8 * (i % BN_BYTES))) & 0xff;
	}
	return (n);
}

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->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;

	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
   property of performing the operation on arrays of different sizes.
   The sizes of those arrays is expressed through cl, which is the
   common length ( basicall, 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.  The code assumes that at most one bit of condition is set.
 * nwords is the number of words to swap.  The code assumes that at least nwords are allocated in both a and b,
 * and that no more than nwords are used by either a or b.
 * a and b cannot be the same number
 */
void
BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
{
	BN_ULONG t;
	int i;

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

	assert(a != b);
	assert((condition & (condition - 1)) == 0);
	assert(sizeof(BN_ULONG) >= sizeof(int));

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

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

#define BN_CONSTTIME_SWAP(ind) \
	do { \
		t = (a->d[ind] ^ b->d[ind]) & condition; \
		a->d[ind] ^= t; \
		b->d[ind] ^= t; \
	} while (0)


	switch (nwords) {
	default:
		for (i = 10; i < nwords; i++)
			BN_CONSTTIME_SWAP(i);
		/* Fallthrough */
	case 10: BN_CONSTTIME_SWAP(9); /* Fallthrough */
	case 9: BN_CONSTTIME_SWAP(8); /* Fallthrough */
	case 8: BN_CONSTTIME_SWAP(7); /* Fallthrough */
	case 7: BN_CONSTTIME_SWAP(6); /* Fallthrough */
	case 6: BN_CONSTTIME_SWAP(5); /* Fallthrough */
	case 5: BN_CONSTTIME_SWAP(4); /* Fallthrough */
	case 4: BN_CONSTTIME_SWAP(3); /* Fallthrough */
	case 3: BN_CONSTTIME_SWAP(2); /* Fallthrough */
	case 2: BN_CONSTTIME_SWAP(1); /* Fallthrough */
	case 1:
		BN_CONSTTIME_SWAP(0);
	}
#undef BN_CONSTTIME_SWAP
}