aboutsummaryrefslogtreecommitdiff
path: root/openssl/crypto/bn/bn_gf2m.c
blob: 527b0fa15be51ada3725d3d77704b26e8f8619ff (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
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
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
/* crypto/bn/bn_gf2m.c */
/* ====================================================================
 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
 *
 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
 * to the OpenSSL project.
 *
 * The ECC Code is licensed pursuant to the OpenSSL open source
 * license provided below.
 *
 * In addition, Sun covenants to all licensees who provide a reciprocal
 * covenant with respect to their own patents if any, not to sue under
 * current and future patent claims necessarily infringed by the making,
 * using, practicing, selling, offering for sale and/or otherwise
 * disposing of the ECC Code as delivered hereunder (or portions thereof),
 * provided that such covenant shall not apply:
 *  1) for code that a licensee deletes from the ECC Code;
 *  2) separates from the ECC Code; or
 *  3) for infringements caused by:
 *       i) the modification of the ECC Code or
 *      ii) the combination of the ECC Code with other software or
 *          devices where such combination causes the infringement.
 *
 * The software is originally written by Sheueling Chang Shantz and
 * Douglas Stebila of Sun Microsystems Laboratories.
 *
 */

/* NOTE: This file is licensed pursuant to the OpenSSL license below
 * and may be modified; but after modifications, the above covenant
 * may no longer apply!  In such cases, the corresponding paragraph
 * ["In addition, Sun covenants ... causes the infringement."] and
 * this note can be edited out; but please keep the Sun copyright
 * notice and attribution. */

/* ====================================================================
 * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
 *
 * 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 above 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 acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED 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 OpenSSL PROJECT OR
 * ITS 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.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

#include <assert.h>
#include <limits.h>
#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"

/* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */
#define MAX_ITERATIONS 50

static const BN_ULONG SQR_tb[16] =
  {     0,     1,     4,     5,    16,    17,    20,    21,
       64,    65,    68,    69,    80,    81,    84,    85 };
/* Platform-specific macros to accelerate squaring. */
#if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
#define SQR1(w) \
    SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
    SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
    SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
    SQR_tb[(w) >> 36 & 0xF] <<  8 | SQR_tb[(w) >> 32 & 0xF]
#define SQR0(w) \
    SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
    SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \
    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]
#endif
#ifdef THIRTY_TWO_BIT
#define SQR1(w) \
    SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
    SQR_tb[(w) >> 20 & 0xF] <<  8 | SQR_tb[(w) >> 16 & 0xF]
#define SQR0(w) \
    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \
    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]
#endif

/* Product of two polynomials a, b each with degree < BN_BITS2 - 1,
 * result is a polynomial r with degree < 2 * BN_BITS - 1
 * The caller MUST ensure that the variables have the right amount
 * of space allocated.
 */
#ifdef THIRTY_TWO_BIT
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
	{
	register BN_ULONG h, l, s;
	BN_ULONG tab[8], top2b = a >> 30; 
	register BN_ULONG a1, a2, a4;

	a1 = a & (0x3FFFFFFF); a2 = a1 << 1; a4 = a2 << 1;

	tab[0] =  0; tab[1] = a1;    tab[2] = a2;    tab[3] = a1^a2;
	tab[4] = a4; tab[5] = a1^a4; tab[6] = a2^a4; tab[7] = a1^a2^a4;

	s = tab[b       & 0x7]; l  = s;
	s = tab[b >>  3 & 0x7]; l ^= s <<  3; h  = s >> 29;
	s = tab[b >>  6 & 0x7]; l ^= s <<  6; h ^= s >> 26;
	s = tab[b >>  9 & 0x7]; l ^= s <<  9; h ^= s >> 23;
	s = tab[b >> 12 & 0x7]; l ^= s << 12; h ^= s >> 20;
	s = tab[b >> 15 & 0x7]; l ^= s << 15; h ^= s >> 17;
	s = tab[b >> 18 & 0x7]; l ^= s << 18; h ^= s >> 14;
	s = tab[b >> 21 & 0x7]; l ^= s << 21; h ^= s >> 11;
	s = tab[b >> 24 & 0x7]; l ^= s << 24; h ^= s >>  8;
	s = tab[b >> 27 & 0x7]; l ^= s << 27; h ^= s >>  5;
	s = tab[b >> 30      ]; l ^= s << 30; h ^= s >>  2;

	/* compensate for the top two bits of a */

	if (top2b & 01) { l ^= b << 30; h ^= b >> 2; } 
	if (top2b & 02) { l ^= b << 31; h ^= b >> 1; } 

	*r1 = h; *r0 = l;
	} 
#endif
#if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
	{
	register BN_ULONG h, l, s;
	BN_ULONG tab[16], top3b = a >> 61;
	register BN_ULONG a1, a2, a4, a8;

	a1 = a & (0x1FFFFFFFFFFFFFFFULL); a2 = a1 << 1; a4 = a2 << 1; a8 = a4 << 1;

	tab[ 0] = 0;     tab[ 1] = a1;       tab[ 2] = a2;       tab[ 3] = a1^a2;
	tab[ 4] = a4;    tab[ 5] = a1^a4;    tab[ 6] = a2^a4;    tab[ 7] = a1^a2^a4;
	tab[ 8] = a8;    tab[ 9] = a1^a8;    tab[10] = a2^a8;    tab[11] = a1^a2^a8;
	tab[12] = a4^a8; tab[13] = a1^a4^a8; tab[14] = a2^a4^a8; tab[15] = a1^a2^a4^a8;

	s = tab[b       & 0xF]; l  = s;
	s = tab[b >>  4 & 0xF]; l ^= s <<  4; h  = s >> 60;
	s = tab[b >>  8 & 0xF]; l ^= s <<  8; h ^= s >> 56;
	s = tab[b >> 12 & 0xF]; l ^= s << 12; h ^= s >> 52;
	s = tab[b >> 16 & 0xF]; l ^= s << 16; h ^= s >> 48;
	s = tab[b >> 20 & 0xF]; l ^= s << 20; h ^= s >> 44;
	s = tab[b >> 24 & 0xF]; l ^= s << 24; h ^= s >> 40;
	s = tab[b >> 28 & 0xF]; l ^= s << 28; h ^= s >> 36;
	s = tab[b >> 32 & 0xF]; l ^= s << 32; h ^= s >> 32;
	s = tab[b >> 36 & 0xF]; l ^= s << 36; h ^= s >> 28;
	s = tab[b >> 40 & 0xF]; l ^= s << 40; h ^= s >> 24;
	s = tab[b >> 44 & 0xF]; l ^= s << 44; h ^= s >> 20;
	s = tab[b >> 48 & 0xF]; l ^= s << 48; h ^= s >> 16;
	s = tab[b >> 52 & 0xF]; l ^= s << 52; h ^= s >> 12;
	s = tab[b >> 56 & 0xF]; l ^= s << 56; h ^= s >>  8;
	s = tab[b >> 60      ]; l ^= s << 60; h ^= s >>  4;

	/* compensate for the top three bits of a */

	if (top3b & 01) { l ^= b << 61; h ^= b >> 3; } 
	if (top3b & 02) { l ^= b << 62; h ^= b >> 2; } 
	if (top3b & 04) { l ^= b << 63; h ^= b >> 1; } 

	*r1 = h; *r0 = l;
	} 
#endif

/* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
 * result is a polynomial r with degree < 4 * BN_BITS2 - 1
 * The caller MUST ensure that the variables have the right amount
 * of space allocated.
 */
static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0, const BN_ULONG b1, const BN_ULONG b0)
	{
	BN_ULONG m1, m0;
	/* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
	bn_GF2m_mul_1x1(r+3, r+2, a1, b1);
	bn_GF2m_mul_1x1(r+1, r, a0, b0);
	bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
	/* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
	r[2] ^= m1 ^ r[1] ^ r[3];  /* h0 ^= m1 ^ l1 ^ h1; */
	r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0;  /* l1 ^= l0 ^ h0 ^ m0; */
	}


/* Add polynomials a and b and store result in r; r could be a or b, a and b 
 * could be equal; r is the bitwise XOR of a and b.
 */
int	BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
	{
	int i;
	const BIGNUM *at, *bt;

	bn_check_top(a);
	bn_check_top(b);

	if (a->top < b->top) { at = b; bt = a; }
	else { at = a; bt = b; }

	if(bn_wexpand(r, at->top) == NULL)
		return 0;

	for (i = 0; i < bt->top; i++)
		{
		r->d[i] = at->d[i] ^ bt->d[i];
		}
	for (; i < at->top; i++)
		{
		r->d[i] = at->d[i];
		}
	
	r->top = at->top;
	bn_correct_top(r);
	
	return 1;
	}


/* Some functions allow for representation of the irreducible polynomials
 * as an int[], say p.  The irreducible f(t) is then of the form:
 *     t^p[0] + t^p[1] + ... + t^p[k]
 * where m = p[0] > p[1] > ... > p[k] = 0.
 */


/* Performs modular reduction of a and store result in r.  r could be a. */
int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
	{
	int j, k;
	int n, dN, d0, d1;
	BN_ULONG zz, *z;

	bn_check_top(a);

	if (!p[0])
		{
		/* reduction mod 1 => return 0 */
		BN_zero(r);
		return 1;
		}

	/* Since the algorithm does reduction in the r value, if a != r, copy
	 * the contents of a into r so we can do reduction in r. 
	 */
	if (a != r)
		{
		if (!bn_wexpand(r, a->top)) return 0;
		for (j = 0; j < a->top; j++)
			{
			r->d[j] = a->d[j];
			}
		r->top = a->top;
		}
	z = r->d;

	/* start reduction */
	dN = p[0] / BN_BITS2;  
	for (j = r->top - 1; j > dN;)
		{
		zz = z[j];
		if (z[j] == 0) { j--; continue; }
		z[j] = 0;

		for (k = 1; p[k] != 0; k++)
			{
			/* reducing component t^p[k] */
			n = p[0] - p[k];
			d0 = n % BN_BITS2;  d1 = BN_BITS2 - d0;
			n /= BN_BITS2; 
			z[j-n] ^= (zz>>d0);
			if (d0) z[j-n-1] ^= (zz<<d1);
			}

		/* reducing component t^0 */
		n = dN;  
		d0 = p[0] % BN_BITS2;
		d1 = BN_BITS2 - d0;
		z[j-n] ^= (zz >> d0);
		if (d0) z[j-n-1] ^= (zz << d1);
		}

	/* final round of reduction */
	while (j == dN)
		{

		d0 = p[0] % BN_BITS2;
		zz = z[dN] >> d0;
		if (zz == 0) break;
		d1 = BN_BITS2 - d0;
		
		/* clear up the top d1 bits */
		if (d0)
			z[dN] = (z[dN] << d1) >> d1;
		else
			z[dN] = 0;
		z[0] ^= zz; /* reduction t^0 component */

		for (k = 1; p[k] != 0; k++)
			{
			BN_ULONG tmp_ulong;

			/* reducing component t^p[k]*/
			n = p[k] / BN_BITS2;   
			d0 = p[k] % BN_BITS2;
			d1 = BN_BITS2 - d0;
			z[n] ^= (zz << d0);
			tmp_ulong = zz >> d1;
                        if (d0 && tmp_ulong)
                                z[n+1] ^= tmp_ulong;
			}

		
		}

	bn_correct_top(r);
	return 1;
	}

/* Performs modular reduction of a by p and store result in r.  r could be a.
 *
 * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_arr function.
 */
int	BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
	{
	int ret = 0;
	const int max = BN_num_bits(p) + 1;
	int *arr=NULL;
	bn_check_top(a);
	bn_check_top(p);
	if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err;
	ret = BN_GF2m_poly2arr(p, arr, max);
	if (!ret || ret > max)
		{
		BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH);
		goto err;
		}
	ret = BN_GF2m_mod_arr(r, a, arr);
	bn_check_top(r);
err:
	if (arr) OPENSSL_free(arr);
	return ret;
	}


/* Compute the product of two polynomials a and b, reduce modulo p, and store
 * the result in r.  r could be a or b; a could be b.
 */
int	BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx)
	{
	int zlen, i, j, k, ret = 0;
	BIGNUM *s;
	BN_ULONG x1, x0, y1, y0, zz[4];

	bn_check_top(a);
	bn_check_top(b);

	if (a == b)
		{
		return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
		}

	BN_CTX_start(ctx);
	if ((s = BN_CTX_get(ctx)) == NULL) goto err;
	
	zlen = a->top + b->top + 4;
	if (!bn_wexpand(s, zlen)) goto err;
	s->top = zlen;

	for (i = 0; i < zlen; i++) s->d[i] = 0;

	for (j = 0; j < b->top; j += 2)
		{
		y0 = b->d[j];
		y1 = ((j+1) == b->top) ? 0 : b->d[j+1];
		for (i = 0; i < a->top; i += 2)
			{
			x0 = a->d[i];
			x1 = ((i+1) == a->top) ? 0 : a->d[i+1];
			bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
			for (k = 0; k < 4; k++) s->d[i+j+k] ^= zz[k];
			}
		}

	bn_correct_top(s);
	if (BN_GF2m_mod_arr(r, s, p))
		ret = 1;
	bn_check_top(r);

err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Compute the product of two polynomials a and b, reduce modulo p, and store
 * the result in r.  r could be a or b; a could equal b.
 *
 * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_mul_arr function.
 */
int	BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx)
	{
	int ret = 0;
	const int max = BN_num_bits(p) + 1;
	int *arr=NULL;
	bn_check_top(a);
	bn_check_top(b);
	bn_check_top(p);
	if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err;
	ret = BN_GF2m_poly2arr(p, arr, max);
	if (!ret || ret > max)
		{
		BNerr(BN_F_BN_GF2M_MOD_MUL,BN_R_INVALID_LENGTH);
		goto err;
		}
	ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
	bn_check_top(r);
err:
	if (arr) OPENSSL_free(arr);
	return ret;
	}


/* Square a, reduce the result mod p, and store it in a.  r could be a. */
int	BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx)
	{
	int i, ret = 0;
	BIGNUM *s;

	bn_check_top(a);
	BN_CTX_start(ctx);
	if ((s = BN_CTX_get(ctx)) == NULL) return 0;
	if (!bn_wexpand(s, 2 * a->top)) goto err;

	for (i = a->top - 1; i >= 0; i--)
		{
		s->d[2*i+1] = SQR1(a->d[i]);
		s->d[2*i  ] = SQR0(a->d[i]);
		}

	s->top = 2 * a->top;
	bn_correct_top(s);
	if (!BN_GF2m_mod_arr(r, s, p)) goto err;
	bn_check_top(r);
	ret = 1;
err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Square a, reduce the result mod p, and store it in a.  r could be a.
 *
 * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_sqr_arr function.
 */
int	BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
	{
	int ret = 0;
	const int max = BN_num_bits(p) + 1;
	int *arr=NULL;

	bn_check_top(a);
	bn_check_top(p);
	if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err;
	ret = BN_GF2m_poly2arr(p, arr, max);
	if (!ret || ret > max)
		{
		BNerr(BN_F_BN_GF2M_MOD_SQR,BN_R_INVALID_LENGTH);
		goto err;
		}
	ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
	bn_check_top(r);
err:
	if (arr) OPENSSL_free(arr);
	return ret;
	}


/* Invert a, reduce modulo p, and store the result in r. r could be a. 
 * Uses Modified Almost Inverse Algorithm (Algorithm 10) from
 *     Hankerson, D., Hernandez, J.L., and Menezes, A.  "Software Implementation
 *     of Elliptic Curve Cryptography Over Binary Fields".
 */
int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
	{
	BIGNUM *b, *c, *u, *v, *tmp;
	int ret = 0;

	bn_check_top(a);
	bn_check_top(p);

	BN_CTX_start(ctx);
	
	b = BN_CTX_get(ctx);
	c = BN_CTX_get(ctx);
	u = BN_CTX_get(ctx);
	v = BN_CTX_get(ctx);
	if (v == NULL) goto err;

	if (!BN_one(b)) goto err;
	if (!BN_GF2m_mod(u, a, p)) goto err;
	if (!BN_copy(v, p)) goto err;

	if (BN_is_zero(u)) goto err;

	while (1)
		{
		while (!BN_is_odd(u))
			{
			if (!BN_rshift1(u, u)) goto err;
			if (BN_is_odd(b))
				{
				if (!BN_GF2m_add(b, b, p)) goto err;
				}
			if (!BN_rshift1(b, b)) goto err;
			}

		if (BN_abs_is_word(u, 1)) break;

		if (BN_num_bits(u) < BN_num_bits(v))
			{
			tmp = u; u = v; v = tmp;
			tmp = b; b = c; c = tmp;
			}
		
		if (!BN_GF2m_add(u, u, v)) goto err;
		if (!BN_GF2m_add(b, b, c)) goto err;
		}


	if (!BN_copy(r, b)) goto err;
	bn_check_top(r);
	ret = 1;

err:
  	BN_CTX_end(ctx);
	return ret;
	}

/* Invert xx, reduce modulo p, and store the result in r. r could be xx. 
 *
 * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_inv function.
 */
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], BN_CTX *ctx)
	{
	BIGNUM *field;
	int ret = 0;

	bn_check_top(xx);
	BN_CTX_start(ctx);
	if ((field = BN_CTX_get(ctx)) == NULL) goto err;
	if (!BN_GF2m_arr2poly(p, field)) goto err;
	
	ret = BN_GF2m_mod_inv(r, xx, field, ctx);
	bn_check_top(r);

err:
	BN_CTX_end(ctx);
	return ret;
	}


#ifndef OPENSSL_SUN_GF2M_DIV
/* Divide y by x, reduce modulo p, and store the result in r. r could be x 
 * or y, x could equal y.
 */
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx)
	{
	BIGNUM *xinv = NULL;
	int ret = 0;

	bn_check_top(y);
	bn_check_top(x);
	bn_check_top(p);

	BN_CTX_start(ctx);
	xinv = BN_CTX_get(ctx);
	if (xinv == NULL) goto err;
	
	if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) goto err;
	if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) goto err;
	bn_check_top(r);
	ret = 1;

err:
	BN_CTX_end(ctx);
	return ret;
	}
#else
/* Divide y by x, reduce modulo p, and store the result in r. r could be x 
 * or y, x could equal y.
 * Uses algorithm Modular_Division_GF(2^m) from 
 *     Chang-Shantz, S.  "From Euclid's GCD to Montgomery Multiplication to 
 *     the Great Divide".
 */
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx)
	{
	BIGNUM *a, *b, *u, *v;
	int ret = 0;

	bn_check_top(y);
	bn_check_top(x);
	bn_check_top(p);

	BN_CTX_start(ctx);
	
	a = BN_CTX_get(ctx);
	b = BN_CTX_get(ctx);
	u = BN_CTX_get(ctx);
	v = BN_CTX_get(ctx);
	if (v == NULL) goto err;

	/* reduce x and y mod p */
	if (!BN_GF2m_mod(u, y, p)) goto err;
	if (!BN_GF2m_mod(a, x, p)) goto err;
	if (!BN_copy(b, p)) goto err;
	
	while (!BN_is_odd(a))
		{
		if (!BN_rshift1(a, a)) goto err;
		if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err;
		if (!BN_rshift1(u, u)) goto err;
		}

	do
		{
		if (BN_GF2m_cmp(b, a) > 0)
			{
			if (!BN_GF2m_add(b, b, a)) goto err;
			if (!BN_GF2m_add(v, v, u)) goto err;
			do
				{
				if (!BN_rshift1(b, b)) goto err;
				if (BN_is_odd(v)) if (!BN_GF2m_add(v, v, p)) goto err;
				if (!BN_rshift1(v, v)) goto err;
				} while (!BN_is_odd(b));
			}
		else if (BN_abs_is_word(a, 1))
			break;
		else
			{
			if (!BN_GF2m_add(a, a, b)) goto err;
			if (!BN_GF2m_add(u, u, v)) goto err;
			do
				{
				if (!BN_rshift1(a, a)) goto err;
				if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err;
				if (!BN_rshift1(u, u)) goto err;
				} while (!BN_is_odd(a));
			}
		} while (1);

	if (!BN_copy(r, u)) goto err;
	bn_check_top(r);
	ret = 1;

err:
  	BN_CTX_end(ctx);
	return ret;
	}
#endif

/* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx 
 * or yy, xx could equal yy.
 *
 * This function calls down to the BN_GF2m_mod_div implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_div function.
 */
int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, const int p[], BN_CTX *ctx)
	{
	BIGNUM *field;
	int ret = 0;

	bn_check_top(yy);
	bn_check_top(xx);

	BN_CTX_start(ctx);
	if ((field = BN_CTX_get(ctx)) == NULL) goto err;
	if (!BN_GF2m_arr2poly(p, field)) goto err;
	
	ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
	bn_check_top(r);

err:
	BN_CTX_end(ctx);
	return ret;
	}


/* Compute the bth power of a, reduce modulo p, and store
 * the result in r.  r could be a.
 * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363.
 */
int	BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx)
	{
	int ret = 0, i, n;
	BIGNUM *u;

	bn_check_top(a);
	bn_check_top(b);

	if (BN_is_zero(b))
		return(BN_one(r));

	if (BN_abs_is_word(b, 1))
		return (BN_copy(r, a) != NULL);

	BN_CTX_start(ctx);
	if ((u = BN_CTX_get(ctx)) == NULL) goto err;
	
	if (!BN_GF2m_mod_arr(u, a, p)) goto err;
	
	n = BN_num_bits(b) - 1;
	for (i = n - 1; i >= 0; i--)
		{
		if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) goto err;
		if (BN_is_bit_set(b, i))
			{
			if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) goto err;
			}
		}
	if (!BN_copy(r, u)) goto err;
	bn_check_top(r);
	ret = 1;
err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Compute the bth power of a, reduce modulo p, and store
 * the result in r.  r could be a.
 *
 * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_exp_arr function.
 */
int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx)
	{
	int ret = 0;
	const int max = BN_num_bits(p) + 1;
	int *arr=NULL;
	bn_check_top(a);
	bn_check_top(b);
	bn_check_top(p);
	if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err;
	ret = BN_GF2m_poly2arr(p, arr, max);
	if (!ret || ret > max)
		{
		BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH);
		goto err;
		}
	ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
	bn_check_top(r);
err:
	if (arr) OPENSSL_free(arr);
	return ret;
	}

/* Compute the square root of a, reduce modulo p, and store
 * the result in r.  r could be a.
 * Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
 */
int	BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx)
	{
	int ret = 0;
	BIGNUM *u;

	bn_check_top(a);

	if (!p[0])
		{
		/* reduction mod 1 => return 0 */
		BN_zero(r);
		return 1;
		}

	BN_CTX_start(ctx);
	if ((u = BN_CTX_get(ctx)) == NULL) goto err;
	
	if (!BN_set_bit(u, p[0] - 1)) goto err;
	ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
	bn_check_top(r);

err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Compute the square root of a, reduce modulo p, and store
 * the result in r.  r could be a.
 *
 * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_sqrt_arr function.
 */
int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
	{
	int ret = 0;
	const int max = BN_num_bits(p) + 1;
	int *arr=NULL;
	bn_check_top(a);
	bn_check_top(p);
	if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err;
	ret = BN_GF2m_poly2arr(p, arr, max);
	if (!ret || ret > max)
		{
		BNerr(BN_F_BN_GF2M_MOD_SQRT,BN_R_INVALID_LENGTH);
		goto err;
		}
	ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
	bn_check_top(r);
err:
	if (arr) OPENSSL_free(arr);
	return ret;
	}

/* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.
 * Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
 */
int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[], BN_CTX *ctx)
	{
	int ret = 0, count = 0, j;
	BIGNUM *a, *z, *rho, *w, *w2, *tmp;

	bn_check_top(a_);

	if (!p[0])
		{
		/* reduction mod 1 => return 0 */
		BN_zero(r);
		return 1;
		}

	BN_CTX_start(ctx);
	a = BN_CTX_get(ctx);
	z = BN_CTX_get(ctx);
	w = BN_CTX_get(ctx);
	if (w == NULL) goto err;

	if (!BN_GF2m_mod_arr(a, a_, p)) goto err;
	
	if (BN_is_zero(a))
		{
		BN_zero(r);
		ret = 1;
		goto err;
		}

	if (p[0] & 0x1) /* m is odd */
		{
		/* compute half-trace of a */
		if (!BN_copy(z, a)) goto err;
		for (j = 1; j <= (p[0] - 1) / 2; j++)
			{
			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
			if (!BN_GF2m_add(z, z, a)) goto err;
			}
		
		}
	else /* m is even */
		{
		rho = BN_CTX_get(ctx);
		w2 = BN_CTX_get(ctx);
		tmp = BN_CTX_get(ctx);
		if (tmp == NULL) goto err;
		do
			{
			if (!BN_rand(rho, p[0], 0, 0)) goto err;
			if (!BN_GF2m_mod_arr(rho, rho, p)) goto err;
			BN_zero(z);
			if (!BN_copy(w, rho)) goto err;
			for (j = 1; j <= p[0] - 1; j++)
				{
				if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;
				if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) goto err;
				if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) goto err;
				if (!BN_GF2m_add(z, z, tmp)) goto err;
				if (!BN_GF2m_add(w, w2, rho)) goto err;
				}
			count++;
			} while (BN_is_zero(w) && (count < MAX_ITERATIONS));
		if (BN_is_zero(w))
			{
			BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,BN_R_TOO_MANY_ITERATIONS);
			goto err;
			}
		}
	
	if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) goto err;
	if (!BN_GF2m_add(w, z, w)) goto err;
	if (BN_GF2m_cmp(w, a))
		{
		BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION);
		goto err;
		}

	if (!BN_copy(r, z)) goto err;
	bn_check_top(r);

	ret = 1;

err:
	BN_CTX_end(ctx);
	return ret;
	}

/* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.
 *
 * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper
 * function is only provided for convenience; for best performance, use the 
 * BN_GF2m_mod_solve_quad_arr function.
 */
int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
	{
	int ret = 0;
	const int max = BN_num_bits(p) + 1;
	int *arr=NULL;
	bn_check_top(a);
	bn_check_top(p);
	if ((arr = (int *)OPENSSL_malloc(sizeof(int) *
						max)) == NULL) goto err;
	ret = BN_GF2m_poly2arr(p, arr, max);
	if (!ret || ret > max)
		{
		BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD,BN_R_INVALID_LENGTH);
		goto err;
		}
	ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
	bn_check_top(r);
err:
	if (arr) OPENSSL_free(arr);
	return ret;
	}

/* Convert the bit-string representation of a polynomial
 * ( \sum_{i=0}^n a_i * x^i) into an array of integers corresponding 
 * to the bits with non-zero coefficient.  Array is terminated with -1.
 * Up to max elements of the array will be filled.  Return value is total
 * number of array elements that would be filled if array was large enough.
 */
int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
	{
	int i, j, k = 0;
	BN_ULONG mask;

	if (BN_is_zero(a))
		return 0;

	for (i = a->top - 1; i >= 0; i--)
		{
		if (!a->d[i])
			/* skip word if a->d[i] == 0 */
			continue;
		mask = BN_TBIT;
		for (j = BN_BITS2 - 1; j >= 0; j--)
			{
			if (a->d[i] & mask) 
				{
				if (k < max) p[k] = BN_BITS2 * i + j;
				k++;
				}
			mask >>= 1;
			}
		}

	if (k < max) {
		p[k] = -1;
		k++;
	}

	return k;
	}

/* Convert the coefficient array representation of a polynomial to a 
 * bit-string.  The array must be terminated by -1.
 */
int BN_GF2m_arr2poly(const int p[], BIGNUM *a)
	{
	int i;

	bn_check_top(a);
	BN_zero(a);
	for (i = 0; p[i] != -1; i++)
		{
		if (BN_set_bit(a, p[i]) == 0)
			return 0;
		}
	bn_check_top(a);

	return 1;
	}