GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libcrypto/bn/bn_gf2m.c Lines: 291 337 86.4 %
Date: 2017-11-13 Branches: 218 323 67.5 %

Line Branch Exec Source
1
/* $OpenBSD: bn_gf2m.c,v 1.23 2017/01/29 17:49:22 beck Exp $ */
2
/* ====================================================================
3
 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
4
 *
5
 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included
6
 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed
7
 * to the OpenSSL project.
8
 *
9
 * The ECC Code is licensed pursuant to the OpenSSL open source
10
 * license provided below.
11
 *
12
 * In addition, Sun covenants to all licensees who provide a reciprocal
13
 * covenant with respect to their own patents if any, not to sue under
14
 * current and future patent claims necessarily infringed by the making,
15
 * using, practicing, selling, offering for sale and/or otherwise
16
 * disposing of the ECC Code as delivered hereunder (or portions thereof),
17
 * provided that such covenant shall not apply:
18
 *  1) for code that a licensee deletes from the ECC Code;
19
 *  2) separates from the ECC Code; or
20
 *  3) for infringements caused by:
21
 *       i) the modification of the ECC Code or
22
 *      ii) the combination of the ECC Code with other software or
23
 *          devices where such combination causes the infringement.
24
 *
25
 * The software is originally written by Sheueling Chang Shantz and
26
 * Douglas Stebila of Sun Microsystems Laboratories.
27
 *
28
 */
29
30
/* NOTE: This file is licensed pursuant to the OpenSSL license below
31
 * and may be modified; but after modifications, the above covenant
32
 * may no longer apply!  In such cases, the corresponding paragraph
33
 * ["In addition, Sun covenants ... causes the infringement."] and
34
 * this note can be edited out; but please keep the Sun copyright
35
 * notice and attribution. */
36
37
/* ====================================================================
38
 * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
39
 *
40
 * Redistribution and use in source and binary forms, with or without
41
 * modification, are permitted provided that the following conditions
42
 * are met:
43
 *
44
 * 1. Redistributions of source code must retain the above copyright
45
 *    notice, this list of conditions and the following disclaimer.
46
 *
47
 * 2. Redistributions in binary form must reproduce the above copyright
48
 *    notice, this list of conditions and the following disclaimer in
49
 *    the documentation and/or other materials provided with the
50
 *    distribution.
51
 *
52
 * 3. All advertising materials mentioning features or use of this
53
 *    software must display the following acknowledgment:
54
 *    "This product includes software developed by the OpenSSL Project
55
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
56
 *
57
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
58
 *    endorse or promote products derived from this software without
59
 *    prior written permission. For written permission, please contact
60
 *    openssl-core@openssl.org.
61
 *
62
 * 5. Products derived from this software may not be called "OpenSSL"
63
 *    nor may "OpenSSL" appear in their names without prior written
64
 *    permission of the OpenSSL Project.
65
 *
66
 * 6. Redistributions of any form whatsoever must retain the following
67
 *    acknowledgment:
68
 *    "This product includes software developed by the OpenSSL Project
69
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
70
 *
71
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
72
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
73
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
74
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
75
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
76
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
77
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
78
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
79
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
80
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
81
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
82
 * OF THE POSSIBILITY OF SUCH DAMAGE.
83
 * ====================================================================
84
 *
85
 * This product includes cryptographic software written by Eric Young
86
 * (eay@cryptsoft.com).  This product includes software written by Tim
87
 * Hudson (tjh@cryptsoft.com).
88
 *
89
 */
90
91
#include <limits.h>
92
#include <stdio.h>
93
94
#include <openssl/opensslconf.h>
95
96
#include <openssl/err.h>
97
98
#include "bn_lcl.h"
99
100
#ifndef OPENSSL_NO_EC2M
101
102
/* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */
103
#define MAX_ITERATIONS 50
104
105
static const BN_ULONG SQR_tb[16] =
106
	{     0,     1,     4,     5,    16,    17,    20,    21,
107
64,    65,    68,    69,    80,    81,    84,    85 };
108
/* Platform-specific macros to accelerate squaring. */
109
#ifdef _LP64
110
#define SQR1(w) \
111
    SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
112
    SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
113
    SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
114
    SQR_tb[(w) >> 36 & 0xF] <<  8 | SQR_tb[(w) >> 32 & 0xF]
115
#define SQR0(w) \
116
    SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
117
    SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
118
    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \
119
    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]
120
#else
121
#define SQR1(w) \
122
    SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
123
    SQR_tb[(w) >> 20 & 0xF] <<  8 | SQR_tb[(w) >> 16 & 0xF]
124
#define SQR0(w) \
125
    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \
126
    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]
127
#endif
128
129
#if !defined(OPENSSL_BN_ASM_GF2m)
130
/* Product of two polynomials a, b each with degree < BN_BITS2 - 1,
131
 * result is a polynomial r with degree < 2 * BN_BITS - 1
132
 * The caller MUST ensure that the variables have the right amount
133
 * of space allocated.
134
 */
135
static void
136
bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)
137
{
138
#ifndef _LP64
139
	BN_ULONG h, l, s;
140
	BN_ULONG tab[8], top2b = a >> 30;
141
	BN_ULONG a1, a2, a4;
142
143
	a1 = a & (0x3FFFFFFF);
144
	a2 = a1 << 1;
145
	a4 = a2 << 1;
146
147
	tab[0] = 0;
148
	tab[1] = a1;
149
	tab[2] = a2;
150
	tab[3] = a1 ^ a2;
151
	tab[4] = a4;
152
	tab[5] = a1 ^ a4;
153
	tab[6] = a2 ^ a4;
154
	tab[7] = a1 ^ a2 ^ a4;
155
156
	s = tab[b & 0x7];
157
	l = s;
158
	s = tab[b >> 3 & 0x7];
159
	l ^= s << 3;
160
	h = s >> 29;
161
	s = tab[b >> 6 & 0x7];
162
	l ^= s <<  6;
163
	h ^= s >> 26;
164
	s = tab[b >> 9 & 0x7];
165
	l ^= s <<  9;
166
	h ^= s >> 23;
167
	s = tab[b >> 12 & 0x7];
168
	l ^= s << 12;
169
	h ^= s >> 20;
170
	s = tab[b >> 15 & 0x7];
171
	l ^= s << 15;
172
	h ^= s >> 17;
173
	s = tab[b >> 18 & 0x7];
174
	l ^= s << 18;
175
	h ^= s >> 14;
176
	s = tab[b >> 21 & 0x7];
177
	l ^= s << 21;
178
	h ^= s >> 11;
179
	s = tab[b >> 24 & 0x7];
180
	l ^= s << 24;
181
	h ^= s >>  8;
182
	s = tab[b >> 27 & 0x7];
183
	l ^= s << 27;
184
	h ^= s >>  5;
185
	s = tab[b >> 30];
186
	l ^= s << 30;
187
	h ^= s >> 2;
188
189
	/* compensate for the top two bits of a */
190
	if (top2b & 01) {
191
		l ^= b << 30;
192
		h ^= b >> 2;
193
	}
194
	if (top2b & 02) {
195
		l ^= b << 31;
196
		h ^= b >> 1;
197
	}
198
199
	*r1 = h;
200
	*r0 = l;
201
#else
202
	BN_ULONG h, l, s;
203
	BN_ULONG tab[16], top3b = a >> 61;
204
	BN_ULONG a1, a2, a4, a8;
205
206
	a1 = a & (0x1FFFFFFFFFFFFFFFULL);
207
	a2 = a1 << 1;
208
	a4 = a2 << 1;
209
	a8 = a4 << 1;
210
211
	tab[0] = 0;
212
	tab[1] = a1;
213
	tab[2] = a2;
214
	tab[3] = a1 ^ a2;
215
	tab[4] = a4;
216
	tab[5] = a1 ^ a4;
217
	tab[6] = a2 ^ a4;
218
	tab[7] = a1 ^ a2 ^ a4;
219
	tab[8] = a8;
220
	tab[9] = a1 ^ a8;
221
	tab[10] = a2 ^ a8;
222
	tab[11] = a1 ^ a2 ^ a8;
223
	tab[12] = a4 ^ a8;
224
	tab[13] = a1 ^ a4 ^ a8;
225
	tab[14] = a2 ^ a4 ^ a8;
226
	tab[15] = a1 ^ a2 ^ a4 ^ a8;
227
228
	s = tab[b & 0xF];
229
	l = s;
230
	s = tab[b >> 4 & 0xF];
231
	l ^= s << 4;
232
	h = s >> 60;
233
	s = tab[b >> 8 & 0xF];
234
	l ^= s << 8;
235
	h ^= s >> 56;
236
	s = tab[b >> 12 & 0xF];
237
	l ^= s << 12;
238
	h ^= s >> 52;
239
	s = tab[b >> 16 & 0xF];
240
	l ^= s << 16;
241
	h ^= s >> 48;
242
	s = tab[b >> 20 & 0xF];
243
	l ^= s << 20;
244
	h ^= s >> 44;
245
	s = tab[b >> 24 & 0xF];
246
	l ^= s << 24;
247
	h ^= s >> 40;
248
	s = tab[b >> 28 & 0xF];
249
	l ^= s << 28;
250
	h ^= s >> 36;
251
	s = tab[b >> 32 & 0xF];
252
	l ^= s << 32;
253
	h ^= s >> 32;
254
	s = tab[b >> 36 & 0xF];
255
	l ^= s << 36;
256
	h ^= s >> 28;
257
	s = tab[b >> 40 & 0xF];
258
	l ^= s << 40;
259
	h ^= s >> 24;
260
	s = tab[b >> 44 & 0xF];
261
	l ^= s << 44;
262
	h ^= s >> 20;
263
	s = tab[b >> 48 & 0xF];
264
	l ^= s << 48;
265
	h ^= s >> 16;
266
	s = tab[b >> 52 & 0xF];
267
	l ^= s << 52;
268
	h ^= s >> 12;
269
	s = tab[b >> 56 & 0xF];
270
	l ^= s << 56;
271
	h ^= s >>  8;
272
	s = tab[b >> 60];
273
	l ^= s << 60;
274
	h ^= s >>  4;
275
276
	/* compensate for the top three bits of a */
277
	if (top3b & 01) {
278
		l ^= b << 61;
279
		h ^= b >> 3;
280
	}
281
	if (top3b & 02) {
282
		l ^= b << 62;
283
		h ^= b >> 2;
284
	}
285
	if (top3b & 04) {
286
		l ^= b << 63;
287
		h ^= b >> 1;
288
	}
289
290
	*r1 = h;
291
	*r0 = l;
292
#endif
293
}
294
295
/* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
296
 * result is a polynomial r with degree < 4 * BN_BITS2 - 1
297
 * The caller MUST ensure that the variables have the right amount
298
 * of space allocated.
299
 */
300
static void
301
bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,
302
    const BN_ULONG b1, const BN_ULONG b0)
303
{
304
	BN_ULONG m1, m0;
305
306
	/* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
307
	bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);
308
	bn_GF2m_mul_1x1(r + 1, r, a0, b0);
309
	bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
310
	/* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
311
	r[2] ^= m1 ^ r[1] ^ r[3];  /* h0 ^= m1 ^ l1 ^ h1; */
312
	r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0;  /* l1 ^= l0 ^ h0 ^ m0; */
313
}
314
#else
315
void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,
316
    BN_ULONG b0);
317
#endif
318
319
/* Add polynomials a and b and store result in r; r could be a or b, a and b
320
 * could be equal; r is the bitwise XOR of a and b.
321
 */
322
int
323
BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
324
{
325
	int i;
326
	const BIGNUM *at, *bt;
327
328
	bn_check_top(a);
329
	bn_check_top(b);
330
331
3616688
	if (a->top < b->top) {
332
		at = b;
333
		bt = a;
334
23017
	} else {
335
		at = a;
336
		bt = b;
337
	}
338
339

3617114
	if (bn_wexpand(r, at->top) == NULL)
340
		return 0;
341
342
22460274
	for (i = 0; i < bt->top; i++) {
343
9421793
		r->d[i] = at->d[i] ^ bt->d[i];
344
	}
345
4171734
	for (; i < at->top; i++) {
346
277523
		r->d[i] = at->d[i];
347
	}
348
349
1808344
	r->top = at->top;
350

9150021
	bn_correct_top(r);
351
352
1808344
	return 1;
353
1808344
}
354
355
356
/* Some functions allow for representation of the irreducible polynomials
357
 * as an int[], say p.  The irreducible f(t) is then of the form:
358
 *     t^p[0] + t^p[1] + ... + t^p[k]
359
 * where m = p[0] > p[1] > ... > p[k] = 0.
360
 */
361
362
363
/* Performs modular reduction of a and store result in r.  r could be a. */
364
int
365
BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
366
{
367
	int j, k;
368
	int n, dN, d0, d1;
369
	BN_ULONG zz, *z;
370
371
	bn_check_top(a);
372
373
14493942
	if (!p[0]) {
374
		/* reduction mod 1 => return 0 */
375
		BN_zero(r);
376
		return 1;
377
	}
378
379
	/* Since the algorithm does reduction in the r value, if a != r, copy
380
	 * the contents of a into r so we can do reduction in r.
381
	 */
382
7246971
	if (a != r) {
383

14493894
		if (!bn_wexpand(r, a->top))
384
			return 0;
385
151957422
		for (j = 0; j < a->top; j++) {
386
68731764
			r->d[j] = a->d[j];
387
		}
388
7246947
		r->top = a->top;
389
7246947
	}
390
7246971
	z = r->d;
391
392
	/* start reduction */
393
7246971
	dN = p[0] / BN_BITS2;
394
114884424
	for (j = r->top - 1; j > dN; ) {
395
66927104
		zz = z[j];
396
66927104
		if (z[j] == 0) {
397
33463726
			j--;
398
33463726
			continue;
399
		}
400
33463378
		z[j] = 0;
401
402
206446712
		for (k = 1; p[k] != 0; k++) {
403
			/* reducing component t^p[k] */
404
69759978
			n = p[0] - p[k];
405
69759978
			d0 = n % BN_BITS2;
406
69759978
			d1 = BN_BITS2 - d0;
407
69759978
			n /= BN_BITS2;
408
69759978
			z[j - n] ^= (zz >> d0);
409
69759978
			if (d0)
410
69732003
				z[j - n - 1] ^= (zz << d1);
411
		}
412
413
		/* reducing component t^0 */
414
		n = dN;
415
33463378
		d0 = p[0] % BN_BITS2;
416
33463378
		d1 = BN_BITS2 - d0;
417
33463378
		z[j - n] ^= (zz >> d0);
418
33463378
		if (d0)
419
33463378
			z[j - n - 1] ^= (zz << d1);
420
	}
421
422
	/* final round of reduction */
423
28107496
	while (j == dN) {
424
425
14048508
		d0 = p[0] % BN_BITS2;
426
14048508
		zz = z[dN] >> d0;
427
14048508
		if (zz == 0)
428
			break;
429
6806777
		d1 = BN_BITS2 - d0;
430
431
		/* clear up the top d1 bits */
432
6806777
		if (d0)
433
6806777
			z[dN] = (z[dN] << d1) >> d1;
434
		else
435
			z[dN] = 0;
436
6806777
		z[0] ^= zz; /* reduction t^0 component */
437
438
41122288
		for (k = 1; p[k] != 0; k++) {
439
			BN_ULONG tmp_ulong;
440
441
			/* reducing component t^p[k]*/
442
13754367
			n = p[k] / BN_BITS2;
443
13754367
			d0 = p[k] % BN_BITS2;
444
13754367
			d1 = BN_BITS2 - d0;
445
13754367
			z[n] ^= (zz << d0);
446

27508734
			if (d0 && (tmp_ulong = zz >> d1))
447
1577526
				z[n + 1] ^= tmp_ulong;
448
		}
449
450
451
	}
452
453

138183763
	bn_correct_top(r);
454
7246971
	return 1;
455
7246971
}
456
457
/* Performs modular reduction of a by p and store result in r.  r could be a.
458
 *
459
 * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
460
 * function is only provided for convenience; for best performance, use the
461
 * BN_GF2m_mod_arr function.
462
 */
463
int
464
BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
465
{
466
	int ret = 0;
467
82412
	int arr[6];
468
469
	bn_check_top(a);
470
	bn_check_top(p);
471
41206
	ret = BN_GF2m_poly2arr(p, arr, sizeof(arr) / sizeof(arr[0]));
472
41206
	if (!ret || ret > (int)(sizeof(arr) / sizeof(arr[0]))) {
473
		BNerror(BN_R_INVALID_LENGTH);
474
		return 0;
475
	}
476
41206
	ret = BN_GF2m_mod_arr(r, a, arr);
477
	bn_check_top(r);
478
41206
	return ret;
479
41206
}
480
481
482
/* Compute the product of two polynomials a and b, reduce modulo p, and store
483
 * the result in r.  r could be a or b; a could be b.
484
 */
485
int
486
BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[],
487
    BN_CTX *ctx)
488
{
489
	int zlen, i, j, k, ret = 0;
490
	BIGNUM *s;
491
7055944
	BN_ULONG x1, x0, y1, y0, zz[4];
492
493
	bn_check_top(a);
494
	bn_check_top(b);
495
496
3527972
	if (a == b) {
497
		return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
498
	}
499
500
3527972
	BN_CTX_start(ctx);
501
3527972
	if ((s = BN_CTX_get(ctx)) == NULL)
502
		goto err;
503
504
3527972
	zlen = a->top + b->top + 4;
505

7055944
	if (!bn_wexpand(s, zlen))
506
		goto err;
507
3527972
	s->top = zlen;
508
509
108577092
	for (i = 0; i < zlen; i++)
510
50760574
		s->d[i] = 0;
511
512
28937318
	for (j = 0; j < b->top; j += 2) {
513
10940687
		y0 = b->d[j];
514
30705137
		y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];
515
88818172
		for (i = 0; i < a->top; i += 2) {
516
33468399
			x0 = a->d[i];
517
91941180
			x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];
518
33468399
			bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
519
334683990
			for (k = 0; k < 4; k++)
520
133873596
				s->d[i + j + k] ^= zz[k];
521
		}
522
	}
523
524

63170569
	bn_correct_top(s);
525
3527972
	if (BN_GF2m_mod_arr(r, s, p))
526
3527972
		ret = 1;
527
	bn_check_top(r);
528
529
err:
530
3527972
	BN_CTX_end(ctx);
531
3527972
	return ret;
532
3527972
}
533
534
/* Compute the product of two polynomials a and b, reduce modulo p, and store
535
 * the result in r.  r could be a or b; a could equal b.
536
 *
537
 * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper
538
 * function is only provided for convenience; for best performance, use the
539
 * BN_GF2m_mod_mul_arr function.
540
 */
541
int
542
BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p,
543
    BN_CTX *ctx)
544
{
545
	int ret = 0;
546
85388
	const int max = BN_num_bits(p) + 1;
547
	int *arr = NULL;
548
549
	bn_check_top(a);
550
	bn_check_top(b);
551
	bn_check_top(p);
552
42694
	if ((arr = reallocarray(NULL, max, sizeof(int))) == NULL)
553
		goto err;
554
42694
	ret = BN_GF2m_poly2arr(p, arr, max);
555

85388
	if (!ret || ret > max) {
556
		BNerror(BN_R_INVALID_LENGTH);
557
		goto err;
558
	}
559
42694
	ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
560
	bn_check_top(r);
561
562
err:
563
42694
	free(arr);
564
42694
	return ret;
565
}
566
567
568
/* Square a, reduce the result mod p, and store it in a.  r could be a. */
569
int
570
BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx)
571
{
572
	int i, ret = 0;
573
	BIGNUM *s;
574
575
	bn_check_top(a);
576
7342544
	BN_CTX_start(ctx);
577
3671272
	if ((s = BN_CTX_get(ctx)) == NULL)
578
		goto err;
579

7342544
	if (!bn_wexpand(s, 2 * a->top))
580
		goto err;
581
582
41213410
	for (i = a->top - 1; i >= 0; i--) {
583
16935433
		s->d[2 * i + 1] = SQR1(a->d[i]);
584
16935433
		s->d[2 * i] = SQR0(a->d[i]);
585
	}
586
587
3671272
	s->top = 2 * a->top;
588

21494254
	bn_correct_top(s);
589
3671272
	if (!BN_GF2m_mod_arr(r, s, p))
590
		goto err;
591
	bn_check_top(r);
592
3671272
	ret = 1;
593
594
err:
595
3671272
	BN_CTX_end(ctx);
596
3671272
	return ret;
597
}
598
599
/* Square a, reduce the result mod p, and store it in a.  r could be a.
600
 *
601
 * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper
602
 * function is only provided for convenience; for best performance, use the
603
 * BN_GF2m_mod_sqr_arr function.
604
 */
605
int
606
BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
607
{
608
	int ret = 0;
609
3024
	const int max = BN_num_bits(p) + 1;
610
	int *arr = NULL;
611
612
	bn_check_top(a);
613
	bn_check_top(p);
614
1512
	if ((arr = reallocarray(NULL, max, sizeof(int))) == NULL)
615
		goto err;
616
1512
	ret = BN_GF2m_poly2arr(p, arr, max);
617

3024
	if (!ret || ret > max) {
618
		BNerror(BN_R_INVALID_LENGTH);
619
		goto err;
620
	}
621
1512
	ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
622
	bn_check_top(r);
623
624
err:
625
1512
	free(arr);
626
1512
	return ret;
627
}
628
629
630
/* Invert a, reduce modulo p, and store the result in r. r could be a.
631
 * Uses Modified Almost Inverse Algorithm (Algorithm 10) from
632
 *     Hankerson, D., Hernandez, J.L., and Menezes, A.  "Software Implementation
633
 *     of Elliptic Curve Cryptography Over Binary Fields".
634
 */
635
int
636
BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
637
{
638
	BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;
639
	int ret = 0;
640
641
	bn_check_top(a);
642
	bn_check_top(p);
643
644
78188
	BN_CTX_start(ctx);
645
646
39094
	if ((b = BN_CTX_get(ctx)) == NULL)
647
		goto err;
648
39094
	if ((c = BN_CTX_get(ctx)) == NULL)
649
		goto err;
650
39094
	if ((u = BN_CTX_get(ctx)) == NULL)
651
		goto err;
652
39094
	if ((v = BN_CTX_get(ctx)) == NULL)
653
		goto err;
654
655
39094
	if (!BN_GF2m_mod(u, a, p))
656
		goto err;
657
39094
	if (BN_is_zero(u))
658
		goto err;
659
660
39094
	if (!BN_copy(v, p))
661
		goto err;
662
#if 0
663
	if (!BN_one(b))
664
		goto err;
665
666
	while (1) {
667
		while (!BN_is_odd(u)) {
668
			if (BN_is_zero(u))
669
				goto err;
670
			if (!BN_rshift1(u, u))
671
				goto err;
672
			if (BN_is_odd(b)) {
673
				if (!BN_GF2m_add(b, b, p))
674
					goto err;
675
			}
676
			if (!BN_rshift1(b, b))
677
				goto err;
678
		}
679
680
		if (BN_abs_is_word(u, 1))
681
			break;
682
683
		if (BN_num_bits(u) < BN_num_bits(v)) {
684
			tmp = u;
685
			u = v;
686
			v = tmp;
687
			tmp = b;
688
			b = c;
689
			c = tmp;
690
		}
691
692
		if (!BN_GF2m_add(u, u, v))
693
			goto err;
694
		if (!BN_GF2m_add(b, b, c))
695
			goto err;
696
	}
697
#else
698
	{
699
39094
		int i,	ubits = BN_num_bits(u),
700
39094
		vbits = BN_num_bits(v),	/* v is copy of p */
701
39094
		top = p->top;
702
		BN_ULONG *udp, *bdp, *vdp, *cdp;
703
704

78188
		if (!bn_wexpand(u, top))
705
                        goto err;
706
39094
		udp = u->d;
707
79478
		for (i = u->top; i < top; i++)
708
645
			udp[i] = 0;
709
39094
		u->top = top;
710

78188
		if (!bn_wexpand(b, top))
711
                        goto err;
712
39094
		bdp = b->d;
713
39094
		bdp[0] = 1;
714
510774
		for (i = 1; i < top; i++)
715
216293
			bdp[i] = 0;
716
39094
		b->top = top;
717

78188
		if (!bn_wexpand(c, top))
718
                        goto err;
719
39094
		cdp = c->d;
720
588962
		for (i = 0; i < top; i++)
721
255387
			cdp[i] = 0;
722
39094
		c->top = top;
723
39094
		vdp = v->d;	/* It pays off to "cache" *->d pointers, because
724
				 * it allows optimizer to be more aggressive.
725
				 * But we don't have to "cache" p->d, because *p
726
				 * is declared 'const'... */
727
12826197
		while (1) {
728

115329516
			while (ubits && !(udp[0]&1)) {
729
				BN_ULONG u0, u1, b0, b1, mask;
730
731
				u0 = udp[0];
732
25616975
				b0 = bdp[0];
733
25616975
				mask = (BN_ULONG)0 - (b0 & 1);
734
25616975
				b0  ^= p->d[0] & mask;
735
381074022
				for (i = 0; i < top - 1; i++) {
736
164920036
					u1 = udp[i + 1];
737
329840072
					udp[i] = ((u0 >> 1) |
738
164920036
					    (u1 << (BN_BITS2 - 1))) & BN_MASK2;
739
					u0 = u1;
740
164920036
					b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);
741
329840072
					bdp[i] = ((b0 >> 1) |
742
164920036
					    (b1 << (BN_BITS2 - 1))) & BN_MASK2;
743
					b0 = b1;
744
				}
745
25616975
				udp[i] = u0 >> 1;
746
25616975
				bdp[i] = b0 >> 1;
747
25616975
				ubits--;
748
			}
749
750
12826197
			if (ubits <= BN_BITS2) {
751
				/* See if poly was reducible. */
752
2038131
				if (udp[0] == 0)
753
					goto err;
754
2038131
				if (udp[0] == 1)
755
					break;
756
			}
757
758
12787103
			if (ubits < vbits) {
759
				i = ubits;
760
				ubits = vbits;
761
				vbits = i;
762
				tmp = u;
763
				u = v;
764
				v = tmp;
765
				tmp = b;
766
				b = c;
767
				c = tmp;
768
				udp = vdp;
769
5126363
				vdp = v->d;
770
				bdp = cdp;
771
5126363
				cdp = c->d;
772
5126363
			}
773
215815494
			for (i = 0; i < top; i++) {
774
95120644
				udp[i] ^= vdp[i];
775
95120644
				bdp[i] ^= cdp[i];
776
			}
777
12787103
			if (ubits == vbits) {
778
				BN_ULONG ul;
779
2550154
				int utop = (ubits - 1) / BN_BITS2;
780
781
5243436
				while ((ul = udp[utop]) == 0 && utop)
782
71564
					utop--;
783
2550154
				ubits = utop*BN_BITS2 + BN_num_bits_word(ul);
784
2550154
			}
785
		}
786

196907
		bn_correct_top(b);
787
39094
	}
788
#endif
789
790
39094
	if (!BN_copy(r, b))
791
		goto err;
792
	bn_check_top(r);
793
39094
	ret = 1;
794
795
err:
796
#ifdef BN_DEBUG /* BN_CTX_end would complain about the expanded form */
797
	bn_correct_top(c);
798
	bn_correct_top(u);
799
	bn_correct_top(v);
800
#endif
801
39094
	BN_CTX_end(ctx);
802
39094
	return ret;
803
39094
}
804
805
/* Invert xx, reduce modulo p, and store the result in r. r could be xx.
806
 *
807
 * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper
808
 * function is only provided for convenience; for best performance, use the
809
 * BN_GF2m_mod_inv function.
810
 */
811
int
812
BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], BN_CTX *ctx)
813
{
814
	BIGNUM *field;
815
	int ret = 0;
816
817
	bn_check_top(xx);
818
	BN_CTX_start(ctx);
819
	if ((field = BN_CTX_get(ctx)) == NULL)
820
		goto err;
821
	if (!BN_GF2m_arr2poly(p, field))
822
		goto err;
823
824
	ret = BN_GF2m_mod_inv(r, xx, field, ctx);
825
	bn_check_top(r);
826
827
err:
828
	BN_CTX_end(ctx);
829
	return ret;
830
}
831
832
833
#ifndef OPENSSL_SUN_GF2M_DIV
834
/* Divide y by x, reduce modulo p, and store the result in r. r could be x
835
 * or y, x could equal y.
836
 */
837
int
838
BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p,
839
    BN_CTX *ctx)
840
{
841
	BIGNUM *xinv = NULL;
842
	int ret = 0;
843
844
	bn_check_top(y);
845
	bn_check_top(x);
846
	bn_check_top(p);
847
848
76988
	BN_CTX_start(ctx);
849
38494
	if ((xinv = BN_CTX_get(ctx)) == NULL)
850
		goto err;
851
852
38494
	if (!BN_GF2m_mod_inv(xinv, x, p, ctx))
853
		goto err;
854
38494
	if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))
855
		goto err;
856
	bn_check_top(r);
857
38494
	ret = 1;
858
859
err:
860
38494
	BN_CTX_end(ctx);
861
38494
	return ret;
862
}
863
#else
864
/* Divide y by x, reduce modulo p, and store the result in r. r could be x
865
 * or y, x could equal y.
866
 * Uses algorithm Modular_Division_GF(2^m) from
867
 *     Chang-Shantz, S.  "From Euclid's GCD to Montgomery Multiplication to
868
 *     the Great Divide".
869
 */
870
int
871
BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p,
872
    BN_CTX *ctx)
873
{
874
	BIGNUM *a, *b, *u, *v;
875
	int ret = 0;
876
877
	bn_check_top(y);
878
	bn_check_top(x);
879
	bn_check_top(p);
880
881
	BN_CTX_start(ctx);
882
883
	if ((a = BN_CTX_get(ctx)) == NULL)
884
		goto err;
885
	if ((b = BN_CTX_get(ctx)) == NULL)
886
		goto err;
887
	if ((u = BN_CTX_get(ctx)) == NULL)
888
		goto err;
889
	if ((v = BN_CTX_get(ctx)) == NULL)
890
		goto err;
891
892
	/* reduce x and y mod p */
893
	if (!BN_GF2m_mod(u, y, p))
894
		goto err;
895
	if (!BN_GF2m_mod(a, x, p))
896
		goto err;
897
	if (!BN_copy(b, p))
898
		goto err;
899
900
	while (!BN_is_odd(a)) {
901
		if (!BN_rshift1(a, a))
902
			goto err;
903
		if (BN_is_odd(u))
904
			if (!BN_GF2m_add(u, u, p))
905
				goto err;
906
		if (!BN_rshift1(u, u))
907
			goto err;
908
	}
909
910
	do {
911
		if (BN_GF2m_cmp(b, a) > 0) {
912
			if (!BN_GF2m_add(b, b, a))
913
				goto err;
914
			if (!BN_GF2m_add(v, v, u))
915
				goto err;
916
			do {
917
				if (!BN_rshift1(b, b))
918
					goto err;
919
				if (BN_is_odd(v))
920
					if (!BN_GF2m_add(v, v, p))
921
						goto err;
922
				if (!BN_rshift1(v, v))
923
					goto err;
924
			} while (!BN_is_odd(b));
925
		} else if (BN_abs_is_word(a, 1))
926
			break;
927
		else {
928
			if (!BN_GF2m_add(a, a, b))
929
				goto err;
930
			if (!BN_GF2m_add(u, u, v))
931
				goto err;
932
			do {
933
				if (!BN_rshift1(a, a))
934
					goto err;
935
				if (BN_is_odd(u))
936
					if (!BN_GF2m_add(u, u, p))
937
						goto err;
938
				if (!BN_rshift1(u, u))
939
					goto err;
940
			} while (!BN_is_odd(a));
941
		}
942
	} while (1);
943
944
	if (!BN_copy(r, u))
945
		goto err;
946
	bn_check_top(r);
947
	ret = 1;
948
949
err:
950
	BN_CTX_end(ctx);
951
	return ret;
952
}
953
#endif
954
955
/* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
956
 * or yy, xx could equal yy.
957
 *
958
 * This function calls down to the BN_GF2m_mod_div implementation; this wrapper
959
 * function is only provided for convenience; for best performance, use the
960
 * BN_GF2m_mod_div function.
961
 */
962
int
963
BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,
964
    const int p[], BN_CTX *ctx)
965
{
966
	BIGNUM *field;
967
	int ret = 0;
968
969
	bn_check_top(yy);
970
	bn_check_top(xx);
971
972
	BN_CTX_start(ctx);
973
	if ((field = BN_CTX_get(ctx)) == NULL)
974
		goto err;
975
	if (!BN_GF2m_arr2poly(p, field))
976
		goto err;
977
978
	ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
979
	bn_check_top(r);
980
981
err:
982
	BN_CTX_end(ctx);
983
	return ret;
984
}
985
986
987
/* Compute the bth power of a, reduce modulo p, and store
988
 * the result in r.  r could be a.
989
 * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363.
990
 */
991
int
992
BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[],
993
    BN_CTX *ctx)
994
{
995
	int ret = 0, i, n;
996
	BIGNUM *u;
997
998
	bn_check_top(a);
999
	bn_check_top(b);
1000
1001
4800
	if (BN_is_zero(b))
1002
		return (BN_one(r));
1003
1004

2400
	if (BN_abs_is_word(b, 1))
1005
		return (BN_copy(r, a) != NULL);
1006
1007
2400
	BN_CTX_start(ctx);
1008
2400
	if ((u = BN_CTX_get(ctx)) == NULL)
1009
		goto err;
1010
1011
2400
	if (!BN_GF2m_mod_arr(u, a, p))
1012
		goto err;
1013
1014
2400
	n = BN_num_bits(b) - 1;
1015
2058000
	for (i = n - 1; i >= 0; i--) {
1016
1026600
		if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx))
1017
			goto err;
1018
1026600
		if (BN_is_bit_set(b, i)) {
1019
466248
			if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx))
1020
				goto err;
1021
		}
1022
	}
1023
2400
	if (!BN_copy(r, u))
1024
		goto err;
1025
	bn_check_top(r);
1026
2400
	ret = 1;
1027
1028
err:
1029
2400
	BN_CTX_end(ctx);
1030
2400
	return ret;
1031
2400
}
1032
1033
/* Compute the bth power of a, reduce modulo p, and store
1034
 * the result in r.  r could be a.
1035
 *
1036
 * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper
1037
 * function is only provided for convenience; for best performance, use the
1038
 * BN_GF2m_mod_exp_arr function.
1039
 */
1040
int
1041
BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p,
1042
    BN_CTX *ctx)
1043
{
1044
	int ret = 0;
1045
3600
	const int max = BN_num_bits(p) + 1;
1046
	int *arr = NULL;
1047
1048
	bn_check_top(a);
1049
	bn_check_top(b);
1050
	bn_check_top(p);
1051
1800
	if ((arr = reallocarray(NULL, max, sizeof(int))) == NULL)
1052
		goto err;
1053
1800
	ret = BN_GF2m_poly2arr(p, arr, max);
1054

3600
	if (!ret || ret > max) {
1055
		BNerror(BN_R_INVALID_LENGTH);
1056
		goto err;
1057
	}
1058
1800
	ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
1059
	bn_check_top(r);
1060
1061
err:
1062
1800
	free(arr);
1063
1800
	return ret;
1064
}
1065
1066
/* Compute the square root of a, reduce modulo p, and store
1067
 * the result in r.  r could be a.
1068
 * Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
1069
 */
1070
int
1071
BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx)
1072
{
1073
	int ret = 0;
1074
	BIGNUM *u;
1075
1076
	bn_check_top(a);
1077
1078
1200
	if (!p[0]) {
1079
		/* reduction mod 1 => return 0 */
1080
		BN_zero(r);
1081
		return 1;
1082
	}
1083
1084
600
	BN_CTX_start(ctx);
1085
600
	if ((u = BN_CTX_get(ctx)) == NULL)
1086
		goto err;
1087
1088
600
	if (!BN_set_bit(u, p[0] - 1))
1089
		goto err;
1090
600
	ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
1091
	bn_check_top(r);
1092
1093
err:
1094
600
	BN_CTX_end(ctx);
1095
600
	return ret;
1096
600
}
1097
1098
/* Compute the square root of a, reduce modulo p, and store
1099
 * the result in r.  r could be a.
1100
 *
1101
 * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper
1102
 * function is only provided for convenience; for best performance, use the
1103
 * BN_GF2m_mod_sqrt_arr function.
1104
 */
1105
int
1106
BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
1107
{
1108
	int ret = 0;
1109
1200
	const int max = BN_num_bits(p) + 1;
1110
	int *arr = NULL;
1111
	bn_check_top(a);
1112
	bn_check_top(p);
1113
600
	if ((arr = reallocarray(NULL, max, sizeof(int))) == NULL)
1114
		goto err;
1115
600
	ret = BN_GF2m_poly2arr(p, arr, max);
1116

1200
	if (!ret || ret > max) {
1117
		BNerror(BN_R_INVALID_LENGTH);
1118
		goto err;
1119
	}
1120
600
	ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
1121
	bn_check_top(r);
1122
1123
err:
1124
600
	free(arr);
1125
600
	return ret;
1126
}
1127
1128
/* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.
1129
 * Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
1130
 */
1131
int
1132
BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
1133
    BN_CTX *ctx)
1134
{
1135
	int ret = 0, count = 0, j;
1136
	BIGNUM *a, *z, *rho, *w, *w2, *tmp;
1137
1138
	bn_check_top(a_);
1139
1140
1368
	if (!p[0]) {
1141
		/* reduction mod 1 => return 0 */
1142
		BN_zero(r);
1143
		return 1;
1144
	}
1145
1146
684
	BN_CTX_start(ctx);
1147
684
	if ((a = BN_CTX_get(ctx)) == NULL)
1148
		goto err;
1149
684
	if ((z = BN_CTX_get(ctx)) == NULL)
1150
		goto err;
1151
684
	if ((w = BN_CTX_get(ctx)) == NULL)
1152
		goto err;
1153
1154
684
	if (!BN_GF2m_mod_arr(a, a_, p))
1155
		goto err;
1156
1157
684
	if (BN_is_zero(a)) {
1158
		BN_zero(r);
1159
		ret = 1;
1160
		goto err;
1161
	}
1162
1163
684
	if (p[0] & 0x1) /* m is odd */
1164
	{
1165
		/* compute half-trace of a */
1166
674
		if (!BN_copy(z, a))
1167
			goto err;
1168
124516
		for (j = 1; j <= (p[0] - 1) / 2; j++) {
1169
61584
			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1170
				goto err;
1171
61584
			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1172
				goto err;
1173
61584
			if (!BN_GF2m_add(z, z, a))
1174
				goto err;
1175
		}
1176
1177
	}
1178
	else /* m is even */
1179
	{
1180
10
		if ((rho = BN_CTX_get(ctx)) == NULL)
1181
			goto err;
1182
10
		if ((w2 = BN_CTX_get(ctx)) == NULL)
1183
			goto err;
1184
10
		if ((tmp = BN_CTX_get(ctx)) == NULL)
1185
			goto err;
1186
10
		do {
1187
24
			if (!BN_rand(rho, p[0], 0, 0))
1188
				goto err;
1189
24
			if (!BN_GF2m_mod_arr(rho, rho, p))
1190
				goto err;
1191
24
			BN_zero(z);
1192
24
			if (!BN_copy(w, rho))
1193
				goto err;
1194
11008
			for (j = 1; j <= p[0] - 1; j++) {
1195
5480
				if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1196
					goto err;
1197
5480
				if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx))
1198
					goto err;
1199
5480
				if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx))
1200
					goto err;
1201
5480
				if (!BN_GF2m_add(z, z, tmp))
1202
					goto err;
1203
5480
				if (!BN_GF2m_add(w, w2, rho))
1204
					goto err;
1205
			}
1206
24
			count++;
1207
24
		} while (BN_is_zero(w) && (count < MAX_ITERATIONS));
1208
10
		if (BN_is_zero(w)) {
1209
			BNerror(BN_R_TOO_MANY_ITERATIONS);
1210
			goto err;
1211
		}
1212
	}
1213
1214
684
	if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx))
1215
		goto err;
1216
684
	if (!BN_GF2m_add(w, z, w))
1217
		goto err;
1218
684
	if (BN_GF2m_cmp(w, a)) {
1219
288
		BNerror(BN_R_NO_SOLUTION);
1220
288
		goto err;
1221
	}
1222
1223
396
	if (!BN_copy(r, z))
1224
		goto err;
1225
	bn_check_top(r);
1226
1227
396
	ret = 1;
1228
1229
err:
1230
684
	BN_CTX_end(ctx);
1231
684
	return ret;
1232
684
}
1233
1234
/* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.
1235
 *
1236
 * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper
1237
 * function is only provided for convenience; for best performance, use the
1238
 * BN_GF2m_mod_solve_quad_arr function.
1239
 */
1240
int
1241
BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
1242
{
1243
	int ret = 0;
1244
1200
	const int max = BN_num_bits(p) + 1;
1245
	int *arr = NULL;
1246
1247
	bn_check_top(a);
1248
	bn_check_top(p);
1249
600
	if ((arr = reallocarray(NULL, max, sizeof(int))) == NULL)
1250
		goto err;
1251
600
	ret = BN_GF2m_poly2arr(p, arr, max);
1252

1200
	if (!ret || ret > max) {
1253
		BNerror(BN_R_INVALID_LENGTH);
1254
		goto err;
1255
	}
1256
600
	ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
1257
	bn_check_top(r);
1258
1259
err:
1260
600
	free(arr);
1261
600
	return ret;
1262
}
1263
1264
/* Convert the bit-string representation of a polynomial
1265
 * ( \sum_{i=0}^n a_i * x^i) into an array of integers corresponding
1266
 * to the bits with non-zero coefficient.  Array is terminated with -1.
1267
 * Up to max elements of the array will be filled.  Return value is total
1268
 * number of array elements that would be filled if array was large enough.
1269
 */
1270
int
1271
BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
1272
{
1273
	int i, j, k = 0;
1274
	BN_ULONG mask;
1275
1276
178080
	if (BN_is_zero(a))
1277
		return 0;
1278
1279
1276638
	for (i = a->top - 1; i >= 0; i--) {
1280
549279
		if (!a->d[i])
1281
			/* skip word if a->d[i] == 0 */
1282
			continue;
1283
		mask = BN_TBIT;
1284
26493350
		for (j = BN_BITS2 - 1; j >= 0; j--) {
1285
13042880
			if (a->d[i] & mask) {
1286
377174
				if (k < max)
1287
377174
					p[k] = BN_BITS2 * i + j;
1288
377174
				k++;
1289
377174
			}
1290
13042880
			mask >>= 1;
1291
		}
1292
	}
1293
1294
89040
	if (k < max) {
1295
89040
		p[k] = -1;
1296
89040
		k++;
1297
89040
	}
1298
1299
89040
	return k;
1300
89040
}
1301
1302
/* Convert the coefficient array representation of a polynomial to a
1303
 * bit-string.  The array must be terminated by -1.
1304
 */
1305
int
1306
BN_GF2m_arr2poly(const int p[], BIGNUM *a)
1307
{
1308
	int i;
1309
1310
	bn_check_top(a);
1311
96
	BN_zero(a);
1312
480
	for (i = 0; p[i] != -1; i++) {
1313
192
		if (BN_set_bit(a, p[i]) == 0)
1314
			return 0;
1315
	}
1316
	bn_check_top(a);
1317
1318
48
	return 1;
1319
48
}
1320
1321
#endif