1 /* crypto/bn/bn_gf2m.c */
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 /*
31 * NOTE: This file is licensed pursuant to the OpenSSL license below and may
32 * be modified; but after modifications, the above covenant may no longer
33 * apply! In such cases, the corresponding paragraph ["In addition, Sun
34 * covenants ... causes the infringement."] and this note can be edited out;
35 * but please keep the Sun copyright notice and attribution.
36 */
37
38 /* ====================================================================
39 * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved.
40 *
41 * Redistribution and use in source and binary forms, with or without
42 * modification, are permitted provided that the following conditions
43 * are met:
44 *
45 * 1. Redistributions of source code must retain the above copyright
46 * notice, this list of conditions and the following disclaimer.
47 *
48 * 2. Redistributions in binary form must reproduce the above copyright
49 * notice, this list of conditions and the following disclaimer in
50 * the documentation and/or other materials provided with the
51 * distribution.
52 *
53 * 3. All advertising materials mentioning features or use of this
54 * software must display the following acknowledgment:
55 * "This product includes software developed by the OpenSSL Project
56 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
57 *
58 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
59 * endorse or promote products derived from this software without
60 * prior written permission. For written permission, please contact
61 * openssl-core@openssl.org.
62 *
63 * 5. Products derived from this software may not be called "OpenSSL"
64 * nor may "OpenSSL" appear in their names without prior written
65 * permission of the OpenSSL Project.
66 *
67 * 6. Redistributions of any form whatsoever must retain the following
68 * acknowledgment:
69 * "This product includes software developed by the OpenSSL Project
70 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
71 *
72 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
73 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
74 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
75 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
76 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
77 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
78 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
79 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
80 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
81 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
82 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
83 * OF THE POSSIBILITY OF SUCH DAMAGE.
84 * ====================================================================
85 *
86 * This product includes cryptographic software written by Eric Young
87 * (eay@cryptsoft.com). This product includes software written by Tim
88 * Hudson (tjh@cryptsoft.com).
89 *
90 */
91
92 #include <assert.h>
93 #include <limits.h>
94 #include <stdio.h>
95 #include "cryptlib.h"
96 #include "bn_lcl.h"
97
98 #ifndef OPENSSL_NO_EC2M
99
100 /*
101 * Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should
102 * fail.
103 */
104 # define MAX_ITERATIONS 50
105
106 static const BN_ULONG SQR_tb[16] = { 0, 1, 4, 5, 16, 17, 20, 21,
107 64, 65, 68, 69, 80, 81, 84, 85
108 };
109
110 /* Platform-specific macros to accelerate squaring. */
111 # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
112 # define SQR1(w) \
113 SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \
114 SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \
115 SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \
116 SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF]
117 # define SQR0(w) \
118 SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \
119 SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \
120 SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
121 SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
122 # endif
123 # ifdef THIRTY_TWO_BIT
124 # define SQR1(w) \
125 SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \
126 SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF]
127 # define SQR0(w) \
128 SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \
129 SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF]
130 # endif
131
132 # if !defined(OPENSSL_BN_ASM_GF2m)
133 /*
134 * Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is
135 * a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that
136 * the variables have the right amount of space allocated.
137 */
138 # ifdef THIRTY_TWO_BIT
bn_GF2m_mul_1x1(BN_ULONG * r1,BN_ULONG * r0,const BN_ULONG a,const BN_ULONG b)139 static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
140 const BN_ULONG b)
141 {
142 register BN_ULONG h, l, s;
143 BN_ULONG tab[8], top2b = a >> 30;
144 register BN_ULONG a1, a2, a4;
145
146 a1 = a & (0x3FFFFFFF);
147 a2 = a1 << 1;
148 a4 = a2 << 1;
149
150 tab[0] = 0;
151 tab[1] = a1;
152 tab[2] = a2;
153 tab[3] = a1 ^ a2;
154 tab[4] = a4;
155 tab[5] = a1 ^ a4;
156 tab[6] = a2 ^ a4;
157 tab[7] = a1 ^ a2 ^ a4;
158
159 s = tab[b & 0x7];
160 l = s;
161 s = tab[b >> 3 & 0x7];
162 l ^= s << 3;
163 h = s >> 29;
164 s = tab[b >> 6 & 0x7];
165 l ^= s << 6;
166 h ^= s >> 26;
167 s = tab[b >> 9 & 0x7];
168 l ^= s << 9;
169 h ^= s >> 23;
170 s = tab[b >> 12 & 0x7];
171 l ^= s << 12;
172 h ^= s >> 20;
173 s = tab[b >> 15 & 0x7];
174 l ^= s << 15;
175 h ^= s >> 17;
176 s = tab[b >> 18 & 0x7];
177 l ^= s << 18;
178 h ^= s >> 14;
179 s = tab[b >> 21 & 0x7];
180 l ^= s << 21;
181 h ^= s >> 11;
182 s = tab[b >> 24 & 0x7];
183 l ^= s << 24;
184 h ^= s >> 8;
185 s = tab[b >> 27 & 0x7];
186 l ^= s << 27;
187 h ^= s >> 5;
188 s = tab[b >> 30];
189 l ^= s << 30;
190 h ^= s >> 2;
191
192 /* compensate for the top two bits of a */
193
194 if (top2b & 01) {
195 l ^= b << 30;
196 h ^= b >> 2;
197 }
198 if (top2b & 02) {
199 l ^= b << 31;
200 h ^= b >> 1;
201 }
202
203 *r1 = h;
204 *r0 = l;
205 }
206 # endif
207 # if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
bn_GF2m_mul_1x1(BN_ULONG * r1,BN_ULONG * r0,const BN_ULONG a,const BN_ULONG b)208 static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
209 const BN_ULONG b)
210 {
211 register BN_ULONG h, l, s;
212 BN_ULONG tab[16], top3b = a >> 61;
213 register BN_ULONG a1, a2, a4, a8;
214
215 a1 = a & (0x1FFFFFFFFFFFFFFFULL);
216 a2 = a1 << 1;
217 a4 = a2 << 1;
218 a8 = a4 << 1;
219
220 tab[0] = 0;
221 tab[1] = a1;
222 tab[2] = a2;
223 tab[3] = a1 ^ a2;
224 tab[4] = a4;
225 tab[5] = a1 ^ a4;
226 tab[6] = a2 ^ a4;
227 tab[7] = a1 ^ a2 ^ a4;
228 tab[8] = a8;
229 tab[9] = a1 ^ a8;
230 tab[10] = a2 ^ a8;
231 tab[11] = a1 ^ a2 ^ a8;
232 tab[12] = a4 ^ a8;
233 tab[13] = a1 ^ a4 ^ a8;
234 tab[14] = a2 ^ a4 ^ a8;
235 tab[15] = a1 ^ a2 ^ a4 ^ a8;
236
237 s = tab[b & 0xF];
238 l = s;
239 s = tab[b >> 4 & 0xF];
240 l ^= s << 4;
241 h = s >> 60;
242 s = tab[b >> 8 & 0xF];
243 l ^= s << 8;
244 h ^= s >> 56;
245 s = tab[b >> 12 & 0xF];
246 l ^= s << 12;
247 h ^= s >> 52;
248 s = tab[b >> 16 & 0xF];
249 l ^= s << 16;
250 h ^= s >> 48;
251 s = tab[b >> 20 & 0xF];
252 l ^= s << 20;
253 h ^= s >> 44;
254 s = tab[b >> 24 & 0xF];
255 l ^= s << 24;
256 h ^= s >> 40;
257 s = tab[b >> 28 & 0xF];
258 l ^= s << 28;
259 h ^= s >> 36;
260 s = tab[b >> 32 & 0xF];
261 l ^= s << 32;
262 h ^= s >> 32;
263 s = tab[b >> 36 & 0xF];
264 l ^= s << 36;
265 h ^= s >> 28;
266 s = tab[b >> 40 & 0xF];
267 l ^= s << 40;
268 h ^= s >> 24;
269 s = tab[b >> 44 & 0xF];
270 l ^= s << 44;
271 h ^= s >> 20;
272 s = tab[b >> 48 & 0xF];
273 l ^= s << 48;
274 h ^= s >> 16;
275 s = tab[b >> 52 & 0xF];
276 l ^= s << 52;
277 h ^= s >> 12;
278 s = tab[b >> 56 & 0xF];
279 l ^= s << 56;
280 h ^= s >> 8;
281 s = tab[b >> 60];
282 l ^= s << 60;
283 h ^= s >> 4;
284
285 /* compensate for the top three bits of a */
286
287 if (top3b & 01) {
288 l ^= b << 61;
289 h ^= b >> 3;
290 }
291 if (top3b & 02) {
292 l ^= b << 62;
293 h ^= b >> 2;
294 }
295 if (top3b & 04) {
296 l ^= b << 63;
297 h ^= b >> 1;
298 }
299
300 *r1 = h;
301 *r0 = l;
302 }
303 # endif
304
305 /*
306 * Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
307 * result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST
308 * ensure that the variables have the right amount of space allocated.
309 */
bn_GF2m_mul_2x2(BN_ULONG * r,const BN_ULONG a1,const BN_ULONG a0,const BN_ULONG b1,const BN_ULONG b0)310 static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,
311 const BN_ULONG b1, const BN_ULONG b0)
312 {
313 BN_ULONG m1, m0;
314 /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
315 bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);
316 bn_GF2m_mul_1x1(r + 1, r, a0, b0);
317 bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
318 /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
319 r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
320 r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
321 }
322 # else
323 void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,
324 BN_ULONG b0);
325 # endif
326
327 /*
328 * Add polynomials a and b and store result in r; r could be a or b, a and b
329 * could be equal; r is the bitwise XOR of a and b.
330 */
BN_GF2m_add(BIGNUM * r,const BIGNUM * a,const BIGNUM * b)331 int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
332 {
333 int i;
334 const BIGNUM *at, *bt;
335
336 bn_check_top(a);
337 bn_check_top(b);
338
339 if (a->top < b->top) {
340 at = b;
341 bt = a;
342 } else {
343 at = a;
344 bt = b;
345 }
346
347 if (bn_wexpand(r, at->top) == NULL)
348 return 0;
349
350 for (i = 0; i < bt->top; i++) {
351 r->d[i] = at->d[i] ^ bt->d[i];
352 }
353 for (; i < at->top; i++) {
354 r->d[i] = at->d[i];
355 }
356
357 r->top = at->top;
358 bn_correct_top(r);
359
360 return 1;
361 }
362
363 /*-
364 * Some functions allow for representation of the irreducible polynomials
365 * as an int[], say p. The irreducible f(t) is then of the form:
366 * t^p[0] + t^p[1] + ... + t^p[k]
367 * where m = p[0] > p[1] > ... > p[k] = 0.
368 */
369
370 /* Performs modular reduction of a and store result in r. r could be a. */
BN_GF2m_mod_arr(BIGNUM * r,const BIGNUM * a,const int p[])371 int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
372 {
373 int j, k;
374 int n, dN, d0, d1;
375 BN_ULONG zz, *z;
376
377 bn_check_top(a);
378
379 if (!p[0]) {
380 /* reduction mod 1 => return 0 */
381 BN_zero(r);
382 return 1;
383 }
384
385 /*
386 * Since the algorithm does reduction in the r value, if a != r, copy the
387 * contents of a into r so we can do reduction in r.
388 */
389 if (a != r) {
390 if (!bn_wexpand(r, a->top))
391 return 0;
392 for (j = 0; j < a->top; j++) {
393 r->d[j] = a->d[j];
394 }
395 r->top = a->top;
396 }
397 z = r->d;
398
399 /* start reduction */
400 dN = p[0] / BN_BITS2;
401 for (j = r->top - 1; j > dN;) {
402 zz = z[j];
403 if (z[j] == 0) {
404 j--;
405 continue;
406 }
407 z[j] = 0;
408
409 for (k = 1; p[k] != 0; k++) {
410 /* reducing component t^p[k] */
411 n = p[0] - p[k];
412 d0 = n % BN_BITS2;
413 d1 = BN_BITS2 - d0;
414 n /= BN_BITS2;
415 z[j - n] ^= (zz >> d0);
416 if (d0)
417 z[j - n - 1] ^= (zz << d1);
418 }
419
420 /* reducing component t^0 */
421 n = dN;
422 d0 = p[0] % BN_BITS2;
423 d1 = BN_BITS2 - d0;
424 z[j - n] ^= (zz >> d0);
425 if (d0)
426 z[j - n - 1] ^= (zz << d1);
427 }
428
429 /* final round of reduction */
430 while (j == dN) {
431
432 d0 = p[0] % BN_BITS2;
433 zz = z[dN] >> d0;
434 if (zz == 0)
435 break;
436 d1 = BN_BITS2 - d0;
437
438 /* clear up the top d1 bits */
439 if (d0)
440 z[dN] = (z[dN] << d1) >> d1;
441 else
442 z[dN] = 0;
443 z[0] ^= zz; /* reduction t^0 component */
444
445 for (k = 1; p[k] != 0; k++) {
446 BN_ULONG tmp_ulong;
447
448 /* reducing component t^p[k] */
449 n = p[k] / BN_BITS2;
450 d0 = p[k] % BN_BITS2;
451 d1 = BN_BITS2 - d0;
452 z[n] ^= (zz << d0);
453 tmp_ulong = zz >> d1;
454 if (d0 && tmp_ulong)
455 z[n + 1] ^= tmp_ulong;
456 }
457
458 }
459
460 bn_correct_top(r);
461 return 1;
462 }
463
464 /*
465 * Performs modular reduction of a by p and store result in r. r could be a.
466 * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
467 * function is only provided for convenience; for best performance, use the
468 * BN_GF2m_mod_arr function.
469 */
BN_GF2m_mod(BIGNUM * r,const BIGNUM * a,const BIGNUM * p)470 int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
471 {
472 int ret = 0;
473 int arr[6];
474 bn_check_top(a);
475 bn_check_top(p);
476 ret = BN_GF2m_poly2arr(p, arr, sizeof(arr) / sizeof(arr[0]));
477 if (!ret || ret > (int)(sizeof(arr) / sizeof(arr[0]))) {
478 BNerr(BN_F_BN_GF2M_MOD, BN_R_INVALID_LENGTH);
479 return 0;
480 }
481 ret = BN_GF2m_mod_arr(r, a, arr);
482 bn_check_top(r);
483 return ret;
484 }
485
486 /*
487 * Compute the product of two polynomials a and b, reduce modulo p, and store
488 * the result in r. r could be a or b; a could be b.
489 */
BN_GF2m_mod_mul_arr(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const int p[],BN_CTX * ctx)490 int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
491 const int p[], BN_CTX *ctx)
492 {
493 int zlen, i, j, k, ret = 0;
494 BIGNUM *s;
495 BN_ULONG x1, x0, y1, y0, zz[4];
496
497 bn_check_top(a);
498 bn_check_top(b);
499
500 if (a == b) {
501 return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
502 }
503
504 BN_CTX_start(ctx);
505 if ((s = BN_CTX_get(ctx)) == NULL)
506 goto err;
507
508 zlen = a->top + b->top + 4;
509 if (!bn_wexpand(s, zlen))
510 goto err;
511 s->top = zlen;
512
513 for (i = 0; i < zlen; i++)
514 s->d[i] = 0;
515
516 for (j = 0; j < b->top; j += 2) {
517 y0 = b->d[j];
518 y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];
519 for (i = 0; i < a->top; i += 2) {
520 x0 = a->d[i];
521 x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];
522 bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
523 for (k = 0; k < 4; k++)
524 s->d[i + j + k] ^= zz[k];
525 }
526 }
527
528 bn_correct_top(s);
529 if (BN_GF2m_mod_arr(r, s, p))
530 ret = 1;
531 bn_check_top(r);
532
533 err:
534 BN_CTX_end(ctx);
535 return ret;
536 }
537
538 /*
539 * Compute the product of two polynomials a and b, reduce modulo p, and store
540 * the result in r. r could be a or b; a could equal b. This function calls
541 * down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is
542 * only provided for convenience; for best performance, use the
543 * BN_GF2m_mod_mul_arr function.
544 */
BN_GF2m_mod_mul(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * p,BN_CTX * ctx)545 int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
546 const BIGNUM *p, BN_CTX *ctx)
547 {
548 int ret = 0;
549 const int max = BN_num_bits(p) + 1;
550 int *arr = NULL;
551 bn_check_top(a);
552 bn_check_top(b);
553 bn_check_top(p);
554 if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL)
555 goto err;
556 ret = BN_GF2m_poly2arr(p, arr, max);
557 if (!ret || ret > max) {
558 BNerr(BN_F_BN_GF2M_MOD_MUL, BN_R_INVALID_LENGTH);
559 goto err;
560 }
561 ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
562 bn_check_top(r);
563 err:
564 if (arr)
565 OPENSSL_free(arr);
566 return ret;
567 }
568
569 /* Square a, reduce the result mod p, and store it in a. r could be a. */
BN_GF2m_mod_sqr_arr(BIGNUM * r,const BIGNUM * a,const int p[],BN_CTX * ctx)570 int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
571 BN_CTX *ctx)
572 {
573 int i, ret = 0;
574 BIGNUM *s;
575
576 bn_check_top(a);
577 BN_CTX_start(ctx);
578 if ((s = BN_CTX_get(ctx)) == NULL)
579 return 0;
580 if (!bn_wexpand(s, 2 * a->top))
581 goto err;
582
583 for (i = a->top - 1; i >= 0; i--) {
584 s->d[2 * i + 1] = SQR1(a->d[i]);
585 s->d[2 * i] = SQR0(a->d[i]);
586 }
587
588 s->top = 2 * a->top;
589 bn_correct_top(s);
590 if (!BN_GF2m_mod_arr(r, s, p))
591 goto err;
592 bn_check_top(r);
593 ret = 1;
594 err:
595 BN_CTX_end(ctx);
596 return ret;
597 }
598
599 /*
600 * Square a, reduce the result mod p, and store it in a. r could be a. This
601 * function calls down to the BN_GF2m_mod_sqr_arr implementation; this
602 * wrapper function is only provided for convenience; for best performance,
603 * use the BN_GF2m_mod_sqr_arr function.
604 */
BN_GF2m_mod_sqr(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)605 int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
606 {
607 int ret = 0;
608 const int max = BN_num_bits(p) + 1;
609 int *arr = NULL;
610
611 bn_check_top(a);
612 bn_check_top(p);
613 if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL)
614 goto err;
615 ret = BN_GF2m_poly2arr(p, arr, max);
616 if (!ret || ret > max) {
617 BNerr(BN_F_BN_GF2M_MOD_SQR, BN_R_INVALID_LENGTH);
618 goto err;
619 }
620 ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
621 bn_check_top(r);
622 err:
623 if (arr)
624 OPENSSL_free(arr);
625 return ret;
626 }
627
628 /*
629 * Invert a, reduce modulo p, and store the result in r. r could be a. Uses
630 * Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D.,
631 * Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic
632 * Curve Cryptography Over Binary Fields".
633 */
BN_GF2m_mod_inv(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)634 int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
635 {
636 BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;
637 int ret = 0;
638
639 bn_check_top(a);
640 bn_check_top(p);
641
642 BN_CTX_start(ctx);
643
644 if ((b = BN_CTX_get(ctx)) == NULL)
645 goto err;
646 if ((c = BN_CTX_get(ctx)) == NULL)
647 goto err;
648 if ((u = BN_CTX_get(ctx)) == NULL)
649 goto err;
650 if ((v = BN_CTX_get(ctx)) == NULL)
651 goto err;
652
653 if (!BN_GF2m_mod(u, a, p))
654 goto err;
655 if (BN_is_zero(u))
656 goto err;
657
658 if (!BN_copy(v, p))
659 goto err;
660 # if 0
661 if (!BN_one(b))
662 goto err;
663
664 while (1) {
665 while (!BN_is_odd(u)) {
666 if (BN_is_zero(u))
667 goto err;
668 if (!BN_rshift1(u, u))
669 goto err;
670 if (BN_is_odd(b)) {
671 if (!BN_GF2m_add(b, b, p))
672 goto err;
673 }
674 if (!BN_rshift1(b, b))
675 goto err;
676 }
677
678 if (BN_abs_is_word(u, 1))
679 break;
680
681 if (BN_num_bits(u) < BN_num_bits(v)) {
682 tmp = u;
683 u = v;
684 v = tmp;
685 tmp = b;
686 b = c;
687 c = tmp;
688 }
689
690 if (!BN_GF2m_add(u, u, v))
691 goto err;
692 if (!BN_GF2m_add(b, b, c))
693 goto err;
694 }
695 # else
696 {
697 int i;
698 int ubits = BN_num_bits(u);
699 int vbits = BN_num_bits(v); /* v is copy of p */
700 int top = p->top;
701 BN_ULONG *udp, *bdp, *vdp, *cdp;
702
703 bn_wexpand(u, top);
704 udp = u->d;
705 for (i = u->top; i < top; i++)
706 udp[i] = 0;
707 u->top = top;
708 bn_wexpand(b, top);
709 bdp = b->d;
710 bdp[0] = 1;
711 for (i = 1; i < top; i++)
712 bdp[i] = 0;
713 b->top = top;
714 bn_wexpand(c, top);
715 cdp = c->d;
716 for (i = 0; i < top; i++)
717 cdp[i] = 0;
718 c->top = top;
719 vdp = v->d; /* It pays off to "cache" *->d pointers,
720 * because it allows optimizer to be more
721 * aggressive. But we don't have to "cache"
722 * p->d, because *p is declared 'const'... */
723 while (1) {
724 while (ubits && !(udp[0] & 1)) {
725 BN_ULONG u0, u1, b0, b1, mask;
726
727 u0 = udp[0];
728 b0 = bdp[0];
729 mask = (BN_ULONG)0 - (b0 & 1);
730 b0 ^= p->d[0] & mask;
731 for (i = 0; i < top - 1; i++) {
732 u1 = udp[i + 1];
733 udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2;
734 u0 = u1;
735 b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);
736 bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2;
737 b0 = b1;
738 }
739 udp[i] = u0 >> 1;
740 bdp[i] = b0 >> 1;
741 ubits--;
742 }
743
744 if (ubits <= BN_BITS2) {
745 if (udp[0] == 0) /* poly was reducible */
746 goto err;
747 if (udp[0] == 1)
748 break;
749 }
750
751 if (ubits < vbits) {
752 i = ubits;
753 ubits = vbits;
754 vbits = i;
755 tmp = u;
756 u = v;
757 v = tmp;
758 tmp = b;
759 b = c;
760 c = tmp;
761 udp = vdp;
762 vdp = v->d;
763 bdp = cdp;
764 cdp = c->d;
765 }
766 for (i = 0; i < top; i++) {
767 udp[i] ^= vdp[i];
768 bdp[i] ^= cdp[i];
769 }
770 if (ubits == vbits) {
771 BN_ULONG ul;
772 int utop = (ubits - 1) / BN_BITS2;
773
774 while ((ul = udp[utop]) == 0 && utop)
775 utop--;
776 ubits = utop * BN_BITS2 + BN_num_bits_word(ul);
777 }
778 }
779 bn_correct_top(b);
780 }
781 # endif
782
783 if (!BN_copy(r, b))
784 goto err;
785 bn_check_top(r);
786 ret = 1;
787
788 err:
789 # ifdef BN_DEBUG /* BN_CTX_end would complain about the
790 * expanded form */
791 bn_correct_top(c);
792 bn_correct_top(u);
793 bn_correct_top(v);
794 # endif
795 BN_CTX_end(ctx);
796 return ret;
797 }
798
799 /*
800 * Invert xx, reduce modulo p, and store the result in r. r could be xx.
801 * This function calls down to the BN_GF2m_mod_inv implementation; this
802 * wrapper function is only provided for convenience; for best performance,
803 * use the BN_GF2m_mod_inv function.
804 */
BN_GF2m_mod_inv_arr(BIGNUM * r,const BIGNUM * xx,const int p[],BN_CTX * ctx)805 int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[],
806 BN_CTX *ctx)
807 {
808 BIGNUM *field;
809 int ret = 0;
810
811 bn_check_top(xx);
812 BN_CTX_start(ctx);
813 if ((field = BN_CTX_get(ctx)) == NULL)
814 goto err;
815 if (!BN_GF2m_arr2poly(p, field))
816 goto err;
817
818 ret = BN_GF2m_mod_inv(r, xx, field, ctx);
819 bn_check_top(r);
820
821 err:
822 BN_CTX_end(ctx);
823 return ret;
824 }
825
826 # ifndef OPENSSL_SUN_GF2M_DIV
827 /*
828 * Divide y by x, reduce modulo p, and store the result in r. r could be x
829 * or y, x could equal y.
830 */
BN_GF2m_mod_div(BIGNUM * r,const BIGNUM * y,const BIGNUM * x,const BIGNUM * p,BN_CTX * ctx)831 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
832 const BIGNUM *p, BN_CTX *ctx)
833 {
834 BIGNUM *xinv = NULL;
835 int ret = 0;
836
837 bn_check_top(y);
838 bn_check_top(x);
839 bn_check_top(p);
840
841 BN_CTX_start(ctx);
842 xinv = BN_CTX_get(ctx);
843 if (xinv == NULL)
844 goto err;
845
846 if (!BN_GF2m_mod_inv(xinv, x, p, ctx))
847 goto err;
848 if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))
849 goto err;
850 bn_check_top(r);
851 ret = 1;
852
853 err:
854 BN_CTX_end(ctx);
855 return ret;
856 }
857 # else
858 /*
859 * Divide y by x, reduce modulo p, and store the result in r. r could be x
860 * or y, x could equal y. Uses algorithm Modular_Division_GF(2^m) from
861 * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to the
862 * Great Divide".
863 */
BN_GF2m_mod_div(BIGNUM * r,const BIGNUM * y,const BIGNUM * x,const BIGNUM * p,BN_CTX * ctx)864 int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
865 const BIGNUM *p, BN_CTX *ctx)
866 {
867 BIGNUM *a, *b, *u, *v;
868 int ret = 0;
869
870 bn_check_top(y);
871 bn_check_top(x);
872 bn_check_top(p);
873
874 BN_CTX_start(ctx);
875
876 a = BN_CTX_get(ctx);
877 b = BN_CTX_get(ctx);
878 u = BN_CTX_get(ctx);
879 v = BN_CTX_get(ctx);
880 if (v == NULL)
881 goto err;
882
883 /* reduce x and y mod p */
884 if (!BN_GF2m_mod(u, y, p))
885 goto err;
886 if (!BN_GF2m_mod(a, x, p))
887 goto err;
888 if (!BN_copy(b, p))
889 goto err;
890
891 while (!BN_is_odd(a)) {
892 if (!BN_rshift1(a, a))
893 goto err;
894 if (BN_is_odd(u))
895 if (!BN_GF2m_add(u, u, p))
896 goto err;
897 if (!BN_rshift1(u, u))
898 goto err;
899 }
900
901 do {
902 if (BN_GF2m_cmp(b, a) > 0) {
903 if (!BN_GF2m_add(b, b, a))
904 goto err;
905 if (!BN_GF2m_add(v, v, u))
906 goto err;
907 do {
908 if (!BN_rshift1(b, b))
909 goto err;
910 if (BN_is_odd(v))
911 if (!BN_GF2m_add(v, v, p))
912 goto err;
913 if (!BN_rshift1(v, v))
914 goto err;
915 } while (!BN_is_odd(b));
916 } else if (BN_abs_is_word(a, 1))
917 break;
918 else {
919 if (!BN_GF2m_add(a, a, b))
920 goto err;
921 if (!BN_GF2m_add(u, u, v))
922 goto err;
923 do {
924 if (!BN_rshift1(a, a))
925 goto err;
926 if (BN_is_odd(u))
927 if (!BN_GF2m_add(u, u, p))
928 goto err;
929 if (!BN_rshift1(u, u))
930 goto err;
931 } while (!BN_is_odd(a));
932 }
933 } while (1);
934
935 if (!BN_copy(r, u))
936 goto err;
937 bn_check_top(r);
938 ret = 1;
939
940 err:
941 BN_CTX_end(ctx);
942 return ret;
943 }
944 # endif
945
946 /*
947 * Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
948 * * or yy, xx could equal yy. This function calls down to the
949 * BN_GF2m_mod_div implementation; this wrapper function is only provided for
950 * convenience; for best performance, use the BN_GF2m_mod_div function.
951 */
BN_GF2m_mod_div_arr(BIGNUM * r,const BIGNUM * yy,const BIGNUM * xx,const int p[],BN_CTX * ctx)952 int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,
953 const int p[], BN_CTX *ctx)
954 {
955 BIGNUM *field;
956 int ret = 0;
957
958 bn_check_top(yy);
959 bn_check_top(xx);
960
961 BN_CTX_start(ctx);
962 if ((field = BN_CTX_get(ctx)) == NULL)
963 goto err;
964 if (!BN_GF2m_arr2poly(p, field))
965 goto err;
966
967 ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
968 bn_check_top(r);
969
970 err:
971 BN_CTX_end(ctx);
972 return ret;
973 }
974
975 /*
976 * Compute the bth power of a, reduce modulo p, and store the result in r. r
977 * could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE
978 * P1363.
979 */
BN_GF2m_mod_exp_arr(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const int p[],BN_CTX * ctx)980 int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
981 const int p[], BN_CTX *ctx)
982 {
983 int ret = 0, i, n;
984 BIGNUM *u;
985
986 bn_check_top(a);
987 bn_check_top(b);
988
989 if (BN_is_zero(b))
990 return (BN_one(r));
991
992 if (BN_abs_is_word(b, 1))
993 return (BN_copy(r, a) != NULL);
994
995 BN_CTX_start(ctx);
996 if ((u = BN_CTX_get(ctx)) == NULL)
997 goto err;
998
999 if (!BN_GF2m_mod_arr(u, a, p))
1000 goto err;
1001
1002 n = BN_num_bits(b) - 1;
1003 for (i = n - 1; i >= 0; i--) {
1004 if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx))
1005 goto err;
1006 if (BN_is_bit_set(b, i)) {
1007 if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx))
1008 goto err;
1009 }
1010 }
1011 if (!BN_copy(r, u))
1012 goto err;
1013 bn_check_top(r);
1014 ret = 1;
1015 err:
1016 BN_CTX_end(ctx);
1017 return ret;
1018 }
1019
1020 /*
1021 * Compute the bth power of a, reduce modulo p, and store the result in r. r
1022 * could be a. This function calls down to the BN_GF2m_mod_exp_arr
1023 * implementation; this wrapper function is only provided for convenience;
1024 * for best performance, use the BN_GF2m_mod_exp_arr function.
1025 */
BN_GF2m_mod_exp(BIGNUM * r,const BIGNUM * a,const BIGNUM * b,const BIGNUM * p,BN_CTX * ctx)1026 int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
1027 const BIGNUM *p, BN_CTX *ctx)
1028 {
1029 int ret = 0;
1030 const int max = BN_num_bits(p) + 1;
1031 int *arr = NULL;
1032 bn_check_top(a);
1033 bn_check_top(b);
1034 bn_check_top(p);
1035 if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL)
1036 goto err;
1037 ret = BN_GF2m_poly2arr(p, arr, max);
1038 if (!ret || ret > max) {
1039 BNerr(BN_F_BN_GF2M_MOD_EXP, BN_R_INVALID_LENGTH);
1040 goto err;
1041 }
1042 ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
1043 bn_check_top(r);
1044 err:
1045 if (arr)
1046 OPENSSL_free(arr);
1047 return ret;
1048 }
1049
1050 /*
1051 * Compute the square root of a, reduce modulo p, and store the result in r.
1052 * r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
1053 */
BN_GF2m_mod_sqrt_arr(BIGNUM * r,const BIGNUM * a,const int p[],BN_CTX * ctx)1054 int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[],
1055 BN_CTX *ctx)
1056 {
1057 int ret = 0;
1058 BIGNUM *u;
1059
1060 bn_check_top(a);
1061
1062 if (!p[0]) {
1063 /* reduction mod 1 => return 0 */
1064 BN_zero(r);
1065 return 1;
1066 }
1067
1068 BN_CTX_start(ctx);
1069 if ((u = BN_CTX_get(ctx)) == NULL)
1070 goto err;
1071
1072 if (!BN_set_bit(u, p[0] - 1))
1073 goto err;
1074 ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
1075 bn_check_top(r);
1076
1077 err:
1078 BN_CTX_end(ctx);
1079 return ret;
1080 }
1081
1082 /*
1083 * Compute the square root of a, reduce modulo p, and store the result in r.
1084 * r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr
1085 * implementation; this wrapper function is only provided for convenience;
1086 * for best performance, use the BN_GF2m_mod_sqrt_arr function.
1087 */
BN_GF2m_mod_sqrt(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)1088 int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
1089 {
1090 int ret = 0;
1091 const int max = BN_num_bits(p) + 1;
1092 int *arr = NULL;
1093 bn_check_top(a);
1094 bn_check_top(p);
1095 if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL)
1096 goto err;
1097 ret = BN_GF2m_poly2arr(p, arr, max);
1098 if (!ret || ret > max) {
1099 BNerr(BN_F_BN_GF2M_MOD_SQRT, BN_R_INVALID_LENGTH);
1100 goto err;
1101 }
1102 ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
1103 bn_check_top(r);
1104 err:
1105 if (arr)
1106 OPENSSL_free(arr);
1107 return ret;
1108 }
1109
1110 /*
1111 * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
1112 * 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
1113 */
BN_GF2m_mod_solve_quad_arr(BIGNUM * r,const BIGNUM * a_,const int p[],BN_CTX * ctx)1114 int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
1115 BN_CTX *ctx)
1116 {
1117 int ret = 0, count = 0, j;
1118 BIGNUM *a, *z, *rho, *w, *w2, *tmp;
1119
1120 bn_check_top(a_);
1121
1122 if (!p[0]) {
1123 /* reduction mod 1 => return 0 */
1124 BN_zero(r);
1125 return 1;
1126 }
1127
1128 BN_CTX_start(ctx);
1129 a = BN_CTX_get(ctx);
1130 z = BN_CTX_get(ctx);
1131 w = BN_CTX_get(ctx);
1132 if (w == NULL)
1133 goto err;
1134
1135 if (!BN_GF2m_mod_arr(a, a_, p))
1136 goto err;
1137
1138 if (BN_is_zero(a)) {
1139 BN_zero(r);
1140 ret = 1;
1141 goto err;
1142 }
1143
1144 if (p[0] & 0x1) { /* m is odd */
1145 /* compute half-trace of a */
1146 if (!BN_copy(z, a))
1147 goto err;
1148 for (j = 1; j <= (p[0] - 1) / 2; j++) {
1149 if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1150 goto err;
1151 if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1152 goto err;
1153 if (!BN_GF2m_add(z, z, a))
1154 goto err;
1155 }
1156
1157 } else { /* m is even */
1158
1159 rho = BN_CTX_get(ctx);
1160 w2 = BN_CTX_get(ctx);
1161 tmp = BN_CTX_get(ctx);
1162 if (tmp == NULL)
1163 goto err;
1164 do {
1165 if (!BN_rand(rho, p[0], 0, 0))
1166 goto err;
1167 if (!BN_GF2m_mod_arr(rho, rho, p))
1168 goto err;
1169 BN_zero(z);
1170 if (!BN_copy(w, rho))
1171 goto err;
1172 for (j = 1; j <= p[0] - 1; j++) {
1173 if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
1174 goto err;
1175 if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx))
1176 goto err;
1177 if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx))
1178 goto err;
1179 if (!BN_GF2m_add(z, z, tmp))
1180 goto err;
1181 if (!BN_GF2m_add(w, w2, rho))
1182 goto err;
1183 }
1184 count++;
1185 } while (BN_is_zero(w) && (count < MAX_ITERATIONS));
1186 if (BN_is_zero(w)) {
1187 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_TOO_MANY_ITERATIONS);
1188 goto err;
1189 }
1190 }
1191
1192 if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx))
1193 goto err;
1194 if (!BN_GF2m_add(w, z, w))
1195 goto err;
1196 if (BN_GF2m_cmp(w, a)) {
1197 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION);
1198 goto err;
1199 }
1200
1201 if (!BN_copy(r, z))
1202 goto err;
1203 bn_check_top(r);
1204
1205 ret = 1;
1206
1207 err:
1208 BN_CTX_end(ctx);
1209 return ret;
1210 }
1211
1212 /*
1213 * Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
1214 * 0. This function calls down to the BN_GF2m_mod_solve_quad_arr
1215 * implementation; this wrapper function is only provided for convenience;
1216 * for best performance, use the BN_GF2m_mod_solve_quad_arr function.
1217 */
BN_GF2m_mod_solve_quad(BIGNUM * r,const BIGNUM * a,const BIGNUM * p,BN_CTX * ctx)1218 int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1219 BN_CTX *ctx)
1220 {
1221 int ret = 0;
1222 const int max = BN_num_bits(p) + 1;
1223 int *arr = NULL;
1224 bn_check_top(a);
1225 bn_check_top(p);
1226 if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL)
1227 goto err;
1228 ret = BN_GF2m_poly2arr(p, arr, max);
1229 if (!ret || ret > max) {
1230 BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD, BN_R_INVALID_LENGTH);
1231 goto err;
1232 }
1233 ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
1234 bn_check_top(r);
1235 err:
1236 if (arr)
1237 OPENSSL_free(arr);
1238 return ret;
1239 }
1240
1241 /*
1242 * Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i *
1243 * x^i) into an array of integers corresponding to the bits with non-zero
1244 * coefficient. Array is terminated with -1. Up to max elements of the array
1245 * will be filled. Return value is total number of array elements that would
1246 * be filled if array was large enough.
1247 */
BN_GF2m_poly2arr(const BIGNUM * a,int p[],int max)1248 int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
1249 {
1250 int i, j, k = 0;
1251 BN_ULONG mask;
1252
1253 if (BN_is_zero(a))
1254 return 0;
1255
1256 for (i = a->top - 1; i >= 0; i--) {
1257 if (!a->d[i])
1258 /* skip word if a->d[i] == 0 */
1259 continue;
1260 mask = BN_TBIT;
1261 for (j = BN_BITS2 - 1; j >= 0; j--) {
1262 if (a->d[i] & mask) {
1263 if (k < max)
1264 p[k] = BN_BITS2 * i + j;
1265 k++;
1266 }
1267 mask >>= 1;
1268 }
1269 }
1270
1271 if (k < max) {
1272 p[k] = -1;
1273 k++;
1274 }
1275
1276 return k;
1277 }
1278
1279 /*
1280 * Convert the coefficient array representation of a polynomial to a
1281 * bit-string. The array must be terminated by -1.
1282 */
BN_GF2m_arr2poly(const int p[],BIGNUM * a)1283 int BN_GF2m_arr2poly(const int p[], BIGNUM *a)
1284 {
1285 int i;
1286
1287 bn_check_top(a);
1288 BN_zero(a);
1289 for (i = 0; p[i] != -1; i++) {
1290 if (BN_set_bit(a, p[i]) == 0)
1291 return 0;
1292 }
1293 bn_check_top(a);
1294
1295 return 1;
1296 }
1297
1298 #endif
1299