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 | /* 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 <assert.h> |
92 | #include <limits.h> |
93 | #include <stdio.h> |
94 | #include "cryptlib.h" |
95 | #include "bn_lcl.h" |
96 | |
97 | #ifndef OPENSSL_NO_EC2M |
98 | |
99 | /* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */ |
100 | #define MAX_ITERATIONS 50 |
101 | |
102 | static const BN_ULONG SQR_tb[16] = |
103 | { 0, 1, 4, 5, 16, 17, 20, 21, |
104 | 64, 65, 68, 69, 80, 81, 84, 85 }; |
105 | /* Platform-specific macros to accelerate squaring. */ |
106 | #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) |
107 | #define SQR1(w) \ |
108 | SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \ |
109 | SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \ |
110 | SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \ |
111 | SQR_tb[(w) >> 36 & 0xF] << 8 | SQR_tb[(w) >> 32 & 0xF] |
112 | #define SQR0(w) \ |
113 | SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \ |
114 | SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \ |
115 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ |
116 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] |
117 | #endif |
118 | #ifdef THIRTY_TWO_BIT |
119 | #define SQR1(w) \ |
120 | SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \ |
121 | SQR_tb[(w) >> 20 & 0xF] << 8 | SQR_tb[(w) >> 16 & 0xF] |
122 | #define SQR0(w) \ |
123 | SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >> 8 & 0xF] << 16 | \ |
124 | SQR_tb[(w) >> 4 & 0xF] << 8 | SQR_tb[(w) & 0xF] |
125 | #endif |
126 | |
127 | #if !defined(OPENSSL_BN_ASM_GF2m) |
128 | /* Product of two polynomials a, b each with degree < BN_BITS2 - 1, |
129 | * result is a polynomial r with degree < 2 * BN_BITS - 1 |
130 | * The caller MUST ensure that the variables have the right amount |
131 | * of space allocated. |
132 | */ |
133 | #ifdef THIRTY_TWO_BIT |
134 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b) |
135 | { |
136 | register BN_ULONG h, l, s; |
137 | BN_ULONG tab[8], top2b = a >> 30; |
138 | register BN_ULONG a1, a2, a4; |
139 | |
140 | a1 = a & (0x3FFFFFFF); a2 = a1 << 1; a4 = a2 << 1; |
141 | |
142 | tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2; |
143 | tab[4] = a4; tab[5] = a1^a4; tab[6] = a2^a4; tab[7] = a1^a2^a4; |
144 | |
145 | s = tab[b & 0x7]; l = s; |
146 | s = tab[b >> 3 & 0x7]; l ^= s << 3; h = s >> 29; |
147 | s = tab[b >> 6 & 0x7]; l ^= s << 6; h ^= s >> 26; |
148 | s = tab[b >> 9 & 0x7]; l ^= s << 9; h ^= s >> 23; |
149 | s = tab[b >> 12 & 0x7]; l ^= s << 12; h ^= s >> 20; |
150 | s = tab[b >> 15 & 0x7]; l ^= s << 15; h ^= s >> 17; |
151 | s = tab[b >> 18 & 0x7]; l ^= s << 18; h ^= s >> 14; |
152 | s = tab[b >> 21 & 0x7]; l ^= s << 21; h ^= s >> 11; |
153 | s = tab[b >> 24 & 0x7]; l ^= s << 24; h ^= s >> 8; |
154 | s = tab[b >> 27 & 0x7]; l ^= s << 27; h ^= s >> 5; |
155 | s = tab[b >> 30 ]; l ^= s << 30; h ^= s >> 2; |
156 | |
157 | /* compensate for the top two bits of a */ |
158 | |
159 | if (top2b & 01) { l ^= b << 30; h ^= b >> 2; } |
160 | if (top2b & 02) { l ^= b << 31; h ^= b >> 1; } |
161 | |
162 | *r1 = h; *r0 = l; |
163 | } |
164 | #endif |
165 | #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG) |
166 | static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b) |
167 | { |
168 | register BN_ULONG h, l, s; |
169 | BN_ULONG tab[16], top3b = a >> 61; |
170 | register BN_ULONG a1, a2, a4, a8; |
171 | |
172 | a1 = a & (0x1FFFFFFFFFFFFFFFULL); a2 = a1 << 1; a4 = a2 << 1; a8 = a4 << 1; |
173 | |
174 | tab[ 0] = 0; tab[ 1] = a1; tab[ 2] = a2; tab[ 3] = a1^a2; |
175 | tab[ 4] = a4; tab[ 5] = a1^a4; tab[ 6] = a2^a4; tab[ 7] = a1^a2^a4; |
176 | tab[ 8] = a8; tab[ 9] = a1^a8; tab[10] = a2^a8; tab[11] = a1^a2^a8; |
177 | tab[12] = a4^a8; tab[13] = a1^a4^a8; tab[14] = a2^a4^a8; tab[15] = a1^a2^a4^a8; |
178 | |
179 | s = tab[b & 0xF]; l = s; |
180 | s = tab[b >> 4 & 0xF]; l ^= s << 4; h = s >> 60; |
181 | s = tab[b >> 8 & 0xF]; l ^= s << 8; h ^= s >> 56; |
182 | s = tab[b >> 12 & 0xF]; l ^= s << 12; h ^= s >> 52; |
183 | s = tab[b >> 16 & 0xF]; l ^= s << 16; h ^= s >> 48; |
184 | s = tab[b >> 20 & 0xF]; l ^= s << 20; h ^= s >> 44; |
185 | s = tab[b >> 24 & 0xF]; l ^= s << 24; h ^= s >> 40; |
186 | s = tab[b >> 28 & 0xF]; l ^= s << 28; h ^= s >> 36; |
187 | s = tab[b >> 32 & 0xF]; l ^= s << 32; h ^= s >> 32; |
188 | s = tab[b >> 36 & 0xF]; l ^= s << 36; h ^= s >> 28; |
189 | s = tab[b >> 40 & 0xF]; l ^= s << 40; h ^= s >> 24; |
190 | s = tab[b >> 44 & 0xF]; l ^= s << 44; h ^= s >> 20; |
191 | s = tab[b >> 48 & 0xF]; l ^= s << 48; h ^= s >> 16; |
192 | s = tab[b >> 52 & 0xF]; l ^= s << 52; h ^= s >> 12; |
193 | s = tab[b >> 56 & 0xF]; l ^= s << 56; h ^= s >> 8; |
194 | s = tab[b >> 60 ]; l ^= s << 60; h ^= s >> 4; |
195 | |
196 | /* compensate for the top three bits of a */ |
197 | |
198 | if (top3b & 01) { l ^= b << 61; h ^= b >> 3; } |
199 | if (top3b & 02) { l ^= b << 62; h ^= b >> 2; } |
200 | if (top3b & 04) { l ^= b << 63; h ^= b >> 1; } |
201 | |
202 | *r1 = h; *r0 = l; |
203 | } |
204 | #endif |
205 | |
206 | /* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1, |
207 | * result is a polynomial r with degree < 4 * BN_BITS2 - 1 |
208 | * The caller MUST ensure that the variables have the right amount |
209 | * of space allocated. |
210 | */ |
211 | 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) |
212 | { |
213 | BN_ULONG m1, m0; |
214 | /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */ |
215 | bn_GF2m_mul_1x1(r+3, r+2, a1, b1); |
216 | bn_GF2m_mul_1x1(r+1, r, a0, b0); |
217 | bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1); |
218 | /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */ |
219 | r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */ |
220 | r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */ |
221 | } |
222 | #else |
223 | void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1, BN_ULONG b0); |
224 | #endif |
225 | |
226 | /* Add polynomials a and b and store result in r; r could be a or b, a and b |
227 | * could be equal; r is the bitwise XOR of a and b. |
228 | */ |
229 | int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) |
230 | { |
231 | int i; |
232 | const BIGNUM *at, *bt; |
233 | |
234 | bn_check_top(a); |
235 | bn_check_top(b); |
236 | |
237 | if (a->top < b->top) { at = b; bt = a; } |
238 | else { at = a; bt = b; } |
239 | |
240 | if(bn_wexpand(r, at->top) == NULL) |
241 | return 0; |
242 | |
243 | for (i = 0; i < bt->top; i++) |
244 | { |
245 | r->d[i] = at->d[i] ^ bt->d[i]; |
246 | } |
247 | for (; i < at->top; i++) |
248 | { |
249 | r->d[i] = at->d[i]; |
250 | } |
251 | |
252 | r->top = at->top; |
253 | bn_correct_top(r); |
254 | |
255 | return 1; |
256 | } |
257 | |
258 | |
259 | /* Some functions allow for representation of the irreducible polynomials |
260 | * as an int[], say p. The irreducible f(t) is then of the form: |
261 | * t^p[0] + t^p[1] + ... + t^p[k] |
262 | * where m = p[0] > p[1] > ... > p[k] = 0. |
263 | */ |
264 | |
265 | |
266 | /* Performs modular reduction of a and store result in r. r could be a. */ |
267 | int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[]) |
268 | { |
269 | int j, k; |
270 | int n, dN, d0, d1; |
271 | BN_ULONG zz, *z; |
272 | |
273 | bn_check_top(a); |
274 | |
275 | if (!p[0]) |
276 | { |
277 | /* reduction mod 1 => return 0 */ |
278 | BN_zero(r); |
279 | return 1; |
280 | } |
281 | |
282 | /* Since the algorithm does reduction in the r value, if a != r, copy |
283 | * the contents of a into r so we can do reduction in r. |
284 | */ |
285 | if (a != r) |
286 | { |
287 | if (!bn_wexpand(r, a->top)) return 0; |
288 | for (j = 0; j < a->top; j++) |
289 | { |
290 | r->d[j] = a->d[j]; |
291 | } |
292 | r->top = a->top; |
293 | } |
294 | z = r->d; |
295 | |
296 | /* start reduction */ |
297 | dN = p[0] / BN_BITS2; |
298 | for (j = r->top - 1; j > dN;) |
299 | { |
300 | zz = z[j]; |
301 | if (z[j] == 0) { j--; continue; } |
302 | z[j] = 0; |
303 | |
304 | for (k = 1; p[k] != 0; k++) |
305 | { |
306 | /* reducing component t^p[k] */ |
307 | n = p[0] - p[k]; |
308 | d0 = n % BN_BITS2; d1 = BN_BITS2 - d0; |
309 | n /= BN_BITS2; |
310 | z[j-n] ^= (zz>>d0); |
311 | if (d0) z[j-n-1] ^= (zz<<d1); |
312 | } |
313 | |
314 | /* reducing component t^0 */ |
315 | n = dN; |
316 | d0 = p[0] % BN_BITS2; |
317 | d1 = BN_BITS2 - d0; |
318 | z[j-n] ^= (zz >> d0); |
319 | if (d0) z[j-n-1] ^= (zz << d1); |
320 | } |
321 | |
322 | /* final round of reduction */ |
323 | while (j == dN) |
324 | { |
325 | |
326 | d0 = p[0] % BN_BITS2; |
327 | zz = z[dN] >> d0; |
328 | if (zz == 0) break; |
329 | d1 = BN_BITS2 - d0; |
330 | |
331 | /* clear up the top d1 bits */ |
332 | if (d0) |
333 | z[dN] = (z[dN] << d1) >> d1; |
334 | else |
335 | z[dN] = 0; |
336 | z[0] ^= zz; /* reduction t^0 component */ |
337 | |
338 | for (k = 1; p[k] != 0; k++) |
339 | { |
340 | BN_ULONG tmp_ulong; |
341 | |
342 | /* reducing component t^p[k]*/ |
343 | n = p[k] / BN_BITS2; |
344 | d0 = p[k] % BN_BITS2; |
345 | d1 = BN_BITS2 - d0; |
346 | z[n] ^= (zz << d0); |
347 | tmp_ulong = zz >> d1; |
348 | if (d0 && tmp_ulong) |
349 | z[n+1] ^= tmp_ulong; |
350 | } |
351 | |
352 | |
353 | } |
354 | |
355 | bn_correct_top(r); |
356 | return 1; |
357 | } |
358 | |
359 | /* Performs modular reduction of a by p and store result in r. r could be a. |
360 | * |
361 | * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper |
362 | * function is only provided for convenience; for best performance, use the |
363 | * BN_GF2m_mod_arr function. |
364 | */ |
365 | int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p) |
366 | { |
367 | int ret = 0; |
368 | int arr[6]; |
369 | bn_check_top(a); |
370 | bn_check_top(p); |
371 | ret = BN_GF2m_poly2arr(p, arr, sizeof(arr)/sizeof(arr[0])); |
372 | if (!ret || ret > (int)(sizeof(arr)/sizeof(arr[0]))) |
373 | { |
374 | BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH); |
375 | return 0; |
376 | } |
377 | ret = BN_GF2m_mod_arr(r, a, arr); |
378 | bn_check_top(r); |
379 | return ret; |
380 | } |
381 | |
382 | |
383 | /* Compute the product of two polynomials a and b, reduce modulo p, and store |
384 | * the result in r. r could be a or b; a could be b. |
385 | */ |
386 | int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx) |
387 | { |
388 | int zlen, i, j, k, ret = 0; |
389 | BIGNUM *s; |
390 | BN_ULONG x1, x0, y1, y0, zz[4]; |
391 | |
392 | bn_check_top(a); |
393 | bn_check_top(b); |
394 | |
395 | if (a == b) |
396 | { |
397 | return BN_GF2m_mod_sqr_arr(r, a, p, ctx); |
398 | } |
399 | |
400 | BN_CTX_start(ctx); |
401 | if ((s = BN_CTX_get(ctx)) == NULL) goto err; |
402 | |
403 | zlen = a->top + b->top + 4; |
404 | if (!bn_wexpand(s, zlen)) goto err; |
405 | s->top = zlen; |
406 | |
407 | for (i = 0; i < zlen; i++) s->d[i] = 0; |
408 | |
409 | for (j = 0; j < b->top; j += 2) |
410 | { |
411 | y0 = b->d[j]; |
412 | y1 = ((j+1) == b->top) ? 0 : b->d[j+1]; |
413 | for (i = 0; i < a->top; i += 2) |
414 | { |
415 | x0 = a->d[i]; |
416 | x1 = ((i+1) == a->top) ? 0 : a->d[i+1]; |
417 | bn_GF2m_mul_2x2(zz, x1, x0, y1, y0); |
418 | for (k = 0; k < 4; k++) s->d[i+j+k] ^= zz[k]; |
419 | } |
420 | } |
421 | |
422 | bn_correct_top(s); |
423 | if (BN_GF2m_mod_arr(r, s, p)) |
424 | ret = 1; |
425 | bn_check_top(r); |
426 | |
427 | err: |
428 | BN_CTX_end(ctx); |
429 | return ret; |
430 | } |
431 | |
432 | /* Compute the product of two polynomials a and b, reduce modulo p, and store |
433 | * the result in r. r could be a or b; a could equal b. |
434 | * |
435 | * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper |
436 | * function is only provided for convenience; for best performance, use the |
437 | * BN_GF2m_mod_mul_arr function. |
438 | */ |
439 | int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx) |
440 | { |
441 | int ret = 0; |
442 | const int max = BN_num_bits(p) + 1; |
443 | int *arr=NULL; |
444 | bn_check_top(a); |
445 | bn_check_top(b); |
446 | bn_check_top(p); |
447 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
448 | ret = BN_GF2m_poly2arr(p, arr, max); |
449 | if (!ret || ret > max) |
450 | { |
451 | BNerr(BN_F_BN_GF2M_MOD_MUL,BN_R_INVALID_LENGTH); |
452 | goto err; |
453 | } |
454 | ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx); |
455 | bn_check_top(r); |
456 | err: |
457 | if (arr) OPENSSL_free(arr); |
458 | return ret; |
459 | } |
460 | |
461 | |
462 | /* Square a, reduce the result mod p, and store it in a. r could be a. */ |
463 | int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx) |
464 | { |
465 | int i, ret = 0; |
466 | BIGNUM *s; |
467 | |
468 | bn_check_top(a); |
469 | BN_CTX_start(ctx); |
470 | if ((s = BN_CTX_get(ctx)) == NULL) return 0; |
471 | if (!bn_wexpand(s, 2 * a->top)) goto err; |
472 | |
473 | for (i = a->top - 1; i >= 0; i--) |
474 | { |
475 | s->d[2*i+1] = SQR1(a->d[i]); |
476 | s->d[2*i ] = SQR0(a->d[i]); |
477 | } |
478 | |
479 | s->top = 2 * a->top; |
480 | bn_correct_top(s); |
481 | if (!BN_GF2m_mod_arr(r, s, p)) goto err; |
482 | bn_check_top(r); |
483 | ret = 1; |
484 | err: |
485 | BN_CTX_end(ctx); |
486 | return ret; |
487 | } |
488 | |
489 | /* Square a, reduce the result mod p, and store it in a. r could be a. |
490 | * |
491 | * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper |
492 | * function is only provided for convenience; for best performance, use the |
493 | * BN_GF2m_mod_sqr_arr function. |
494 | */ |
495 | int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
496 | { |
497 | int ret = 0; |
498 | const int max = BN_num_bits(p) + 1; |
499 | int *arr=NULL; |
500 | |
501 | bn_check_top(a); |
502 | bn_check_top(p); |
503 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
504 | ret = BN_GF2m_poly2arr(p, arr, max); |
505 | if (!ret || ret > max) |
506 | { |
507 | BNerr(BN_F_BN_GF2M_MOD_SQR,BN_R_INVALID_LENGTH); |
508 | goto err; |
509 | } |
510 | ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx); |
511 | bn_check_top(r); |
512 | err: |
513 | if (arr) OPENSSL_free(arr); |
514 | return ret; |
515 | } |
516 | |
517 | |
518 | /* Invert a, reduce modulo p, and store the result in r. r could be a. |
519 | * Uses Modified Almost Inverse Algorithm (Algorithm 10) from |
520 | * Hankerson, D., Hernandez, J.L., and Menezes, A. "Software Implementation |
521 | * of Elliptic Curve Cryptography Over Binary Fields". |
522 | */ |
523 | int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
524 | { |
525 | BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp; |
526 | int ret = 0; |
527 | |
528 | bn_check_top(a); |
529 | bn_check_top(p); |
530 | |
531 | BN_CTX_start(ctx); |
532 | |
533 | if ((b = BN_CTX_get(ctx))==NULL) goto err; |
534 | if ((c = BN_CTX_get(ctx))==NULL) goto err; |
535 | if ((u = BN_CTX_get(ctx))==NULL) goto err; |
536 | if ((v = BN_CTX_get(ctx))==NULL) goto err; |
537 | |
538 | if (!BN_GF2m_mod(u, a, p)) goto err; |
539 | if (BN_is_zero(u)) goto err; |
540 | |
541 | if (!BN_copy(v, p)) goto err; |
542 | #if 0 |
543 | if (!BN_one(b)) goto err; |
544 | |
545 | while (1) |
546 | { |
547 | while (!BN_is_odd(u)) |
548 | { |
549 | if (BN_is_zero(u)) goto err; |
550 | if (!BN_rshift1(u, u)) goto err; |
551 | if (BN_is_odd(b)) |
552 | { |
553 | if (!BN_GF2m_add(b, b, p)) goto err; |
554 | } |
555 | if (!BN_rshift1(b, b)) goto err; |
556 | } |
557 | |
558 | if (BN_abs_is_word(u, 1)) break; |
559 | |
560 | if (BN_num_bits(u) < BN_num_bits(v)) |
561 | { |
562 | tmp = u; u = v; v = tmp; |
563 | tmp = b; b = c; c = tmp; |
564 | } |
565 | |
566 | if (!BN_GF2m_add(u, u, v)) goto err; |
567 | if (!BN_GF2m_add(b, b, c)) goto err; |
568 | } |
569 | #else |
570 | { |
571 | int i, ubits = BN_num_bits(u), |
572 | vbits = BN_num_bits(v), /* v is copy of p */ |
573 | top = p->top; |
574 | BN_ULONG *udp,*bdp,*vdp,*cdp; |
575 | |
576 | bn_wexpand(u,top); udp = u->d; |
577 | for (i=u->top;i<top;i++) udp[i] = 0; |
578 | u->top = top; |
579 | bn_wexpand(b,top); bdp = b->d; |
580 | bdp[0] = 1; |
581 | for (i=1;i<top;i++) bdp[i] = 0; |
582 | b->top = top; |
583 | bn_wexpand(c,top); cdp = c->d; |
584 | for (i=0;i<top;i++) cdp[i] = 0; |
585 | c->top = top; |
586 | vdp = v->d; /* It pays off to "cache" *->d pointers, because |
587 | * it allows optimizer to be more aggressive. |
588 | * But we don't have to "cache" p->d, because *p |
589 | * is declared 'const'... */ |
590 | while (1) |
591 | { |
592 | while (ubits && !(udp[0]&1)) |
593 | { |
594 | BN_ULONG u0,u1,b0,b1,mask; |
595 | |
596 | u0 = udp[0]; |
597 | b0 = bdp[0]; |
598 | mask = (BN_ULONG)0-(b0&1); |
599 | b0 ^= p->d[0]&mask; |
600 | for (i=0;i<top-1;i++) |
601 | { |
602 | u1 = udp[i+1]; |
603 | udp[i] = ((u0>>1)|(u1<<(BN_BITS2-1)))&BN_MASK2; |
604 | u0 = u1; |
605 | b1 = bdp[i+1]^(p->d[i+1]&mask); |
606 | bdp[i] = ((b0>>1)|(b1<<(BN_BITS2-1)))&BN_MASK2; |
607 | b0 = b1; |
608 | } |
609 | udp[i] = u0>>1; |
610 | bdp[i] = b0>>1; |
611 | ubits--; |
612 | } |
613 | |
614 | if (ubits<=BN_BITS2 && udp[0]==1) break; |
615 | |
616 | if (ubits<vbits) |
617 | { |
618 | i = ubits; ubits = vbits; vbits = i; |
619 | tmp = u; u = v; v = tmp; |
620 | tmp = b; b = c; c = tmp; |
621 | udp = vdp; vdp = v->d; |
622 | bdp = cdp; cdp = c->d; |
623 | } |
624 | for(i=0;i<top;i++) |
625 | { |
626 | udp[i] ^= vdp[i]; |
627 | bdp[i] ^= cdp[i]; |
628 | } |
629 | if (ubits==vbits) |
630 | { |
631 | BN_ULONG ul; |
632 | int utop = (ubits-1)/BN_BITS2; |
633 | |
634 | while ((ul=udp[utop])==0 && utop) utop--; |
635 | ubits = utop*BN_BITS2 + BN_num_bits_word(ul); |
636 | } |
637 | } |
638 | bn_correct_top(b); |
639 | } |
640 | #endif |
641 | |
642 | if (!BN_copy(r, b)) goto err; |
643 | bn_check_top(r); |
644 | ret = 1; |
645 | |
646 | err: |
647 | #ifdef BN_DEBUG /* BN_CTX_end would complain about the expanded form */ |
648 | bn_correct_top(c); |
649 | bn_correct_top(u); |
650 | bn_correct_top(v); |
651 | #endif |
652 | BN_CTX_end(ctx); |
653 | return ret; |
654 | } |
655 | |
656 | /* Invert xx, reduce modulo p, and store the result in r. r could be xx. |
657 | * |
658 | * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper |
659 | * function is only provided for convenience; for best performance, use the |
660 | * BN_GF2m_mod_inv function. |
661 | */ |
662 | int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], BN_CTX *ctx) |
663 | { |
664 | BIGNUM *field; |
665 | int ret = 0; |
666 | |
667 | bn_check_top(xx); |
668 | BN_CTX_start(ctx); |
669 | if ((field = BN_CTX_get(ctx)) == NULL) goto err; |
670 | if (!BN_GF2m_arr2poly(p, field)) goto err; |
671 | |
672 | ret = BN_GF2m_mod_inv(r, xx, field, ctx); |
673 | bn_check_top(r); |
674 | |
675 | err: |
676 | BN_CTX_end(ctx); |
677 | return ret; |
678 | } |
679 | |
680 | |
681 | #ifndef OPENSSL_SUN_GF2M_DIV |
682 | /* Divide y by x, reduce modulo p, and store the result in r. r could be x |
683 | * or y, x could equal y. |
684 | */ |
685 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx) |
686 | { |
687 | BIGNUM *xinv = NULL; |
688 | int ret = 0; |
689 | |
690 | bn_check_top(y); |
691 | bn_check_top(x); |
692 | bn_check_top(p); |
693 | |
694 | BN_CTX_start(ctx); |
695 | xinv = BN_CTX_get(ctx); |
696 | if (xinv == NULL) goto err; |
697 | |
698 | if (!BN_GF2m_mod_inv(xinv, x, p, ctx)) goto err; |
699 | if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx)) goto err; |
700 | bn_check_top(r); |
701 | ret = 1; |
702 | |
703 | err: |
704 | BN_CTX_end(ctx); |
705 | return ret; |
706 | } |
707 | #else |
708 | /* Divide y by x, reduce modulo p, and store the result in r. r could be x |
709 | * or y, x could equal y. |
710 | * Uses algorithm Modular_Division_GF(2^m) from |
711 | * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to |
712 | * the Great Divide". |
713 | */ |
714 | int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p, BN_CTX *ctx) |
715 | { |
716 | BIGNUM *a, *b, *u, *v; |
717 | int ret = 0; |
718 | |
719 | bn_check_top(y); |
720 | bn_check_top(x); |
721 | bn_check_top(p); |
722 | |
723 | BN_CTX_start(ctx); |
724 | |
725 | a = BN_CTX_get(ctx); |
726 | b = BN_CTX_get(ctx); |
727 | u = BN_CTX_get(ctx); |
728 | v = BN_CTX_get(ctx); |
729 | if (v == NULL) goto err; |
730 | |
731 | /* reduce x and y mod p */ |
732 | if (!BN_GF2m_mod(u, y, p)) goto err; |
733 | if (!BN_GF2m_mod(a, x, p)) goto err; |
734 | if (!BN_copy(b, p)) goto err; |
735 | |
736 | while (!BN_is_odd(a)) |
737 | { |
738 | if (!BN_rshift1(a, a)) goto err; |
739 | if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err; |
740 | if (!BN_rshift1(u, u)) goto err; |
741 | } |
742 | |
743 | do |
744 | { |
745 | if (BN_GF2m_cmp(b, a) > 0) |
746 | { |
747 | if (!BN_GF2m_add(b, b, a)) goto err; |
748 | if (!BN_GF2m_add(v, v, u)) goto err; |
749 | do |
750 | { |
751 | if (!BN_rshift1(b, b)) goto err; |
752 | if (BN_is_odd(v)) if (!BN_GF2m_add(v, v, p)) goto err; |
753 | if (!BN_rshift1(v, v)) goto err; |
754 | } while (!BN_is_odd(b)); |
755 | } |
756 | else if (BN_abs_is_word(a, 1)) |
757 | break; |
758 | else |
759 | { |
760 | if (!BN_GF2m_add(a, a, b)) goto err; |
761 | if (!BN_GF2m_add(u, u, v)) goto err; |
762 | do |
763 | { |
764 | if (!BN_rshift1(a, a)) goto err; |
765 | if (BN_is_odd(u)) if (!BN_GF2m_add(u, u, p)) goto err; |
766 | if (!BN_rshift1(u, u)) goto err; |
767 | } while (!BN_is_odd(a)); |
768 | } |
769 | } while (1); |
770 | |
771 | if (!BN_copy(r, u)) goto err; |
772 | bn_check_top(r); |
773 | ret = 1; |
774 | |
775 | err: |
776 | BN_CTX_end(ctx); |
777 | return ret; |
778 | } |
779 | #endif |
780 | |
781 | /* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx |
782 | * or yy, xx could equal yy. |
783 | * |
784 | * This function calls down to the BN_GF2m_mod_div implementation; this wrapper |
785 | * function is only provided for convenience; for best performance, use the |
786 | * BN_GF2m_mod_div function. |
787 | */ |
788 | int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, const int p[], BN_CTX *ctx) |
789 | { |
790 | BIGNUM *field; |
791 | int ret = 0; |
792 | |
793 | bn_check_top(yy); |
794 | bn_check_top(xx); |
795 | |
796 | BN_CTX_start(ctx); |
797 | if ((field = BN_CTX_get(ctx)) == NULL) goto err; |
798 | if (!BN_GF2m_arr2poly(p, field)) goto err; |
799 | |
800 | ret = BN_GF2m_mod_div(r, yy, xx, field, ctx); |
801 | bn_check_top(r); |
802 | |
803 | err: |
804 | BN_CTX_end(ctx); |
805 | return ret; |
806 | } |
807 | |
808 | |
809 | /* Compute the bth power of a, reduce modulo p, and store |
810 | * the result in r. r could be a. |
811 | * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363. |
812 | */ |
813 | int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[], BN_CTX *ctx) |
814 | { |
815 | int ret = 0, i, n; |
816 | BIGNUM *u; |
817 | |
818 | bn_check_top(a); |
819 | bn_check_top(b); |
820 | |
821 | if (BN_is_zero(b)) |
822 | return(BN_one(r)); |
823 | |
824 | if (BN_abs_is_word(b, 1)) |
825 | return (BN_copy(r, a) != NULL); |
826 | |
827 | BN_CTX_start(ctx); |
828 | if ((u = BN_CTX_get(ctx)) == NULL) goto err; |
829 | |
830 | if (!BN_GF2m_mod_arr(u, a, p)) goto err; |
831 | |
832 | n = BN_num_bits(b) - 1; |
833 | for (i = n - 1; i >= 0; i--) |
834 | { |
835 | if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) goto err; |
836 | if (BN_is_bit_set(b, i)) |
837 | { |
838 | if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) goto err; |
839 | } |
840 | } |
841 | if (!BN_copy(r, u)) goto err; |
842 | bn_check_top(r); |
843 | ret = 1; |
844 | err: |
845 | BN_CTX_end(ctx); |
846 | return ret; |
847 | } |
848 | |
849 | /* Compute the bth power of a, reduce modulo p, and store |
850 | * the result in r. r could be a. |
851 | * |
852 | * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper |
853 | * function is only provided for convenience; for best performance, use the |
854 | * BN_GF2m_mod_exp_arr function. |
855 | */ |
856 | int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx) |
857 | { |
858 | int ret = 0; |
859 | const int max = BN_num_bits(p) + 1; |
860 | int *arr=NULL; |
861 | bn_check_top(a); |
862 | bn_check_top(b); |
863 | bn_check_top(p); |
864 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
865 | ret = BN_GF2m_poly2arr(p, arr, max); |
866 | if (!ret || ret > max) |
867 | { |
868 | BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH); |
869 | goto err; |
870 | } |
871 | ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx); |
872 | bn_check_top(r); |
873 | err: |
874 | if (arr) OPENSSL_free(arr); |
875 | return ret; |
876 | } |
877 | |
878 | /* Compute the square root of a, reduce modulo p, and store |
879 | * the result in r. r could be a. |
880 | * Uses exponentiation as in algorithm A.4.1 from IEEE P1363. |
881 | */ |
882 | int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx) |
883 | { |
884 | int ret = 0; |
885 | BIGNUM *u; |
886 | |
887 | bn_check_top(a); |
888 | |
889 | if (!p[0]) |
890 | { |
891 | /* reduction mod 1 => return 0 */ |
892 | BN_zero(r); |
893 | return 1; |
894 | } |
895 | |
896 | BN_CTX_start(ctx); |
897 | if ((u = BN_CTX_get(ctx)) == NULL) goto err; |
898 | |
899 | if (!BN_set_bit(u, p[0] - 1)) goto err; |
900 | ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx); |
901 | bn_check_top(r); |
902 | |
903 | err: |
904 | BN_CTX_end(ctx); |
905 | return ret; |
906 | } |
907 | |
908 | /* Compute the square root of a, reduce modulo p, and store |
909 | * the result in r. r could be a. |
910 | * |
911 | * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper |
912 | * function is only provided for convenience; for best performance, use the |
913 | * BN_GF2m_mod_sqrt_arr function. |
914 | */ |
915 | int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
916 | { |
917 | int ret = 0; |
918 | const int max = BN_num_bits(p) + 1; |
919 | int *arr=NULL; |
920 | bn_check_top(a); |
921 | bn_check_top(p); |
922 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * max)) == NULL) goto err; |
923 | ret = BN_GF2m_poly2arr(p, arr, max); |
924 | if (!ret || ret > max) |
925 | { |
926 | BNerr(BN_F_BN_GF2M_MOD_SQRT,BN_R_INVALID_LENGTH); |
927 | goto err; |
928 | } |
929 | ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx); |
930 | bn_check_top(r); |
931 | err: |
932 | if (arr) OPENSSL_free(arr); |
933 | return ret; |
934 | } |
935 | |
936 | /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0. |
937 | * Uses algorithms A.4.7 and A.4.6 from IEEE P1363. |
938 | */ |
939 | int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[], BN_CTX *ctx) |
940 | { |
941 | int ret = 0, count = 0, j; |
942 | BIGNUM *a, *z, *rho, *w, *w2, *tmp; |
943 | |
944 | bn_check_top(a_); |
945 | |
946 | if (!p[0]) |
947 | { |
948 | /* reduction mod 1 => return 0 */ |
949 | BN_zero(r); |
950 | return 1; |
951 | } |
952 | |
953 | BN_CTX_start(ctx); |
954 | a = BN_CTX_get(ctx); |
955 | z = BN_CTX_get(ctx); |
956 | w = BN_CTX_get(ctx); |
957 | if (w == NULL) goto err; |
958 | |
959 | if (!BN_GF2m_mod_arr(a, a_, p)) goto err; |
960 | |
961 | if (BN_is_zero(a)) |
962 | { |
963 | BN_zero(r); |
964 | ret = 1; |
965 | goto err; |
966 | } |
967 | |
968 | if (p[0] & 0x1) /* m is odd */ |
969 | { |
970 | /* compute half-trace of a */ |
971 | if (!BN_copy(z, a)) goto err; |
972 | for (j = 1; j <= (p[0] - 1) / 2; j++) |
973 | { |
974 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err; |
975 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err; |
976 | if (!BN_GF2m_add(z, z, a)) goto err; |
977 | } |
978 | |
979 | } |
980 | else /* m is even */ |
981 | { |
982 | rho = BN_CTX_get(ctx); |
983 | w2 = BN_CTX_get(ctx); |
984 | tmp = BN_CTX_get(ctx); |
985 | if (tmp == NULL) goto err; |
986 | do |
987 | { |
988 | if (!BN_rand(rho, p[0], 0, 0)) goto err; |
989 | if (!BN_GF2m_mod_arr(rho, rho, p)) goto err; |
990 | BN_zero(z); |
991 | if (!BN_copy(w, rho)) goto err; |
992 | for (j = 1; j <= p[0] - 1; j++) |
993 | { |
994 | if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err; |
995 | if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) goto err; |
996 | if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) goto err; |
997 | if (!BN_GF2m_add(z, z, tmp)) goto err; |
998 | if (!BN_GF2m_add(w, w2, rho)) goto err; |
999 | } |
1000 | count++; |
1001 | } while (BN_is_zero(w) && (count < MAX_ITERATIONS)); |
1002 | if (BN_is_zero(w)) |
1003 | { |
1004 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,BN_R_TOO_MANY_ITERATIONS); |
1005 | goto err; |
1006 | } |
1007 | } |
1008 | |
1009 | if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) goto err; |
1010 | if (!BN_GF2m_add(w, z, w)) goto err; |
1011 | if (BN_GF2m_cmp(w, a)) |
1012 | { |
1013 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION); |
1014 | goto err; |
1015 | } |
1016 | |
1017 | if (!BN_copy(r, z)) goto err; |
1018 | bn_check_top(r); |
1019 | |
1020 | ret = 1; |
1021 | |
1022 | err: |
1023 | BN_CTX_end(ctx); |
1024 | return ret; |
1025 | } |
1026 | |
1027 | /* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns 0. |
1028 | * |
1029 | * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper |
1030 | * function is only provided for convenience; for best performance, use the |
1031 | * BN_GF2m_mod_solve_quad_arr function. |
1032 | */ |
1033 | int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx) |
1034 | { |
1035 | int ret = 0; |
1036 | const int max = BN_num_bits(p) + 1; |
1037 | int *arr=NULL; |
1038 | bn_check_top(a); |
1039 | bn_check_top(p); |
1040 | if ((arr = (int *)OPENSSL_malloc(sizeof(int) * |
1041 | max)) == NULL) goto err; |
1042 | ret = BN_GF2m_poly2arr(p, arr, max); |
1043 | if (!ret || ret > max) |
1044 | { |
1045 | BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD,BN_R_INVALID_LENGTH); |
1046 | goto err; |
1047 | } |
1048 | ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx); |
1049 | bn_check_top(r); |
1050 | err: |
1051 | if (arr) OPENSSL_free(arr); |
1052 | return ret; |
1053 | } |
1054 | |
1055 | /* Convert the bit-string representation of a polynomial |
1056 | * ( \sum_{i=0}^n a_i * x^i) into an array of integers corresponding |
1057 | * to the bits with non-zero coefficient. Array is terminated with -1. |
1058 | * Up to max elements of the array will be filled. Return value is total |
1059 | * number of array elements that would be filled if array was large enough. |
1060 | */ |
1061 | int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max) |
1062 | { |
1063 | int i, j, k = 0; |
1064 | BN_ULONG mask; |
1065 | |
1066 | if (BN_is_zero(a)) |
1067 | return 0; |
1068 | |
1069 | for (i = a->top - 1; i >= 0; i--) |
1070 | { |
1071 | if (!a->d[i]) |
1072 | /* skip word if a->d[i] == 0 */ |
1073 | continue; |
1074 | mask = BN_TBIT; |
1075 | for (j = BN_BITS2 - 1; j >= 0; j--) |
1076 | { |
1077 | if (a->d[i] & mask) |
1078 | { |
1079 | if (k < max) p[k] = BN_BITS2 * i + j; |
1080 | k++; |
1081 | } |
1082 | mask >>= 1; |
1083 | } |
1084 | } |
1085 | |
1086 | if (k < max) { |
1087 | p[k] = -1; |
1088 | k++; |
1089 | } |
1090 | |
1091 | return k; |
1092 | } |
1093 | |
1094 | /* Convert the coefficient array representation of a polynomial to a |
1095 | * bit-string. The array must be terminated by -1. |
1096 | */ |
1097 | int BN_GF2m_arr2poly(const int p[], BIGNUM *a) |
1098 | { |
1099 | int i; |
1100 | |
1101 | bn_check_top(a); |
1102 | BN_zero(a); |
1103 | for (i = 0; p[i] != -1; i++) |
1104 | { |
1105 | if (BN_set_bit(a, p[i]) == 0) |
1106 | return 0; |
1107 | } |
1108 | bn_check_top(a); |
1109 | |
1110 | return 1; |
1111 | } |
1112 | |
1113 | #endif |
1114 | |