OLD | NEW |
| (Empty) |
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, c
onst 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_ULON
G 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 i
nt 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 wrap
per | |
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 BIGNU
M *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 *c
tx) | |
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 wrap
per | |
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)) got
o 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)) got
o 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 i
nt 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 wrap
per | |
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 wra
pper | |
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_CT
X *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 er
r; | |
996 if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) go
to 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_ITER
ATIONS); | |
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; th
is 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 | |
OLD | NEW |