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 |