openssl/crypto/bn/bn_gf2m.c - Issue 2072073002: Delete bundled copy of OpenSSL and replace with README.

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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

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