Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.8/site-packages/ecdsa/ecdsa.py: 80%

1#! /usr/bin/env python 

2 

3""" 

4Low level implementation of Elliptic-Curve Digital Signatures. 

5 

6.. note :: 

7 You're most likely looking for the :py:class:`~ecdsa.keys` module. 

8 This is a low-level implementation of the ECDSA that operates on 

9 integers, not byte strings. 

10 

11NOTE: This a low level implementation of ECDSA, for normal applications 

12you should be looking at the keys.py module. 

13 

14Classes and methods for elliptic-curve signatures: 

15private keys, public keys, signatures, 

16and definitions of prime-modulus curves. 

17 

18Example: 

19 

20.. code-block:: python 

21 

22 # (In real-life applications, you would probably want to 

23 # protect against defects in SystemRandom.) 

24 from random import SystemRandom 

25 randrange = SystemRandom().randrange 

26 

27 # Generate a public/private key pair using the NIST Curve P-192: 

28 

29 g = generator_192 

30 n = g.order() 

31 secret = randrange( 1, n ) 

32 pubkey = Public_key( g, g * secret ) 

33 privkey = Private_key( pubkey, secret ) 

34 

35 # Signing a hash value: 

36 

37 hash = randrange( 1, n ) 

38 signature = privkey.sign( hash, randrange( 1, n ) ) 

39 

40 # Verifying a signature for a hash value: 

41 

42 if pubkey.verifies( hash, signature ): 

43 print_("Demo verification succeeded.") 

44 else: 

45 print_("*** Demo verification failed.") 

46 

47 # Verification fails if the hash value is modified: 

48 

49 if pubkey.verifies( hash-1, signature ): 

50 print_("**** Demo verification failed to reject tampered hash.") 

51 else: 

52 print_("Demo verification correctly rejected tampered hash.") 

53 

54Revision history: 

55 2005.12.31 - Initial version. 

56 

57 2008.11.25 - Substantial revisions introducing new classes. 

58 

59 2009.05.16 - Warn against using random.randrange in real applications. 

60 

61 2009.05.17 - Use random.SystemRandom by default. 

62 

63Originally written in 2005 by Peter Pearson and placed in the public domain, 

64modified as part of the python-ecdsa package. 

65""" 

66 

67from six import int2byte, b 

68from . import ellipticcurve 

69from . import numbertheory 

70from .util import bit_length 

71from ._compat import remove_whitespace 

72 

73 

74class RSZeroError(RuntimeError): 

75 pass 

76 

77 

78class InvalidPointError(RuntimeError): 

79 pass 

80 

81 

82class Signature(object): 

83 """ 

84 ECDSA signature. 

85 

86 :ivar int r: the ``r`` element of the ECDSA signature 

87 :ivar int s: the ``s`` element of the ECDSA signature 

88 """ 

89 

90 def __init__(self, r, s): 

91 self.r = r 

92 self.s = s 

93 

94 def recover_public_keys(self, hash, generator): 

95 """ 

96 Returns two public keys for which the signature is valid 

97 

98 :param int hash: signed hash 

99 :param AbstractPoint generator: is the generator used in creation 

100 of the signature 

101 :rtype: tuple(Public_key, Public_key) 

102 :return: a pair of public keys that can validate the signature 

103 """ 

104 curve = generator.curve() 

105 n = generator.order() 

106 r = self.r 

107 s = self.s 

108 e = hash 

109 x = r 

110 

111 # Compute the curve point with x as x-coordinate 

112 alpha = ( 

113 pow(x, 3, curve.p()) + (curve.a() * x) + curve.b() 

114 ) % curve.p() 

115 beta = numbertheory.square_root_mod_prime(alpha, curve.p()) 

116 y = beta if beta % 2 == 0 else curve.p() - beta 

117 

118 # Compute the public key 

119 R1 = ellipticcurve.PointJacobi(curve, x, y, 1, n) 

120 Q1 = numbertheory.inverse_mod(r, n) * (s * R1 + (-e % n) * generator) 

121 Pk1 = Public_key(generator, Q1) 

122 

123 # And the second solution 

124 R2 = ellipticcurve.PointJacobi(curve, x, -y, 1, n) 

125 Q2 = numbertheory.inverse_mod(r, n) * (s * R2 + (-e % n) * generator) 

126 Pk2 = Public_key(generator, Q2) 

127 

128 return [Pk1, Pk2] 

129 

130 

131class Public_key(object): 

132 """Public key for ECDSA.""" 

133 

134 def __init__(self, generator, point, verify=True): 

135 """Low level ECDSA public key object. 

136 

137 :param generator: the Point that generates the group (the base point) 

138 :param point: the Point that defines the public key 

139 :param bool verify: if True check if point is valid point on curve 

140 

141 :raises InvalidPointError: if the point parameters are invalid or 

142 point does not lay on the curve 

143 """ 

144 

145 self.curve = generator.curve() 

146 self.generator = generator 

147 self.point = point 

148 n = generator.order() 

149 p = self.curve.p() 

150 if not (0 <= point.x() < p) or not (0 <= point.y() < p): 

151 raise InvalidPointError( 

152 "The public point has x or y out of range." 

153 ) 

154 if verify and not self.curve.contains_point(point.x(), point.y()): 

155 raise InvalidPointError("Point does not lay on the curve") 

156 if not n: 

157 raise InvalidPointError("Generator point must have order.") 

158 # for curve parameters with base point with cofactor 1, all points 

159 # that are on the curve are scalar multiples of the base point, so 

160 # verifying that is not necessary. See Section 3.2.2.1 of SEC 1 v2 

161 if ( 

162 verify 

163 and self.curve.cofactor() != 1 

164 and not n * point == ellipticcurve.INFINITY 

165 ): 

166 raise InvalidPointError("Generator point order is bad.") 

167 

168 def __eq__(self, other): 

169 """Return True if the keys are identical, False otherwise. 

170 

171 Note: for comparison, only placement on the same curve and point 

172 equality is considered, use of the same generator point is not 

173 considered. 

174 """ 

175 if isinstance(other, Public_key): 

176 return self.curve == other.curve and self.point == other.point 

177 return NotImplemented 

178 

179 def __ne__(self, other): 

180 """Return False if the keys are identical, True otherwise.""" 

181 return not self == other 

182 

183 def verifies(self, hash, signature): 

184 """Verify that signature is a valid signature of hash. 

185 Return True if the signature is valid. 

186 """ 

187 

188 # From X9.62 J.3.1. 

189 

190 G = self.generator 

191 n = G.order() 

192 r = signature.r 

193 s = signature.s 

194 if r < 1 or r > n - 1: 

195 return False 

196 if s < 1 or s > n - 1: 

197 return False 

198 c = numbertheory.inverse_mod(s, n) 

199 u1 = (hash * c) % n 

200 u2 = (r * c) % n 

201 if hasattr(G, "mul_add"): 

202 xy = G.mul_add(u1, self.point, u2) 

203 else: 

204 xy = u1 * G + u2 * self.point 

205 v = xy.x() % n 

206 return v == r 

207 

208 

209class Private_key(object): 

210 """Private key for ECDSA.""" 

211 

212 def __init__(self, public_key, secret_multiplier): 

213 """public_key is of class Public_key; 

214 secret_multiplier is a large integer. 

215 """ 

216 

217 self.public_key = public_key 

218 self.secret_multiplier = secret_multiplier 

219 

220 def __eq__(self, other): 

221 """Return True if the points are identical, False otherwise.""" 

222 if isinstance(other, Private_key): 

223 return ( 

224 self.public_key == other.public_key 

225 and self.secret_multiplier == other.secret_multiplier 

226 ) 

227 return NotImplemented 

228 

229 def __ne__(self, other): 

230 """Return False if the points are identical, True otherwise.""" 

231 return not self == other 

232 

233 def sign(self, hash, random_k): 

234 """Return a signature for the provided hash, using the provided 

235 random nonce. It is absolutely vital that random_k be an unpredictable 

236 number in the range [1, self.public_key.point.order()-1]. If 

237 an attacker can guess random_k, he can compute our private key from a 

238 single signature. Also, if an attacker knows a few high-order 

239 bits (or a few low-order bits) of random_k, he can compute our private 

240 key from many signatures. The generation of nonces with adequate 

241 cryptographic strength is very difficult and far beyond the scope 

242 of this comment. 

243 

244 May raise RuntimeError, in which case retrying with a new 

245 random value k is in order. 

246 """ 

247 

248 G = self.public_key.generator 

249 n = G.order() 

250 k = random_k % n 

251 # Fix the bit-length of the random nonce, 

252 # so that it doesn't leak via timing. 

253 # This does not change that ks = k mod n 

254 ks = k + n 

255 kt = ks + n 

256 if bit_length(ks) == bit_length(n): 

257 p1 = kt * G 

258 else: 

259 p1 = ks * G 

260 r = p1.x() % n 

261 if r == 0: 

262 raise RSZeroError("amazingly unlucky random number r") 

263 s = ( 

264 numbertheory.inverse_mod(k, n) 

265 * (hash + (self.secret_multiplier * r) % n) 

266 ) % n 

267 if s == 0: 

268 raise RSZeroError("amazingly unlucky random number s") 

269 return Signature(r, s) 

270 

271 

272def int_to_string(x): 

273 """Convert integer x into a string of bytes, as per X9.62.""" 

274 assert x >= 0 

275 if x == 0: 

276 return b("\0") 

277 result = [] 

278 while x: 

279 ordinal = x & 0xFF 

280 result.append(int2byte(ordinal)) 

281 x >>= 8 

282 

283 result.reverse() 

284 return b("").join(result) 

285 

286 

287def string_to_int(s): 

288 """Convert a string of bytes into an integer, as per X9.62.""" 

289 result = 0 

290 for c in s: 

291 if not isinstance(c, int): 

292 c = ord(c) 

293 result = 256 * result + c 

294 return result 

295 

296 

297def digest_integer(m): 

298 """Convert an integer into a string of bytes, compute 

299 its SHA-1 hash, and convert the result to an integer.""" 

300 # 

301 # I don't expect this function to be used much. I wrote 

302 # it in order to be able to duplicate the examples 

303 # in ECDSAVS. 

304 # 

305 from hashlib import sha1 

306 

307 return string_to_int(sha1(int_to_string(m)).digest()) 

308 

309 

310def point_is_valid(generator, x, y): 

311 """Is (x,y) a valid public key based on the specified generator?""" 

312 

313 # These are the tests specified in X9.62. 

314 

315 n = generator.order() 

316 curve = generator.curve() 

317 p = curve.p() 

318 if not (0 <= x < p) or not (0 <= y < p): 

319 return False 

320 if not curve.contains_point(x, y): 

321 return False 

322 if ( 

323 curve.cofactor() != 1 

324 and not n * ellipticcurve.PointJacobi(curve, x, y, 1) 

325 == ellipticcurve.INFINITY 

326 ): 

327 return False 

328 return True 

329 

330 

331# secp112r1 curve 

332_p = int(remove_whitespace("DB7C 2ABF62E3 5E668076 BEAD208B"), 16) 

333# s = 00F50B02 8E4D696E 67687561 51752904 72783FB1 

334_a = int(remove_whitespace("DB7C 2ABF62E3 5E668076 BEAD2088"), 16) 

335_b = int(remove_whitespace("659E F8BA0439 16EEDE89 11702B22"), 16) 

336_Gx = int(remove_whitespace("09487239 995A5EE7 6B55F9C2 F098"), 16) 

337_Gy = int(remove_whitespace("A89C E5AF8724 C0A23E0E 0FF77500"), 16) 

338_r = int(remove_whitespace("DB7C 2ABF62E3 5E7628DF AC6561C5"), 16) 

339_h = 1 

340curve_112r1 = ellipticcurve.CurveFp(_p, _a, _b, _h) 

341generator_112r1 = ellipticcurve.PointJacobi( 

342 curve_112r1, _Gx, _Gy, 1, _r, generator=True 

343) 

344 

345 

346# secp112r2 curve 

347_p = int(remove_whitespace("DB7C 2ABF62E3 5E668076 BEAD208B"), 16) 

348# s = 022757A1 114D69E 67687561 51755316 C05E0BD4 

349_a = int(remove_whitespace("6127 C24C05F3 8A0AAAF6 5C0EF02C"), 16) 

350_b = int(remove_whitespace("51DE F1815DB5 ED74FCC3 4C85D709"), 16) 

351_Gx = int(remove_whitespace("4BA30AB5 E892B4E1 649DD092 8643"), 16) 

352_Gy = int(remove_whitespace("ADCD 46F5882E 3747DEF3 6E956E97"), 16) 

353_r = int(remove_whitespace("36DF 0AAFD8B8 D7597CA1 0520D04B"), 16) 

354_h = 4 

355curve_112r2 = ellipticcurve.CurveFp(_p, _a, _b, _h) 

356generator_112r2 = ellipticcurve.PointJacobi( 

357 curve_112r2, _Gx, _Gy, 1, _r, generator=True 

358) 

359 

360 

361# secp128r1 curve 

362_p = int(remove_whitespace("FFFFFFFD FFFFFFFF FFFFFFFF FFFFFFFF"), 16) 

363# S = 000E0D4D 69E6768 75615175 0CC03A44 73D03679 

364# a and b are mod p, so a is equal to p-3, or simply -3 

365# _a = -3 

366_b = int(remove_whitespace("E87579C1 1079F43D D824993C 2CEE5ED3"), 16) 

367_Gx = int(remove_whitespace("161FF752 8B899B2D 0C28607C A52C5B86"), 16) 

368_Gy = int(remove_whitespace("CF5AC839 5BAFEB13 C02DA292 DDED7A83"), 16) 

369_r = int(remove_whitespace("FFFFFFFE 00000000 75A30D1B 9038A115"), 16) 

370_h = 1 

371curve_128r1 = ellipticcurve.CurveFp(_p, -3, _b, _h) 

372generator_128r1 = ellipticcurve.PointJacobi( 

373 curve_128r1, _Gx, _Gy, 1, _r, generator=True 

374) 

375 

376 

377# secp160r1 

378_p = int(remove_whitespace("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 7FFFFFFF"), 16) 

379# S = 1053CDE4 2C14D696 E6768756 1517533B F3F83345 

380# a and b are mod p, so a is equal to p-3, or simply -3 

381# _a = -3 

382_b = int(remove_whitespace("1C97BEFC 54BD7A8B 65ACF89F 81D4D4AD C565FA45"), 16) 

383_Gx = int( 

384 remove_whitespace("4A96B568 8EF57328 46646989 68C38BB9 13CBFC82"), 

385 16, 

386) 

387_Gy = int( 

388 remove_whitespace("23A62855 3168947D 59DCC912 04235137 7AC5FB32"), 

389 16, 

390) 

391_r = int( 

392 remove_whitespace("01 00000000 00000000 0001F4C8 F927AED3 CA752257"), 

393 16, 

394) 

395_h = 1 

396curve_160r1 = ellipticcurve.CurveFp(_p, -3, _b, _h) 

397generator_160r1 = ellipticcurve.PointJacobi( 

398 curve_160r1, _Gx, _Gy, 1, _r, generator=True 

399) 

400 

401 

402# NIST Curve P-192: 

403_p = 6277101735386680763835789423207666416083908700390324961279 

404_r = 6277101735386680763835789423176059013767194773182842284081 

405# s = 0x3045ae6fc8422f64ed579528d38120eae12196d5L 

406# c = 0x3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65L 

407_b = int( 

408 remove_whitespace( 

409 """ 

410 64210519 E59C80E7 0FA7E9AB 72243049 FEB8DEEC C146B9B1""" 

411 ), 

412 16, 

413) 

414_Gx = int( 

415 remove_whitespace( 

416 """ 

417 188DA80E B03090F6 7CBF20EB 43A18800 F4FF0AFD 82FF1012""" 

418 ), 

419 16, 

420) 

421_Gy = int( 

422 remove_whitespace( 

423 """ 

424 07192B95 FFC8DA78 631011ED 6B24CDD5 73F977A1 1E794811""" 

425 ), 

426 16, 

427) 

428 

429curve_192 = ellipticcurve.CurveFp(_p, -3, _b, 1) 

430generator_192 = ellipticcurve.PointJacobi( 

431 curve_192, _Gx, _Gy, 1, _r, generator=True 

432) 

433 

434 

435# NIST Curve P-224: 

436_p = int( 

437 remove_whitespace( 

438 """ 

439 2695994666715063979466701508701963067355791626002630814351 

440 0066298881""" 

441 ) 

442) 

443_r = int( 

444 remove_whitespace( 

445 """ 

446 2695994666715063979466701508701962594045780771442439172168 

447 2722368061""" 

448 ) 

449) 

450# s = 0xbd71344799d5c7fcdc45b59fa3b9ab8f6a948bc5L 

451# c = 0x5b056c7e11dd68f40469ee7f3c7a7d74f7d121116506d031218291fbL 

452_b = int( 

453 remove_whitespace( 

454 """ 

455 B4050A85 0C04B3AB F5413256 5044B0B7 D7BFD8BA 270B3943 

456 2355FFB4""" 

457 ), 

458 16, 

459) 

460_Gx = int( 

461 remove_whitespace( 

462 """ 

463 B70E0CBD 6BB4BF7F 321390B9 4A03C1D3 56C21122 343280D6 

464 115C1D21""" 

465 ), 

466 16, 

467) 

468_Gy = int( 

469 remove_whitespace( 

470 """ 

471 BD376388 B5F723FB 4C22DFE6 CD4375A0 5A074764 44D58199 

472 85007E34""" 

473 ), 

474 16, 

475) 

476 

477curve_224 = ellipticcurve.CurveFp(_p, -3, _b, 1) 

478generator_224 = ellipticcurve.PointJacobi( 

479 curve_224, _Gx, _Gy, 1, _r, generator=True 

480) 

481 

482# NIST Curve P-256: 

483_p = int( 

484 remove_whitespace( 

485 """ 

486 1157920892103562487626974469494075735300861434152903141955 

487 33631308867097853951""" 

488 ) 

489) 

490_r = int( 

491 remove_whitespace( 

492 """ 

493 115792089210356248762697446949407573529996955224135760342 

494 422259061068512044369""" 

495 ) 

496) 

497# s = 0xc49d360886e704936a6678e1139d26b7819f7e90L 

498# c = 0x7efba1662985be9403cb055c75d4f7e0ce8d84a9c5114abcaf3177680104fa0dL 

499_b = int( 

500 remove_whitespace( 

501 """ 

502 5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 

503 3BCE3C3E 27D2604B""" 

504 ), 

505 16, 

506) 

507_Gx = int( 

508 remove_whitespace( 

509 """ 

510 6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 

511 F4A13945 D898C296""" 

512 ), 

513 16, 

514) 

515_Gy = int( 

516 remove_whitespace( 

517 """ 

518 4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE 

519 CBB64068 37BF51F5""" 

520 ), 

521 16, 

522) 

523 

524curve_256 = ellipticcurve.CurveFp(_p, -3, _b, 1) 

525generator_256 = ellipticcurve.PointJacobi( 

526 curve_256, _Gx, _Gy, 1, _r, generator=True 

527) 

528 

529# NIST Curve P-384: 

530_p = int( 

531 remove_whitespace( 

532 """ 

533 3940200619639447921227904010014361380507973927046544666794 

534 8293404245721771496870329047266088258938001861606973112319""" 

535 ) 

536) 

537_r = int( 

538 remove_whitespace( 

539 """ 

540 3940200619639447921227904010014361380507973927046544666794 

541 6905279627659399113263569398956308152294913554433653942643""" 

542 ) 

543) 

544# s = 0xa335926aa319a27a1d00896a6773a4827acdac73L 

545# c = int(remove_whitespace( 

546# """ 

547# 79d1e655 f868f02f ff48dcde e14151dd b80643c1 406d0ca1 

548# 0dfe6fc5 2009540a 495e8042 ea5f744f 6e184667 cc722483""" 

549# ), 16) 

550_b = int( 

551 remove_whitespace( 

552 """ 

553 B3312FA7 E23EE7E4 988E056B E3F82D19 181D9C6E FE814112 

554 0314088F 5013875A C656398D 8A2ED19D 2A85C8ED D3EC2AEF""" 

555 ), 

556 16, 

557) 

558_Gx = int( 

559 remove_whitespace( 

560 """ 

561 AA87CA22 BE8B0537 8EB1C71E F320AD74 6E1D3B62 8BA79B98 

562 59F741E0 82542A38 5502F25D BF55296C 3A545E38 72760AB7""" 

563 ), 

564 16, 

565) 

566_Gy = int( 

567 remove_whitespace( 

568 """ 

569 3617DE4A 96262C6F 5D9E98BF 9292DC29 F8F41DBD 289A147C 

570 E9DA3113 B5F0B8C0 0A60B1CE 1D7E819D 7A431D7C 90EA0E5F""" 

571 ), 

572 16, 

573) 

574 

575curve_384 = ellipticcurve.CurveFp(_p, -3, _b, 1) 

576generator_384 = ellipticcurve.PointJacobi( 

577 curve_384, _Gx, _Gy, 1, _r, generator=True 

578) 

579 

580# NIST Curve P-521: 

581_p = int( 

582 "686479766013060971498190079908139321726943530014330540939" 

583 "446345918554318339765605212255964066145455497729631139148" 

584 "0858037121987999716643812574028291115057151" 

585) 

586_r = int( 

587 "686479766013060971498190079908139321726943530014330540939" 

588 "446345918554318339765539424505774633321719753296399637136" 

589 "3321113864768612440380340372808892707005449" 

590) 

591# s = 0xd09e8800291cb85396cc6717393284aaa0da64baL 

592# c = int(remove_whitespace( 

593# """ 

594# 0b4 8bfa5f42 0a349495 39d2bdfc 264eeeeb 077688e4 

595# 4fbf0ad8 f6d0edb3 7bd6b533 28100051 8e19f1b9 ffbe0fe9 

596# ed8a3c22 00b8f875 e523868c 70c1e5bf 55bad637""" 

597# ), 16) 

598_b = int( 

599 remove_whitespace( 

600 """ 

601 051 953EB961 8E1C9A1F 929A21A0 B68540EE A2DA725B 

602 99B315F3 B8B48991 8EF109E1 56193951 EC7E937B 1652C0BD 

603 3BB1BF07 3573DF88 3D2C34F1 EF451FD4 6B503F00""" 

604 ), 

605 16, 

606) 

607_Gx = int( 

608 remove_whitespace( 

609 """ 

610 C6 858E06B7 0404E9CD 9E3ECB66 2395B442 9C648139 

611 053FB521 F828AF60 6B4D3DBA A14B5E77 EFE75928 FE1DC127 

612 A2FFA8DE 3348B3C1 856A429B F97E7E31 C2E5BD66""" 

613 ), 

614 16, 

615) 

616_Gy = int( 

617 remove_whitespace( 

618 """ 

619 118 39296A78 9A3BC004 5C8A5FB4 2C7D1BD9 98F54449 

620 579B4468 17AFBD17 273E662C 97EE7299 5EF42640 C550B901 

621 3FAD0761 353C7086 A272C240 88BE9476 9FD16650""" 

622 ), 

623 16, 

624) 

625 

626curve_521 = ellipticcurve.CurveFp(_p, -3, _b, 1) 

627generator_521 = ellipticcurve.PointJacobi( 

628 curve_521, _Gx, _Gy, 1, _r, generator=True 

629) 

630 

631# Certicom secp256-k1 

632_a = 0x0000000000000000000000000000000000000000000000000000000000000000 

633_b = 0x0000000000000000000000000000000000000000000000000000000000000007 

634_p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F 

635_Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798 

636_Gy = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8 

637_r = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 

638 

639curve_secp256k1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

640generator_secp256k1 = ellipticcurve.PointJacobi( 

641 curve_secp256k1, _Gx, _Gy, 1, _r, generator=True 

642) 

643 

644# Brainpool P-160-r1 

645_a = 0x340E7BE2A280EB74E2BE61BADA745D97E8F7C300 

646_b = 0x1E589A8595423412134FAA2DBDEC95C8D8675E58 

647_p = 0xE95E4A5F737059DC60DFC7AD95B3D8139515620F 

648_Gx = 0xBED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3 

649_Gy = 0x1667CB477A1A8EC338F94741669C976316DA6321 

650_q = 0xE95E4A5F737059DC60DF5991D45029409E60FC09 

651 

652curve_brainpoolp160r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

653generator_brainpoolp160r1 = ellipticcurve.PointJacobi( 

654 curve_brainpoolp160r1, _Gx, _Gy, 1, _q, generator=True 

655) 

656 

657# Brainpool P-160-t1 

658_a = 0xE95E4A5F737059DC60DFC7AD95B3D8139515620C 

659_b = 0x7A556B6DAE535B7B51ED2C4D7DAA7A0B5C55F380 

660# _z = 0x24DBFF5DEC9B986BBFE5295A29BFBAE45E0F5D0B 

661_Gx = 0xB199B13B9B34EFC1397E64BAEB05ACC265FF2378 

662_Gy = 0xADD6718B7C7C1961F0991B842443772152C9E0AD 

663_q = 0xE95E4A5F737059DC60DF5991D45029409E60FC09 

664curve_brainpoolp160t1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

665generator_brainpoolp160t1 = ellipticcurve.PointJacobi( 

666 curve_brainpoolp160t1, _Gx, _Gy, 1, _q, generator=True 

667) 

668 

669# Brainpool P-192-r1 

670_a = 0x6A91174076B1E0E19C39C031FE8685C1CAE040E5C69A28EF 

671_b = 0x469A28EF7C28CCA3DC721D044F4496BCCA7EF4146FBF25C9 

672_p = 0xC302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297 

673_Gx = 0xC0A0647EAAB6A48753B033C56CB0F0900A2F5C4853375FD6 

674_Gy = 0x14B690866ABD5BB88B5F4828C1490002E6773FA2FA299B8F 

675_q = 0xC302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1 

676 

677curve_brainpoolp192r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

678generator_brainpoolp192r1 = ellipticcurve.PointJacobi( 

679 curve_brainpoolp192r1, _Gx, _Gy, 1, _q, generator=True 

680) 

681 

682# Brainpool P-192-t1 

683_a = 0xC302F41D932A36CDA7A3463093D18DB78FCE476DE1A86294 

684_b = 0x13D56FFAEC78681E68F9DEB43B35BEC2FB68542E27897B79 

685# _z = 0x1B6F5CC8DB4DC7AF19458A9CB80DC2295E5EB9C3732104CB 

686_Gx = 0x3AE9E58C82F63C30282E1FE7BBF43FA72C446AF6F4618129 

687_Gy = 0x097E2C5667C2223A902AB5CA449D0084B7E5B3DE7CCC01C9 

688_q = 0xC302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1 

689 

690curve_brainpoolp192t1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

691generator_brainpoolp192t1 = ellipticcurve.PointJacobi( 

692 curve_brainpoolp192t1, _Gx, _Gy, 1, _q, generator=True 

693) 

694 

695# Brainpool P-224-r1 

696_a = 0x68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43 

697_b = 0x2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B 

698_p = 0xD7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF 

699_Gx = 0x0D9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D 

700_Gy = 0x58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD 

701_q = 0xD7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F 

702 

703curve_brainpoolp224r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

704generator_brainpoolp224r1 = ellipticcurve.PointJacobi( 

705 curve_brainpoolp224r1, _Gx, _Gy, 1, _q, generator=True 

706) 

707 

708# Brainpool P-224-t1 

709_a = 0xD7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FC 

710_b = 0x4B337D934104CD7BEF271BF60CED1ED20DA14C08B3BB64F18A60888D 

711# _z = 0x2DF271E14427A346910CF7A2E6CFA7B3F484E5C2CCE1C8B730E28B3F 

712_Gx = 0x6AB1E344CE25FF3896424E7FFE14762ECB49F8928AC0C76029B4D580 

713_Gy = 0x0374E9F5143E568CD23F3F4D7C0D4B1E41C8CC0D1C6ABD5F1A46DB4C 

714_q = 0xD7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F 

715 

716curve_brainpoolp224t1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

717generator_brainpoolp224t1 = ellipticcurve.PointJacobi( 

718 curve_brainpoolp224t1, _Gx, _Gy, 1, _q, generator=True 

719) 

720 

721# Brainpool P-256-r1 

722_a = 0x7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9 

723_b = 0x26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6 

724_p = 0xA9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377 

725_Gx = 0x8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262 

726_Gy = 0x547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997 

727_q = 0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7 

728 

729curve_brainpoolp256r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

730generator_brainpoolp256r1 = ellipticcurve.PointJacobi( 

731 curve_brainpoolp256r1, _Gx, _Gy, 1, _q, generator=True 

732) 

733 

734# Brainpool P-256-t1 

735_a = 0xA9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5374 

736_b = 0x662C61C430D84EA4FE66A7733D0B76B7BF93EBC4AF2F49256AE58101FEE92B04 

737# _z = 0x3E2D4BD9597B58639AE7AA669CAB9837CF5CF20A2C852D10F655668DFC150EF0 

738_Gx = 0xA3E8EB3CC1CFE7B7732213B23A656149AFA142C47AAFBC2B79A191562E1305F4 

739_Gy = 0x2D996C823439C56D7F7B22E14644417E69BCB6DE39D027001DABE8F35B25C9BE 

740_q = 0xA9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7 

741 

742curve_brainpoolp256t1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

743generator_brainpoolp256t1 = ellipticcurve.PointJacobi( 

744 curve_brainpoolp256t1, _Gx, _Gy, 1, _q, generator=True 

745) 

746 

747# Brainpool P-320-r1 

748_a = int( 

749 remove_whitespace( 

750 """ 

751 3EE30B568FBAB0F883CCEBD46D3F3BB8A2A73513F5EB79DA66190EB085FFA9 

752 F492F375A97D860EB4""" 

753 ), 

754 16, 

755) 

756_b = int( 

757 remove_whitespace( 

758 """ 

759 520883949DFDBC42D3AD198640688A6FE13F41349554B49ACC31DCCD884539 

760 816F5EB4AC8FB1F1A6""" 

761 ), 

762 16, 

763) 

764_p = int( 

765 remove_whitespace( 

766 """ 

767 D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC 

768 28FCD412B1F1B32E27""" 

769 ), 

770 16, 

771) 

772_Gx = int( 

773 remove_whitespace( 

774 """ 

775 43BD7E9AFB53D8B85289BCC48EE5BFE6F20137D10A087EB6E7871E2A10A599 

776 C710AF8D0D39E20611""" 

777 ), 

778 16, 

779) 

780_Gy = int( 

781 remove_whitespace( 

782 """ 

783 14FDD05545EC1CC8AB4093247F77275E0743FFED117182EAA9C77877AAAC6A 

784 C7D35245D1692E8EE1""" 

785 ), 

786 16, 

787) 

788_q = int( 

789 remove_whitespace( 

790 """ 

791 D35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658 

792 E98691555B44C59311""" 

793 ), 

794 16, 

795) 

796 

797curve_brainpoolp320r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

798generator_brainpoolp320r1 = ellipticcurve.PointJacobi( 

799 curve_brainpoolp320r1, _Gx, _Gy, 1, _q, generator=True 

800) 

801 

802# Brainpool P-320-t1 

803_a = int( 

804 remove_whitespace( 

805 """ 

806 D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC 

807 28FCD412B1F1B32E24""" 

808 ), 

809 16, 

810) 

811_b = int( 

812 remove_whitespace( 

813 """ 

814 A7F561E038EB1ED560B3D147DB782013064C19F27ED27C6780AAF77FB8A547 

815 CEB5B4FEF422340353""" 

816 ), 

817 16, 

818) 

819# _z = int( 

820# remove_whitespace( 

821# """ 

822# 15F75CAF668077F7E85B42EB01F0A81FF56ECD6191D55CB82B7D861458A18F 

823# EFC3E5AB7496F3C7B1""" 

824# ), 

825# 16, 

826# ) 

827_Gx = int( 

828 remove_whitespace( 

829 """ 

830 925BE9FB01AFC6FB4D3E7D4990010F813408AB106C4F09CB7EE07868CC136F 

831 FF3357F624A21BED52""" 

832 ), 

833 16, 

834) 

835_Gy = int( 

836 remove_whitespace( 

837 """ 

838 63BA3A7A27483EBF6671DBEF7ABB30EBEE084E58A0B077AD42A5A0989D1EE7 

839 1B1B9BC0455FB0D2C3""" 

840 ), 

841 16, 

842) 

843_q = int( 

844 remove_whitespace( 

845 """ 

846 D35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658 

847 E98691555B44C59311""" 

848 ), 

849 16, 

850) 

851 

852curve_brainpoolp320t1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

853generator_brainpoolp320t1 = ellipticcurve.PointJacobi( 

854 curve_brainpoolp320t1, _Gx, _Gy, 1, _q, generator=True 

855) 

856 

857# Brainpool P-384-r1 

858_a = int( 

859 remove_whitespace( 

860 """ 

861 7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F9 

862 0F8AA5814A503AD4EB04A8C7DD22CE2826""" 

863 ), 

864 16, 

865) 

866_b = int( 

867 remove_whitespace( 

868 """ 

869 04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62 

870 D57CB4390295DBC9943AB78696FA504C11""" 

871 ), 

872 16, 

873) 

874_p = int( 

875 remove_whitespace( 

876 """ 

877 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711 

878 23ACD3A729901D1A71874700133107EC53""" 

879 ), 

880 16, 

881) 

882_Gx = int( 

883 remove_whitespace( 

884 """ 

885 1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10 

886 E8E826E03436D646AAEF87B2E247D4AF1E""" 

887 ), 

888 16, 

889) 

890_Gy = int( 

891 remove_whitespace( 

892 """ 

893 8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF991292 

894 80E4646217791811142820341263C5315""" 

895 ), 

896 16, 

897) 

898_q = int( 

899 remove_whitespace( 

900 """ 

901 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425 

902 A7CF3AB6AF6B7FC3103B883202E9046565""" 

903 ), 

904 16, 

905) 

906 

907curve_brainpoolp384r1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

908generator_brainpoolp384r1 = ellipticcurve.PointJacobi( 

909 curve_brainpoolp384r1, _Gx, _Gy, 1, _q, generator=True 

910) 

911 

912_a = int( 

913 remove_whitespace( 

914 """ 

915 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711 

916 23ACD3A729901D1A71874700133107EC50""" 

917 ), 

918 16, 

919) 

920_b = int( 

921 remove_whitespace( 

922 """ 

923 7F519EADA7BDA81BD826DBA647910F8C4B9346ED8CCDC64E4B1ABD11756DCE 

924 1D2074AA263B88805CED70355A33B471EE""" 

925 ), 

926 16, 

927) 

928# _z = int( 

929# remove_whitespace( 

930# """ 

931# 41DFE8DD399331F7166A66076734A89CD0D2BCDB7D068E44E1F378F41ECBAE 

932# 97D2D63DBC87BCCDDCCC5DA39E8589291C""" 

933# ), 

934# 16, 

935# ) 

936_Gx = int( 

937 remove_whitespace( 

938 """ 

939 18DE98B02DB9A306F2AFCD7235F72A819B80AB12EBD653172476FECD462AAB 

940 FFC4FF191B946A5F54D8D0AA2F418808CC""" 

941 ), 

942 16, 

943) 

944_Gy = int( 

945 remove_whitespace( 

946 """ 

947 25AB056962D30651A114AFD2755AD336747F93475B7A1FCA3B88F2B6A208CC 

948 FE469408584DC2B2912675BF5B9E582928""" 

949 ), 

950 16, 

951) 

952_q = int( 

953 remove_whitespace( 

954 """ 

955 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425 

956 A7CF3AB6AF6B7FC3103B883202E9046565""" 

957 ), 

958 16, 

959) 

960 

961curve_brainpoolp384t1 = ellipticcurve.CurveFp(_p, _a, _b, 1) 

962generator_brainpoolp384t1 = ellipticcurve.PointJacobi( 

963 curve_brainpoolp384t1, _Gx, _Gy, 1, _q, generator=True 

964) 

965 

966# Brainpool P-512-r1 

967_a = int( 

968 remove_whitespace( 

969 """ 

970 7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863 

971 BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA""" 

972 ), 

973 16, 

974) 

975_b = int( 

976 remove_whitespace( 

977 """ 

978 3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117 

979 A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723""" 

980 ), 

981 16, 

982) 

983_p = int( 

984 remove_whitespace( 

985 """ 

986 AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308 

987 717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3""" 

988 ), 

989 16, 

990) 

991_Gx = int( 

992 remove_whitespace( 

993 """