1{-# LANGUAGE DeriveDataTypeable #-} 2-- | 3-- Module : Crypto.PubKey.ECC.Types 4-- License : BSD-style 5-- Maintainer : Vincent Hanquez <vincent@snarc.org> 6-- Stability : Experimental 7-- Portability : Excellent 8-- 9-- References: 10-- <https://tools.ietf.org/html/rfc5915> 11-- 12module Crypto.PubKey.ECC.Types 13 ( Curve(..) 14 , Point(..) 15 , PublicPoint 16 , PrivateNumber 17 , CurveBinary(..) 18 , CurvePrime(..) 19 , common_curve 20 , curveSizeBits 21 , ecc_fx 22 , ecc_p 23 , CurveCommon(..) 24 -- * Recommended curves definition 25 , CurveName(..) 26 , getCurveByName 27 ) where 28 29import Data.Data 30import Crypto.Internal.Imports 31import Crypto.Number.Basic (numBits) 32 33-- | Define either a binary curve or a prime curve. 34data Curve = CurveF2m CurveBinary -- ^ ��(2^m) 35 | CurveFP CurvePrime -- ^ ��p 36 deriving (Show,Read,Eq,Data) 37 38-- | ECC Public Point 39type PublicPoint = Point 40 41-- | ECC Private Number 42type PrivateNumber = Integer 43 44-- | Define a point on a curve. 45data Point = Point Integer Integer 46 | PointO -- ^ Point at Infinity 47 deriving (Show,Read,Eq,Data) 48 49instance NFData Point where 50 rnf (Point x y) = x `seq` y `seq` () 51 rnf PointO = () 52 53-- | Define an elliptic curve in ��(2^m). 54-- The firt parameter is the Integer representatioin of the irreducible polynomial f(x). 55data CurveBinary = CurveBinary Integer CurveCommon 56 deriving (Show,Read,Eq,Data) 57 58instance NFData CurveBinary where 59 rnf (CurveBinary i cc) = i `seq` cc `seq` () 60 61-- | Define an elliptic curve in ��p. 62-- The first parameter is the Prime Number. 63data CurvePrime = CurvePrime Integer CurveCommon 64 deriving (Show,Read,Eq,Data) 65 66-- | Parameters in common between binary and prime curves. 67common_curve :: Curve -> CurveCommon 68common_curve (CurveF2m (CurveBinary _ cc)) = cc 69common_curve (CurveFP (CurvePrime _ cc)) = cc 70 71-- | Irreducible polynomial representing the characteristic of a CurveBinary. 72ecc_fx :: CurveBinary -> Integer 73ecc_fx (CurveBinary fx _) = fx 74 75-- | Prime number representing the characteristic of a CurvePrime. 76ecc_p :: CurvePrime -> Integer 77ecc_p (CurvePrime p _) = p 78 79-- | Define common parameters in a curve definition 80-- of the form: y^2 = x^3 + ax + b. 81data CurveCommon = CurveCommon 82 { ecc_a :: Integer -- ^ curve parameter a 83 , ecc_b :: Integer -- ^ curve parameter b 84 , ecc_g :: Point -- ^ base point 85 , ecc_n :: Integer -- ^ order of G 86 , ecc_h :: Integer -- ^ cofactor 87 } deriving (Show,Read,Eq,Data) 88 89-- | Define names for known recommended curves. 90data CurveName = 91 SEC_p112r1 92 | SEC_p112r2 93 | SEC_p128r1 94 | SEC_p128r2 95 | SEC_p160k1 96 | SEC_p160r1 97 | SEC_p160r2 98 | SEC_p192k1 99 | SEC_p192r1 -- aka prime192v1 100 | SEC_p224k1 101 | SEC_p224r1 102 | SEC_p256k1 103 | SEC_p256r1 -- aka prime256v1 104 | SEC_p384r1 105 | SEC_p521r1 106 | SEC_t113r1 107 | SEC_t113r2 108 | SEC_t131r1 109 | SEC_t131r2 110 | SEC_t163k1 111 | SEC_t163r1 112 | SEC_t163r2 113 | SEC_t193r1 114 | SEC_t193r2 115 | SEC_t233k1 -- aka NIST K-233 116 | SEC_t233r1 117 | SEC_t239k1 118 | SEC_t283k1 119 | SEC_t283r1 120 | SEC_t409k1 121 | SEC_t409r1 122 | SEC_t571k1 123 | SEC_t571r1 124 deriving (Show,Read,Eq,Ord,Enum,Bounded,Data) 125 126{- 127curvesOIDs :: [ (CurveName, [Integer]) ] 128curvesOIDs = 129 [ (SEC_p112r1, [1,3,132,0,6]) 130 , (SEC_p112r2, [1,3,132,0,7]) 131 , (SEC_p128r1, [1,3,132,0,28]) 132 , (SEC_p128r2, [1,3,132,0,29]) 133 , (SEC_p160k1, [1,3,132,0,9]) 134 , (SEC_p160r1, [1,3,132,0,8]) 135 , (SEC_p160r2, [1,3,132,0,30]) 136 , (SEC_p192k1, [1,3,132,0,31]) 137 , (SEC_p192r1, [1,2,840,10045,3,1,1]) 138 , (SEC_p224k1, [1,3,132,0,32]) 139 , (SEC_p224r1, [1,3,132,0,33]) 140 , (SEC_p256k1, [1,3,132,0,10]) 141 , (SEC_p256r1, [1,2,840,10045,3,1,7]) 142 , (SEC_p384r1, [1,3,132,0,34]) 143 , (SEC_p521r1, [1,3,132,0,35]) 144 , (SEC_t113r1, [1,3,132,0,4]) 145 , (SEC_t113r2, [1,3,132,0,5]) 146 , (SEC_t131r1, [1,3,132,0,22]) 147 , (SEC_t131r2, [1,3,132,0,23]) 148 , (SEC_t163k1, [1,3,132,0,1]) 149 , (SEC_t163r1, [1,3,132,0,2]) 150 , (SEC_t163r2, [1,3,132,0,15]) 151 , (SEC_t193r1, [1,3,132,0,24]) 152 , (SEC_t193r2, [1,3,132,0,25]) 153 , (SEC_t233k1, [1,3,132,0,26]) 154 , (SEC_t233r1, [1,3,132,0,27]) 155 , (SEC_t239k1, [1,3,132,0,3]) 156 , (SEC_t283k1, [1,3,132,0,16]) 157 , (SEC_t283r1, [1,3,132,0,17]) 158 , (SEC_t409k1, [1,3,132,0,36]) 159 , (SEC_t409r1, [1,3,132,0,37]) 160 , (SEC_t571k1, [1,3,132,0,38]) 161 , (SEC_t571r1, [1,3,132,0,39]) 162 ] 163-} 164 165-- | get the size of the curve in bits 166curveSizeBits :: Curve -> Int 167curveSizeBits (CurveFP c) = numBits (ecc_p c) 168curveSizeBits (CurveF2m c) = numBits (ecc_fx c) - 1 169 170-- | Get the curve definition associated with a recommended known curve name. 171getCurveByName :: CurveName -> Curve 172getCurveByName SEC_p112r1 = CurveFP $ CurvePrime 173 0xdb7c2abf62e35e668076bead208b 174 (CurveCommon 175 { ecc_a = 0xdb7c2abf62e35e668076bead2088 176 , ecc_b = 0x659ef8ba043916eede8911702b22 177 , ecc_g = Point 0x09487239995a5ee76b55f9c2f098 178 0xa89ce5af8724c0a23e0e0ff77500 179 , ecc_n = 0xdb7c2abf62e35e7628dfac6561c5 180 , ecc_h = 1 181 }) 182getCurveByName SEC_p112r2 = CurveFP $ CurvePrime 183 0xdb7c2abf62e35e668076bead208b 184 (CurveCommon 185 { ecc_a = 0x6127c24c05f38a0aaaf65c0ef02c 186 , ecc_b = 0x51def1815db5ed74fcc34c85d709 187 , ecc_g = Point 0x4ba30ab5e892b4e1649dd0928643 188 0xadcd46f5882e3747def36e956e97 189 , ecc_n = 0x36df0aafd8b8d7597ca10520d04b 190 , ecc_h = 4 191 }) 192getCurveByName SEC_p128r1 = CurveFP $ CurvePrime 193 0xfffffffdffffffffffffffffffffffff 194 (CurveCommon 195 { ecc_a = 0xfffffffdfffffffffffffffffffffffc 196 , ecc_b = 0xe87579c11079f43dd824993c2cee5ed3 197 , ecc_g = Point 0x161ff7528b899b2d0c28607ca52c5b86 198 0xcf5ac8395bafeb13c02da292dded7a83 199 , ecc_n = 0xfffffffe0000000075a30d1b9038a115 200 , ecc_h = 1 201 }) 202getCurveByName SEC_p128r2 = CurveFP $ CurvePrime 203 0xfffffffdffffffffffffffffffffffff 204 (CurveCommon 205 { ecc_a = 0xd6031998d1b3bbfebf59cc9bbff9aee1 206 , ecc_b = 0x5eeefca380d02919dc2c6558bb6d8a5d 207 , ecc_g = Point 0x7b6aa5d85e572983e6fb32a7cdebc140 208 0x27b6916a894d3aee7106fe805fc34b44 209 , ecc_n = 0x3fffffff7fffffffbe0024720613b5a3 210 , ecc_h = 4 211 }) 212getCurveByName SEC_p160k1 = CurveFP $ CurvePrime 213 0x00fffffffffffffffffffffffffffffffeffffac73 214 (CurveCommon 215 { ecc_a = 0x000000000000000000000000000000000000000000 216 , ecc_b = 0x000000000000000000000000000000000000000007 217 , ecc_g = Point 0x003b4c382ce37aa192a4019e763036f4f5dd4d7ebb 218 0x00938cf935318fdced6bc28286531733c3f03c4fee 219 , ecc_n = 0x0100000000000000000001b8fa16dfab9aca16b6b3 220 , ecc_h = 1 221 }) 222getCurveByName SEC_p160r1 = CurveFP $ CurvePrime 223 0x00ffffffffffffffffffffffffffffffff7fffffff 224 (CurveCommon 225 { ecc_a = 0x00ffffffffffffffffffffffffffffffff7ffffffc 226 , ecc_b = 0x001c97befc54bd7a8b65acf89f81d4d4adc565fa45 227 , ecc_g = Point 0x004a96b5688ef573284664698968c38bb913cbfc82 228 0x0023a628553168947d59dcc912042351377ac5fb32 229 , ecc_n = 0x0100000000000000000001f4c8f927aed3ca752257 230 , ecc_h = 1 231 }) 232getCurveByName SEC_p160r2 = CurveFP $ CurvePrime 233 0x00fffffffffffffffffffffffffffffffeffffac73 234 (CurveCommon 235 { ecc_a = 0x00fffffffffffffffffffffffffffffffeffffac70 236 , ecc_b = 0x00b4e134d3fb59eb8bab57274904664d5af50388ba 237 , ecc_g = Point 0x0052dcb034293a117e1f4ff11b30f7199d3144ce6d 238 0x00feaffef2e331f296e071fa0df9982cfea7d43f2e 239 , ecc_n = 0x0100000000000000000000351ee786a818f3a1a16b 240 , ecc_h = 1 241 }) 242getCurveByName SEC_p192k1 = CurveFP $ CurvePrime 243 0xfffffffffffffffffffffffffffffffffffffffeffffee37 244 (CurveCommon 245 { ecc_a = 0x000000000000000000000000000000000000000000000000 246 , ecc_b = 0x000000000000000000000000000000000000000000000003 247 , ecc_g = Point 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d 248 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d 249 , ecc_n = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d 250 , ecc_h = 1 251 }) 252getCurveByName SEC_p192r1 = CurveFP $ CurvePrime 253 0xfffffffffffffffffffffffffffffffeffffffffffffffff 254 (CurveCommon 255 { ecc_a = 0xfffffffffffffffffffffffffffffffefffffffffffffffc 256 , ecc_b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1 257 , ecc_g = Point 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012 258 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811 259 , ecc_n = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831 260 , ecc_h = 1 261 }) 262getCurveByName SEC_p224k1 = CurveFP $ CurvePrime 263 0x00fffffffffffffffffffffffffffffffffffffffffffffffeffffe56d 264 (CurveCommon 265 { ecc_a = 0x0000000000000000000000000000000000000000000000000000000000 266 , ecc_b = 0x0000000000000000000000000000000000000000000000000000000005 267 , ecc_g = Point 0x00a1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c 268 0x007e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5 269 , ecc_n = 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 270 , ecc_h = 1 271 }) 272getCurveByName SEC_p224r1 = CurveFP $ CurvePrime 273 0xffffffffffffffffffffffffffffffff000000000000000000000001 274 (CurveCommon 275 { ecc_a = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe 276 , ecc_b = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4 277 , ecc_g = Point 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21 278 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34 279 , ecc_n = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d 280 , ecc_h = 1 281 }) 282getCurveByName SEC_p256k1 = CurveFP $ CurvePrime 283 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f 284 (CurveCommon 285 { ecc_a = 0x0000000000000000000000000000000000000000000000000000000000000000 286 , ecc_b = 0x0000000000000000000000000000000000000000000000000000000000000007 287 , ecc_g = Point 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 288 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8 289 , ecc_n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 290 , ecc_h = 1 291 }) 292getCurveByName SEC_p256r1 = CurveFP $ CurvePrime 293 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff 294 (CurveCommon 295 { ecc_a = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc 296 , ecc_b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b 297 , ecc_g = Point 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 298 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 299 , ecc_n = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 300 , ecc_h = 1 301 }) 302getCurveByName SEC_p384r1 = CurveFP $ CurvePrime 303 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff 304 (CurveCommon 305 { ecc_a = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc 306 , ecc_b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef 307 , ecc_g = Point 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7 308 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f 309 , ecc_n = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973 310 , ecc_h = 1 311 }) 312getCurveByName SEC_p521r1 = CurveFP $ CurvePrime 313 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 314 (CurveCommon 315 { ecc_a = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc 316 , ecc_b = 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00 317 , ecc_g = Point 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66 318 0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650 319 , ecc_n = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409 320 , ecc_h = 1 321 }) 322getCurveByName SEC_t113r1 = CurveF2m $ CurveBinary 323 0x020000000000000000000000000201 324 (CurveCommon 325 { ecc_a = 0x003088250ca6e7c7fe649ce85820f7 326 , ecc_b = 0x00e8bee4d3e2260744188be0e9c723 327 , ecc_g = Point 0x009d73616f35f4ab1407d73562c10f 328 0x00a52830277958ee84d1315ed31886 329 , ecc_n = 0x0100000000000000d9ccec8a39e56f 330 , ecc_h = 2 331 }) 332getCurveByName SEC_t113r2 = CurveF2m $ CurveBinary 333 0x020000000000000000000000000201 334 (CurveCommon 335 { ecc_a = 0x00689918dbec7e5a0dd6dfc0aa55c7 336 , ecc_b = 0x0095e9a9ec9b297bd4bf36e059184f 337 , ecc_g = Point 0x01a57a6a7b26ca5ef52fcdb8164797 338 0x00b3adc94ed1fe674c06e695baba1d 339 , ecc_n = 0x010000000000000108789b2496af93 340 , ecc_h = 2 341 }) 342getCurveByName SEC_t131r1 = CurveF2m $ CurveBinary 343 0x080000000000000000000000000000010d 344 (CurveCommon 345 { ecc_a = 0x07a11b09a76b562144418ff3ff8c2570b8 346 , ecc_b = 0x0217c05610884b63b9c6c7291678f9d341 347 , ecc_g = Point 0x0081baf91fdf9833c40f9c181343638399 348 0x078c6e7ea38c001f73c8134b1b4ef9e150 349 , ecc_n = 0x0400000000000000023123953a9464b54d 350 , ecc_h = 2 351 }) 352getCurveByName SEC_t131r2 = CurveF2m $ CurveBinary 353 0x080000000000000000000000000000010d 354 (CurveCommon 355 { ecc_a = 0x03e5a88919d7cafcbf415f07c2176573b2 356 , ecc_b = 0x04b8266a46c55657ac734ce38f018f2192 357 , ecc_g = Point 0x0356dcd8f2f95031ad652d23951bb366a8 358 0x0648f06d867940a5366d9e265de9eb240f 359 , ecc_n = 0x0400000000000000016954a233049ba98f 360 , ecc_h = 2 361 }) 362getCurveByName SEC_t163k1 = CurveF2m $ CurveBinary 363 0x0800000000000000000000000000000000000000c9 364 (CurveCommon 365 { ecc_a = 0x000000000000000000000000000000000000000001 366 , ecc_b = 0x000000000000000000000000000000000000000001 367 , ecc_g = Point 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8 368 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9 369 , ecc_n = 0x04000000000000000000020108a2e0cc0d99f8a5ef 370 , ecc_h = 2 371 }) 372getCurveByName SEC_t163r1 = CurveF2m $ CurveBinary 373 0x0800000000000000000000000000000000000000c9 374 (CurveCommon 375 { ecc_a = 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2 376 , ecc_b = 0x0713612dcddcb40aab946bda29ca91f73af958afd9 377 , ecc_g = Point 0x0369979697ab43897789566789567f787a7876a654 378 0x00435edb42efafb2989d51fefce3c80988f41ff883 379 , ecc_n = 0x03ffffffffffffffffffff48aab689c29ca710279b 380 , ecc_h = 2 381 }) 382getCurveByName SEC_t163r2 = CurveF2m $ CurveBinary 383 0x0800000000000000000000000000000000000000c9 384 (CurveCommon 385 { ecc_a = 0x000000000000000000000000000000000000000001 386 , ecc_b = 0x020a601907b8c953ca1481eb10512f78744a3205fd 387 , ecc_g = Point 0x03f0eba16286a2d57ea0991168d4994637e8343e36 388 0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1 389 , ecc_n = 0x040000000000000000000292fe77e70c12a4234c33 390 , ecc_h = 2 391 }) 392getCurveByName SEC_t193r1 = CurveF2m $ CurveBinary 393 0x02000000000000000000000000000000000000000000008001 394 (CurveCommon 395 { ecc_a = 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01 396 , ecc_b = 0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814 397 , ecc_g = Point 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1 398 0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05 399 , ecc_n = 0x01000000000000000000000000c7f34a778f443acc920eba49 400 , ecc_h = 2 401 }) 402getCurveByName SEC_t193r2 = CurveF2m $ CurveBinary 403 0x02000000000000000000000000000000000000000000008001 404 (CurveCommon 405 { ecc_a = 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b 406 , ecc_b = 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae 407 , ecc_g = Point 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f 408 0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c 409 , ecc_n = 0x010000000000000000000000015aab561b005413ccd4ee99d5 410 , ecc_h = 2 411 }) 412getCurveByName SEC_t233k1 = CurveF2m $ CurveBinary 413 0x020000000000000000000000000000000000000004000000000000000001 414 (CurveCommon 415 { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000 416 , ecc_b = 0x000000000000000000000000000000000000000000000000000000000001 417 , ecc_g = Point 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126 418 0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3 419 , ecc_n = 0x008000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf 420 , ecc_h = 4 421 }) 422getCurveByName SEC_t233r1 = CurveF2m $ CurveBinary 423 0x020000000000000000000000000000000000000004000000000000000001 424 (CurveCommon 425 { ecc_a = 0x000000000000000000000000000000000000000000000000000000000001 426 , ecc_b = 0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad 427 , ecc_g = Point 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b 428 0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052 429 , ecc_n = 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7 430 , ecc_h = 2 431 }) 432getCurveByName SEC_t239k1 = CurveF2m $ CurveBinary 433 0x800000000000000000004000000000000000000000000000000000000001 434 (CurveCommon 435 { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000 436 , ecc_b = 0x000000000000000000000000000000000000000000000000000000000001 437 , ecc_g = Point 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc 438 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca 439 , ecc_n = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5 440 , ecc_h = 4 441 }) 442getCurveByName SEC_t283k1 = CurveF2m $ CurveBinary 443 0x0800000000000000000000000000000000000000000000000000000000000000000010a1 444 (CurveCommon 445 { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000 446 , ecc_b = 0x000000000000000000000000000000000000000000000000000000000000000000000001 447 , ecc_g = Point 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836 448 0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259 449 , ecc_n = 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61 450 , ecc_h = 4 451 }) 452getCurveByName SEC_t283r1 = CurveF2m $ CurveBinary 453 0x0800000000000000000000000000000000000000000000000000000000000000000010a1 454 (CurveCommon 455 { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000001 456 , ecc_b = 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5 457 , ecc_g = Point 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053 458 0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4 459 , ecc_n = 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 460 , ecc_h = 2 461 }) 462getCurveByName SEC_t409k1 = CurveF2m $ CurveBinary 463 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 464 (CurveCommon 465 { ecc_a = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 466 , ecc_b = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 467 , ecc_g = Point 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746 468 0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b 469 , ecc_n = 0x007ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf 470 , ecc_h = 4 471 }) 472getCurveByName SEC_t409r1 = CurveF2m $ CurveBinary 473 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 474 (CurveCommon 475 { ecc_a = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 476 , ecc_b = 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f 477 , ecc_g = Point 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7 478 0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706 479 , ecc_n = 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 480 , ecc_h = 2 481 }) 482getCurveByName SEC_t571k1 = CurveF2m $ CurveBinary 483 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 484 (CurveCommon 485 { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 486 , ecc_b = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 487 , ecc_g = Point 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972 488 0x0349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3 489 , ecc_n = 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001 490 , ecc_h = 4 491 }) 492getCurveByName SEC_t571r1 = CurveF2m $ CurveBinary 493 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 494 (CurveCommon 495 { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 496 , ecc_b = 0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a 497 , ecc_g = Point 0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19 498 0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b 499 , ecc_n = 0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47 500 , ecc_h = 2 501 }) 502