1{-# LANGUAGE DeriveDataTypeable #-} 2{-# LANGUAGE GeneralizedNewtypeDeriving #-} 3-- | 4-- Module : Crypto.ECC.Simple.Types 5-- License : BSD-style 6-- Maintainer : Vincent Hanquez <vincent@snarc.org> 7-- Stability : Experimental 8-- Portability : Excellent 9-- 10-- References: 11-- <https://tools.ietf.org/html/rfc5915> 12-- 13{-# OPTIONS_GHC -fno-warn-missing-signatures #-} 14module Crypto.ECC.Simple.Types 15 ( Curve(..) 16 , Point(..) 17 , Scalar(..) 18 , CurveType(..) 19 , CurveBinaryParam(..) 20 , CurvePrimeParam(..) 21 , curveSizeBits 22 , curveSizeBytes 23 , CurveParameters(..) 24 -- * Specific curves definition 25 , SEC_p112r1(..) 26 , SEC_p112r2(..) 27 , SEC_p128r1(..) 28 , SEC_p128r2(..) 29 , SEC_p160k1(..) 30 , SEC_p160r1(..) 31 , SEC_p160r2(..) 32 , SEC_p192k1(..) 33 , SEC_p192r1(..) -- aka prime192v1 34 , SEC_p224k1(..) 35 , SEC_p224r1(..) 36 , SEC_p256k1(..) 37 , SEC_p256r1(..) -- aka prime256v1 38 , SEC_p384r1(..) 39 , SEC_p521r1(..) 40 , SEC_t113r1(..) 41 , SEC_t113r2(..) 42 , SEC_t131r1(..) 43 , SEC_t131r2(..) 44 , SEC_t163k1(..) 45 , SEC_t163r1(..) 46 , SEC_t163r2(..) 47 , SEC_t193r1(..) 48 , SEC_t193r2(..) 49 , SEC_t233k1(..) -- aka NIST K-233 50 , SEC_t233r1(..) 51 , SEC_t239k1(..) 52 , SEC_t283k1(..) 53 , SEC_t283r1(..) 54 , SEC_t409k1(..) 55 , SEC_t409r1(..) 56 , SEC_t571k1(..) 57 , SEC_t571r1(..) 58 ) where 59 60import Data.Data 61import Crypto.Internal.Imports 62import Crypto.Number.Basic (numBits) 63 64class Curve curve where 65 curveParameters :: proxy curve -> CurveParameters curve 66 curveType :: proxy curve -> CurveType 67 68-- | get the size of the curve in bits 69curveSizeBits :: Curve curve => proxy curve -> Int 70curveSizeBits proxy = 71 case curveType proxy of 72 CurvePrime (CurvePrimeParam p) -> numBits p 73 CurveBinary (CurveBinaryParam c) -> numBits c - 1 74 75-- | get the size of the curve in bytes 76curveSizeBytes :: Curve curve => proxy curve -> Int 77curveSizeBytes proxy = (curveSizeBits proxy + 7) `div` 8 78 79-- | Define common parameters in a curve definition 80-- of the form: y^2 = x^3 + ax + b. 81data CurveParameters curve = CurveParameters 82 { curveEccA :: Integer -- ^ curve parameter a 83 , curveEccB :: Integer -- ^ curve parameter b 84 , curveEccG :: Point curve -- ^ base point 85 , curveEccN :: Integer -- ^ order of G 86 , curveEccH :: Integer -- ^ cofactor 87 } deriving (Show,Eq,Data) 88 89newtype CurveBinaryParam = CurveBinaryParam Integer 90 deriving (Show,Read,Eq,Data) 91 92newtype CurvePrimeParam = CurvePrimeParam Integer 93 deriving (Show,Read,Eq,Data) 94 95data CurveType = 96 CurveBinary CurveBinaryParam 97 | CurvePrime CurvePrimeParam 98 deriving (Show,Read,Eq,Data) 99 100-- | ECC Private Number 101newtype Scalar curve = Scalar Integer 102 deriving (Show,Read,Eq,Data,NFData) 103 104-- | Define a point on a curve. 105data Point curve = 106 Point Integer Integer 107 | PointO -- ^ Point at Infinity 108 deriving (Show,Read,Eq,Data) 109 110instance NFData (Point curve) where 111 rnf (Point x y) = x `seq` y `seq` () 112 rnf PointO = () 113 114data SEC_p112r1 = SEC_p112r1 deriving (Show,Read,Eq) 115data SEC_p112r2 = SEC_p112r2 deriving (Show,Read,Eq) 116data SEC_p128r1 = SEC_p128r1 deriving (Show,Read,Eq) 117data SEC_p128r2 = SEC_p128r2 deriving (Show,Read,Eq) 118data SEC_p160k1 = SEC_p160k1 deriving (Show,Read,Eq) 119data SEC_p160r1 = SEC_p160r1 deriving (Show,Read,Eq) 120data SEC_p160r2 = SEC_p160r2 deriving (Show,Read,Eq) 121data SEC_p192k1 = SEC_p192k1 deriving (Show,Read,Eq) 122data SEC_p192r1 = SEC_p192r1 deriving (Show,Read,Eq) 123data SEC_p224k1 = SEC_p224k1 deriving (Show,Read,Eq) 124data SEC_p224r1 = SEC_p224r1 deriving (Show,Read,Eq) 125data SEC_p256k1 = SEC_p256k1 deriving (Show,Read,Eq) 126data SEC_p256r1 = SEC_p256r1 deriving (Show,Read,Eq) 127data SEC_p384r1 = SEC_p384r1 deriving (Show,Read,Eq) 128data SEC_p521r1 = SEC_p521r1 deriving (Show,Read,Eq) 129data SEC_t113r1 = SEC_t113r1 deriving (Show,Read,Eq) 130data SEC_t113r2 = SEC_t113r2 deriving (Show,Read,Eq) 131data SEC_t131r1 = SEC_t131r1 deriving (Show,Read,Eq) 132data SEC_t131r2 = SEC_t131r2 deriving (Show,Read,Eq) 133data SEC_t163k1 = SEC_t163k1 deriving (Show,Read,Eq) 134data SEC_t163r1 = SEC_t163r1 deriving (Show,Read,Eq) 135data SEC_t163r2 = SEC_t163r2 deriving (Show,Read,Eq) 136data SEC_t193r1 = SEC_t193r1 deriving (Show,Read,Eq) 137data SEC_t193r2 = SEC_t193r2 deriving (Show,Read,Eq) 138data SEC_t233k1 = SEC_t233k1 deriving (Show,Read,Eq) 139data SEC_t233r1 = SEC_t233r1 deriving (Show,Read,Eq) 140data SEC_t239k1 = SEC_t239k1 deriving (Show,Read,Eq) 141data SEC_t283k1 = SEC_t283k1 deriving (Show,Read,Eq) 142data SEC_t283r1 = SEC_t283r1 deriving (Show,Read,Eq) 143data SEC_t409k1 = SEC_t409k1 deriving (Show,Read,Eq) 144data SEC_t409r1 = SEC_t409r1 deriving (Show,Read,Eq) 145data SEC_t571k1 = SEC_t571k1 deriving (Show,Read,Eq) 146data SEC_t571r1 = SEC_t571r1 deriving (Show,Read,Eq) 147 148-- | Define names for known recommended curves. 149instance Curve SEC_p112r1 where 150 curveType _ = typeSEC_p112r1 151 curveParameters _ = paramSEC_p112r1 152 153instance Curve SEC_p112r2 where 154 curveType _ = typeSEC_p112r2 155 curveParameters _ = paramSEC_p112r2 156 157instance Curve SEC_p128r1 where 158 curveType _ = typeSEC_p128r1 159 curveParameters _ = paramSEC_p128r1 160 161instance Curve SEC_p128r2 where 162 curveType _ = typeSEC_p128r2 163 curveParameters _ = paramSEC_p128r2 164 165instance Curve SEC_p160k1 where 166 curveType _ = typeSEC_p160k1 167 curveParameters _ = paramSEC_p160k1 168 169instance Curve SEC_p160r1 where 170 curveType _ = typeSEC_p160r1 171 curveParameters _ = paramSEC_p160r1 172 173instance Curve SEC_p160r2 where 174 curveType _ = typeSEC_p160r2 175 curveParameters _ = paramSEC_p160r2 176 177instance Curve SEC_p192k1 where 178 curveType _ = typeSEC_p192k1 179 curveParameters _ = paramSEC_p192k1 180 181instance Curve SEC_p192r1 where 182 curveType _ = typeSEC_p192r1 183 curveParameters _ = paramSEC_p192r1 184 185instance Curve SEC_p224k1 where 186 curveType _ = typeSEC_p224k1 187 curveParameters _ = paramSEC_p224k1 188 189instance Curve SEC_p224r1 where 190 curveType _ = typeSEC_p224r1 191 curveParameters _ = paramSEC_p224r1 192 193instance Curve SEC_p256k1 where 194 curveType _ = typeSEC_p256k1 195 curveParameters _ = paramSEC_p256k1 196 197instance Curve SEC_p256r1 where 198 curveType _ = typeSEC_p256r1 199 curveParameters _ = paramSEC_p256r1 200 201instance Curve SEC_p384r1 where 202 curveType _ = typeSEC_p384r1 203 curveParameters _ = paramSEC_p384r1 204 205instance Curve SEC_p521r1 where 206 curveType _ = typeSEC_p521r1 207 curveParameters _ = paramSEC_p521r1 208 209instance Curve SEC_t113r1 where 210 curveType _ = typeSEC_t113r1 211 curveParameters _ = paramSEC_t113r1 212 213instance Curve SEC_t113r2 where 214 curveType _ = typeSEC_t113r2 215 curveParameters _ = paramSEC_t113r2 216 217instance Curve SEC_t131r1 where 218 curveType _ = typeSEC_t131r1 219 curveParameters _ = paramSEC_t131r1 220 221instance Curve SEC_t131r2 where 222 curveType _ = typeSEC_t131r2 223 curveParameters _ = paramSEC_t131r2 224 225instance Curve SEC_t163k1 where 226 curveType _ = typeSEC_t163k1 227 curveParameters _ = paramSEC_t163k1 228 229instance Curve SEC_t163r1 where 230 curveType _ = typeSEC_t163r1 231 curveParameters _ = paramSEC_t163r1 232 233instance Curve SEC_t163r2 where 234 curveType _ = typeSEC_t163r2 235 curveParameters _ = paramSEC_t163r2 236 237instance Curve SEC_t193r1 where 238 curveType _ = typeSEC_t193r1 239 curveParameters _ = paramSEC_t193r1 240 241instance Curve SEC_t193r2 where 242 curveType _ = typeSEC_t193r2 243 curveParameters _ = paramSEC_t193r2 244 245instance Curve SEC_t233k1 where 246 curveType _ = typeSEC_t233k1 247 curveParameters _ = paramSEC_t233k1 248 249instance Curve SEC_t233r1 where 250 curveType _ = typeSEC_t233r1 251 curveParameters _ = paramSEC_t233r1 252 253instance Curve SEC_t239k1 where 254 curveType _ = typeSEC_t239k1 255 curveParameters _ = paramSEC_t239k1 256 257instance Curve SEC_t283k1 where 258 curveType _ = typeSEC_t283k1 259 curveParameters _ = paramSEC_t283k1 260 261instance Curve SEC_t283r1 where 262 curveType _ = typeSEC_t283r1 263 curveParameters _ = paramSEC_t283r1 264 265instance Curve SEC_t409k1 where 266 curveType _ = typeSEC_t409k1 267 curveParameters _ = paramSEC_t409k1 268 269instance Curve SEC_t409r1 where 270 curveType _ = typeSEC_t409r1 271 curveParameters _ = paramSEC_t409r1 272 273instance Curve SEC_t571k1 where 274 curveType _ = typeSEC_t571k1 275 curveParameters _ = paramSEC_t571k1 276 277instance Curve SEC_t571r1 where 278 curveType _ = typeSEC_t571r1 279 curveParameters _ = paramSEC_t571r1 280 281{- 282curvesOIDs :: [ (CurveName, [Integer]) ] 283curvesOIDs = 284 [ (SEC_p112r1, [1,3,132,0,6]) 285 , (SEC_p112r2, [1,3,132,0,7]) 286 , (SEC_p128r1, [1,3,132,0,28]) 287 , (SEC_p128r2, [1,3,132,0,29]) 288 , (SEC_p160k1, [1,3,132,0,9]) 289 , (SEC_p160r1, [1,3,132,0,8]) 290 , (SEC_p160r2, [1,3,132,0,30]) 291 , (SEC_p192k1, [1,3,132,0,31]) 292 , (SEC_p192r1, [1,2,840,10045,3,1,1]) 293 , (SEC_p224k1, [1,3,132,0,32]) 294 , (SEC_p224r1, [1,3,132,0,33]) 295 , (SEC_p256k1, [1,3,132,0,10]) 296 , (SEC_p256r1, [1,2,840,10045,3,1,7]) 297 , (SEC_p384r1, [1,3,132,0,34]) 298 , (SEC_p521r1, [1,3,132,0,35]) 299 , (SEC_t113r1, [1,3,132,0,4]) 300 , (SEC_t113r2, [1,3,132,0,5]) 301 , (SEC_t131r1, [1,3,132,0,22]) 302 , (SEC_t131r2, [1,3,132,0,23]) 303 , (SEC_t163k1, [1,3,132,0,1]) 304 , (SEC_t163r1, [1,3,132,0,2]) 305 , (SEC_t163r2, [1,3,132,0,15]) 306 , (SEC_t193r1, [1,3,132,0,24]) 307 , (SEC_t193r2, [1,3,132,0,25]) 308 , (SEC_t233k1, [1,3,132,0,26]) 309 , (SEC_t233r1, [1,3,132,0,27]) 310 , (SEC_t239k1, [1,3,132,0,3]) 311 , (SEC_t283k1, [1,3,132,0,16]) 312 , (SEC_t283r1, [1,3,132,0,17]) 313 , (SEC_t409k1, [1,3,132,0,36]) 314 , (SEC_t409r1, [1,3,132,0,37]) 315 , (SEC_t571k1, [1,3,132,0,38]) 316 , (SEC_t571r1, [1,3,132,0,39]) 317 ] 318-} 319 320typeSEC_p112r1 = CurvePrime $ CurvePrimeParam 0xdb7c2abf62e35e668076bead208b 321paramSEC_p112r1 = CurveParameters 322 { curveEccA = 0xdb7c2abf62e35e668076bead2088 323 , curveEccB = 0x659ef8ba043916eede8911702b22 324 , curveEccG = Point 0x09487239995a5ee76b55f9c2f098 325 0xa89ce5af8724c0a23e0e0ff77500 326 , curveEccN = 0xdb7c2abf62e35e7628dfac6561c5 327 , curveEccH = 1 328 } 329typeSEC_p112r2 = CurvePrime $ CurvePrimeParam 0xdb7c2abf62e35e668076bead208b 330paramSEC_p112r2 = CurveParameters 331 { curveEccA = 0x6127c24c05f38a0aaaf65c0ef02c 332 , curveEccB = 0x51def1815db5ed74fcc34c85d709 333 , curveEccG = Point 0x4ba30ab5e892b4e1649dd0928643 334 0xadcd46f5882e3747def36e956e97 335 , curveEccN = 0x36df0aafd8b8d7597ca10520d04b 336 , curveEccH = 4 337 } 338typeSEC_p128r1 = CurvePrime $ CurvePrimeParam 0xfffffffdffffffffffffffffffffffff 339paramSEC_p128r1 = CurveParameters 340 { curveEccA = 0xfffffffdfffffffffffffffffffffffc 341 , curveEccB = 0xe87579c11079f43dd824993c2cee5ed3 342 , curveEccG = Point 0x161ff7528b899b2d0c28607ca52c5b86 343 0xcf5ac8395bafeb13c02da292dded7a83 344 , curveEccN = 0xfffffffe0000000075a30d1b9038a115 345 , curveEccH = 1 346 } 347typeSEC_p128r2 = CurvePrime $ CurvePrimeParam 0xfffffffdffffffffffffffffffffffff 348paramSEC_p128r2 = CurveParameters 349 { curveEccA = 0xd6031998d1b3bbfebf59cc9bbff9aee1 350 , curveEccB = 0x5eeefca380d02919dc2c6558bb6d8a5d 351 , curveEccG = Point 0x7b6aa5d85e572983e6fb32a7cdebc140 352 0x27b6916a894d3aee7106fe805fc34b44 353 , curveEccN = 0x3fffffff7fffffffbe0024720613b5a3 354 , curveEccH = 4 355 } 356typeSEC_p160k1 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffeffffac73 357paramSEC_p160k1 = CurveParameters 358 { curveEccA = 0x000000000000000000000000000000000000000000 359 , curveEccB = 0x000000000000000000000000000000000000000007 360 , curveEccG = Point 0x003b4c382ce37aa192a4019e763036f4f5dd4d7ebb 361 0x00938cf935318fdced6bc28286531733c3f03c4fee 362 , curveEccN = 0x0100000000000000000001b8fa16dfab9aca16b6b3 363 , curveEccH = 1 364 } 365typeSEC_p160r1 = CurvePrime $ CurvePrimeParam 0x00ffffffffffffffffffffffffffffffff7fffffff 366paramSEC_p160r1 = CurveParameters 367 { curveEccA = 0x00ffffffffffffffffffffffffffffffff7ffffffc 368 , curveEccB = 0x001c97befc54bd7a8b65acf89f81d4d4adc565fa45 369 , curveEccG = Point 0x004a96b5688ef573284664698968c38bb913cbfc82 370 0x0023a628553168947d59dcc912042351377ac5fb32 371 , curveEccN = 0x0100000000000000000001f4c8f927aed3ca752257 372 , curveEccH = 1 373 } 374typeSEC_p160r2 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffeffffac73 375paramSEC_p160r2 = CurveParameters 376 { curveEccA = 0x00fffffffffffffffffffffffffffffffeffffac70 377 , curveEccB = 0x00b4e134d3fb59eb8bab57274904664d5af50388ba 378 , curveEccG = Point 0x0052dcb034293a117e1f4ff11b30f7199d3144ce6d 379 0x00feaffef2e331f296e071fa0df9982cfea7d43f2e 380 , curveEccN = 0x0100000000000000000000351ee786a818f3a1a16b 381 , curveEccH = 1 382 } 383typeSEC_p192k1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffeffffee37 384paramSEC_p192k1 = CurveParameters 385 { curveEccA = 0x000000000000000000000000000000000000000000000000 386 , curveEccB = 0x000000000000000000000000000000000000000000000003 387 , curveEccG = Point 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d 388 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d 389 , curveEccN = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d 390 , curveEccH = 1 391 } 392typeSEC_p192r1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffeffffffffffffffff 393paramSEC_p192r1 = CurveParameters 394 { curveEccA = 0xfffffffffffffffffffffffffffffffefffffffffffffffc 395 , curveEccB = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1 396 , curveEccG = Point 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012 397 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811 398 , curveEccN = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831 399 , curveEccH = 1 400 } 401typeSEC_p224k1 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffffffffffffffffffeffffe56d 402paramSEC_p224k1 = CurveParameters 403 { curveEccA = 0x0000000000000000000000000000000000000000000000000000000000 404 , curveEccB = 0x0000000000000000000000000000000000000000000000000000000005 405 , curveEccG = Point 0x00a1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c 406 0x007e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5 407 , curveEccN = 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 408 , curveEccH = 1 409 } 410typeSEC_p224r1 = CurvePrime $ CurvePrimeParam 0xffffffffffffffffffffffffffffffff000000000000000000000001 411paramSEC_p224r1 = CurveParameters 412 { curveEccA = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe 413 , curveEccB = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4 414 , curveEccG = Point 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21 415 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34 416 , curveEccN = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d 417 , curveEccH = 1 418 } 419typeSEC_p256k1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f 420paramSEC_p256k1 = CurveParameters 421 { curveEccA = 0x0000000000000000000000000000000000000000000000000000000000000000 422 , curveEccB = 0x0000000000000000000000000000000000000000000000000000000000000007 423 , curveEccG = Point 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 424 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8 425 , curveEccN = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 426 , curveEccH = 1 427 } 428typeSEC_p256r1 = CurvePrime $ CurvePrimeParam 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff 429paramSEC_p256r1 = CurveParameters 430 { curveEccA = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc 431 , curveEccB = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b 432 , curveEccG = Point 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 433 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 434 , curveEccN = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 435 , curveEccH = 1 436 } 437typeSEC_p384r1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff 438paramSEC_p384r1 = CurveParameters 439 { curveEccA = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc 440 , curveEccB = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef 441 , curveEccG = Point 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7 442 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f 443 , curveEccN = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973 444 , curveEccH = 1 445 } 446typeSEC_p521r1 = CurvePrime $ CurvePrimeParam 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 447paramSEC_p521r1 = CurveParameters 448 { curveEccA = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc 449 , curveEccB = 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00 450 , curveEccG = Point 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66 451 0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650 452 , curveEccN = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409 453 , curveEccH = 1 454 } 455typeSEC_t113r1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000201 456paramSEC_t113r1 = CurveParameters 457 { curveEccA = 0x003088250ca6e7c7fe649ce85820f7 458 , curveEccB = 0x00e8bee4d3e2260744188be0e9c723 459 , curveEccG = Point 0x009d73616f35f4ab1407d73562c10f 460 0x00a52830277958ee84d1315ed31886 461 , curveEccN = 0x0100000000000000d9ccec8a39e56f 462 , curveEccH = 2 463 } 464typeSEC_t113r2 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000201 465paramSEC_t113r2 = CurveParameters 466 { curveEccA = 0x00689918dbec7e5a0dd6dfc0aa55c7 467 , curveEccB = 0x0095e9a9ec9b297bd4bf36e059184f 468 , curveEccG = Point 0x01a57a6a7b26ca5ef52fcdb8164797 469 0x00b3adc94ed1fe674c06e695baba1d 470 , curveEccN = 0x010000000000000108789b2496af93 471 , curveEccH = 2 472 } 473typeSEC_t131r1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000010d 474paramSEC_t131r1 = CurveParameters 475 { curveEccA = 0x07a11b09a76b562144418ff3ff8c2570b8 476 , curveEccB = 0x0217c05610884b63b9c6c7291678f9d341 477 , curveEccG = Point 0x0081baf91fdf9833c40f9c181343638399 478 0x078c6e7ea38c001f73c8134b1b4ef9e150 479 , curveEccN = 0x0400000000000000023123953a9464b54d 480 , curveEccH = 2 481 } 482typeSEC_t131r2 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000010d 483paramSEC_t131r2 = CurveParameters 484 { curveEccA = 0x03e5a88919d7cafcbf415f07c2176573b2 485 , curveEccB = 0x04b8266a46c55657ac734ce38f018f2192 486 , curveEccG = Point 0x0356dcd8f2f95031ad652d23951bb366a8 487 0x0648f06d867940a5366d9e265de9eb240f 488 , curveEccN = 0x0400000000000000016954a233049ba98f 489 , curveEccH = 2 490 } 491typeSEC_t163k1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9 492paramSEC_t163k1 = CurveParameters 493 { curveEccA = 0x000000000000000000000000000000000000000001 494 , curveEccB = 0x000000000000000000000000000000000000000001 495 , curveEccG = Point 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8 496 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9 497 , curveEccN = 0x04000000000000000000020108a2e0cc0d99f8a5ef 498 , curveEccH = 2 499 } 500typeSEC_t163r1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9 501paramSEC_t163r1 = CurveParameters 502 { curveEccA = 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2 503 , curveEccB = 0x0713612dcddcb40aab946bda29ca91f73af958afd9 504 , curveEccG = Point 0x0369979697ab43897789566789567f787a7876a654 505 0x00435edb42efafb2989d51fefce3c80988f41ff883 506 , curveEccN = 0x03ffffffffffffffffffff48aab689c29ca710279b 507 , curveEccH = 2 508 } 509typeSEC_t163r2 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9 510paramSEC_t163r2 = CurveParameters 511 { curveEccA = 0x000000000000000000000000000000000000000001 512 , curveEccB = 0x020a601907b8c953ca1481eb10512f78744a3205fd 513 , curveEccG = Point 0x03f0eba16286a2d57ea0991168d4994637e8343e36 514 0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1 515 , curveEccN = 0x040000000000000000000292fe77e70c12a4234c33 516 , curveEccH = 2 517 } 518typeSEC_t193r1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000008001 519paramSEC_t193r1 = CurveParameters 520 { curveEccA = 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01 521 , curveEccB = 0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814 522 , curveEccG = Point 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1 523 0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05 524 , curveEccN = 0x01000000000000000000000000c7f34a778f443acc920eba49 525 , curveEccH = 2 526 } 527typeSEC_t193r2 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000008001 528paramSEC_t193r2 = CurveParameters 529 { curveEccA = 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b 530 , curveEccB = 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae 531 , curveEccG = Point 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f 532 0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c 533 , curveEccN = 0x010000000000000000000000015aab561b005413ccd4ee99d5 534 , curveEccH = 2 535 } 536typeSEC_t233k1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000000000000000004000000000000000001 537paramSEC_t233k1 = CurveParameters 538 { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000 539 , curveEccB = 0x000000000000000000000000000000000000000000000000000000000001 540 , curveEccG = Point 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126 541 0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3 542 , curveEccN = 0x008000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf 543 , curveEccH = 4 544 } 545typeSEC_t233r1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000000000000000004000000000000000001 546paramSEC_t233r1 = CurveParameters 547 { curveEccA = 0x000000000000000000000000000000000000000000000000000000000001 548 , curveEccB = 0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad 549 , curveEccG = Point 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b 550 0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052 551 , curveEccN = 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7 552 , curveEccH = 2 553 } 554typeSEC_t239k1 = CurveBinary $ CurveBinaryParam 0x800000000000000000004000000000000000000000000000000000000001 555paramSEC_t239k1 = CurveParameters 556 { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000 557 , curveEccB = 0x000000000000000000000000000000000000000000000000000000000001 558 , curveEccG = Point 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc 559 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca 560 , curveEccN = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5 561 , curveEccH = 4 562 } 563typeSEC_t283k1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000000000000000000000000000000010a1 564paramSEC_t283k1 = CurveParameters 565 { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000 566 , curveEccB = 0x000000000000000000000000000000000000000000000000000000000000000000000001 567 , curveEccG = Point 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836 568 0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259 569 , curveEccN = 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61 570 , curveEccH = 4 571 } 572typeSEC_t283r1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000000000000000000000000000000010a1 573paramSEC_t283r1 = CurveParameters 574 { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000001 575 , curveEccB = 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5 576 , curveEccG = Point 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053 577 0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4 578 , curveEccN = 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 579 , curveEccH = 2 580 } 581typeSEC_t409k1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 582paramSEC_t409k1 = CurveParameters 583 { curveEccA = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 584 , curveEccB = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 585 , curveEccG = Point 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746 586 0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b 587 , curveEccN = 0x007ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf 588 , curveEccH = 4 589 } 590typeSEC_t409r1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 591paramSEC_t409r1 = CurveParameters 592 { curveEccA = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 593 , curveEccB = 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f 594 , curveEccG = Point 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7 595 0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706 596 , curveEccN = 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 597 , curveEccH = 2 598 } 599typeSEC_t571k1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 600paramSEC_t571k1 = CurveParameters 601 { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 602 , curveEccB = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 603 , curveEccG = Point 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972 604 0x0349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3 605 , curveEccN = 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001 606 , curveEccH = 4 607 } 608typeSEC_t571r1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 609paramSEC_t571r1 = CurveParameters 610 { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 611 , curveEccB = 0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a 612 , curveEccG = Point 0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19 613 0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b 614 , curveEccN = 0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47 615 , curveEccH = 2 616 } 617