{-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module      : Crypto.PubKey.ECC.types
-- License     : BSD-style
-- Maintainer  : Vincent Hanquez <vincent@snarc.org>
-- Stability   : Experimental
-- Portability : Excellent
--
-- references:
--   <https://tools.ietf.org/html/rfc5915>
--
module Crypto.PubKey.ECC.Types
    ( Curve(..)
    , Point(..)
    , PublicPoint
    , PrivateNumber
    , CurveBinary(..)
    , CurvePrime(..)
    , common_curve
    , curveSizeBits
    , ecc_fx
    , ecc_p
    , CurveCommon(..)
    -- * recommended curves definition
    , CurveName(..)
    , getCurveByName
    ) where

import           Data.Data
import           Crypto.Internal.Imports
import           Crypto.Number.Basic (numBits)

-- | Define either a binary curve or a prime curve.
data Curve = CurveF2m CurveBinary -- ^ 𝔽(2^m)
           | CurveFP  CurvePrime  -- ^ 𝔽p
           deriving (Show,Read,Eq,Data,Typeable)

-- | ECC Public Point
type PublicPoint = Point

-- | ECC Private Number
type PrivateNumber = Integer

-- | Define a point on a curve.
data Point = Point Integer Integer
           | PointO -- ^ Point at Infinity
           deriving (Show,Read,Eq,Data,Typeable)

instance NFData Point where
    rnf (Point x y) = x `seq` y `seq` ()
    rnf PointO = ()

-- | Define an elliptic curve in 𝔽(2^m).
-- The firt parameter is the Integer representatioin of the irreducible polynomial f(x).
data CurveBinary = CurveBinary Integer CurveCommon
    deriving (Show,Read,Eq,Data,Typeable)

instance NFData CurveBinary where
    rnf (CurveBinary i cc) = i `seq` cc `seq` ()

-- | Define an elliptic curve in 𝔽p.
-- The first parameter is the Prime Number.
data CurvePrime = CurvePrime Integer CurveCommon
    deriving (Show,Read,Eq,Data,Typeable)

-- | Parameters in common between binary and prime curves.
common_curve :: Curve -> CurveCommon
common_curve (CurveF2m (CurveBinary _ cc)) = cc
common_curve (CurveFP  (CurvePrime  _ cc)) = cc

-- | Irreducible polynomial representing the characteristic of a CurveBinary.
ecc_fx :: CurveBinary -> Integer
ecc_fx (CurveBinary fx _) = fx

-- | Prime number representing the characteristic of a CurvePrime.
ecc_p :: CurvePrime -> Integer
ecc_p (CurvePrime p _) = p

-- | Define common parameters in a curve definition
-- of the form: y^2 = x^3 + ax + b.
data CurveCommon = CurveCommon
    { ecc_a :: Integer -- ^ curve parameter a
    , ecc_b :: Integer -- ^ curve parameter b
    , ecc_g :: Point   -- ^ base point
    , ecc_n :: Integer -- ^ order of G
    , ecc_h :: Integer -- ^ cofactor
    } deriving (Show,Read,Eq,Data,Typeable)

-- | Define names for known recommended curves.
data CurveName =
      SEC_p112r1
    | SEC_p112r2
    | SEC_p128r1
    | SEC_p128r2
    | SEC_p160k1
    | SEC_p160r1
    | SEC_p160r2
    | SEC_p192k1
    | SEC_p192r1 -- aka prime192v1
    | SEC_p224k1
    | SEC_p224r1
    | SEC_p256k1
    | SEC_p256r1 -- aka prime256v1
    | SEC_p384r1
    | SEC_p521r1
    | SEC_t113r1
    | SEC_t113r2
    | SEC_t131r1
    | SEC_t131r2
    | SEC_t163k1
    | SEC_t163r1
    | SEC_t163r2
    | SEC_t193r1
    | SEC_t193r2
    | SEC_t233k1 -- aka NIST K-233
    | SEC_t233r1
    | SEC_t239k1
    | SEC_t283k1
    | SEC_t283r1
    | SEC_t409k1
    | SEC_t409r1
    | SEC_t571k1
    | SEC_t571r1
    deriving (Show,Read,Eq,Ord,Enum,Bounded,Data,Typeable)

{-
curvesOIDs :: [ (CurveName, [Integer]) ]
curvesOIDs =
    [ (SEC_p112r1, [1,3,132,0,6])
    , (SEC_p112r2, [1,3,132,0,7])
    , (SEC_p128r1, [1,3,132,0,28])
    , (SEC_p128r2, [1,3,132,0,29])
    , (SEC_p160k1, [1,3,132,0,9])
    , (SEC_p160r1, [1,3,132,0,8])
    , (SEC_p160r2, [1,3,132,0,30])
    , (SEC_p192k1, [1,3,132,0,31])
    , (SEC_p192r1, [1,2,840,10045,3,1,1])
    , (SEC_p224k1, [1,3,132,0,32])
    , (SEC_p224r1, [1,3,132,0,33])
    , (SEC_p256k1, [1,3,132,0,10])
    , (SEC_p256r1, [1,2,840,10045,3,1,7])
    , (SEC_p384r1, [1,3,132,0,34])
    , (SEC_p521r1, [1,3,132,0,35])
    , (SEC_t113r1, [1,3,132,0,4])
    , (SEC_t113r2, [1,3,132,0,5])
    , (SEC_t131r1, [1,3,132,0,22])
    , (SEC_t131r2, [1,3,132,0,23])
    , (SEC_t163k1, [1,3,132,0,1])
    , (SEC_t163r1, [1,3,132,0,2])
    , (SEC_t163r2, [1,3,132,0,15])
    , (SEC_t193r1, [1,3,132,0,24])
    , (SEC_t193r2, [1,3,132,0,25])
    , (SEC_t233k1, [1,3,132,0,26])
    , (SEC_t233r1, [1,3,132,0,27])
    , (SEC_t239k1, [1,3,132,0,3])
    , (SEC_t283k1, [1,3,132,0,16])
    , (SEC_t283r1, [1,3,132,0,17])
    , (SEC_t409k1, [1,3,132,0,36])
    , (SEC_t409r1, [1,3,132,0,37])
    , (SEC_t571k1, [1,3,132,0,38])
    , (SEC_t571r1, [1,3,132,0,39])
    ]
-}

-- | get the size of the curve in bits
curveSizeBits :: Curve -> Int
curveSizeBits (CurveFP  c) = numBits (ecc_p  c)
curveSizeBits (CurveF2m c) = numBits (ecc_fx c) - 1

-- | Get the curve definition associated with a recommended known curve name.
getCurveByName :: CurveName -> Curve
getCurveByName SEC_p112r1 = CurveFP  $ CurvePrime
    0xdb7c2abf62e35e668076bead208b
    (CurveCommon
        { ecc_a = 0xdb7c2abf62e35e668076bead2088
        , ecc_b = 0x659ef8ba043916eede8911702b22
        , ecc_g = Point 0x09487239995a5ee76b55f9c2f098
                        0xa89ce5af8724c0a23e0e0ff77500
        , ecc_n = 0xdb7c2abf62e35e7628dfac6561c5
        , ecc_h = 1
        })
getCurveByName SEC_p112r2 = CurveFP  $ CurvePrime
    0xdb7c2abf62e35e668076bead208b
    (CurveCommon
        { ecc_a = 0x6127c24c05f38a0aaaf65c0ef02c
        , ecc_b = 0x51def1815db5ed74fcc34c85d709
        , ecc_g = Point 0x4ba30ab5e892b4e1649dd0928643
                        0xadcd46f5882e3747def36e956e97
        , ecc_n = 0x36df0aafd8b8d7597ca10520d04b
        , ecc_h = 4
        })
getCurveByName SEC_p128r1 = CurveFP  $ CurvePrime
    0xfffffffdffffffffffffffffffffffff
    (CurveCommon
        { ecc_a = 0xfffffffdfffffffffffffffffffffffc
        , ecc_b = 0xe87579c11079f43dd824993c2cee5ed3
        , ecc_g = Point 0x161ff7528b899b2d0c28607ca52c5b86
                        0xcf5ac8395bafeb13c02da292dded7a83
        , ecc_n = 0xfffffffe0000000075a30d1b9038a115
        , ecc_h = 1
        })
getCurveByName SEC_p128r2 = CurveFP  $ CurvePrime
    0xfffffffdffffffffffffffffffffffff
    (CurveCommon
        { ecc_a = 0xd6031998d1b3bbfebf59cc9bbff9aee1
        , ecc_b = 0x5eeefca380d02919dc2c6558bb6d8a5d
        , ecc_g = Point 0x7b6aa5d85e572983e6fb32a7cdebc140
                        0x27b6916a894d3aee7106fe805fc34b44
        , ecc_n = 0x3fffffff7fffffffbe0024720613b5a3
        , ecc_h = 4
        })
getCurveByName SEC_p160k1 = CurveFP  $ CurvePrime
    0x00fffffffffffffffffffffffffffffffeffffac73
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000
        , ecc_b = 0x000000000000000000000000000000000000000007
        , ecc_g = Point 0x003b4c382ce37aa192a4019e763036f4f5dd4d7ebb
                        0x00938cf935318fdced6bc28286531733c3f03c4fee
        , ecc_n = 0x0100000000000000000001b8fa16dfab9aca16b6b3
        , ecc_h = 1
        })
getCurveByName SEC_p160r1 = CurveFP  $ CurvePrime
    0x00ffffffffffffffffffffffffffffffff7fffffff
    (CurveCommon
        { ecc_a = 0x00ffffffffffffffffffffffffffffffff7ffffffc
        , ecc_b = 0x001c97befc54bd7a8b65acf89f81d4d4adc565fa45
        , ecc_g = Point 0x004a96b5688ef573284664698968c38bb913cbfc82
                        0x0023a628553168947d59dcc912042351377ac5fb32
        , ecc_n = 0x0100000000000000000001f4c8f927aed3ca752257
        , ecc_h = 1
        })
getCurveByName SEC_p160r2 = CurveFP  $ CurvePrime
    0x00fffffffffffffffffffffffffffffffeffffac73
    (CurveCommon
        { ecc_a = 0x00fffffffffffffffffffffffffffffffeffffac70
        , ecc_b = 0x00b4e134d3fb59eb8bab57274904664d5af50388ba
        , ecc_g = Point 0x0052dcb034293a117e1f4ff11b30f7199d3144ce6d
                        0x00feaffef2e331f296e071fa0df9982cfea7d43f2e
        , ecc_n = 0x0100000000000000000000351ee786a818f3a1a16b
        , ecc_h = 1
        })
getCurveByName SEC_p192k1 = CurveFP  $ CurvePrime
    0xfffffffffffffffffffffffffffffffffffffffeffffee37
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000
        , ecc_b = 0x000000000000000000000000000000000000000000000003
        , ecc_g = Point 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d
                        0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d
        , ecc_n = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d
        , ecc_h = 1
        })
getCurveByName SEC_p192r1 = CurveFP  $ CurvePrime
    0xfffffffffffffffffffffffffffffffeffffffffffffffff
    (CurveCommon
        { ecc_a = 0xfffffffffffffffffffffffffffffffefffffffffffffffc
        , ecc_b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
        , ecc_g = Point 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
                        0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
        , ecc_n = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831
        , ecc_h = 1
        })
getCurveByName SEC_p224k1 = CurveFP  $ CurvePrime
    0x00fffffffffffffffffffffffffffffffffffffffffffffffeffffe56d
    (CurveCommon
        { ecc_a = 0x0000000000000000000000000000000000000000000000000000000000
        , ecc_b = 0x0000000000000000000000000000000000000000000000000000000005
        , ecc_g = Point 0x00a1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c
                        0x007e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5
        , ecc_n = 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7
        , ecc_h = 1
        })
getCurveByName SEC_p224r1 = CurveFP  $ CurvePrime
    0xffffffffffffffffffffffffffffffff000000000000000000000001
    (CurveCommon
        { ecc_a = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe
        , ecc_b = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
        , ecc_g = Point 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
                        0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
        , ecc_n = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d
        , ecc_h = 1
        })
getCurveByName SEC_p256k1 = CurveFP  $ CurvePrime
    0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
    (CurveCommon
        { ecc_a = 0x0000000000000000000000000000000000000000000000000000000000000000
        , ecc_b = 0x0000000000000000000000000000000000000000000000000000000000000007
        , ecc_g = Point 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
                        0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
        , ecc_n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
        , ecc_h = 1
        })
getCurveByName SEC_p256r1 = CurveFP  $ CurvePrime
    0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
    (CurveCommon
        { ecc_a = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
        , ecc_b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
        , ecc_g = Point 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
                        0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
        , ecc_n = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
        , ecc_h = 1
        })
getCurveByName SEC_p384r1 = CurveFP  $ CurvePrime
    0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
    (CurveCommon
        { ecc_a = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc
        , ecc_b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
        , ecc_g = Point 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7
                        0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f
        , ecc_n = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973
        , ecc_h = 1
        })
getCurveByName SEC_p521r1 = CurveFP  $ CurvePrime
    0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
    (CurveCommon
        { ecc_a = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
        , ecc_b = 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
        , ecc_g = Point 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
                        0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650
        , ecc_n = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409
        , ecc_h = 1
        })
getCurveByName SEC_t113r1 = CurveF2m $ CurveBinary
    0x020000000000000000000000000201
    (CurveCommon
        { ecc_a = 0x003088250ca6e7c7fe649ce85820f7
        , ecc_b = 0x00e8bee4d3e2260744188be0e9c723
        , ecc_g = Point 0x009d73616f35f4ab1407d73562c10f
                        0x00a52830277958ee84d1315ed31886
        , ecc_n = 0x0100000000000000d9ccec8a39e56f
        , ecc_h = 2
        })
getCurveByName SEC_t113r2 = CurveF2m $ CurveBinary
    0x020000000000000000000000000201
    (CurveCommon
        { ecc_a = 0x00689918dbec7e5a0dd6dfc0aa55c7
        , ecc_b = 0x0095e9a9ec9b297bd4bf36e059184f
        , ecc_g = Point 0x01a57a6a7b26ca5ef52fcdb8164797
                        0x00b3adc94ed1fe674c06e695baba1d
        , ecc_n = 0x010000000000000108789b2496af93
        , ecc_h = 2
        })
getCurveByName SEC_t131r1 = CurveF2m $ CurveBinary
    0x080000000000000000000000000000010d
    (CurveCommon
        { ecc_a = 0x07a11b09a76b562144418ff3ff8c2570b8
        , ecc_b = 0x0217c05610884b63b9c6c7291678f9d341
        , ecc_g = Point 0x0081baf91fdf9833c40f9c181343638399
                        0x078c6e7ea38c001f73c8134b1b4ef9e150
        , ecc_n = 0x0400000000000000023123953a9464b54d
        , ecc_h = 2
        })
getCurveByName SEC_t131r2 = CurveF2m $ CurveBinary
    0x080000000000000000000000000000010d
    (CurveCommon
        { ecc_a = 0x03e5a88919d7cafcbf415f07c2176573b2
        , ecc_b = 0x04b8266a46c55657ac734ce38f018f2192
        , ecc_g = Point 0x0356dcd8f2f95031ad652d23951bb366a8
                        0x0648f06d867940a5366d9e265de9eb240f
        , ecc_n = 0x0400000000000000016954a233049ba98f
        , ecc_h = 2
        })
getCurveByName SEC_t163k1 = CurveF2m $ CurveBinary
    0x0800000000000000000000000000000000000000c9
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000001
        , ecc_b = 0x000000000000000000000000000000000000000001
        , ecc_g = Point 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8
                        0x0289070fb05d38ff58321f2e800536d538ccdaa3d9
        , ecc_n = 0x04000000000000000000020108a2e0cc0d99f8a5ef
        , ecc_h = 2
        })
getCurveByName SEC_t163r1 = CurveF2m $ CurveBinary
    0x0800000000000000000000000000000000000000c9
    (CurveCommon
        { ecc_a = 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2
        , ecc_b = 0x0713612dcddcb40aab946bda29ca91f73af958afd9
        , ecc_g = Point 0x0369979697ab43897789566789567f787a7876a654
                        0x00435edb42efafb2989d51fefce3c80988f41ff883
        , ecc_n = 0x03ffffffffffffffffffff48aab689c29ca710279b
        , ecc_h = 2
        })
getCurveByName SEC_t163r2 = CurveF2m $ CurveBinary
    0x0800000000000000000000000000000000000000c9
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000001
        , ecc_b = 0x020a601907b8c953ca1481eb10512f78744a3205fd
        , ecc_g = Point 0x03f0eba16286a2d57ea0991168d4994637e8343e36
                        0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1
        , ecc_n = 0x040000000000000000000292fe77e70c12a4234c33
        , ecc_h = 2
        })
getCurveByName SEC_t193r1 = CurveF2m $ CurveBinary
    0x02000000000000000000000000000000000000000000008001
    (CurveCommon
        { ecc_a = 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01
        , ecc_b = 0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814
        , ecc_g = Point 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1
                        0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05
        , ecc_n = 0x01000000000000000000000000c7f34a778f443acc920eba49
        , ecc_h = 2
        })
getCurveByName SEC_t193r2 = CurveF2m $ CurveBinary
    0x02000000000000000000000000000000000000000000008001
    (CurveCommon
        { ecc_a = 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b
        , ecc_b = 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae
        , ecc_g = Point 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f
                        0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c
        , ecc_n = 0x010000000000000000000000015aab561b005413ccd4ee99d5
        , ecc_h = 2
        })
getCurveByName SEC_t233k1 = CurveF2m $ CurveBinary
    0x020000000000000000000000000000000000000004000000000000000001
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000
        , ecc_b = 0x000000000000000000000000000000000000000000000000000000000001
        , ecc_g = Point 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126
                        0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3
        , ecc_n = 0x008000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf
        , ecc_h = 4
        })
getCurveByName SEC_t233r1 = CurveF2m $ CurveBinary
    0x020000000000000000000000000000000000000004000000000000000001
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000000000000001
        , ecc_b = 0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad
        , ecc_g = Point 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b
                        0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052
        , ecc_n = 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7
        , ecc_h = 2
        })
getCurveByName SEC_t239k1 = CurveF2m $ CurveBinary
    0x800000000000000000004000000000000000000000000000000000000001
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000
        , ecc_b = 0x000000000000000000000000000000000000000000000000000000000001
        , ecc_g = Point 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc
                        0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca
        , ecc_n = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5
        , ecc_h = 4
        })
getCurveByName SEC_t283k1 = CurveF2m $ CurveBinary
    0x0800000000000000000000000000000000000000000000000000000000000000000010a1
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000
        , ecc_b = 0x000000000000000000000000000000000000000000000000000000000000000000000001
        , ecc_g = Point 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836
                        0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259
        , ecc_n = 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61
        , ecc_h = 4
        })
getCurveByName SEC_t283r1 = CurveF2m $ CurveBinary
    0x0800000000000000000000000000000000000000000000000000000000000000000010a1
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000001
        , ecc_b = 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5
        , ecc_g = Point 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053
                        0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4
        , ecc_n = 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307
        , ecc_h = 2
        })
getCurveByName SEC_t409k1 = CurveF2m $ CurveBinary
    0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
    (CurveCommon
        { ecc_a = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
        , ecc_b = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
        , ecc_g = Point 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746
                        0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b
        , ecc_n = 0x007ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf
        , ecc_h = 4
        })
getCurveByName SEC_t409r1 = CurveF2m $ CurveBinary
    0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
    (CurveCommon
        { ecc_a = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
        , ecc_b = 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f
        , ecc_g = Point 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7
                        0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706
        , ecc_n = 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173
        , ecc_h = 2
        })
getCurveByName SEC_t571k1 = CurveF2m $ CurveBinary
    0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
        , ecc_b = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
        , ecc_g = Point 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972
                        0x0349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3
        , ecc_n = 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001
        , ecc_h = 4
        })
getCurveByName SEC_t571r1 = CurveF2m $ CurveBinary
    0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425
    (CurveCommon
        { ecc_a = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
        , ecc_b = 0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a
        , ecc_g = Point 0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19
                        0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b
        , ecc_n = 0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47
        , ecc_h = 2
        })