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

    import Data.Data
    import Data.Tuple (swap)
    import Data.ASN1.OID

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    data Curve = CurveF2m CurveBinary -- ^ 𝔽(2^m)
               | CurveFP  CurvePrime  -- ^ 𝔽p
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    -- | 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
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    -- The firt parameter is the Integer representatioin of the irreducible polynomial f(x).
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    -- | Define an elliptic curve in 𝔽p.
    -- The first parameter is the Prime Number.
    data CurvePrime = CurvePrime Integer CurveCommon
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    Data,Typeable)

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

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

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

    -- | Define common parameters in a curve definition
    -- of the form: y^2 = x^3 + ax + b.
    data CurveCommon = CurveCommon
        { CurveCommon -> Integer
    ecc_a :: Integer -- ^ curve parameter a
        , CurveCommon -> Integer
    ecc_b :: Integer -- ^ curve parameter b
        , CurveCommon -> Point
    ecc_g :: Point   -- ^ base point
        , CurveCommon -> Integer
    ecc_n :: Integer -- ^ order of G
        , CurveCommon -> Integer
    ecc_h :: Integer -- ^ cofactor
        } deriving (Int -> CurveCommon -> ShowS
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    (forall d. Data d => c (t d)) -> Maybe (c CurveCommon)
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c CurveCommon)
    $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c CurveCommon)
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c CurveCommon)
    $cgmapT :: (forall b. Data b => b -> b) -> CurveCommon -> CurveCommon
    gmapT :: (forall b. Data b => b -> b) -> CurveCommon -> CurveCommon
    $cgmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveCommon -> r
    gmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveCommon -> r
    $cgmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveCommon -> r
    gmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveCommon -> r
    $cgmapQ :: forall u. (forall d. Data d => d -> u) -> CurveCommon -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> CurveCommon -> [u]
    $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CurveCommon -> u
    gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CurveCommon -> u
    $cgmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CurveCommon -> m CurveCommon
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CurveCommon -> m CurveCommon
    $cgmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveCommon -> m CurveCommon
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveCommon -> m CurveCommon
    $cgmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveCommon -> m CurveCommon
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveCommon -> m CurveCommon
    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 (Int -> CurveName -> ShowS
    [CurveName] -> ShowS
    CurveName -> String
    (Int -> CurveName -> ShowS)
    -> (CurveName -> String)
    -> ([CurveName] -> ShowS)
    -> Show CurveName
    forall a.
    (Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
    $cshowsPrec :: Int -> CurveName -> ShowS
    showsPrec :: Int -> CurveName -> ShowS
    $cshow :: CurveName -> String
    show :: CurveName -> String
    $cshowList :: [CurveName] -> ShowS
    showList :: [CurveName] -> ShowS
    Show,ReadPrec [CurveName]
    ReadPrec CurveName
    Int -> ReadS CurveName
    ReadS [CurveName]
    (Int -> ReadS CurveName)
    -> ReadS [CurveName]
    -> ReadPrec CurveName
    -> ReadPrec [CurveName]
    -> Read CurveName
    forall a.
    (Int -> ReadS a)
    -> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
    $creadsPrec :: Int -> ReadS CurveName
    readsPrec :: Int -> ReadS CurveName
    $creadList :: ReadS [CurveName]
    readList :: ReadS [CurveName]
    $creadPrec :: ReadPrec CurveName
    readPrec :: ReadPrec CurveName
    $creadListPrec :: ReadPrec [CurveName]
    readListPrec :: ReadPrec [CurveName]
    Read,CurveName -> CurveName -> Bool
    (CurveName -> CurveName -> Bool)
    -> (CurveName -> CurveName -> Bool) -> Eq CurveName
    forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
    $c== :: CurveName -> CurveName -> Bool
    == :: CurveName -> CurveName -> Bool
    $c/= :: CurveName -> CurveName -> Bool
    /= :: CurveName -> CurveName -> Bool
    Eq,Eq CurveName
    Eq CurveName =>
    (CurveName -> CurveName -> Ordering)
    -> (CurveName -> CurveName -> Bool)
    -> (CurveName -> CurveName -> Bool)
    -> (CurveName -> CurveName -> Bool)
    -> (CurveName -> CurveName -> Bool)
    -> (CurveName -> CurveName -> CurveName)
    -> (CurveName -> CurveName -> CurveName)
    -> Ord CurveName
    CurveName -> CurveName -> Bool
    CurveName -> CurveName -> Ordering
    CurveName -> CurveName -> CurveName
    forall a.
    Eq a =>
    (a -> a -> Ordering)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> Bool)
    -> (a -> a -> a)
    -> (a -> a -> a)
    -> Ord a
    $ccompare :: CurveName -> CurveName -> Ordering
    compare :: CurveName -> CurveName -> Ordering
    $c< :: CurveName -> CurveName -> Bool
    < :: CurveName -> CurveName -> Bool
    $c<= :: CurveName -> CurveName -> Bool
    <= :: CurveName -> CurveName -> Bool
    $c> :: CurveName -> CurveName -> Bool
    > :: CurveName -> CurveName -> Bool
    $c>= :: CurveName -> CurveName -> Bool
    >= :: CurveName -> CurveName -> Bool
    $cmax :: CurveName -> CurveName -> CurveName
    max :: CurveName -> CurveName -> CurveName
    $cmin :: CurveName -> CurveName -> CurveName
    min :: CurveName -> CurveName -> CurveName
    Ord,Int -> CurveName
    CurveName -> Int
    CurveName -> [CurveName]
    CurveName -> CurveName
    CurveName -> CurveName -> [CurveName]
    CurveName -> CurveName -> CurveName -> [CurveName]
    (CurveName -> CurveName)
    -> (CurveName -> CurveName)
    -> (Int -> CurveName)
    -> (CurveName -> Int)
    -> (CurveName -> [CurveName])
    -> (CurveName -> CurveName -> [CurveName])
    -> (CurveName -> CurveName -> [CurveName])
    -> (CurveName -> CurveName -> CurveName -> [CurveName])
    -> Enum CurveName
    forall a.
    (a -> a)
    -> (a -> a)
    -> (Int -> a)
    -> (a -> Int)
    -> (a -> [a])
    -> (a -> a -> [a])
    -> (a -> a -> [a])
    -> (a -> a -> a -> [a])
    -> Enum a
    $csucc :: CurveName -> CurveName
    succ :: CurveName -> CurveName
    $cpred :: CurveName -> CurveName
    pred :: CurveName -> CurveName
    $ctoEnum :: Int -> CurveName
    toEnum :: Int -> CurveName
    $cfromEnum :: CurveName -> Int
    fromEnum :: CurveName -> Int
    $cenumFrom :: CurveName -> [CurveName]
    enumFrom :: CurveName -> [CurveName]
    $cenumFromThen :: CurveName -> CurveName -> [CurveName]
    enumFromThen :: CurveName -> CurveName -> [CurveName]
    $cenumFromTo :: CurveName -> CurveName -> [CurveName]
    enumFromTo :: CurveName -> CurveName -> [CurveName]
    $cenumFromThenTo :: CurveName -> CurveName -> CurveName -> [CurveName]
    enumFromThenTo :: CurveName -> CurveName -> CurveName -> [CurveName]
    Enum,Typeable CurveName
    Typeable CurveName =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> CurveName -> c CurveName)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c CurveName)
    -> (CurveName -> Constr)
    -> (CurveName -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c CurveName))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CurveName))
    -> ((forall b. Data b => b -> b) -> CurveName -> CurveName)
    -> (forall r r'.
        (r -> r' -> r)
        -> r -> (forall d. Data d => d -> r') -> CurveName -> r)
    -> (forall r r'.
        (r' -> r -> r)
        -> r -> (forall d. Data d => d -> r') -> CurveName -> r)
    -> (forall u. (forall d. Data d => d -> u) -> CurveName -> [u])
    -> (forall u.
        Int -> (forall d. Data d => d -> u) -> CurveName -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> CurveName -> m CurveName)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> CurveName -> m CurveName)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> CurveName -> m CurveName)
    -> Data CurveName
    CurveName -> Constr
    CurveName -> DataType
    (forall b. Data b => b -> b) -> CurveName -> CurveName
    forall a.
    Typeable a =>
    (forall (c :: * -> *).
     (forall d b. Data d => c (d -> b) -> d -> c b)
     -> (forall g. g -> c g) -> a -> c a)
    -> (forall (c :: * -> *).
        (forall b r. Data b => c (b -> r) -> c r)
        -> (forall r. r -> c r) -> Constr -> c a)
    -> (a -> Constr)
    -> (a -> DataType)
    -> (forall (t :: * -> *) (c :: * -> *).
        Typeable t =>
        (forall d. Data d => c (t d)) -> Maybe (c a))
    -> (forall (t :: * -> * -> *) (c :: * -> *).
        Typeable t =>
        (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a))
    -> ((forall b. Data b => b -> b) -> a -> a)
    -> (forall r r'.
        (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall r r'.
        (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r)
    -> (forall u. (forall d. Data d => d -> u) -> a -> [u])
    -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u)
    -> (forall (m :: * -> *).
        Monad m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> (forall (m :: * -> *).
        MonadPlus m =>
        (forall d. Data d => d -> m d) -> a -> m a)
    -> Data a
    forall u. Int -> (forall d. Data d => d -> u) -> CurveName -> u
    forall u. (forall d. Data d => d -> u) -> CurveName -> [u]
    forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveName -> r
    forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveName -> r
    forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c CurveName
    forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> CurveName -> c CurveName
    forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c CurveName)
    forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CurveName)
    $cgfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> CurveName -> c CurveName
    gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> CurveName -> c CurveName
    $cgunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c CurveName
    gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c CurveName
    $ctoConstr :: CurveName -> Constr
    toConstr :: CurveName -> Constr
    $cdataTypeOf :: CurveName -> DataType
    dataTypeOf :: CurveName -> DataType
    $cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c CurveName)
    dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c CurveName)
    $cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CurveName)
    dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c CurveName)
    $cgmapT :: (forall b. Data b => b -> b) -> CurveName -> CurveName
    gmapT :: (forall b. Data b => b -> b) -> CurveName -> CurveName
    $cgmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveName -> r
    gmapQl :: forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveName -> r
    $cgmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveName -> r
    gmapQr :: forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> CurveName -> r
    $cgmapQ :: forall u. (forall d. Data d => d -> u) -> CurveName -> [u]
    gmapQ :: forall u. (forall d. Data d => d -> u) -> CurveName -> [u]
    $cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CurveName -> u
    gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> CurveName -> u
    $cgmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    gmapM :: forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    $cgmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    gmapMp :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    $cgmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    gmapMo :: forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> CurveName -> m CurveName
    Data,Typeable)

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

    instance OIDable CurveName where
        getObjectID :: CurveName -> OID
    getObjectID CurveName
    cn = OID -> (OID -> OID) -> Maybe OID -> OID
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe (String -> OID
    forall a. HasCallStack => String -> a
    error (String
    "no oid for: " String -> ShowS
    forall a. [a] -> [a] -> [a]
    ++ CurveName -> String
    forall a. Show a => a -> String
    show CurveName
    cn)) OID -> OID
    forall a. a -> a
    id (Maybe OID -> OID) -> Maybe OID -> OID
    forall a b. (a -> b) -> a -> b
    $ CurveName -> [(CurveName, OID)] -> Maybe OID
    forall a b. Eq a => a -> [(a, b)] -> Maybe b
    lookup CurveName
    cn [(CurveName, OID)]
    curvesOIDs

    instance OIDNameable CurveName where
        fromObjectID :: OID -> Maybe CurveName
    fromObjectID OID
    oid = OID -> [(CurveName, OID)] -> Maybe CurveName
    forall {a} {b}. Eq a => a -> [(b, a)] -> Maybe b
    lookupSnd OID
    oid [(CurveName, OID)]
    curvesOIDs
          where lookupSnd :: a -> [(b, a)] -> Maybe b
    lookupSnd a
    x = a -> [(a, b)] -> Maybe b
    forall a b. Eq a => a -> [(a, b)] -> Maybe b
    lookup a
    x ([(a, b)] -> Maybe b)
    -> ([(b, a)] -> [(a, b)]) -> [(b, a)] -> Maybe b
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . ((b, a) -> (a, b)) -> [(b, a)] -> [(a, b)]
    forall a b. (a -> b) -> [a] -> [b]
    map (b, a) -> (a, b)
    forall a b. (a, b) -> (b, a)
    swap

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