-- |
-- Module      : Crypto.ECC
-- License     : BSD-style
-- Maintainer  : Vincent Hanquez <vincent@snarc.org>
-- Stability   : experimental
-- Portability : unknown
--
-- Elliptic Curve Cryptography
--
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ScopedTypeVariables #-}
module Crypto.ECC
    ( Curve_P256R1(..)
    , Curve_P384R1(..)
    , Curve_P521R1(..)
    , Curve_X25519(..)
    , Curve_X448(..)
    , Curve_Edwards25519(..)
    , EllipticCurve(..)
    , EllipticCurveDH(..)
    , EllipticCurveArith(..)
    , EllipticCurveBasepointArith(..)
    , KeyPair(..)
    , SharedSecret(..)
    ) where

import qualified Crypto.PubKey.ECC.P256 as P256
import qualified Crypto.ECC.Edwards25519 as Edwards25519
import qualified Crypto.ECC.Simple.Types as Simple
import qualified Crypto.ECC.Simple.Prim as Simple
import           Crypto.Random
import           Crypto.Error
import           Crypto.Internal.Imports
import           Crypto.Internal.ByteArray (ByteArray, ByteArrayAccess, ScrubbedBytes)
import qualified Crypto.Internal.ByteArray as B
import           Crypto.Number.Basic (numBits)
import           Crypto.Number.Serialize (i2ospOf_, os2ip)
import qualified Crypto.Number.Serialize.LE as LE
import qualified Crypto.PubKey.Curve25519 as X25519
import qualified Crypto.PubKey.Curve448 as X448
import           Data.ByteArray (convert)
import           Data.Data (Data())
import           Data.Kind (Type)
import           Data.Proxy

-- | An elliptic curve key pair composed of the private part (a scalar), and
-- the associated point.
data KeyPair curve = KeyPair
    { forall curve. KeyPair curve -> Point curve
keypairGetPublic  :: !(Point curve)
    , forall curve. KeyPair curve -> Scalar curve
keypairGetPrivate :: !(Scalar curve)
    }

newtype SharedSecret = SharedSecret ScrubbedBytes
    deriving (SharedSecret -> SharedSecret -> Bool
(SharedSecret -> SharedSecret -> Bool)
-> (SharedSecret -> SharedSecret -> Bool) -> Eq SharedSecret
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: SharedSecret -> SharedSecret -> Bool
== :: SharedSecret -> SharedSecret -> Bool
$c/= :: SharedSecret -> SharedSecret -> Bool
/= :: SharedSecret -> SharedSecret -> Bool
Eq, SharedSecret -> Int
(SharedSecret -> Int)
-> (forall p a. SharedSecret -> (Ptr p -> IO a) -> IO a)
-> (forall p. SharedSecret -> Ptr p -> IO ())
-> ByteArrayAccess SharedSecret
forall p. SharedSecret -> Ptr p -> IO ()
forall ba.
(ba -> Int)
-> (forall p a. ba -> (Ptr p -> IO a) -> IO a)
-> (forall p. ba -> Ptr p -> IO ())
-> ByteArrayAccess ba
forall p a. SharedSecret -> (Ptr p -> IO a) -> IO a
$clength :: SharedSecret -> Int
length :: SharedSecret -> Int
$cwithByteArray :: forall p a. SharedSecret -> (Ptr p -> IO a) -> IO a
withByteArray :: forall p a. SharedSecret -> (Ptr p -> IO a) -> IO a
$ccopyByteArrayToPtr :: forall p. SharedSecret -> Ptr p -> IO ()
copyByteArrayToPtr :: forall p. SharedSecret -> Ptr p -> IO ()
ByteArrayAccess, SharedSecret -> ()
(SharedSecret -> ()) -> NFData SharedSecret
forall a. (a -> ()) -> NFData a
$crnf :: SharedSecret -> ()
rnf :: SharedSecret -> ()
NFData)

class EllipticCurve curve where
    -- | Point on an Elliptic Curve
    type Point curve  :: Type

    -- | Scalar in the Elliptic Curve domain
    type Scalar curve :: Type

    -- | Generate a new random scalar on the curve.
    -- The scalar will represent a number between 1 and the order of the curve non included
    curveGenerateScalar :: MonadRandom randomly => proxy curve -> randomly (Scalar curve)

    -- | Generate a new random keypair
    curveGenerateKeyPair :: MonadRandom randomly => proxy curve -> randomly (KeyPair curve)

    -- | Get the curve size in bits
    curveSizeBits :: proxy curve -> Int

    -- | Encode a elliptic curve point into binary form
    encodePoint :: ByteArray bs => proxy curve -> Point curve -> bs

    -- | Try to decode the binary form of an elliptic curve point
    decodePoint :: ByteArray bs => proxy curve -> bs -> CryptoFailable (Point curve)

class EllipticCurve curve => EllipticCurveDH curve where
    -- | Generate a Diffie hellman secret value.
    --
    -- This is generally just the .x coordinate of the resulting point, that
    -- is not hashed.
    --
    -- use `pointSmul` to keep the result in Point format.
    --
    -- /WARNING:/ Curve implementations may return a special value or an
    -- exception when the public point lies in a subgroup of small order.
    -- This function is adequate when the scalar is in expected range and
    -- contributory behaviour is not needed.  Otherwise use 'ecdh'.
    ecdhRaw :: proxy curve -> Scalar curve -> Point curve -> SharedSecret
    ecdhRaw proxy curve
prx Scalar curve
s = CryptoFailable SharedSecret -> SharedSecret
forall a. CryptoFailable a -> a
throwCryptoError (CryptoFailable SharedSecret -> SharedSecret)
-> (Point curve -> CryptoFailable SharedSecret)
-> Point curve
-> SharedSecret
forall b c a. (b -> c) -> (a -> b) -> a -> c
. proxy curve
-> Scalar curve -> Point curve -> CryptoFailable SharedSecret
forall curve (proxy :: * -> *).
EllipticCurveDH curve =>
proxy curve
-> Scalar curve -> Point curve -> CryptoFailable SharedSecret
forall (proxy :: * -> *).
proxy curve
-> Scalar curve -> Point curve -> CryptoFailable SharedSecret
ecdh proxy curve
prx Scalar curve
s

    -- | Generate a Diffie hellman secret value and verify that the result
    -- is not the point at infinity.
    --
    -- This additional test avoids risks existing with function 'ecdhRaw'.
    -- Implementations always return a 'CryptoError' instead of a special
    -- value or an exception.
    ecdh :: proxy curve -> Scalar curve -> Point curve -> CryptoFailable SharedSecret

class (EllipticCurve curve, Eq (Point curve)) => EllipticCurveArith curve where
    -- | Add points on a curve
    pointAdd :: proxy curve -> Point curve -> Point curve -> Point curve

    -- | Negate a curve point
    pointNegate :: proxy curve -> Point curve -> Point curve

    -- | Scalar Multiplication on a curve
    pointSmul :: proxy curve -> Scalar curve -> Point curve -> Point curve

--   -- | Scalar Inverse
--   scalarInverse :: Scalar curve -> Scalar curve

class (EllipticCurveArith curve, Eq (Scalar curve)) => EllipticCurveBasepointArith curve where
    -- | Get the curve order size in bits
    curveOrderBits :: proxy curve -> Int

    -- | Multiply a scalar with the curve base point
    pointBaseSmul :: proxy curve -> Scalar curve -> Point curve

    -- | Multiply the point @p@ with @s2@ and add a lifted to curve value @s1@
    pointsSmulVarTime :: proxy curve -> Scalar curve -> Scalar curve -> Point curve -> Point curve
    pointsSmulVarTime proxy curve
prx Scalar curve
s1 Scalar curve
s2 Point curve
p = proxy curve -> Point curve -> Point curve -> Point curve
forall curve (proxy :: * -> *).
EllipticCurveArith curve =>
proxy curve -> Point curve -> Point curve -> Point curve
forall (proxy :: * -> *).
proxy curve -> Point curve -> Point curve -> Point curve
pointAdd proxy curve
prx (proxy curve -> Scalar curve -> Point curve
forall curve (proxy :: * -> *).
EllipticCurveBasepointArith curve =>
proxy curve -> Scalar curve -> Point curve
forall (proxy :: * -> *).
proxy curve -> Scalar curve -> Point curve
pointBaseSmul proxy curve
prx Scalar curve
s1) (proxy curve -> Scalar curve -> Point curve -> Point curve
forall curve (proxy :: * -> *).
EllipticCurveArith curve =>
proxy curve -> Scalar curve -> Point curve -> Point curve
forall (proxy :: * -> *).
proxy curve -> Scalar curve -> Point curve -> Point curve
pointSmul proxy curve
prx Scalar curve
s2 Point curve
p)

    -- | Encode an elliptic curve scalar into big-endian form
    encodeScalar :: ByteArray bs => proxy curve -> Scalar curve -> bs

    -- | Try to decode the big-endian form of an elliptic curve scalar
    decodeScalar :: ByteArray bs => proxy curve -> bs -> CryptoFailable (Scalar curve)

    -- | Convert an elliptic curve scalar to an integer
    scalarToInteger :: proxy curve -> Scalar curve -> Integer

    -- | Try to create an elliptic curve scalar from an integer
    scalarFromInteger :: proxy curve -> Integer -> CryptoFailable (Scalar curve)

    -- | Add two scalars and reduce modulo the curve order
    scalarAdd :: proxy curve -> Scalar curve -> Scalar curve -> Scalar curve

    -- | Multiply two scalars and reduce modulo the curve order
    scalarMul :: proxy curve -> Scalar curve -> Scalar curve -> Scalar curve

-- | P256 Curve
--
-- also known as P256
data Curve_P256R1 = Curve_P256R1
    deriving (Int -> Curve_P256R1 -> ShowS
[Curve_P256R1] -> ShowS
Curve_P256R1 -> String
(Int -> Curve_P256R1 -> ShowS)
-> (Curve_P256R1 -> String)
-> ([Curve_P256R1] -> ShowS)
-> Show Curve_P256R1
forall a.
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$cshowsPrec :: Int -> Curve_P256R1 -> ShowS
showsPrec :: Int -> Curve_P256R1 -> ShowS
$cshow :: Curve_P256R1 -> String
show :: Curve_P256R1 -> String
$cshowList :: [Curve_P256R1] -> ShowS
showList :: [Curve_P256R1] -> ShowS
Show,Typeable Curve_P256R1
Typeable Curve_P256R1 =>
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-> ((forall b. Data b => b -> b) -> Curve_P256R1 -> Curve_P256R1)
-> (forall r r'.
    (r -> r' -> r)
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-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1)
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-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1)
-> Data Curve_P256R1
Curve_P256R1 -> Constr
Curve_P256R1 -> DataType
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forall a.
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-> (forall u. (forall d. Data d => d -> u) -> a -> [u])
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-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
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    (forall d. Data d => d -> m d) -> a -> m a)
-> (forall (m :: * -> *).
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-> Data a
forall u. Int -> (forall d. Data d => d -> u) -> Curve_P256R1 -> u
forall u. (forall d. Data d => d -> u) -> Curve_P256R1 -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P256R1 -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P256R1 -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1
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forall (c :: * -> *).
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-> (forall r. r -> c r) -> Constr -> c Curve_P256R1
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(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P256R1 -> c Curve_P256R1
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P256R1)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P256R1)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P256R1 -> c Curve_P256R1
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P256R1 -> c Curve_P256R1
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P256R1
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P256R1
$ctoConstr :: Curve_P256R1 -> Constr
toConstr :: Curve_P256R1 -> Constr
$cdataTypeOf :: Curve_P256R1 -> DataType
dataTypeOf :: Curve_P256R1 -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P256R1)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P256R1)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P256R1)
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P256R1)
$cgmapT :: (forall b. Data b => b -> b) -> Curve_P256R1 -> Curve_P256R1
gmapT :: (forall b. Data b => b -> b) -> Curve_P256R1 -> Curve_P256R1
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P256R1 -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P256R1 -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P256R1 -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P256R1 -> r
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_P256R1 -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_P256R1 -> [u]
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_P256R1 -> u
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_P256R1 -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P256R1 -> m Curve_P256R1
Data)

instance EllipticCurve Curve_P256R1 where
    type Point Curve_P256R1 = P256.Point
    type Scalar Curve_P256R1 = P256.Scalar
    curveSizeBits :: forall (proxy :: * -> *). proxy Curve_P256R1 -> Int
curveSizeBits proxy Curve_P256R1
_ = Int
256
    curveGenerateScalar :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_P256R1 -> randomly (Scalar Curve_P256R1)
curveGenerateScalar proxy Curve_P256R1
_ = randomly Scalar
randomly (Scalar Curve_P256R1)
forall (randomly :: * -> *).
MonadRandom randomly =>
randomly Scalar
P256.scalarGenerate
    curveGenerateKeyPair :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_P256R1 -> randomly (KeyPair Curve_P256R1)
curveGenerateKeyPair proxy Curve_P256R1
_ = Scalar -> KeyPair Curve_P256R1
forall {curve}.
(Point curve ~ Point, Scalar curve ~ Scalar) =>
Scalar -> KeyPair curve
toKeyPair (Scalar -> KeyPair Curve_P256R1)
-> randomly Scalar -> randomly (KeyPair Curve_P256R1)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> randomly Scalar
forall (randomly :: * -> *).
MonadRandom randomly =>
randomly Scalar
P256.scalarGenerate
      where toKeyPair :: Scalar -> KeyPair curve
toKeyPair Scalar
scalar = Point curve -> Scalar curve -> KeyPair curve
forall curve. Point curve -> Scalar curve -> KeyPair curve
KeyPair (Scalar -> Point
P256.toPoint Scalar
scalar) Scalar
Scalar curve
scalar
    encodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P256R1 -> Point Curve_P256R1 -> bs
encodePoint proxy Curve_P256R1
_ Point Curve_P256R1
p = bs
forall bs. ByteArray bs => bs
mxy
      where
        mxy :: forall bs. ByteArray bs => bs
        mxy :: forall bs. ByteArray bs => bs
mxy = [bs] -> bs
forall bin bout.
(ByteArrayAccess bin, ByteArray bout) =>
[bin] -> bout
B.concat [bs
uncompressed, bs
xy]
          where
            uncompressed, xy :: bs
            uncompressed :: bs
uncompressed = Word8 -> bs
forall a. ByteArray a => Word8 -> a
B.singleton Word8
4
            xy :: bs
xy = Point -> bs
forall ba. ByteArray ba => Point -> ba
P256.pointToBinary Point
Point Curve_P256R1
p
    decodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P256R1 -> bs -> CryptoFailable (Point Curve_P256R1)
decodePoint proxy Curve_P256R1
_ bs
mxy = case bs -> Maybe (Word8, bs)
forall a. ByteArray a => a -> Maybe (Word8, a)
B.uncons bs
mxy of
        Maybe (Word8, bs)
Nothing -> CryptoError -> CryptoFailable Point
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_PointSizeInvalid
        Just (Word8
m,bs
xy)
            -- uncompressed
            | Word8
m Word8 -> Word8 -> Bool
forall a. Eq a => a -> a -> Bool
== Word8
4 -> bs -> CryptoFailable Point
forall ba. ByteArrayAccess ba => ba -> CryptoFailable Point
P256.pointFromBinary bs
xy
            | Bool
otherwise -> CryptoError -> CryptoFailable Point
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_PointFormatInvalid

instance EllipticCurveArith Curve_P256R1 where
    pointAdd :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Point Curve_P256R1 -> Point Curve_P256R1 -> Point Curve_P256R1
pointAdd  proxy Curve_P256R1
_ Point Curve_P256R1
a Point Curve_P256R1
b = Point -> Point -> Point
P256.pointAdd Point
Point Curve_P256R1
a Point
Point Curve_P256R1
b
    pointNegate :: forall (proxy :: * -> *).
proxy Curve_P256R1 -> Point Curve_P256R1 -> Point Curve_P256R1
pointNegate proxy Curve_P256R1
_ Point Curve_P256R1
p = Point -> Point
P256.pointNegate Point
Point Curve_P256R1
p
    pointSmul :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Scalar Curve_P256R1 -> Point Curve_P256R1 -> Point Curve_P256R1
pointSmul proxy Curve_P256R1
_ Scalar Curve_P256R1
s Point Curve_P256R1
p = Scalar -> Point -> Point
P256.pointMul Scalar
Scalar Curve_P256R1
s Point
Point Curve_P256R1
p

instance EllipticCurveDH Curve_P256R1 where
    ecdhRaw :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Scalar Curve_P256R1 -> Point Curve_P256R1 -> SharedSecret
ecdhRaw proxy Curve_P256R1
_ Scalar Curve_P256R1
s Point Curve_P256R1
p = ScrubbedBytes -> SharedSecret
SharedSecret (ScrubbedBytes -> SharedSecret) -> ScrubbedBytes -> SharedSecret
forall a b. (a -> b) -> a -> b
$ Scalar -> Point -> ScrubbedBytes
forall binary. ByteArray binary => Scalar -> Point -> binary
P256.pointDh Scalar
Scalar Curve_P256R1
s Point
Point Curve_P256R1
p
    ecdh :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Scalar Curve_P256R1
-> Point Curve_P256R1
-> CryptoFailable SharedSecret
ecdh  proxy Curve_P256R1
prx Scalar Curve_P256R1
s Point Curve_P256R1
p = SharedSecret -> CryptoFailable SharedSecret
checkNonZeroDH (proxy Curve_P256R1
-> Scalar Curve_P256R1 -> Point Curve_P256R1 -> SharedSecret
forall curve (proxy :: * -> *).
EllipticCurveDH curve =>
proxy curve -> Scalar curve -> Point curve -> SharedSecret
forall (proxy :: * -> *).
proxy Curve_P256R1
-> Scalar Curve_P256R1 -> Point Curve_P256R1 -> SharedSecret
ecdhRaw proxy Curve_P256R1
prx Scalar Curve_P256R1
s Point Curve_P256R1
p)

instance EllipticCurveBasepointArith Curve_P256R1 where
    curveOrderBits :: forall (proxy :: * -> *). proxy Curve_P256R1 -> Int
curveOrderBits proxy Curve_P256R1
_ = Int
256
    pointBaseSmul :: forall (proxy :: * -> *).
proxy Curve_P256R1 -> Scalar Curve_P256R1 -> Point Curve_P256R1
pointBaseSmul proxy Curve_P256R1
_ = Scalar -> Point
Scalar Curve_P256R1 -> Point Curve_P256R1
P256.toPoint
    pointsSmulVarTime :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Scalar Curve_P256R1
-> Scalar Curve_P256R1
-> Point Curve_P256R1
-> Point Curve_P256R1
pointsSmulVarTime proxy Curve_P256R1
_ = Scalar -> Scalar -> Point -> Point
Scalar Curve_P256R1
-> Scalar Curve_P256R1 -> Point Curve_P256R1 -> Point Curve_P256R1
P256.pointsMulVarTime
    encodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P256R1 -> Scalar Curve_P256R1 -> bs
encodeScalar proxy Curve_P256R1
_ = Scalar -> bs
Scalar Curve_P256R1 -> bs
forall ba. ByteArray ba => Scalar -> ba
P256.scalarToBinary
    decodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P256R1 -> bs -> CryptoFailable (Scalar Curve_P256R1)
decodeScalar proxy Curve_P256R1
_ = bs -> CryptoFailable Scalar
bs -> CryptoFailable (Scalar Curve_P256R1)
forall ba. ByteArrayAccess ba => ba -> CryptoFailable Scalar
P256.scalarFromBinary
    scalarToInteger :: forall (proxy :: * -> *).
proxy Curve_P256R1 -> Scalar Curve_P256R1 -> Integer
scalarToInteger proxy Curve_P256R1
_ = Scalar -> Integer
Scalar Curve_P256R1 -> Integer
P256.scalarToInteger
    scalarFromInteger :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Integer -> CryptoFailable (Scalar Curve_P256R1)
scalarFromInteger proxy Curve_P256R1
_ = Integer -> CryptoFailable Scalar
Integer -> CryptoFailable (Scalar Curve_P256R1)
P256.scalarFromInteger
    scalarAdd :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Scalar Curve_P256R1
-> Scalar Curve_P256R1
-> Scalar Curve_P256R1
scalarAdd proxy Curve_P256R1
_ = Scalar -> Scalar -> Scalar
Scalar Curve_P256R1 -> Scalar Curve_P256R1 -> Scalar Curve_P256R1
P256.scalarAdd
    scalarMul :: forall (proxy :: * -> *).
proxy Curve_P256R1
-> Scalar Curve_P256R1
-> Scalar Curve_P256R1
-> Scalar Curve_P256R1
scalarMul proxy Curve_P256R1
_ = Scalar -> Scalar -> Scalar
Scalar Curve_P256R1 -> Scalar Curve_P256R1 -> Scalar Curve_P256R1
P256.scalarMul

data Curve_P384R1 = Curve_P384R1
    deriving (Int -> Curve_P384R1 -> ShowS
[Curve_P384R1] -> ShowS
Curve_P384R1 -> String
(Int -> Curve_P384R1 -> ShowS)
-> (Curve_P384R1 -> String)
-> ([Curve_P384R1] -> ShowS)
-> Show Curve_P384R1
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> Curve_P384R1 -> ShowS
showsPrec :: Int -> Curve_P384R1 -> ShowS
$cshow :: Curve_P384R1 -> String
show :: Curve_P384R1 -> String
$cshowList :: [Curve_P384R1] -> ShowS
showList :: [Curve_P384R1] -> ShowS
Show,Typeable Curve_P384R1
Typeable Curve_P384R1 =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g) -> Curve_P384R1 -> c Curve_P384R1)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c Curve_P384R1)
-> (Curve_P384R1 -> Constr)
-> (Curve_P384R1 -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c Curve_P384R1))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c Curve_P384R1))
-> ((forall b. Data b => b -> b) -> Curve_P384R1 -> Curve_P384R1)
-> (forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r)
-> (forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r)
-> (forall u. (forall d. Data d => d -> u) -> Curve_P384R1 -> [u])
-> (forall u.
    Int -> (forall d. Data d => d -> u) -> Curve_P384R1 -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1)
-> Data Curve_P384R1
Curve_P384R1 -> Constr
Curve_P384R1 -> DataType
(forall b. Data b => b -> b) -> Curve_P384R1 -> Curve_P384R1
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) -> Curve_P384R1 -> u
forall u. (forall d. Data d => d -> u) -> Curve_P384R1 -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P384R1
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P384R1 -> c Curve_P384R1
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P384R1)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P384R1)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P384R1 -> c Curve_P384R1
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P384R1 -> c Curve_P384R1
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P384R1
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P384R1
$ctoConstr :: Curve_P384R1 -> Constr
toConstr :: Curve_P384R1 -> Constr
$cdataTypeOf :: Curve_P384R1 -> DataType
dataTypeOf :: Curve_P384R1 -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P384R1)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P384R1)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P384R1)
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P384R1)
$cgmapT :: (forall b. Data b => b -> b) -> Curve_P384R1 -> Curve_P384R1
gmapT :: (forall b. Data b => b -> b) -> Curve_P384R1 -> Curve_P384R1
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P384R1 -> r
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_P384R1 -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_P384R1 -> [u]
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_P384R1 -> u
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_P384R1 -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P384R1 -> m Curve_P384R1
Data)

instance EllipticCurve Curve_P384R1 where
    type Point Curve_P384R1 = Simple.Point Simple.SEC_p384r1
    type Scalar Curve_P384R1 = Simple.Scalar Simple.SEC_p384r1
    curveSizeBits :: forall (proxy :: * -> *). proxy Curve_P384R1 -> Int
curveSizeBits proxy Curve_P384R1
_ = Int
384
    curveGenerateScalar :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_P384R1 -> randomly (Scalar Curve_P384R1)
curveGenerateScalar proxy Curve_P384R1
_ = randomly (Scalar SEC_p384r1)
randomly (Scalar Curve_P384R1)
forall (randomly :: * -> *) curve.
(MonadRandom randomly, Curve curve) =>
randomly (Scalar curve)
Simple.scalarGenerate
    curveGenerateKeyPair :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_P384R1 -> randomly (KeyPair Curve_P384R1)
curveGenerateKeyPair proxy Curve_P384R1
_ = Scalar SEC_p384r1 -> KeyPair Curve_P384R1
forall {curve} {curve}.
(Point curve ~ Point curve, Scalar curve ~ Scalar curve,
 Curve curve) =>
Scalar curve -> KeyPair curve
toKeyPair (Scalar SEC_p384r1 -> KeyPair Curve_P384R1)
-> randomly (Scalar SEC_p384r1) -> randomly (KeyPair Curve_P384R1)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> randomly (Scalar SEC_p384r1)
forall (randomly :: * -> *) curve.
(MonadRandom randomly, Curve curve) =>
randomly (Scalar curve)
Simple.scalarGenerate
      where toKeyPair :: Scalar curve -> KeyPair curve
toKeyPair Scalar curve
scalar = Point curve -> Scalar curve -> KeyPair curve
forall curve. Point curve -> Scalar curve -> KeyPair curve
KeyPair (Scalar curve -> Point curve
forall curve. Curve curve => Scalar curve -> Point curve
Simple.pointBaseMul Scalar curve
scalar) Scalar curve
Scalar curve
scalar
    encodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P384R1 -> Point Curve_P384R1 -> bs
encodePoint proxy Curve_P384R1
_ Point Curve_P384R1
point = Point SEC_p384r1 -> bs
forall curve bs. (Curve curve, ByteArray bs) => Point curve -> bs
encodeECPoint Point SEC_p384r1
Point Curve_P384R1
point
    decodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P384R1 -> bs -> CryptoFailable (Point Curve_P384R1)
decodePoint proxy Curve_P384R1
_ bs
bs = bs -> CryptoFailable (Point SEC_p384r1)
forall curve bs.
(Curve curve, ByteArray bs) =>
bs -> CryptoFailable (Point curve)
decodeECPoint bs
bs

instance EllipticCurveArith Curve_P384R1 where
    pointAdd :: forall (proxy :: * -> *).
proxy Curve_P384R1
-> Point Curve_P384R1 -> Point Curve_P384R1 -> Point Curve_P384R1
pointAdd proxy Curve_P384R1
_ Point Curve_P384R1
a Point Curve_P384R1
b = Point SEC_p384r1 -> Point SEC_p384r1 -> Point SEC_p384r1
forall curve.
Curve curve =>
Point curve -> Point curve -> Point curve
Simple.pointAdd Point SEC_p384r1
Point Curve_P384R1
a Point SEC_p384r1
Point Curve_P384R1
b
    pointNegate :: forall (proxy :: * -> *).
proxy Curve_P384R1 -> Point Curve_P384R1 -> Point Curve_P384R1
pointNegate proxy Curve_P384R1
_ Point Curve_P384R1
p = Point SEC_p384r1 -> Point SEC_p384r1
forall curve. Curve curve => Point curve -> Point curve
Simple.pointNegate Point SEC_p384r1
Point Curve_P384R1
p
    pointSmul :: forall (proxy :: * -> *).
proxy Curve_P384R1
-> Scalar Curve_P384R1 -> Point Curve_P384R1 -> Point Curve_P384R1
pointSmul proxy Curve_P384R1
_ Scalar Curve_P384R1
s Point Curve_P384R1
p = Scalar SEC_p384r1 -> Point SEC_p384r1 -> Point SEC_p384r1
forall curve.
Curve curve =>
Scalar curve -> Point curve -> Point curve
Simple.pointMul Scalar SEC_p384r1
Scalar Curve_P384R1
s Point SEC_p384r1
Point Curve_P384R1
p

instance EllipticCurveDH Curve_P384R1 where
    ecdh :: forall (proxy :: * -> *).
proxy Curve_P384R1
-> Scalar Curve_P384R1
-> Point Curve_P384R1
-> CryptoFailable SharedSecret
ecdh proxy Curve_P384R1
_ Scalar Curve_P384R1
s Point Curve_P384R1
p = Proxy SEC_p384r1 -> Point SEC_p384r1 -> CryptoFailable SharedSecret
forall curve.
Curve curve =>
Proxy curve -> Point curve -> CryptoFailable SharedSecret
encodeECShared Proxy SEC_p384r1
prx (Scalar SEC_p384r1 -> Point SEC_p384r1 -> Point SEC_p384r1
forall curve.
Curve curve =>
Scalar curve -> Point curve -> Point curve
Simple.pointMul Scalar SEC_p384r1
Scalar Curve_P384R1
s Point SEC_p384r1
Point Curve_P384R1
p)
      where
        prx :: Proxy SEC_p384r1
prx = Proxy SEC_p384r1
forall {k} (t :: k). Proxy t
Proxy :: Proxy Simple.SEC_p384r1

instance EllipticCurveBasepointArith Curve_P384R1 where
    curveOrderBits :: forall (proxy :: * -> *). proxy Curve_P384R1 -> Int
curveOrderBits proxy Curve_P384R1
_ = Int
384
    pointBaseSmul :: forall (proxy :: * -> *).
proxy Curve_P384R1 -> Scalar Curve_P384R1 -> Point Curve_P384R1
pointBaseSmul proxy Curve_P384R1
_ = Scalar SEC_p384r1 -> Point SEC_p384r1
Scalar Curve_P384R1 -> Point Curve_P384R1
forall curve. Curve curve => Scalar curve -> Point curve
Simple.pointBaseMul
    pointsSmulVarTime :: forall (proxy :: * -> *).
proxy Curve_P384R1
-> Scalar Curve_P384R1
-> Scalar Curve_P384R1
-> Point Curve_P384R1
-> Point Curve_P384R1
pointsSmulVarTime proxy Curve_P384R1
_ = Scalar SEC_p384r1
-> Scalar SEC_p384r1 -> Point SEC_p384r1 -> Point SEC_p384r1
Scalar Curve_P384R1
-> Scalar Curve_P384R1 -> Point Curve_P384R1 -> Point Curve_P384R1
forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Point curve -> Point curve
ecPointsMulVarTime
    encodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P384R1 -> Scalar Curve_P384R1 -> bs
encodeScalar proxy Curve_P384R1
_ = Scalar SEC_p384r1 -> bs
Scalar Curve_P384R1 -> bs
forall curve bs. (Curve curve, ByteArray bs) => Scalar curve -> bs
ecScalarToBinary
    decodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P384R1 -> bs -> CryptoFailable (Scalar Curve_P384R1)
decodeScalar proxy Curve_P384R1
_ = bs -> CryptoFailable (Scalar SEC_p384r1)
bs -> CryptoFailable (Scalar Curve_P384R1)
forall curve bs.
(Curve curve, ByteArrayAccess bs) =>
bs -> CryptoFailable (Scalar curve)
ecScalarFromBinary
    scalarToInteger :: forall (proxy :: * -> *).
proxy Curve_P384R1 -> Scalar Curve_P384R1 -> Integer
scalarToInteger proxy Curve_P384R1
_ = Scalar SEC_p384r1 -> Integer
Scalar Curve_P384R1 -> Integer
forall curve. Scalar curve -> Integer
ecScalarToInteger
    scalarFromInteger :: forall (proxy :: * -> *).
proxy Curve_P384R1
-> Integer -> CryptoFailable (Scalar Curve_P384R1)
scalarFromInteger proxy Curve_P384R1
_ = Integer -> CryptoFailable (Scalar SEC_p384r1)
Integer -> CryptoFailable (Scalar Curve_P384R1)
forall curve.
Curve curve =>
Integer -> CryptoFailable (Scalar curve)
ecScalarFromInteger
    scalarAdd :: forall (proxy :: * -> *).
proxy Curve_P384R1
-> Scalar Curve_P384R1
-> Scalar Curve_P384R1
-> Scalar Curve_P384R1
scalarAdd proxy Curve_P384R1
_ = Scalar SEC_p384r1 -> Scalar SEC_p384r1 -> Scalar SEC_p384r1
Scalar Curve_P384R1 -> Scalar Curve_P384R1 -> Scalar Curve_P384R1
forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Scalar curve
ecScalarAdd
    scalarMul :: forall (proxy :: * -> *).
proxy Curve_P384R1
-> Scalar Curve_P384R1
-> Scalar Curve_P384R1
-> Scalar Curve_P384R1
scalarMul proxy Curve_P384R1
_ = Scalar SEC_p384r1 -> Scalar SEC_p384r1 -> Scalar SEC_p384r1
Scalar Curve_P384R1 -> Scalar Curve_P384R1 -> Scalar Curve_P384R1
forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Scalar curve
ecScalarMul

data Curve_P521R1 = Curve_P521R1
    deriving (Int -> Curve_P521R1 -> ShowS
[Curve_P521R1] -> ShowS
Curve_P521R1 -> String
(Int -> Curve_P521R1 -> ShowS)
-> (Curve_P521R1 -> String)
-> ([Curve_P521R1] -> ShowS)
-> Show Curve_P521R1
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> Curve_P521R1 -> ShowS
showsPrec :: Int -> Curve_P521R1 -> ShowS
$cshow :: Curve_P521R1 -> String
show :: Curve_P521R1 -> String
$cshowList :: [Curve_P521R1] -> ShowS
showList :: [Curve_P521R1] -> ShowS
Show,Typeable Curve_P521R1
Typeable Curve_P521R1 =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g) -> Curve_P521R1 -> c Curve_P521R1)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c Curve_P521R1)
-> (Curve_P521R1 -> Constr)
-> (Curve_P521R1 -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c Curve_P521R1))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c Curve_P521R1))
-> ((forall b. Data b => b -> b) -> Curve_P521R1 -> Curve_P521R1)
-> (forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r)
-> (forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r)
-> (forall u. (forall d. Data d => d -> u) -> Curve_P521R1 -> [u])
-> (forall u.
    Int -> (forall d. Data d => d -> u) -> Curve_P521R1 -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1)
-> Data Curve_P521R1
Curve_P521R1 -> Constr
Curve_P521R1 -> DataType
(forall b. Data b => b -> b) -> Curve_P521R1 -> Curve_P521R1
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) -> Curve_P521R1 -> u
forall u. (forall d. Data d => d -> u) -> Curve_P521R1 -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P521R1
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P521R1 -> c Curve_P521R1
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P521R1)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P521R1)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P521R1 -> c Curve_P521R1
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_P521R1 -> c Curve_P521R1
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P521R1
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_P521R1
$ctoConstr :: Curve_P521R1 -> Constr
toConstr :: Curve_P521R1 -> Constr
$cdataTypeOf :: Curve_P521R1 -> DataType
dataTypeOf :: Curve_P521R1 -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P521R1)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_P521R1)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P521R1)
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_P521R1)
$cgmapT :: (forall b. Data b => b -> b) -> Curve_P521R1 -> Curve_P521R1
gmapT :: (forall b. Data b => b -> b) -> Curve_P521R1 -> Curve_P521R1
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_P521R1 -> r
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_P521R1 -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_P521R1 -> [u]
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_P521R1 -> u
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_P521R1 -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_P521R1 -> m Curve_P521R1
Data)

instance EllipticCurve Curve_P521R1 where
    type Point Curve_P521R1 = Simple.Point Simple.SEC_p521r1
    type Scalar Curve_P521R1 = Simple.Scalar Simple.SEC_p521r1
    curveSizeBits :: forall (proxy :: * -> *). proxy Curve_P521R1 -> Int
curveSizeBits proxy Curve_P521R1
_ = Int
521
    curveGenerateScalar :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_P521R1 -> randomly (Scalar Curve_P521R1)
curveGenerateScalar proxy Curve_P521R1
_ = randomly (Scalar SEC_p521r1)
randomly (Scalar Curve_P521R1)
forall (randomly :: * -> *) curve.
(MonadRandom randomly, Curve curve) =>
randomly (Scalar curve)
Simple.scalarGenerate
    curveGenerateKeyPair :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_P521R1 -> randomly (KeyPair Curve_P521R1)
curveGenerateKeyPair proxy Curve_P521R1
_ = Scalar SEC_p521r1 -> KeyPair Curve_P521R1
forall {curve} {curve}.
(Point curve ~ Point curve, Scalar curve ~ Scalar curve,
 Curve curve) =>
Scalar curve -> KeyPair curve
toKeyPair (Scalar SEC_p521r1 -> KeyPair Curve_P521R1)
-> randomly (Scalar SEC_p521r1) -> randomly (KeyPair Curve_P521R1)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> randomly (Scalar SEC_p521r1)
forall (randomly :: * -> *) curve.
(MonadRandom randomly, Curve curve) =>
randomly (Scalar curve)
Simple.scalarGenerate
      where toKeyPair :: Scalar curve -> KeyPair curve
toKeyPair Scalar curve
scalar = Point curve -> Scalar curve -> KeyPair curve
forall curve. Point curve -> Scalar curve -> KeyPair curve
KeyPair (Scalar curve -> Point curve
forall curve. Curve curve => Scalar curve -> Point curve
Simple.pointBaseMul Scalar curve
scalar) Scalar curve
Scalar curve
scalar
    encodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P521R1 -> Point Curve_P521R1 -> bs
encodePoint proxy Curve_P521R1
_ Point Curve_P521R1
point = Point SEC_p521r1 -> bs
forall curve bs. (Curve curve, ByteArray bs) => Point curve -> bs
encodeECPoint Point SEC_p521r1
Point Curve_P521R1
point
    decodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P521R1 -> bs -> CryptoFailable (Point Curve_P521R1)
decodePoint proxy Curve_P521R1
_ bs
bs = bs -> CryptoFailable (Point SEC_p521r1)
forall curve bs.
(Curve curve, ByteArray bs) =>
bs -> CryptoFailable (Point curve)
decodeECPoint bs
bs

instance EllipticCurveArith Curve_P521R1 where
    pointAdd :: forall (proxy :: * -> *).
proxy Curve_P521R1
-> Point Curve_P521R1 -> Point Curve_P521R1 -> Point Curve_P521R1
pointAdd proxy Curve_P521R1
_ Point Curve_P521R1
a Point Curve_P521R1
b = Point SEC_p521r1 -> Point SEC_p521r1 -> Point SEC_p521r1
forall curve.
Curve curve =>
Point curve -> Point curve -> Point curve
Simple.pointAdd Point SEC_p521r1
Point Curve_P521R1
a Point SEC_p521r1
Point Curve_P521R1
b
    pointNegate :: forall (proxy :: * -> *).
proxy Curve_P521R1 -> Point Curve_P521R1 -> Point Curve_P521R1
pointNegate proxy Curve_P521R1
_ Point Curve_P521R1
p = Point SEC_p521r1 -> Point SEC_p521r1
forall curve. Curve curve => Point curve -> Point curve
Simple.pointNegate Point SEC_p521r1
Point Curve_P521R1
p
    pointSmul :: forall (proxy :: * -> *).
proxy Curve_P521R1
-> Scalar Curve_P521R1 -> Point Curve_P521R1 -> Point Curve_P521R1
pointSmul proxy Curve_P521R1
_ Scalar Curve_P521R1
s Point Curve_P521R1
p = Scalar SEC_p521r1 -> Point SEC_p521r1 -> Point SEC_p521r1
forall curve.
Curve curve =>
Scalar curve -> Point curve -> Point curve
Simple.pointMul Scalar SEC_p521r1
Scalar Curve_P521R1
s Point SEC_p521r1
Point Curve_P521R1
p

instance EllipticCurveDH Curve_P521R1 where
    ecdh :: forall (proxy :: * -> *).
proxy Curve_P521R1
-> Scalar Curve_P521R1
-> Point Curve_P521R1
-> CryptoFailable SharedSecret
ecdh proxy Curve_P521R1
_ Scalar Curve_P521R1
s Point Curve_P521R1
p = Proxy SEC_p521r1 -> Point SEC_p521r1 -> CryptoFailable SharedSecret
forall curve.
Curve curve =>
Proxy curve -> Point curve -> CryptoFailable SharedSecret
encodeECShared Proxy SEC_p521r1
prx (Scalar SEC_p521r1 -> Point SEC_p521r1 -> Point SEC_p521r1
forall curve.
Curve curve =>
Scalar curve -> Point curve -> Point curve
Simple.pointMul Scalar SEC_p521r1
Scalar Curve_P521R1
s Point SEC_p521r1
Point Curve_P521R1
p)
      where
        prx :: Proxy SEC_p521r1
prx = Proxy SEC_p521r1
forall {k} (t :: k). Proxy t
Proxy :: Proxy Simple.SEC_p521r1

instance EllipticCurveBasepointArith Curve_P521R1 where
    curveOrderBits :: forall (proxy :: * -> *). proxy Curve_P521R1 -> Int
curveOrderBits proxy Curve_P521R1
_ = Int
521
    pointBaseSmul :: forall (proxy :: * -> *).
proxy Curve_P521R1 -> Scalar Curve_P521R1 -> Point Curve_P521R1
pointBaseSmul proxy Curve_P521R1
_ = Scalar SEC_p521r1 -> Point SEC_p521r1
Scalar Curve_P521R1 -> Point Curve_P521R1
forall curve. Curve curve => Scalar curve -> Point curve
Simple.pointBaseMul
    pointsSmulVarTime :: forall (proxy :: * -> *).
proxy Curve_P521R1
-> Scalar Curve_P521R1
-> Scalar Curve_P521R1
-> Point Curve_P521R1
-> Point Curve_P521R1
pointsSmulVarTime proxy Curve_P521R1
_ = Scalar SEC_p521r1
-> Scalar SEC_p521r1 -> Point SEC_p521r1 -> Point SEC_p521r1
Scalar Curve_P521R1
-> Scalar Curve_P521R1 -> Point Curve_P521R1 -> Point Curve_P521R1
forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Point curve -> Point curve
ecPointsMulVarTime
    encodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P521R1 -> Scalar Curve_P521R1 -> bs
encodeScalar proxy Curve_P521R1
_ = Scalar SEC_p521r1 -> bs
Scalar Curve_P521R1 -> bs
forall curve bs. (Curve curve, ByteArray bs) => Scalar curve -> bs
ecScalarToBinary
    decodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_P521R1 -> bs -> CryptoFailable (Scalar Curve_P521R1)
decodeScalar proxy Curve_P521R1
_ = bs -> CryptoFailable (Scalar SEC_p521r1)
bs -> CryptoFailable (Scalar Curve_P521R1)
forall curve bs.
(Curve curve, ByteArrayAccess bs) =>
bs -> CryptoFailable (Scalar curve)
ecScalarFromBinary
    scalarToInteger :: forall (proxy :: * -> *).
proxy Curve_P521R1 -> Scalar Curve_P521R1 -> Integer
scalarToInteger proxy Curve_P521R1
_ = Scalar SEC_p521r1 -> Integer
Scalar Curve_P521R1 -> Integer
forall curve. Scalar curve -> Integer
ecScalarToInteger
    scalarFromInteger :: forall (proxy :: * -> *).
proxy Curve_P521R1
-> Integer -> CryptoFailable (Scalar Curve_P521R1)
scalarFromInteger proxy Curve_P521R1
_ = Integer -> CryptoFailable (Scalar SEC_p521r1)
Integer -> CryptoFailable (Scalar Curve_P521R1)
forall curve.
Curve curve =>
Integer -> CryptoFailable (Scalar curve)
ecScalarFromInteger
    scalarAdd :: forall (proxy :: * -> *).
proxy Curve_P521R1
-> Scalar Curve_P521R1
-> Scalar Curve_P521R1
-> Scalar Curve_P521R1
scalarAdd proxy Curve_P521R1
_ = Scalar SEC_p521r1 -> Scalar SEC_p521r1 -> Scalar SEC_p521r1
Scalar Curve_P521R1 -> Scalar Curve_P521R1 -> Scalar Curve_P521R1
forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Scalar curve
ecScalarAdd
    scalarMul :: forall (proxy :: * -> *).
proxy Curve_P521R1
-> Scalar Curve_P521R1
-> Scalar Curve_P521R1
-> Scalar Curve_P521R1
scalarMul proxy Curve_P521R1
_ = Scalar SEC_p521r1 -> Scalar SEC_p521r1 -> Scalar SEC_p521r1
Scalar Curve_P521R1 -> Scalar Curve_P521R1 -> Scalar Curve_P521R1
forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Scalar curve
ecScalarMul

data Curve_X25519 = Curve_X25519
    deriving (Int -> Curve_X25519 -> ShowS
[Curve_X25519] -> ShowS
Curve_X25519 -> String
(Int -> Curve_X25519 -> ShowS)
-> (Curve_X25519 -> String)
-> ([Curve_X25519] -> ShowS)
-> Show Curve_X25519
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> Curve_X25519 -> ShowS
showsPrec :: Int -> Curve_X25519 -> ShowS
$cshow :: Curve_X25519 -> String
show :: Curve_X25519 -> String
$cshowList :: [Curve_X25519] -> ShowS
showList :: [Curve_X25519] -> ShowS
Show,Typeable Curve_X25519
Typeable Curve_X25519 =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g) -> Curve_X25519 -> c Curve_X25519)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c Curve_X25519)
-> (Curve_X25519 -> Constr)
-> (Curve_X25519 -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c Curve_X25519))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c Curve_X25519))
-> ((forall b. Data b => b -> b) -> Curve_X25519 -> Curve_X25519)
-> (forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r)
-> (forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r)
-> (forall u. (forall d. Data d => d -> u) -> Curve_X25519 -> [u])
-> (forall u.
    Int -> (forall d. Data d => d -> u) -> Curve_X25519 -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519)
-> Data Curve_X25519
Curve_X25519 -> Constr
Curve_X25519 -> DataType
(forall b. Data b => b -> b) -> Curve_X25519 -> Curve_X25519
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) -> Curve_X25519 -> u
forall u. (forall d. Data d => d -> u) -> Curve_X25519 -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_X25519
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_X25519 -> c Curve_X25519
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_X25519)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_X25519)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_X25519 -> c Curve_X25519
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_X25519 -> c Curve_X25519
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_X25519
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_X25519
$ctoConstr :: Curve_X25519 -> Constr
toConstr :: Curve_X25519 -> Constr
$cdataTypeOf :: Curve_X25519 -> DataType
dataTypeOf :: Curve_X25519 -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_X25519)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_X25519)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_X25519)
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_X25519)
$cgmapT :: (forall b. Data b => b -> b) -> Curve_X25519 -> Curve_X25519
gmapT :: (forall b. Data b => b -> b) -> Curve_X25519 -> Curve_X25519
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X25519 -> r
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_X25519 -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_X25519 -> [u]
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_X25519 -> u
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_X25519 -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X25519 -> m Curve_X25519
Data)

instance EllipticCurve Curve_X25519 where
    type Point Curve_X25519 = X25519.PublicKey
    type Scalar Curve_X25519 = X25519.SecretKey
    curveSizeBits :: forall (proxy :: * -> *). proxy Curve_X25519 -> Int
curveSizeBits proxy Curve_X25519
_ = Int
255
    curveGenerateScalar :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_X25519 -> randomly (Scalar Curve_X25519)
curveGenerateScalar proxy Curve_X25519
_ = randomly SecretKey
randomly (Scalar Curve_X25519)
forall (m :: * -> *). MonadRandom m => m SecretKey
X25519.generateSecretKey
    curveGenerateKeyPair :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_X25519 -> randomly (KeyPair Curve_X25519)
curveGenerateKeyPair proxy Curve_X25519
_ = do
        SecretKey
s <- randomly SecretKey
forall (m :: * -> *). MonadRandom m => m SecretKey
X25519.generateSecretKey
        KeyPair Curve_X25519 -> randomly (KeyPair Curve_X25519)
forall a. a -> randomly a
forall (m :: * -> *) a. Monad m => a -> m a
return (KeyPair Curve_X25519 -> randomly (KeyPair Curve_X25519))
-> KeyPair Curve_X25519 -> randomly (KeyPair Curve_X25519)
forall a b. (a -> b) -> a -> b
$ Point Curve_X25519 -> Scalar Curve_X25519 -> KeyPair Curve_X25519
forall curve. Point curve -> Scalar curve -> KeyPair curve
KeyPair (SecretKey -> PublicKey
X25519.toPublic SecretKey
s) SecretKey
Scalar Curve_X25519
s
    encodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_X25519 -> Point Curve_X25519 -> bs
encodePoint proxy Curve_X25519
_ Point Curve_X25519
p = PublicKey -> bs
forall bin bout.
(ByteArrayAccess bin, ByteArray bout) =>
bin -> bout
B.convert PublicKey
Point Curve_X25519
p
    decodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_X25519 -> bs -> CryptoFailable (Point Curve_X25519)
decodePoint proxy Curve_X25519
_ bs
bs = bs -> CryptoFailable PublicKey
forall bs. ByteArrayAccess bs => bs -> CryptoFailable PublicKey
X25519.publicKey bs
bs

instance EllipticCurveDH Curve_X25519 where
    ecdhRaw :: forall (proxy :: * -> *).
proxy Curve_X25519
-> Scalar Curve_X25519 -> Point Curve_X25519 -> SharedSecret
ecdhRaw proxy Curve_X25519
_ Scalar Curve_X25519
s Point Curve_X25519
p = ScrubbedBytes -> SharedSecret
SharedSecret (ScrubbedBytes -> SharedSecret) -> ScrubbedBytes -> SharedSecret
forall a b. (a -> b) -> a -> b
$ DhSecret -> ScrubbedBytes
forall bin bout.
(ByteArrayAccess bin, ByteArray bout) =>
bin -> bout
convert DhSecret
secret
      where secret :: DhSecret
secret = PublicKey -> SecretKey -> DhSecret
X25519.dh PublicKey
Point Curve_X25519
p SecretKey
Scalar Curve_X25519
s
    ecdh :: forall (proxy :: * -> *).
proxy Curve_X25519
-> Scalar Curve_X25519
-> Point Curve_X25519
-> CryptoFailable SharedSecret
ecdh proxy Curve_X25519
prx Scalar Curve_X25519
s Point Curve_X25519
p = SharedSecret -> CryptoFailable SharedSecret
checkNonZeroDH (proxy Curve_X25519
-> Scalar Curve_X25519 -> Point Curve_X25519 -> SharedSecret
forall curve (proxy :: * -> *).
EllipticCurveDH curve =>
proxy curve -> Scalar curve -> Point curve -> SharedSecret
forall (proxy :: * -> *).
proxy Curve_X25519
-> Scalar Curve_X25519 -> Point Curve_X25519 -> SharedSecret
ecdhRaw proxy Curve_X25519
prx Scalar Curve_X25519
s Point Curve_X25519
p)

data Curve_X448 = Curve_X448
    deriving (Int -> Curve_X448 -> ShowS
[Curve_X448] -> ShowS
Curve_X448 -> String
(Int -> Curve_X448 -> ShowS)
-> (Curve_X448 -> String)
-> ([Curve_X448] -> ShowS)
-> Show Curve_X448
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> Curve_X448 -> ShowS
showsPrec :: Int -> Curve_X448 -> ShowS
$cshow :: Curve_X448 -> String
show :: Curve_X448 -> String
$cshowList :: [Curve_X448] -> ShowS
showList :: [Curve_X448] -> ShowS
Show,Typeable Curve_X448
Typeable Curve_X448 =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g) -> Curve_X448 -> c Curve_X448)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c Curve_X448)
-> (Curve_X448 -> Constr)
-> (Curve_X448 -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c Curve_X448))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c Curve_X448))
-> ((forall b. Data b => b -> b) -> Curve_X448 -> Curve_X448)
-> (forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r)
-> (forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r)
-> (forall u. (forall d. Data d => d -> u) -> Curve_X448 -> [u])
-> (forall u.
    Int -> (forall d. Data d => d -> u) -> Curve_X448 -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448)
-> Data Curve_X448
Curve_X448 -> Constr
Curve_X448 -> DataType
(forall b. Data b => b -> b) -> Curve_X448 -> Curve_X448
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) -> Curve_X448 -> u
forall u. (forall d. Data d => d -> u) -> Curve_X448 -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_X448
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_X448 -> c Curve_X448
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_X448)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Curve_X448)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_X448 -> c Curve_X448
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Curve_X448 -> c Curve_X448
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_X448
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_X448
$ctoConstr :: Curve_X448 -> Constr
toConstr :: Curve_X448 -> Constr
$cdataTypeOf :: Curve_X448 -> DataType
dataTypeOf :: Curve_X448 -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_X448)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_X448)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Curve_X448)
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Curve_X448)
$cgmapT :: (forall b. Data b => b -> b) -> Curve_X448 -> Curve_X448
gmapT :: (forall b. Data b => b -> b) -> Curve_X448 -> Curve_X448
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_X448 -> r
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_X448 -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_X448 -> [u]
$cgmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_X448 -> u
gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Curve_X448 -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d) -> Curve_X448 -> m Curve_X448
Data)

instance EllipticCurve Curve_X448 where
    type Point Curve_X448 = X448.PublicKey
    type Scalar Curve_X448 = X448.SecretKey
    curveSizeBits :: forall (proxy :: * -> *). proxy Curve_X448 -> Int
curveSizeBits proxy Curve_X448
_ = Int
448
    curveGenerateScalar :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_X448 -> randomly (Scalar Curve_X448)
curveGenerateScalar proxy Curve_X448
_ = randomly SecretKey
randomly (Scalar Curve_X448)
forall (m :: * -> *). MonadRandom m => m SecretKey
X448.generateSecretKey
    curveGenerateKeyPair :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_X448 -> randomly (KeyPair Curve_X448)
curveGenerateKeyPair proxy Curve_X448
_ = do
        SecretKey
s <- randomly SecretKey
forall (m :: * -> *). MonadRandom m => m SecretKey
X448.generateSecretKey
        KeyPair Curve_X448 -> randomly (KeyPair Curve_X448)
forall a. a -> randomly a
forall (m :: * -> *) a. Monad m => a -> m a
return (KeyPair Curve_X448 -> randomly (KeyPair Curve_X448))
-> KeyPair Curve_X448 -> randomly (KeyPair Curve_X448)
forall a b. (a -> b) -> a -> b
$ Point Curve_X448 -> Scalar Curve_X448 -> KeyPair Curve_X448
forall curve. Point curve -> Scalar curve -> KeyPair curve
KeyPair (SecretKey -> PublicKey
X448.toPublic SecretKey
s) SecretKey
Scalar Curve_X448
s
    encodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_X448 -> Point Curve_X448 -> bs
encodePoint proxy Curve_X448
_ Point Curve_X448
p = PublicKey -> bs
forall bin bout.
(ByteArrayAccess bin, ByteArray bout) =>
bin -> bout
B.convert PublicKey
Point Curve_X448
p
    decodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_X448 -> bs -> CryptoFailable (Point Curve_X448)
decodePoint proxy Curve_X448
_ bs
bs = bs -> CryptoFailable PublicKey
forall bs. ByteArrayAccess bs => bs -> CryptoFailable PublicKey
X448.publicKey bs
bs

instance EllipticCurveDH Curve_X448 where
    ecdhRaw :: forall (proxy :: * -> *).
proxy Curve_X448
-> Scalar Curve_X448 -> Point Curve_X448 -> SharedSecret
ecdhRaw proxy Curve_X448
_ Scalar Curve_X448
s Point Curve_X448
p = ScrubbedBytes -> SharedSecret
SharedSecret (ScrubbedBytes -> SharedSecret) -> ScrubbedBytes -> SharedSecret
forall a b. (a -> b) -> a -> b
$ DhSecret -> ScrubbedBytes
forall bin bout.
(ByteArrayAccess bin, ByteArray bout) =>
bin -> bout
convert DhSecret
secret
      where secret :: DhSecret
secret = PublicKey -> SecretKey -> DhSecret
X448.dh PublicKey
Point Curve_X448
p SecretKey
Scalar Curve_X448
s
    ecdh :: forall (proxy :: * -> *).
proxy Curve_X448
-> Scalar Curve_X448
-> Point Curve_X448
-> CryptoFailable SharedSecret
ecdh proxy Curve_X448
prx Scalar Curve_X448
s Point Curve_X448
p = SharedSecret -> CryptoFailable SharedSecret
checkNonZeroDH (proxy Curve_X448
-> Scalar Curve_X448 -> Point Curve_X448 -> SharedSecret
forall curve (proxy :: * -> *).
EllipticCurveDH curve =>
proxy curve -> Scalar curve -> Point curve -> SharedSecret
forall (proxy :: * -> *).
proxy Curve_X448
-> Scalar Curve_X448 -> Point Curve_X448 -> SharedSecret
ecdhRaw proxy Curve_X448
prx Scalar Curve_X448
s Point Curve_X448
p)

data Curve_Edwards25519 = Curve_Edwards25519
    deriving (Int -> Curve_Edwards25519 -> ShowS
[Curve_Edwards25519] -> ShowS
Curve_Edwards25519 -> String
(Int -> Curve_Edwards25519 -> ShowS)
-> (Curve_Edwards25519 -> String)
-> ([Curve_Edwards25519] -> ShowS)
-> Show Curve_Edwards25519
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> Curve_Edwards25519 -> ShowS
showsPrec :: Int -> Curve_Edwards25519 -> ShowS
$cshow :: Curve_Edwards25519 -> String
show :: Curve_Edwards25519 -> String
$cshowList :: [Curve_Edwards25519] -> ShowS
showList :: [Curve_Edwards25519] -> ShowS
Show,Typeable Curve_Edwards25519
Typeable Curve_Edwards25519 =>
(forall (c :: * -> *).
 (forall d b. Data d => c (d -> b) -> d -> c b)
 -> (forall g. g -> c g)
 -> Curve_Edwards25519
 -> c Curve_Edwards25519)
-> (forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c Curve_Edwards25519)
-> (Curve_Edwards25519 -> Constr)
-> (Curve_Edwards25519 -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c Curve_Edwards25519))
-> (forall (t :: * -> * -> *) (c :: * -> *).
    Typeable t =>
    (forall d e. (Data d, Data e) => c (t d e))
    -> Maybe (c Curve_Edwards25519))
-> ((forall b. Data b => b -> b)
    -> Curve_Edwards25519 -> Curve_Edwards25519)
-> (forall r r'.
    (r -> r' -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r)
-> (forall r r'.
    (r' -> r -> r)
    -> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r)
-> (forall u.
    (forall d. Data d => d -> u) -> Curve_Edwards25519 -> [u])
-> (forall u.
    Int -> (forall d. Data d => d -> u) -> Curve_Edwards25519 -> u)
-> (forall (m :: * -> *).
    Monad m =>
    (forall d. Data d => d -> m d)
    -> Curve_Edwards25519 -> m Curve_Edwards25519)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d)
    -> Curve_Edwards25519 -> m Curve_Edwards25519)
-> (forall (m :: * -> *).
    MonadPlus m =>
    (forall d. Data d => d -> m d)
    -> Curve_Edwards25519 -> m Curve_Edwards25519)
-> Data Curve_Edwards25519
Curve_Edwards25519 -> Constr
Curve_Edwards25519 -> DataType
(forall b. Data b => b -> b)
-> Curve_Edwards25519 -> Curve_Edwards25519
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) -> Curve_Edwards25519 -> u
forall u. (forall d. Data d => d -> u) -> Curve_Edwards25519 -> [u]
forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r
forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r
forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_Edwards25519
forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> Curve_Edwards25519
-> c Curve_Edwards25519
forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_Edwards25519)
forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_Edwards25519)
$cgfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> Curve_Edwards25519
-> c Curve_Edwards25519
gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g)
-> Curve_Edwards25519
-> c Curve_Edwards25519
$cgunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_Edwards25519
gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c Curve_Edwards25519
$ctoConstr :: Curve_Edwards25519 -> Constr
toConstr :: Curve_Edwards25519 -> Constr
$cdataTypeOf :: Curve_Edwards25519 -> DataType
dataTypeOf :: Curve_Edwards25519 -> DataType
$cdataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_Edwards25519)
dataCast1 :: forall (t :: * -> *) (c :: * -> *).
Typeable t =>
(forall d. Data d => c (t d)) -> Maybe (c Curve_Edwards25519)
$cdataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_Edwards25519)
dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e))
-> Maybe (c Curve_Edwards25519)
$cgmapT :: (forall b. Data b => b -> b)
-> Curve_Edwards25519 -> Curve_Edwards25519
gmapT :: (forall b. Data b => b -> b)
-> Curve_Edwards25519 -> Curve_Edwards25519
$cgmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r
gmapQl :: forall r r'.
(r -> r' -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r
$cgmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r
gmapQr :: forall r r'.
(r' -> r -> r)
-> r -> (forall d. Data d => d -> r') -> Curve_Edwards25519 -> r
$cgmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_Edwards25519 -> [u]
gmapQ :: forall u. (forall d. Data d => d -> u) -> Curve_Edwards25519 -> [u]
$cgmapQi :: forall u.
Int -> (forall d. Data d => d -> u) -> Curve_Edwards25519 -> u
gmapQi :: forall u.
Int -> (forall d. Data d => d -> u) -> Curve_Edwards25519 -> u
$cgmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
gmapM :: forall (m :: * -> *).
Monad m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
$cgmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
gmapMp :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
$cgmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
gmapMo :: forall (m :: * -> *).
MonadPlus m =>
(forall d. Data d => d -> m d)
-> Curve_Edwards25519 -> m Curve_Edwards25519
Data)

instance EllipticCurve Curve_Edwards25519 where
    type Point Curve_Edwards25519 = Edwards25519.Point
    type Scalar Curve_Edwards25519 = Edwards25519.Scalar
    curveSizeBits :: forall (proxy :: * -> *). proxy Curve_Edwards25519 -> Int
curveSizeBits proxy Curve_Edwards25519
_ = Int
255
    curveGenerateScalar :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_Edwards25519 -> randomly (Scalar Curve_Edwards25519)
curveGenerateScalar proxy Curve_Edwards25519
_ = randomly Scalar
randomly (Scalar Curve_Edwards25519)
forall (randomly :: * -> *).
MonadRandom randomly =>
randomly Scalar
Edwards25519.scalarGenerate
    curveGenerateKeyPair :: forall (randomly :: * -> *) (proxy :: * -> *).
MonadRandom randomly =>
proxy Curve_Edwards25519 -> randomly (KeyPair Curve_Edwards25519)
curveGenerateKeyPair proxy Curve_Edwards25519
_ = Scalar -> KeyPair Curve_Edwards25519
forall {curve}.
(Point curve ~ Point, Scalar curve ~ Scalar) =>
Scalar -> KeyPair curve
toKeyPair (Scalar -> KeyPair Curve_Edwards25519)
-> randomly Scalar -> randomly (KeyPair Curve_Edwards25519)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> randomly Scalar
forall (randomly :: * -> *).
MonadRandom randomly =>
randomly Scalar
Edwards25519.scalarGenerate
      where toKeyPair :: Scalar -> KeyPair curve
toKeyPair Scalar
scalar = Point curve -> Scalar curve -> KeyPair curve
forall curve. Point curve -> Scalar curve -> KeyPair curve
KeyPair (Scalar -> Point
Edwards25519.toPoint Scalar
scalar) Scalar
Scalar curve
scalar
    encodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_Edwards25519 -> Point Curve_Edwards25519 -> bs
encodePoint proxy Curve_Edwards25519
_ Point Curve_Edwards25519
point = Point -> bs
forall bs. ByteArray bs => Point -> bs
Edwards25519.pointEncode Point
Point Curve_Edwards25519
point
    decodePoint :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_Edwards25519
-> bs -> CryptoFailable (Point Curve_Edwards25519)
decodePoint proxy Curve_Edwards25519
_ bs
bs = bs -> CryptoFailable Point
forall bs. ByteArrayAccess bs => bs -> CryptoFailable Point
Edwards25519.pointDecode bs
bs

instance EllipticCurveArith Curve_Edwards25519 where
    pointAdd :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Point Curve_Edwards25519
-> Point Curve_Edwards25519
-> Point Curve_Edwards25519
pointAdd proxy Curve_Edwards25519
_ Point Curve_Edwards25519
a Point Curve_Edwards25519
b = Point -> Point -> Point
Edwards25519.pointAdd Point
Point Curve_Edwards25519
a Point
Point Curve_Edwards25519
b
    pointNegate :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Point Curve_Edwards25519 -> Point Curve_Edwards25519
pointNegate proxy Curve_Edwards25519
_ Point Curve_Edwards25519
p = Point -> Point
Edwards25519.pointNegate Point
Point Curve_Edwards25519
p
    pointSmul :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Point Curve_Edwards25519
-> Point Curve_Edwards25519
pointSmul proxy Curve_Edwards25519
_ Scalar Curve_Edwards25519
s Point Curve_Edwards25519
p = Scalar -> Point -> Point
Edwards25519.pointMul Scalar
Scalar Curve_Edwards25519
s Point
Point Curve_Edwards25519
p

instance EllipticCurveBasepointArith Curve_Edwards25519 where
    curveOrderBits :: forall (proxy :: * -> *). proxy Curve_Edwards25519 -> Int
curveOrderBits proxy Curve_Edwards25519
_ = Int
253
    pointBaseSmul :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Scalar Curve_Edwards25519 -> Point Curve_Edwards25519
pointBaseSmul proxy Curve_Edwards25519
_ = Scalar -> Point
Scalar Curve_Edwards25519 -> Point Curve_Edwards25519
Edwards25519.toPoint
    pointsSmulVarTime :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Point Curve_Edwards25519
-> Point Curve_Edwards25519
pointsSmulVarTime proxy Curve_Edwards25519
_ = Scalar -> Scalar -> Point -> Point
Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Point Curve_Edwards25519
-> Point Curve_Edwards25519
Edwards25519.pointsMulVarTime
    encodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_Edwards25519 -> Scalar Curve_Edwards25519 -> bs
encodeScalar proxy Curve_Edwards25519
_ = bs -> bs
forall bs. ByteArray bs => bs -> bs
B.reverse (bs -> bs) -> (Scalar -> bs) -> Scalar -> bs
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Scalar -> bs
forall bs. ByteArray bs => Scalar -> bs
Edwards25519.scalarEncode
    decodeScalar :: forall bs (proxy :: * -> *).
ByteArray bs =>
proxy Curve_Edwards25519
-> bs -> CryptoFailable (Scalar Curve_Edwards25519)
decodeScalar proxy Curve_Edwards25519
_ bs
bs
        | bs -> Int
forall ba. ByteArrayAccess ba => ba -> Int
B.length bs
bs Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
32 = bs -> CryptoFailable Scalar
forall bs. ByteArrayAccess bs => bs -> CryptoFailable Scalar
Edwards25519.scalarDecodeLong (bs -> bs
forall bs. ByteArray bs => bs -> bs
B.reverse bs
bs)
        | Bool
otherwise         = CryptoError -> CryptoFailable Scalar
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_SecretKeySizeInvalid
    scalarToInteger :: forall (proxy :: * -> *).
proxy Curve_Edwards25519 -> Scalar Curve_Edwards25519 -> Integer
scalarToInteger proxy Curve_Edwards25519
_ Scalar Curve_Edwards25519
s = Bytes -> Integer
forall ba. ByteArrayAccess ba => ba -> Integer
LE.os2ip (Scalar -> Bytes
forall bs. ByteArray bs => Scalar -> bs
Edwards25519.scalarEncode Scalar
Scalar Curve_Edwards25519
s :: B.Bytes)
    scalarFromInteger :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Integer -> CryptoFailable (Scalar Curve_Edwards25519)
scalarFromInteger proxy Curve_Edwards25519
_ Integer
i =
        case Int -> Integer -> Maybe Bytes
forall ba. ByteArray ba => Int -> Integer -> Maybe ba
LE.i2ospOf Int
32 Integer
i of
            Maybe Bytes
Nothing -> CryptoError -> CryptoFailable Scalar
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_SecretKeySizeInvalid
            Just Bytes
bs -> Bytes -> CryptoFailable Scalar
forall bs. ByteArrayAccess bs => bs -> CryptoFailable Scalar
Edwards25519.scalarDecodeLong (Bytes
bs :: B.Bytes)
    scalarAdd :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519
scalarAdd proxy Curve_Edwards25519
_ = Scalar -> Scalar -> Scalar
Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519 -> Scalar Curve_Edwards25519
Edwards25519.scalarAdd
    scalarMul :: forall (proxy :: * -> *).
proxy Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519
scalarMul proxy Curve_Edwards25519
_ = Scalar -> Scalar -> Scalar
Scalar Curve_Edwards25519
-> Scalar Curve_Edwards25519 -> Scalar Curve_Edwards25519
Edwards25519.scalarMul

checkNonZeroDH :: SharedSecret -> CryptoFailable SharedSecret
checkNonZeroDH :: SharedSecret -> CryptoFailable SharedSecret
checkNonZeroDH s :: SharedSecret
s@(SharedSecret ScrubbedBytes
b)
    | ScrubbedBytes -> Bool
forall ba. ByteArrayAccess ba => ba -> Bool
B.constAllZero ScrubbedBytes
b = CryptoError -> CryptoFailable SharedSecret
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_ScalarMultiplicationInvalid
    | Bool
otherwise        = SharedSecret -> CryptoFailable SharedSecret
forall a. a -> CryptoFailable a
CryptoPassed SharedSecret
s

encodeECShared :: Simple.Curve curve => Proxy curve -> Simple.Point curve -> CryptoFailable SharedSecret
encodeECShared :: forall curve.
Curve curve =>
Proxy curve -> Point curve -> CryptoFailable SharedSecret
encodeECShared Proxy curve
_   Point curve
Simple.PointO      = CryptoError -> CryptoFailable SharedSecret
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_ScalarMultiplicationInvalid
encodeECShared Proxy curve
prx (Simple.Point Integer
x Integer
_) = SharedSecret -> CryptoFailable SharedSecret
forall a. a -> CryptoFailable a
CryptoPassed (SharedSecret -> CryptoFailable SharedSecret)
-> (ScrubbedBytes -> SharedSecret)
-> ScrubbedBytes
-> CryptoFailable SharedSecret
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ScrubbedBytes -> SharedSecret
SharedSecret (ScrubbedBytes -> CryptoFailable SharedSecret)
-> ScrubbedBytes -> CryptoFailable SharedSecret
forall a b. (a -> b) -> a -> b
$ Int -> Integer -> ScrubbedBytes
forall ba. ByteArray ba => Int -> Integer -> ba
i2ospOf_ (Proxy curve -> Int
forall curve (proxy :: * -> *). Curve curve => proxy curve -> Int
Simple.curveSizeBytes Proxy curve
prx) Integer
x

encodeECPoint :: forall curve bs . (Simple.Curve curve, ByteArray bs) => Simple.Point curve -> bs
encodeECPoint :: forall curve bs. (Curve curve, ByteArray bs) => Point curve -> bs
encodeECPoint Point curve
Simple.PointO      = String -> bs
forall a. HasCallStack => String -> a
error String
"encodeECPoint: cannot serialize point at infinity"
encodeECPoint (Simple.Point Integer
x Integer
y) = [bs] -> bs
forall bin bout.
(ByteArrayAccess bin, ByteArray bout) =>
[bin] -> bout
B.concat [bs
uncompressed,bs
xb,bs
yb]
  where
    size :: Int
size = Proxy curve -> Int
forall curve (proxy :: * -> *). Curve curve => proxy curve -> Int
Simple.curveSizeBytes (Proxy curve
forall {k} (t :: k). Proxy t
Proxy :: Proxy curve)
    uncompressed, xb, yb :: bs
    uncompressed :: bs
uncompressed = Word8 -> bs
forall a. ByteArray a => Word8 -> a
B.singleton Word8
4
    xb :: bs
xb = Int -> Integer -> bs
forall ba. ByteArray ba => Int -> Integer -> ba
i2ospOf_ Int
size Integer
x
    yb :: bs
yb = Int -> Integer -> bs
forall ba. ByteArray ba => Int -> Integer -> ba
i2ospOf_ Int
size Integer
y

decodeECPoint :: (Simple.Curve curve, ByteArray bs) => bs -> CryptoFailable (Simple.Point curve)
decodeECPoint :: forall curve bs.
(Curve curve, ByteArray bs) =>
bs -> CryptoFailable (Point curve)
decodeECPoint bs
mxy = case bs -> Maybe (Word8, bs)
forall a. ByteArray a => a -> Maybe (Word8, a)
B.uncons bs
mxy of
    Maybe (Word8, bs)
Nothing     -> CryptoError -> CryptoFailable (Point curve)
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_PointSizeInvalid
    Just (Word8
m,bs
xy)
        -- uncompressed
        | Word8
m Word8 -> Word8 -> Bool
forall a. Eq a => a -> a -> Bool
== Word8
4 ->
            let siz :: Int
siz = bs -> Int
forall ba. ByteArrayAccess ba => ba -> Int
B.length bs
xy Int -> Int -> Int
forall a. Integral a => a -> a -> a
`div` Int
2
                (bs
xb,bs
yb) = Int -> bs -> (bs, bs)
forall bs. ByteArray bs => Int -> bs -> (bs, bs)
B.splitAt Int
siz bs
xy
                x :: Integer
x = bs -> Integer
forall ba. ByteArrayAccess ba => ba -> Integer
os2ip bs
xb
                y :: Integer
y = bs -> Integer
forall ba. ByteArrayAccess ba => ba -> Integer
os2ip bs
yb
             in (Integer, Integer) -> CryptoFailable (Point curve)
forall curve.
Curve curve =>
(Integer, Integer) -> CryptoFailable (Point curve)
Simple.pointFromIntegers (Integer
x,Integer
y)
        | Bool
otherwise -> CryptoError -> CryptoFailable (Point curve)
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_PointFormatInvalid

ecPointsMulVarTime :: forall curve . Simple.Curve curve
                   => Simple.Scalar curve
                   -> Simple.Scalar curve -> Simple.Point curve
                   -> Simple.Point curve
ecPointsMulVarTime :: forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Point curve -> Point curve
ecPointsMulVarTime Scalar curve
n1 = Scalar curve
-> Point curve -> Scalar curve -> Point curve -> Point curve
forall curve.
Curve curve =>
Scalar curve
-> Point curve -> Scalar curve -> Point curve -> Point curve
Simple.pointAddTwoMuls Scalar curve
n1 Point curve
g
  where g :: Point curve
g = CurveParameters curve -> Point curve
forall curve. CurveParameters curve -> Point curve
Simple.curveEccG (CurveParameters curve -> Point curve)
-> CurveParameters curve -> Point curve
forall a b. (a -> b) -> a -> b
$ Proxy curve -> CurveParameters curve
forall curve (proxy :: * -> *).
Curve curve =>
proxy curve -> CurveParameters curve
forall (proxy :: * -> *). proxy curve -> CurveParameters curve
Simple.curveParameters (Proxy curve
forall {k} (t :: k). Proxy t
Proxy :: Proxy curve)

ecScalarFromBinary :: forall curve bs . (Simple.Curve curve, ByteArrayAccess bs)
                   => bs -> CryptoFailable (Simple.Scalar curve)
ecScalarFromBinary :: forall curve bs.
(Curve curve, ByteArrayAccess bs) =>
bs -> CryptoFailable (Scalar curve)
ecScalarFromBinary bs
ba
    | bs -> Int
forall ba. ByteArrayAccess ba => ba -> Int
B.length bs
ba Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
/= Int
size = CryptoError -> CryptoFailable (Scalar curve)
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_SecretKeySizeInvalid
    | Bool
otherwise           = Scalar curve -> CryptoFailable (Scalar curve)
forall a. a -> CryptoFailable a
CryptoPassed (Integer -> Scalar curve
forall curve. Integer -> Scalar curve
Simple.Scalar (Integer -> Scalar curve) -> Integer -> Scalar curve
forall a b. (a -> b) -> a -> b
$ bs -> Integer
forall ba. ByteArrayAccess ba => ba -> Integer
os2ip bs
ba)
  where size :: Int
size = Proxy curve -> Int
forall curve (proxy :: * -> *). Curve curve => proxy curve -> Int
ecCurveOrderBytes (Proxy curve
forall {k} (t :: k). Proxy t
Proxy :: Proxy curve)

ecScalarToBinary :: forall curve bs . (Simple.Curve curve, ByteArray bs)
                 => Simple.Scalar curve -> bs
ecScalarToBinary :: forall curve bs. (Curve curve, ByteArray bs) => Scalar curve -> bs
ecScalarToBinary (Simple.Scalar Integer
s) = Int -> Integer -> bs
forall ba. ByteArray ba => Int -> Integer -> ba
i2ospOf_ Int
size Integer
s
  where size :: Int
size = Proxy curve -> Int
forall curve (proxy :: * -> *). Curve curve => proxy curve -> Int
ecCurveOrderBytes (Proxy curve
forall {k} (t :: k). Proxy t
Proxy :: Proxy curve)

ecScalarFromInteger :: forall curve . Simple.Curve curve
                    => Integer -> CryptoFailable (Simple.Scalar curve)
ecScalarFromInteger :: forall curve.
Curve curve =>
Integer -> CryptoFailable (Scalar curve)
ecScalarFromInteger Integer
s
    | Integer -> Int
numBits Integer
s Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
nb = CryptoError -> CryptoFailable (Scalar curve)
forall a. CryptoError -> CryptoFailable a
CryptoFailed CryptoError
CryptoError_SecretKeySizeInvalid
    | Bool
otherwise      = Scalar curve -> CryptoFailable (Scalar curve)
forall a. a -> CryptoFailable a
CryptoPassed (Integer -> Scalar curve
forall curve. Integer -> Scalar curve
Simple.Scalar Integer
s)
  where nb :: Int
nb = Int
8 Int -> Int -> Int
forall a. Num a => a -> a -> a
* Proxy curve -> Int
forall curve (proxy :: * -> *). Curve curve => proxy curve -> Int
ecCurveOrderBytes (Proxy curve
forall {k} (t :: k). Proxy t
Proxy :: Proxy curve)

ecScalarToInteger :: Simple.Scalar curve -> Integer
ecScalarToInteger :: forall curve. Scalar curve -> Integer
ecScalarToInteger (Simple.Scalar Integer
s) = Integer
s

ecCurveOrderBytes :: Simple.Curve c => proxy c -> Int
ecCurveOrderBytes :: forall curve (proxy :: * -> *). Curve curve => proxy curve -> Int
ecCurveOrderBytes proxy c
prx = (Integer -> Int
numBits Integer
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
7) Int -> Int -> Int
forall a. Integral a => a -> a -> a
`div` Int
8
  where n :: Integer
n = CurveParameters c -> Integer
forall curve. CurveParameters curve -> Integer
Simple.curveEccN (CurveParameters c -> Integer) -> CurveParameters c -> Integer
forall a b. (a -> b) -> a -> b
$ proxy c -> CurveParameters c
forall curve (proxy :: * -> *).
Curve curve =>
proxy curve -> CurveParameters curve
forall (proxy :: * -> *). proxy c -> CurveParameters c
Simple.curveParameters proxy c
prx

ecScalarAdd :: forall curve . Simple.Curve curve
            => Simple.Scalar curve -> Simple.Scalar curve -> Simple.Scalar curve
ecScalarAdd :: forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Scalar curve
ecScalarAdd (Simple.Scalar Integer
a) (Simple.Scalar Integer
b) = Integer -> Scalar curve
forall curve. Integer -> Scalar curve
Simple.Scalar ((Integer
a Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
+ Integer
b) Integer -> Integer -> Integer
forall a. Integral a => a -> a -> a
`mod` Integer
n)
  where n :: Integer
n = CurveParameters curve -> Integer
forall curve. CurveParameters curve -> Integer
Simple.curveEccN (CurveParameters curve -> Integer)
-> CurveParameters curve -> Integer
forall a b. (a -> b) -> a -> b
$ Proxy curve -> CurveParameters curve
forall curve (proxy :: * -> *).
Curve curve =>
proxy curve -> CurveParameters curve
forall (proxy :: * -> *). proxy curve -> CurveParameters curve
Simple.curveParameters (Proxy curve
forall {k} (t :: k). Proxy t
Proxy :: Proxy curve)

ecScalarMul :: forall curve . Simple.Curve curve
            => Simple.Scalar curve -> Simple.Scalar curve -> Simple.Scalar curve
ecScalarMul :: forall curve.
Curve curve =>
Scalar curve -> Scalar curve -> Scalar curve
ecScalarMul (Simple.Scalar Integer
a) (Simple.Scalar Integer
b) = Integer -> Scalar curve
forall curve. Integer -> Scalar curve
Simple.Scalar ((Integer
a Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
* Integer
b) Integer -> Integer -> Integer
forall a. Integral a => a -> a -> a
`mod` Integer
n)
  where n :: Integer
n = CurveParameters curve -> Integer
forall curve. CurveParameters curve -> Integer
Simple.curveEccN (CurveParameters curve -> Integer)
-> CurveParameters curve -> Integer
forall a b. (a -> b) -> a -> b
$ Proxy curve -> CurveParameters curve
forall curve (proxy :: * -> *).
Curve curve =>
proxy curve -> CurveParameters curve
forall (proxy :: * -> *). proxy curve -> CurveParameters curve
Simple.curveParameters (Proxy curve
forall {k} (t :: k). Proxy t
Proxy :: Proxy curve)