[ECC] Improve the code base to allow multiples different implementations

* Use TypeFamilies; need to see what to do for older GHC versions
* Start implementing some API related to ECIES

Crypto/ECC.hs

@@ -0,0 +1,112 @@
+-- |
+-- Module      : Crypto.ECC
+-- License     : BSD-style
+-- Maintainer  : Vincent Hanquez <vincent@snarc.org>
+-- Stability   : experimental
+-- Portability : unknown
+--
+-- Elliptic Curve Cryptography
+--
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE TypeFamilies #-}
+module Crypto.ECC
+    ( Curve_P256R1(..)
+    , Curve_P521R1(..)
+    , EllipticCurve(..)
+    , EllipticCurveDH(..)
+    , EllipticCurveArith(..)
+    , KeyPair(..)
+    , SharedSecret(..)
+    ) where
+
+import qualified Crypto.PubKey.ECC.P256 as P256
+import qualified Crypto.PubKey.ECC.Types as H
+import qualified Crypto.PubKey.ECC.Prim as H
+import           Crypto.Random
+import           Crypto.Internal.ByteArray (ByteArrayAccess, ScrubbedBytes)
+import           Data.Function (on)
+
+-- | An elliptic curve key pair composed of the private part (a scalar), and
+-- the associated point.
+data KeyPair curve = KeyPair
+    { keypairGetPublic  :: !(Point curve)
+    , keypairGetPrivate :: !(Scalar curve)
+    }
+
+newtype SharedSecret = SharedSecret ScrubbedBytes
+    deriving (Eq, ByteArrayAccess)
+
+class EllipticCurve curve where
+    -- | Point on an Elliptic Curve
+    data Point curve  :: *
+
+    -- | Scalar in the Elliptic Curve domain
+    data Scalar curve :: *
+
+    -- | get the order of the Curve
+    curveGetOrder :: curve -> Integer
+
+    -- | get the curve related to a point on a curve
+    curveOfPoint :: Point curve -> curve
+
+    -- | get the curve related to a curve's scalar
+    curveOfScalar :: Scalar curve -> curve
+
+    -- | get the base point of the Curve
+    curveGetBasePoint :: Point curve
+
+    -- | 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 => randomly (Scalar curve)
+
+    -- | Generate a new random keypair
+    curveGenerateKeyPair :: MonadRandom randomly => randomly (KeyPair curve)
+
+class EllipticCurve curve => EllipticCurveDH curve where
+    -- | Generate a Diffie hellman secret
+    ecdh :: Scalar curve -> Point curve -> SharedSecret
+
+class EllipticCurve curve => EllipticCurveArith curve where
+    -- | Add points on a curve
+    pointAdd :: Point curve -> Point curve -> Point curve
+
+    -- | Scalar Multiplication on a curve
+    pointSmul :: Scalar curve -> Point curve -> Point curve
+
+-- | P256 Curve
+--
+-- also known as P256
+data Curve_P256R1 = Curve_P256R1
+
+instance EllipticCurve Curve_P256R1 where
+    newtype Point Curve_P256R1 = P256Point { unP256Point :: P256.Point }
+    newtype Scalar Curve_P256R1 = P256Scalar { unP256Scalar :: P256.Scalar }
+    curveGetOrder     _ = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
+    curveGetBasePoint = P256Point P256.pointBase
+    curveOfScalar _ = Curve_P256R1
+    curveOfPoint _ = Curve_P256R1
+    curveGenerateScalar = P256Scalar <$> P256.scalarGenerate
+    curveGenerateKeyPair = toKeyPair <$> P256.scalarGenerate
+      where toKeyPair scalar = KeyPair (P256Point $ P256.toPoint scalar) (P256Scalar scalar)
+instance EllipticCurveArith Curve_P256R1 where
+    pointAdd  a b = P256Point $ (P256.pointAdd `on` unP256Point) a b
+    pointSmul s p = P256Point $ P256.pointMul (unP256Scalar s) (unP256Point p)
+instance EllipticCurveDH Curve_P256R1 where
+    ecdh s p = undefined
+
+data Curve_P521R1 = Curve_P521R1
+
+instance EllipticCurve Curve_P521R1 where
+    newtype Point Curve_P521R1 = P521Point { unP521Point :: H.Point }
+    newtype Scalar Curve_P521R1 = P521Scalar { unP521Scalar :: H.PrivateNumber }
+    curveGetOrder _ = H.ecc_n $ H.common_curve $ H.getCurveByName H.SEC_p521r1
+    curveGetBasePoint = P521Point $ H.ecc_g $ H.common_curve $ H.getCurveByName H.SEC_p521r1
+    curveOfScalar _ = Curve_P521R1
+    curveOfPoint _ = Curve_P521R1
+    curveGenerateScalar = P521Scalar <$> H.scalarGenerate (H.getCurveByName H.SEC_p521r1)
+    curveGenerateKeyPair = toKeyPair <$> H.scalarGenerate (H.getCurveByName H.SEC_p521r1)
+      where toKeyPair scalar = KeyPair (P521Point $ H.pointBaseMul (H.getCurveByName H.SEC_p521r1) scalar) (P521Scalar scalar)
+instance EllipticCurveArith Curve_P521R1 where
+    pointAdd a b = P521Point $ (H.pointAdd (H.getCurveByName H.SEC_p521r1) `on` unP521Point) a b
+    pointSmul s p = P521Point (H.pointMul (H.getCurveByName H.SEC_p521r1) (unP521Scalar s) (unP521Point p))
+

Crypto/PubKey/ECIES.hs

@@ -0,0 +1,33 @@
+-- |
+-- Module      : Crypto.PubKey.ECIES
+-- License     : BSD-style
+-- Maintainer  : Vincent Hanquez <vincent@snarc.org>
+-- Stability   : experimental
+-- Portability : unknown
+--
+-- IES with Elliptic curve <https://en.wikipedia.org/wiki/Integrated_Encryption_Scheme>
+--
+module Crypto.PubKey.ECIES
+    ( deriveEncrypt
+    , deriveDecrypt
+    ) where
+
+import           Crypto.ECC
+import           Crypto.Random
+
+-- | Generate random a new Shared secret and the associated point
+-- to do a ECIES style encryption
+deriveEncrypt :: (MonadRandom randomly, EllipticCurveDH curve)
+              => Point curve -- ^ the public key of the receiver
+              -> randomly (Point curve, SharedSecret)
+deriveEncrypt pub = do
+    (KeyPair rPoint rScalar) <- curveGenerateKeyPair
+    return (rPoint, ecdh rScalar pub)
+
+-- | Derive the shared secret with the receiver key
+-- and the R point of the scheme.
+deriveDecrypt :: EllipticCurveDH curve
+              => Point curve  -- ^ The received R (supposedly, randomly generate on the encrypt side)
+              -> Scalar curve -- ^ The secret key of the receiver
+              -> SharedSecret
+deriveDecrypt point secret = ecdh secret point

cryptonite.cabal

@@ -101,6 +101,7 @@ Library
                      Crypto.ConstructHash.MiyaguchiPreneel
                      Crypto.Data.AFIS
                      Crypto.Data.Padding
+                     Crypto.ECC
                      Crypto.Error
                      Crypto.MAC.CMAC
                      Crypto.MAC.Poly1305
@@ -129,6 +130,7 @@ Library
                      Crypto.PubKey.ECC.ECDSA
                      Crypto.PubKey.ECC.P256
                      Crypto.PubKey.ECC.Types
+                     Crypto.PubKey.ECIES
                      Crypto.PubKey.Ed25519
                      Crypto.PubKey.Ed448
                      Crypto.PubKey.RSA