Rewriting ECC

Crypto/ECC.hs

@@ -0,0 +1,236 @@
+-- |
+-- Module      : Crypto.ECC
+-- License     : BSD-style
+-- Maintainer  : Vincent Hanquez <[email protected]>
+-- Stability   : experimental
+-- Portability : unknown
+--
+-- Elliptic Curve Cryptography
+--
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+module Crypto.ECC
+    ( Curve_P256R1(..)
+    , Curve_P384R1(..)
+    , Curve_P521R1(..)
+    , Curve_X25519(..)
+    , 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.Error
+import           Crypto.Internal.Imports
+import           Crypto.Internal.ByteArray (ByteArray, ByteArrayAccess, ScrubbedBytes)
+import qualified Crypto.Internal.ByteArray as B
+import           Crypto.Number.Serialize (i2ospOf_, os2ip)
+import qualified Crypto.PubKey.Curve25519 as X25519
+import           Data.Function (on)
+import           Data.ByteArray (convert)
+
+-- | 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)
+
+    encodePoint :: ByteArray bs => Point curve -> bs
+    decodePoint :: ByteArray bs => bs -> CryptoFailable (Point curve)
+
+instance {-# OVERLAPPABLE #-} Show (Point a) where
+    show _ = undefined
+
+instance {-# OVERLAPPABLE #-} Eq (Point a) where
+    _ == _ = undefined
+
+instance {-# OVERLAPPABLE #-} Show (Scalar a) where
+    show _ = undefined
+
+instance {-# OVERLAPPABLE #-} Eq (Scalar a) where
+    _ == _ = undefined
+
+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.
+    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
+
+--   -- | Scalar Inverse
+--   scalarInverse :: Scalar curve -> Scalar 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 } deriving (Eq,Show)
+    newtype Scalar Curve_P256R1 = P256Scalar { unP256Scalar :: P256.Scalar } deriving (Eq,Show)
+    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)
+    encodePoint (P256Point p) = encodeECPoint x y 32
+      where
+        (x,y) = P256.pointToIntegers p
+    decodePoint bs = fromPoint <$> decodeECPoint bs
+      where fromPoint (H.Point x y) = P256Point $ P256.pointFromIntegers (x,y)
+            fromPoint H.PointO      = error "impossible happened: fromPoint is infinite"
+
+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 = shared
+      where
+        (x, _) = P256.pointToIntegers $ unP256Point $ pointSmul s p
+        len = 32 -- (256 + 7) `div` 8
+        shared = SharedSecret $ i2ospOf_ len x
+
+data Curve_P384R1 = Curve_P384R1
+
+instance EllipticCurve Curve_P384R1 where
+    newtype Point Curve_P384R1 = P384Point { unP384Point :: H.Point } deriving (Eq,Show)
+    newtype Scalar Curve_P384R1 = P384Scalar { unP384Scalar :: H.PrivateNumber } deriving (Eq,Show)
+    curveGetOrder _ = H.ecc_n $ H.common_curve $ H.getCurveByName H.SEC_p384r1
+    curveGetBasePoint = P384Point $ H.ecc_g $ H.common_curve $ H.getCurveByName H.SEC_p384r1
+    curveOfScalar _ = Curve_P384R1
+    curveOfPoint _ = Curve_P384R1
+    curveGenerateScalar = P384Scalar <$> H.scalarGenerate (H.getCurveByName H.SEC_p384r1)
+    curveGenerateKeyPair = toKeyPair <$> H.scalarGenerate (H.getCurveByName H.SEC_p384r1)
+      where toKeyPair scalar = KeyPair (P384Point $ H.pointBaseMul (H.getCurveByName H.SEC_p384r1) scalar) (P384Scalar scalar)
+    encodePoint (P384Point (H.Point x y)) = encodeECPoint x y 48
+    encodePoint (P384Point _)             = error "encodePoint P384"
+    decodePoint bs = P384Point <$> decodeECPoint bs
+
+instance EllipticCurveArith Curve_P384R1 where
+    pointAdd a b = P384Point $ (H.pointAdd (H.getCurveByName H.SEC_p384r1) `on` unP384Point) a b
+    pointSmul s p = P384Point (H.pointMul (H.getCurveByName H.SEC_p384r1) (unP384Scalar s) (unP384Point p))
+
+instance EllipticCurveDH Curve_P384R1 where
+    ecdh s p = shared
+      where
+        H.Point x _ = unP384Point $ pointSmul s p
+        len = 48 -- (384 + 7) `div` 8
+        shared = SharedSecret $ i2ospOf_ len x
+
+data Curve_P521R1 = Curve_P521R1
+
+instance EllipticCurve Curve_P521R1 where
+    newtype Point Curve_P521R1 = P521Point { unP521Point :: H.Point } deriving (Eq,Show)
+    newtype Scalar Curve_P521R1 = P521Scalar { unP521Scalar :: H.PrivateNumber } deriving (Eq,Show)
+    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)
+    encodePoint (P521Point (H.Point x y)) = encodeECPoint x y 66
+    encodePoint (P521Point _)             = error "encodePoint P521"
+    decodePoint bs = P521Point <$> decodeECPoint bs
+
+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))
+
+instance EllipticCurveDH Curve_P521R1 where
+    ecdh s p = shared
+      where
+        H.Point x _ = unP521Point $ pointSmul s p
+        len = 66 -- (521 + 7) `div` 8
+        shared = SharedSecret $ i2ospOf_ len x
+
+data Curve_X25519 = Curve_X25519
+
+instance EllipticCurve Curve_X25519 where
+    newtype Point Curve_X25519 = X25519Point X25519.PublicKey deriving (Eq,Show)
+    newtype Scalar Curve_X25519 = X25519Scalar X25519.SecretKey deriving (Eq,Show)
+    curveGetOrder     _ = undefined
+    curveGetBasePoint = undefined
+    curveOfScalar _ = Curve_X25519
+    curveOfPoint _ = Curve_X25519
+    curveGenerateScalar = X25519Scalar <$> X25519.generateSecretKey
+    curveGenerateKeyPair = do
+        s <- X25519.generateSecretKey
+        let p = X25519.toPublic s
+        return $ KeyPair (X25519Point p) (X25519Scalar s)
+    encodePoint (X25519Point p) = B.convert p
+    decodePoint bs = X25519Point <$> X25519.publicKey bs
+
+instance EllipticCurveDH Curve_X25519 where
+    ecdh (X25519Scalar s) (X25519Point p) = SharedSecret $ convert secret
+      where
+        secret = X25519.dh p s
+
+encodeECPoint :: forall bs. ByteArray bs => Integer -> Integer -> Int -> bs
+encodeECPoint x y siz = B.concat [uncompressed,xb,yb]
+  where
+    uncompressed, xb, yb :: bs
+    uncompressed = B.singleton 4
+    xb = i2ospOf_ siz x
+    yb = i2ospOf_ siz y
+
+decodeECPoint :: ByteArray bs => bs -> CryptoFailable H.Point
+decodeECPoint mxy = case B.uncons mxy of
+    Nothing     -> CryptoFailed $ CryptoError_PointSizeInvalid
+    Just (m,xy)
+        -- uncompressed
+        | m == 4 ->
+            let siz = B.length xy `div` 2
+                (xb,yb) = B.splitAt siz xy
+                x = os2ip xb
+                y = os2ip yb
+             in CryptoPassed $ H.Point x y
+        | otherwise -> CryptoFailed $ CryptoError_PointFormatInvalid