diff --git a/Crypto/ECC.hs b/Crypto/ECC.hs new file mode 100644 index 00000000..e2897dae --- /dev/null +++ b/Crypto/ECC.hs @@ -0,0 +1,198 @@ +-- | +-- Module : Crypto.ECC +-- License : BSD-style +-- Maintainer : Vincent Hanquez +-- 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.ECC.Simple.Types as Simple +import qualified Crypto.ECC.Simple.Prim as Simple +import Crypto.Random +import Crypto.Error +import Crypto.Internal.Proxy +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 + type Point curve :: * + + -- | Scalar in the Elliptic Curve domain + type Scalar 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 => 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. + ecdh :: proxy curve -> Scalar curve -> Point curve -> SharedSecret + +class EllipticCurve curve => EllipticCurveArith curve where + -- | Add points on a curve + pointAdd :: proxy curve -> Point 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 + +-- | P256 Curve +-- +-- also known as P256 +data Curve_P256R1 = Curve_P256R1 + +instance EllipticCurve Curve_P256R1 where + type Point Curve_P256R1 = P256.Point + type Scalar Curve_P256R1 = P256.Scalar + curveSizeBits _ = 256 + curveGenerateScalar _ = P256.scalarGenerate + curveGenerateKeyPair _ = toKeyPair <$> P256.scalarGenerate + where toKeyPair scalar = KeyPair (P256.toPoint scalar) scalar + encodePoint _ p = P256.pointToBinary p + decodePoint _ bs = P256.pointFromBinary bs + +instance EllipticCurveArith Curve_P256R1 where + pointAdd _ a b = P256.pointAdd a b + pointSmul _ s p = P256.pointMul s p + +instance EllipticCurveDH Curve_P256R1 where + ecdh _ s p = SharedSecret $ P256.pointDh s p + +data Curve_P384R1 = Curve_P384R1 + +instance EllipticCurve Curve_P384R1 where + type Point Curve_P384R1 = Simple.Point Simple.SEC_p384r1 + type Scalar Curve_P384R1 = Simple.Scalar Simple.SEC_p384r1 + curveSizeBits _ = 384 + curveGenerateScalar _ = Simple.scalarGenerate + curveGenerateKeyPair _ = toKeyPair <$> Simple.scalarGenerate + where toKeyPair scalar = KeyPair (Simple.pointBaseMul scalar) scalar + encodePoint _ point = encodeECPoint point + decodePoint _ bs = decodeECPoint bs + +instance EllipticCurveArith Curve_P384R1 where + pointAdd _ a b = Simple.pointAdd a b + pointSmul _ s p = Simple.pointMul s p + +instance EllipticCurveDH Curve_P384R1 where + ecdh _ s p = SharedSecret $ i2ospOf_ (curveSizeBytes prx) x + where + prx = Proxy :: Proxy Curve_P384R1 + Simple.Point x _ = pointSmul prx s p + +data Curve_P521R1 = Curve_P521R1 + +instance EllipticCurve Curve_P521R1 where + type Point Curve_P521R1 = Simple.Point Simple.SEC_p521r1 + type Scalar Curve_P521R1 = Simple.Scalar Simple.SEC_p521r1 + curveSizeBits _ = 521 + curveGenerateScalar _ = Simple.scalarGenerate + curveGenerateKeyPair _ = toKeyPair <$> Simple.scalarGenerate + where toKeyPair scalar = KeyPair (Simple.pointBaseMul scalar) scalar + encodePoint _ point = encodeECPoint point + decodePoint _ bs = decodeECPoint bs + +instance EllipticCurveArith Curve_P521R1 where + pointAdd _ a b = Simple.pointAdd a b + pointSmul _ s p = Simple.pointMul s p + +instance EllipticCurveDH Curve_P521R1 where + ecdh _ s p = SharedSecret $ i2ospOf_ (curveSizeBytes prx) x + where + prx = Proxy :: Proxy Curve_P521R1 + Simple.Point x _ = pointSmul prx s p + +data Curve_X25519 = Curve_X25519 + +instance EllipticCurve Curve_X25519 where + type Point Curve_X25519 = X25519.PublicKey + type Scalar Curve_X25519 = X25519.SecretKey + curveSizeBits _ = 255 + curveGenerateScalar _ = X25519.generateSecretKey + curveGenerateKeyPair _ = do + s <- X25519.generateSecretKey + return $ KeyPair (X25519.toPublic s) s + encodePoint _ p = B.convert p + decodePoint _ bs = X25519.publicKey bs + +instance EllipticCurveDH Curve_X25519 where + ecdh _ s p = SharedSecret $ convert secret + where secret = X25519.dh p s + +encodeECPoint :: forall curve bs . (Simple.Curve curve, ByteArray bs) => Simple.Point curve -> bs +encodeECPoint Simple.PointO = error "encodeECPoint: cannot serialize point at infinity" +encodeECPoint (Simple.Point x y) = B.concat [uncompressed,xb,yb] + where + size = Simple.curveSizeBytes (Proxy :: Proxy curve) + uncompressed, xb, yb :: bs + uncompressed = B.singleton 4 + xb = i2ospOf_ size x + yb = i2ospOf_ size y + +decodeECPoint :: (Simple.Curve curve, ByteArray bs) => bs -> CryptoFailable (Simple.Point curve) +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 Simple.pointFromIntegers (x,y) + | otherwise -> CryptoFailed $ CryptoError_PointFormatInvalid + +curveSizeBytes :: EllipticCurve c => Proxy c -> Int +curveSizeBytes proxy = (curveSizeBits proxy + 7) `div` 8 diff --git a/Crypto/ECC/Simple/Prim.hs b/Crypto/ECC/Simple/Prim.hs new file mode 100644 index 00000000..4a36b054 --- /dev/null +++ b/Crypto/ECC/Simple/Prim.hs @@ -0,0 +1,207 @@ +-- | Elliptic Curve Arithmetic. +-- +-- /WARNING:/ These functions are vulnerable to timing attacks. +{-# LANGUAGE ScopedTypeVariables #-} +module Crypto.ECC.Simple.Prim + ( scalarGenerate + , scalarFromInteger + , pointAdd + , pointDouble + , pointBaseMul + , pointMul + , pointAddTwoMuls + , pointFromIntegers + , isPointAtInfinity + , isPointValid + ) where + +import Data.Maybe +import Crypto.Internal.Imports +import Crypto.Internal.Proxy +import Crypto.Number.ModArithmetic +import Crypto.Number.F2m +import Crypto.Number.Generate (generateBetween) +import Crypto.ECC.Simple.Types +import Crypto.Error +import Crypto.Random + +-- | Generate a valid scalar for a specific Curve +scalarGenerate :: forall randomly curve . (MonadRandom randomly, Curve curve) => randomly (Scalar curve) +scalarGenerate = + Scalar <$> generateBetween 1 (n - 1) + where + n = curveEccN $ curveParameters (Proxy :: Proxy curve) + +scalarFromInteger :: forall curve . Curve curve => Integer -> CryptoFailable (Scalar curve) +scalarFromInteger n + | n < 0 || n >= mx = CryptoFailed $ CryptoError_EcScalarOutOfBounds + | otherwise = CryptoPassed $ Scalar n + where + mx = case curveType (Proxy :: Proxy curve) of + CurveBinary (CurveBinaryParam b) -> b + CurvePrime (CurvePrimeParam p) -> p + +--TODO: Extract helper function for `fromMaybe PointO...` + +-- | Elliptic Curve point negation: +-- @pointNegate p@ returns point @q@ such that @pointAdd p q == PointO@. +pointNegate :: Curve curve => Point curve -> Point curve +pointNegate PointO = PointO +pointNegate point@(Point x y) = + case curveType point of + CurvePrime {} -> Point x (-y) + CurveBinary {} -> Point x (x `addF2m` y) + +-- | Elliptic Curve point addition. +-- +-- /WARNING:/ Vulnerable to timing attacks. +pointAdd :: Curve curve => Point curve -> Point curve -> Point curve +pointAdd PointO PointO = PointO +pointAdd PointO q = q +pointAdd p PointO = p +pointAdd p q + | p == q = pointDouble p + | p == pointNegate q = PointO +pointAdd point@(Point xp yp) (Point xq yq) = + case ty of + CurvePrime (CurvePrimeParam pr) -> fromMaybe PointO $ do + s <- divmod (yp - yq) (xp - xq) pr + let xr = (s ^ (2::Int) - xp - xq) `mod` pr + yr = (s * (xp - xr) - yp) `mod` pr + return $ Point xr yr + CurveBinary (CurveBinaryParam fx) -> fromMaybe PointO $ do + s <- divF2m fx (yp `addF2m` yq) (xp `addF2m` xq) + let xr = mulF2m fx s s `addF2m` s `addF2m` xp `addF2m` xq `addF2m` a + yr = mulF2m fx s (xp `addF2m` xr) `addF2m` xr `addF2m` yp + return $ Point xr yr + where + ty = curveType point + cc = curveParameters point + a = curveEccA cc + +-- | Elliptic Curve point doubling. +-- +-- /WARNING:/ Vulnerable to timing attacks. +-- +-- This perform the following calculation: +-- > lambda = (3 * xp ^ 2 + a) / 2 yp +-- > xr = lambda ^ 2 - 2 xp +-- > yr = lambda (xp - xr) - yp +-- +-- With binary curve: +-- > xp == 0 => P = O +-- > otherwise => +-- > s = xp + (yp / xp) +-- > xr = s ^ 2 + s + a +-- > yr = xp ^ 2 + (s+1) * xr +-- +pointDouble :: Curve curve => Point curve -> Point curve +pointDouble PointO = PointO +pointDouble point@(Point xp yp) = + case ty of + CurvePrime (CurvePrimeParam pr) -> fromMaybe PointO $ do + lambda <- divmod (3 * xp ^ (2::Int) + a) (2 * yp) pr + let xr = (lambda ^ (2::Int) - 2 * xp) `mod` pr + yr = (lambda * (xp - xr) - yp) `mod` pr + return $ Point xr yr + CurveBinary (CurveBinaryParam fx) + | xp == 0 -> PointO + | otherwise -> fromMaybe PointO $ do + s <- return . addF2m xp =<< divF2m fx yp xp + let xr = mulF2m fx s s `addF2m` s `addF2m` a + yr = mulF2m fx xp xp `addF2m` mulF2m fx xr (s `addF2m` 1) + return $ Point xr yr + where + ty = curveType point + cc = curveParameters point + a = curveEccA cc + +-- | Elliptic curve point multiplication using the base +-- +-- /WARNING:/ Vulnerable to timing attacks. +pointBaseMul :: Curve curve => Scalar curve -> Point curve +pointBaseMul n = pointMul n (curveEccG $ curveParameters (Proxy :: Proxy curve)) + +-- | Elliptic curve point multiplication (double and add algorithm). +-- +-- /WARNING:/ Vulnerable to timing attacks. +pointMul :: Curve curve => Scalar curve -> Point curve -> Point curve +pointMul _ PointO = PointO +pointMul (Scalar n) p + | n == 0 = PointO + | n == 1 = p + | odd n = pointAdd p (pointMul (Scalar (n - 1)) p) + | otherwise = pointMul (Scalar (n `div` 2)) (pointDouble p) + +-- | Elliptic curve double-scalar multiplication (uses Shamir's trick). +-- +-- > pointAddTwoMuls n1 p1 n2 p2 == pointAdd (pointMul n1 p1) +-- > (pointMul n2 p2) +-- +-- /WARNING:/ Vulnerable to timing attacks. +pointAddTwoMuls :: Curve curve => Scalar curve -> Point curve -> Scalar curve -> Point curve -> Point curve +pointAddTwoMuls _ PointO _ PointO = PointO +pointAddTwoMuls _ PointO n2 p2 = pointMul n2 p2 +pointAddTwoMuls n1 p1 _ PointO = pointMul n1 p1 +pointAddTwoMuls (Scalar n1) p1 (Scalar n2) p2 = go (n1, n2) + where + p0 = pointAdd p1 p2 + + go (0, 0 ) = PointO + go (k1, k2) = + let q = pointDouble $ go (k1 `div` 2, k2 `div` 2) + in case (odd k1, odd k2) of + (True , True ) -> pointAdd p0 q + (True , False ) -> pointAdd p1 q + (False , True ) -> pointAdd p2 q + (False , False ) -> q + +-- | Check if a point is the point at infinity. +isPointAtInfinity :: Point curve -> Bool +isPointAtInfinity PointO = True +isPointAtInfinity _ = False + +-- | Make a point on a curve from integer (x,y) coordinate +-- +-- if the point is not valid related to the curve then an error is +-- returned instead of a point +pointFromIntegers :: forall curve . Curve curve => (Integer, Integer) -> CryptoFailable (Point curve) +pointFromIntegers (x,y) + | isPointValid (Proxy :: Proxy curve) x y = CryptoPassed $ Point x y + | otherwise = CryptoFailed $ CryptoError_PointCoordinatesInvalid + +-- | check if a point is on specific curve +-- +-- This perform three checks: +-- +-- * x is not out of range +-- * y is not out of range +-- * the equation @y^2 = x^3 + a*x + b (mod p)@ holds +isPointValid :: Curve curve => proxy curve -> Integer -> Integer -> Bool +isPointValid proxy x y = + case ty of + CurvePrime (CurvePrimeParam p) -> + let a = curveEccA cc + b = curveEccB cc + eqModP z1 z2 = (z1 `mod` p) == (z2 `mod` p) + isValid e = e >= 0 && e < p + in isValid x && isValid y && (y ^ (2 :: Int)) `eqModP` (x ^ (3 :: Int) + a * x + b) + CurveBinary (CurveBinaryParam fx) -> + let a = curveEccA cc + b = curveEccB cc + add = addF2m + mul = mulF2m fx + isValid e = modF2m fx e == e + in and [ isValid x + , isValid y + , ((((x `add` a) `mul` x `add` y) `mul` x) `add` b `add` (squareF2m fx y)) == 0 + ] + where + ty = curveType proxy + cc = curveParameters proxy + +-- | div and mod +divmod :: Integer -> Integer -> Integer -> Maybe Integer +divmod y x m = do + i <- inverse (x `mod` m) m + return $ y * i `mod` m diff --git a/Crypto/ECC/Simple/Types.hs b/Crypto/ECC/Simple/Types.hs new file mode 100644 index 00000000..c97daa29 --- /dev/null +++ b/Crypto/ECC/Simple/Types.hs @@ -0,0 +1,615 @@ +{-# LANGUAGE DeriveDataTypeable #-} +-- | +-- Module : Crypto.ECC.Simple.Types +-- License : BSD-style +-- Maintainer : Vincent Hanquez +-- Stability : Experimental +-- Portability : Excellent +-- +-- references: +-- +-- +{-# OPTIONS_GHC -fno-warn-missing-signatures #-} +module Crypto.ECC.Simple.Types + ( Curve(..) + , Point(..) + , Scalar(..) + , CurveType(..) + , CurveBinaryParam(..) + , CurvePrimeParam(..) + , curveSizeBits + , curveSizeBytes + , CurveParameters(..) + -- * specific curves definition + , SEC_p112r1(..) + , SEC_p112r2(..) + , SEC_p128r1(..) + , SEC_p128r2(..) + , SEC_p160k1(..) + , SEC_p160r1(..) + , SEC_p160r2(..) + , SEC_p192k1(..) + , SEC_p192r1(..) -- aka prime192v1 + , SEC_p224k1(..) + , SEC_p224r1(..) + , SEC_p256k1(..) + , SEC_p256r1(..) -- aka prime256v1 + , SEC_p384r1(..) + , SEC_p521r1(..) + , SEC_t113r1(..) + , SEC_t113r2(..) + , SEC_t131r1(..) + , SEC_t131r2(..) + , SEC_t163k1(..) + , SEC_t163r1(..) + , SEC_t163r2(..) + , SEC_t193r1(..) + , SEC_t193r2(..) + , SEC_t233k1(..) -- aka NIST K-233 + , SEC_t233r1(..) + , SEC_t239k1(..) + , SEC_t283k1(..) + , SEC_t283r1(..) + , SEC_t409k1(..) + , SEC_t409r1(..) + , SEC_t571k1(..) + , SEC_t571r1(..) + ) where + +import Data.Data +import Crypto.Internal.Imports +import Crypto.Number.Basic (numBits) + +class Curve curve where + curveParameters :: proxy curve -> CurveParameters curve + curveType :: proxy curve -> CurveType + +-- | get the size of the curve in bits +curveSizeBits :: Curve curve => proxy curve -> Int +curveSizeBits proxy = + case curveType proxy of + CurvePrime (CurvePrimeParam p) -> numBits p + CurveBinary (CurveBinaryParam c) -> numBits c - 1 + +-- | get the size of the curve in bytes +curveSizeBytes :: Curve curve => proxy curve -> Int +curveSizeBytes proxy = (curveSizeBits proxy + 7) `div` 8 + +-- | Define common parameters in a curve definition +-- of the form: y^2 = x^3 + ax + b. +data CurveParameters curve = CurveParameters + { curveEccA :: Integer -- ^ curve parameter a + , curveEccB :: Integer -- ^ curve parameter b + , curveEccG :: Point curve -- ^ base point + , curveEccN :: Integer -- ^ order of G + , curveEccH :: Integer -- ^ cofactor + } deriving (Show,Eq,Data,Typeable) + +newtype CurveBinaryParam = CurveBinaryParam Integer + deriving (Show,Read,Eq,Data,Typeable) + +newtype CurvePrimeParam = CurvePrimeParam Integer + deriving (Show,Read,Eq,Data,Typeable) + +data CurveType = + CurveBinary CurveBinaryParam + | CurvePrime CurvePrimeParam + deriving (Show,Read,Eq,Data,Typeable) + +-- | ECC Private Number +newtype Scalar curve = Scalar Integer + deriving (Show,Read,Eq,Data,Typeable) + +-- | Define a point on a curve. +data Point curve = + Point Integer Integer + | PointO -- ^ Point at Infinity + deriving (Show,Read,Eq,Data,Typeable) + +instance NFData (Point curve) where + rnf (Point x y) = x `seq` y `seq` () + rnf PointO = () + +data SEC_p112r1 = SEC_p112r1 deriving (Show,Read,Eq) +data SEC_p112r2 = SEC_p112r2 deriving (Show,Read,Eq) +data SEC_p128r1 = SEC_p128r1 deriving (Show,Read,Eq) +data SEC_p128r2 = SEC_p128r2 deriving (Show,Read,Eq) +data SEC_p160k1 = SEC_p160k1 deriving (Show,Read,Eq) +data SEC_p160r1 = SEC_p160r1 deriving (Show,Read,Eq) +data SEC_p160r2 = SEC_p160r2 deriving (Show,Read,Eq) +data SEC_p192k1 = SEC_p192k1 deriving (Show,Read,Eq) +data SEC_p192r1 = SEC_p192r1 deriving (Show,Read,Eq) +data SEC_p224k1 = SEC_p224k1 deriving (Show,Read,Eq) +data SEC_p224r1 = SEC_p224r1 deriving (Show,Read,Eq) +data SEC_p256k1 = SEC_p256k1 deriving (Show,Read,Eq) +data SEC_p256r1 = SEC_p256r1 deriving (Show,Read,Eq) +data SEC_p384r1 = SEC_p384r1 deriving (Show,Read,Eq) +data SEC_p521r1 = SEC_p521r1 deriving (Show,Read,Eq) +data SEC_t113r1 = SEC_t113r1 deriving (Show,Read,Eq) +data SEC_t113r2 = SEC_t113r2 deriving (Show,Read,Eq) +data SEC_t131r1 = SEC_t131r1 deriving (Show,Read,Eq) +data SEC_t131r2 = SEC_t131r2 deriving (Show,Read,Eq) +data SEC_t163k1 = SEC_t163k1 deriving (Show,Read,Eq) +data SEC_t163r1 = SEC_t163r1 deriving (Show,Read,Eq) +data SEC_t163r2 = SEC_t163r2 deriving (Show,Read,Eq) +data SEC_t193r1 = SEC_t193r1 deriving (Show,Read,Eq) +data SEC_t193r2 = SEC_t193r2 deriving (Show,Read,Eq) +data SEC_t233k1 = SEC_t233k1 deriving (Show,Read,Eq) +data SEC_t233r1 = SEC_t233r1 deriving (Show,Read,Eq) +data SEC_t239k1 = SEC_t239k1 deriving (Show,Read,Eq) +data SEC_t283k1 = SEC_t283k1 deriving (Show,Read,Eq) +data SEC_t283r1 = SEC_t283r1 deriving (Show,Read,Eq) +data SEC_t409k1 = SEC_t409k1 deriving (Show,Read,Eq) +data SEC_t409r1 = SEC_t409r1 deriving (Show,Read,Eq) +data SEC_t571k1 = SEC_t571k1 deriving (Show,Read,Eq) +data SEC_t571r1 = SEC_t571r1 deriving (Show,Read,Eq) + +-- | Define names for known recommended curves. +instance Curve SEC_p112r1 where + curveType _ = typeSEC_p112r1 + curveParameters _ = paramSEC_p112r1 + +instance Curve SEC_p112r2 where + curveType _ = typeSEC_p112r2 + curveParameters _ = paramSEC_p112r2 + +instance Curve SEC_p128r1 where + curveType _ = typeSEC_p128r1 + curveParameters _ = paramSEC_p128r1 + +instance Curve SEC_p128r2 where + curveType _ = typeSEC_p128r2 + curveParameters _ = paramSEC_p128r2 + +instance Curve SEC_p160k1 where + curveType _ = typeSEC_p160k1 + curveParameters _ = paramSEC_p160k1 + +instance Curve SEC_p160r1 where + curveType _ = typeSEC_p160r1 + curveParameters _ = paramSEC_p160r1 + +instance Curve SEC_p160r2 where + curveType _ = typeSEC_p160r2 + curveParameters _ = paramSEC_p160r2 + +instance Curve SEC_p192k1 where + curveType _ = typeSEC_p192k1 + curveParameters _ = paramSEC_p192k1 + +instance Curve SEC_p192r1 where + curveType _ = typeSEC_p192r1 + curveParameters _ = paramSEC_p192r1 + +instance Curve SEC_p224k1 where + curveType _ = typeSEC_p224k1 + curveParameters _ = paramSEC_p224k1 + +instance Curve SEC_p224r1 where + curveType _ = typeSEC_p224r1 + curveParameters _ = paramSEC_p224r1 + +instance Curve SEC_p256k1 where + curveType _ = typeSEC_p256k1 + curveParameters _ = paramSEC_p256k1 + +instance Curve SEC_p256r1 where + curveType _ = typeSEC_p256r1 + curveParameters _ = paramSEC_p256r1 + +instance Curve SEC_p384r1 where + curveType _ = typeSEC_p384r1 + curveParameters _ = paramSEC_p384r1 + +instance Curve SEC_p521r1 where + curveType _ = typeSEC_p521r1 + curveParameters _ = paramSEC_p521r1 + +instance Curve SEC_t113r1 where + curveType _ = typeSEC_t113r1 + curveParameters _ = paramSEC_t113r1 + +instance Curve SEC_t113r2 where + curveType _ = typeSEC_t113r2 + curveParameters _ = paramSEC_t113r2 + +instance Curve SEC_t131r1 where + curveType _ = typeSEC_t131r1 + curveParameters _ = paramSEC_t131r1 + +instance Curve SEC_t131r2 where + curveType _ = typeSEC_t131r2 + curveParameters _ = paramSEC_t131r2 + +instance Curve SEC_t163k1 where + curveType _ = typeSEC_t163k1 + curveParameters _ = paramSEC_t163k1 + +instance Curve SEC_t163r1 where + curveType _ = typeSEC_t163r1 + curveParameters _ = paramSEC_t163r1 + +instance Curve SEC_t163r2 where + curveType _ = typeSEC_t163r2 + curveParameters _ = paramSEC_t163r2 + +instance Curve SEC_t193r1 where + curveType _ = typeSEC_t193r1 + curveParameters _ = paramSEC_t193r1 + +instance Curve SEC_t193r2 where + curveType _ = typeSEC_t193r2 + curveParameters _ = paramSEC_t193r2 + +instance Curve SEC_t233k1 where + curveType _ = typeSEC_t233k1 + curveParameters _ = paramSEC_t233k1 + +instance Curve SEC_t233r1 where + curveType _ = typeSEC_t233r1 + curveParameters _ = paramSEC_t233r1 + +instance Curve SEC_t239k1 where + curveType _ = typeSEC_t239k1 + curveParameters _ = paramSEC_t239k1 + +instance Curve SEC_t283k1 where + curveType _ = typeSEC_t283k1 + curveParameters _ = paramSEC_t283k1 + +instance Curve SEC_t283r1 where + curveType _ = typeSEC_t283r1 + curveParameters _ = paramSEC_t283r1 + +instance Curve SEC_t409k1 where + curveType _ = typeSEC_t409k1 + curveParameters _ = paramSEC_t409k1 + +instance Curve SEC_t409r1 where + curveType _ = typeSEC_t409r1 + curveParameters _ = paramSEC_t409r1 + +instance Curve SEC_t571k1 where + curveType _ = typeSEC_t571k1 + curveParameters _ = paramSEC_t571k1 + +instance Curve SEC_t571r1 where + curveType _ = typeSEC_t571r1 + curveParameters _ = paramSEC_t571r1 + +{- +curvesOIDs :: [ (CurveName, [Integer]) ] +curvesOIDs = + [ (SEC_p112r1, [1,3,132,0,6]) + , (SEC_p112r2, [1,3,132,0,7]) + , (SEC_p128r1, [1,3,132,0,28]) + , (SEC_p128r2, [1,3,132,0,29]) + , (SEC_p160k1, [1,3,132,0,9]) + , (SEC_p160r1, [1,3,132,0,8]) + , (SEC_p160r2, [1,3,132,0,30]) + , (SEC_p192k1, [1,3,132,0,31]) + , (SEC_p192r1, [1,2,840,10045,3,1,1]) + , (SEC_p224k1, [1,3,132,0,32]) + , (SEC_p224r1, [1,3,132,0,33]) + , (SEC_p256k1, [1,3,132,0,10]) + , (SEC_p256r1, [1,2,840,10045,3,1,7]) + , (SEC_p384r1, [1,3,132,0,34]) + , (SEC_p521r1, [1,3,132,0,35]) + , (SEC_t113r1, [1,3,132,0,4]) + , (SEC_t113r2, [1,3,132,0,5]) + , (SEC_t131r1, [1,3,132,0,22]) + , (SEC_t131r2, [1,3,132,0,23]) + , (SEC_t163k1, [1,3,132,0,1]) + , (SEC_t163r1, [1,3,132,0,2]) + , (SEC_t163r2, [1,3,132,0,15]) + , (SEC_t193r1, [1,3,132,0,24]) + , (SEC_t193r2, [1,3,132,0,25]) + , (SEC_t233k1, [1,3,132,0,26]) + , (SEC_t233r1, [1,3,132,0,27]) + , (SEC_t239k1, [1,3,132,0,3]) + , (SEC_t283k1, [1,3,132,0,16]) + , (SEC_t283r1, [1,3,132,0,17]) + , (SEC_t409k1, [1,3,132,0,36]) + , (SEC_t409r1, [1,3,132,0,37]) + , (SEC_t571k1, [1,3,132,0,38]) + , (SEC_t571r1, [1,3,132,0,39]) + ] +-} + +typeSEC_p112r1 = CurvePrime $ CurvePrimeParam 0xdb7c2abf62e35e668076bead208b +paramSEC_p112r1 = CurveParameters + { curveEccA = 0xdb7c2abf62e35e668076bead2088 + , curveEccB = 0x659ef8ba043916eede8911702b22 + , curveEccG = Point 0x09487239995a5ee76b55f9c2f098 + 0xa89ce5af8724c0a23e0e0ff77500 + , curveEccN = 0xdb7c2abf62e35e7628dfac6561c5 + , curveEccH = 1 + } +typeSEC_p112r2 = CurvePrime $ CurvePrimeParam 0xdb7c2abf62e35e668076bead208b +paramSEC_p112r2 = CurveParameters + { curveEccA = 0x6127c24c05f38a0aaaf65c0ef02c + , curveEccB = 0x51def1815db5ed74fcc34c85d709 + , curveEccG = Point 0x4ba30ab5e892b4e1649dd0928643 + 0xadcd46f5882e3747def36e956e97 + , curveEccN = 0x36df0aafd8b8d7597ca10520d04b + , curveEccH = 4 + } +typeSEC_p128r1 = CurvePrime $ CurvePrimeParam 0xfffffffdffffffffffffffffffffffff +paramSEC_p128r1 = CurveParameters + { curveEccA = 0xfffffffdfffffffffffffffffffffffc + , curveEccB = 0xe87579c11079f43dd824993c2cee5ed3 + , curveEccG = Point 0x161ff7528b899b2d0c28607ca52c5b86 + 0xcf5ac8395bafeb13c02da292dded7a83 + , curveEccN = 0xfffffffe0000000075a30d1b9038a115 + , curveEccH = 1 + } +typeSEC_p128r2 = CurvePrime $ CurvePrimeParam 0xfffffffdffffffffffffffffffffffff +paramSEC_p128r2 = CurveParameters + { curveEccA = 0xd6031998d1b3bbfebf59cc9bbff9aee1 + , curveEccB = 0x5eeefca380d02919dc2c6558bb6d8a5d + , curveEccG = Point 0x7b6aa5d85e572983e6fb32a7cdebc140 + 0x27b6916a894d3aee7106fe805fc34b44 + , curveEccN = 0x3fffffff7fffffffbe0024720613b5a3 + , curveEccH = 4 + } +typeSEC_p160k1 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffeffffac73 +paramSEC_p160k1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000 + , curveEccB = 0x000000000000000000000000000000000000000007 + , curveEccG = Point 0x003b4c382ce37aa192a4019e763036f4f5dd4d7ebb + 0x00938cf935318fdced6bc28286531733c3f03c4fee + , curveEccN = 0x0100000000000000000001b8fa16dfab9aca16b6b3 + , curveEccH = 1 + } +typeSEC_p160r1 = CurvePrime $ CurvePrimeParam 0x00ffffffffffffffffffffffffffffffff7fffffff +paramSEC_p160r1 = CurveParameters + { curveEccA = 0x00ffffffffffffffffffffffffffffffff7ffffffc + , curveEccB = 0x001c97befc54bd7a8b65acf89f81d4d4adc565fa45 + , curveEccG = Point 0x004a96b5688ef573284664698968c38bb913cbfc82 + 0x0023a628553168947d59dcc912042351377ac5fb32 + , curveEccN = 0x0100000000000000000001f4c8f927aed3ca752257 + , curveEccH = 1 + } +typeSEC_p160r2 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffeffffac73 +paramSEC_p160r2 = CurveParameters + { curveEccA = 0x00fffffffffffffffffffffffffffffffeffffac70 + , curveEccB = 0x00b4e134d3fb59eb8bab57274904664d5af50388ba + , curveEccG = Point 0x0052dcb034293a117e1f4ff11b30f7199d3144ce6d + 0x00feaffef2e331f296e071fa0df9982cfea7d43f2e + , curveEccN = 0x0100000000000000000000351ee786a818f3a1a16b + , curveEccH = 1 + } +typeSEC_p192k1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffeffffee37 +paramSEC_p192k1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000 + , curveEccB = 0x000000000000000000000000000000000000000000000003 + , curveEccG = Point 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d + 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d + , curveEccN = 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d + , curveEccH = 1 + } +typeSEC_p192r1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffeffffffffffffffff +paramSEC_p192r1 = CurveParameters + { curveEccA = 0xfffffffffffffffffffffffffffffffefffffffffffffffc + , curveEccB = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1 + , curveEccG = Point 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012 + 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811 + , curveEccN = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831 + , curveEccH = 1 + } +typeSEC_p224k1 = CurvePrime $ CurvePrimeParam 0x00fffffffffffffffffffffffffffffffffffffffffffffffeffffe56d +paramSEC_p224k1 = CurveParameters + { curveEccA = 0x0000000000000000000000000000000000000000000000000000000000 + , curveEccB = 0x0000000000000000000000000000000000000000000000000000000005 + , curveEccG = Point 0x00a1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c + 0x007e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5 + , curveEccN = 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 + , curveEccH = 1 + } +typeSEC_p224r1 = CurvePrime $ CurvePrimeParam 0xffffffffffffffffffffffffffffffff000000000000000000000001 +paramSEC_p224r1 = CurveParameters + { curveEccA = 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe + , curveEccB = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4 + , curveEccG = Point 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21 + 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34 + , curveEccN = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d + , curveEccH = 1 + } +typeSEC_p256k1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f +paramSEC_p256k1 = CurveParameters + { curveEccA = 0x0000000000000000000000000000000000000000000000000000000000000000 + , curveEccB = 0x0000000000000000000000000000000000000000000000000000000000000007 + , curveEccG = Point 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 + 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8 + , curveEccN = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 + , curveEccH = 1 + } +typeSEC_p256r1 = CurvePrime $ CurvePrimeParam 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff +paramSEC_p256r1 = CurveParameters + { curveEccA = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc + , curveEccB = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b + , curveEccG = Point 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 + 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 + , curveEccN = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 + , curveEccH = 1 + } +typeSEC_p384r1 = CurvePrime $ CurvePrimeParam 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff +paramSEC_p384r1 = CurveParameters + { curveEccA = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc + , curveEccB = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef + , curveEccG = Point 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7 + 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f + , curveEccN = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973 + , curveEccH = 1 + } +typeSEC_p521r1 = CurvePrime $ CurvePrimeParam 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff +paramSEC_p521r1 = CurveParameters + { curveEccA = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc + , curveEccB = 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00 + , curveEccG = Point 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66 + 0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650 + , curveEccN = 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409 + , curveEccH = 1 + } +typeSEC_t113r1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000201 +paramSEC_t113r1 = CurveParameters + { curveEccA = 0x003088250ca6e7c7fe649ce85820f7 + , curveEccB = 0x00e8bee4d3e2260744188be0e9c723 + , curveEccG = Point 0x009d73616f35f4ab1407d73562c10f + 0x00a52830277958ee84d1315ed31886 + , curveEccN = 0x0100000000000000d9ccec8a39e56f + , curveEccH = 2 + } +typeSEC_t113r2 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000201 +paramSEC_t113r2 = CurveParameters + { curveEccA = 0x00689918dbec7e5a0dd6dfc0aa55c7 + , curveEccB = 0x0095e9a9ec9b297bd4bf36e059184f + , curveEccG = Point 0x01a57a6a7b26ca5ef52fcdb8164797 + 0x00b3adc94ed1fe674c06e695baba1d + , curveEccN = 0x010000000000000108789b2496af93 + , curveEccH = 2 + } +typeSEC_t131r1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000010d +paramSEC_t131r1 = CurveParameters + { curveEccA = 0x07a11b09a76b562144418ff3ff8c2570b8 + , curveEccB = 0x0217c05610884b63b9c6c7291678f9d341 + , curveEccG = Point 0x0081baf91fdf9833c40f9c181343638399 + 0x078c6e7ea38c001f73c8134b1b4ef9e150 + , curveEccN = 0x0400000000000000023123953a9464b54d + , curveEccH = 2 + } +typeSEC_t131r2 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000010d +paramSEC_t131r2 = CurveParameters + { curveEccA = 0x03e5a88919d7cafcbf415f07c2176573b2 + , curveEccB = 0x04b8266a46c55657ac734ce38f018f2192 + , curveEccG = Point 0x0356dcd8f2f95031ad652d23951bb366a8 + 0x0648f06d867940a5366d9e265de9eb240f + , curveEccN = 0x0400000000000000016954a233049ba98f + , curveEccH = 2 + } +typeSEC_t163k1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9 +paramSEC_t163k1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000001 + , curveEccB = 0x000000000000000000000000000000000000000001 + , curveEccG = Point 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8 + 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9 + , curveEccN = 0x04000000000000000000020108a2e0cc0d99f8a5ef + , curveEccH = 2 + } +typeSEC_t163r1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9 +paramSEC_t163r1 = CurveParameters + { curveEccA = 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2 + , curveEccB = 0x0713612dcddcb40aab946bda29ca91f73af958afd9 + , curveEccG = Point 0x0369979697ab43897789566789567f787a7876a654 + 0x00435edb42efafb2989d51fefce3c80988f41ff883 + , curveEccN = 0x03ffffffffffffffffffff48aab689c29ca710279b + , curveEccH = 2 + } +typeSEC_t163r2 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000c9 +paramSEC_t163r2 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000001 + , curveEccB = 0x020a601907b8c953ca1481eb10512f78744a3205fd + , curveEccG = Point 0x03f0eba16286a2d57ea0991168d4994637e8343e36 + 0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1 + , curveEccN = 0x040000000000000000000292fe77e70c12a4234c33 + , curveEccH = 2 + } +typeSEC_t193r1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000008001 +paramSEC_t193r1 = CurveParameters + { curveEccA = 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01 + , curveEccB = 0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814 + , curveEccG = Point 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1 + 0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05 + , curveEccN = 0x01000000000000000000000000c7f34a778f443acc920eba49 + , curveEccH = 2 + } +typeSEC_t193r2 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000008001 +paramSEC_t193r2 = CurveParameters + { curveEccA = 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b + , curveEccB = 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae + , curveEccG = Point 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f + 0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c + , curveEccN = 0x010000000000000000000000015aab561b005413ccd4ee99d5 + , curveEccH = 2 + } +typeSEC_t233k1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000000000000000004000000000000000001 +paramSEC_t233k1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000 + , curveEccB = 0x000000000000000000000000000000000000000000000000000000000001 + , curveEccG = Point 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126 + 0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3 + , curveEccN = 0x008000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf + , curveEccH = 4 + } +typeSEC_t233r1 = CurveBinary $ CurveBinaryParam 0x020000000000000000000000000000000000000004000000000000000001 +paramSEC_t233r1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000000000000001 + , curveEccB = 0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad + , curveEccG = Point 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b + 0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052 + , curveEccN = 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7 + , curveEccH = 2 + } +typeSEC_t239k1 = CurveBinary $ CurveBinaryParam 0x800000000000000000004000000000000000000000000000000000000001 +paramSEC_t239k1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000 + , curveEccB = 0x000000000000000000000000000000000000000000000000000000000001 + , curveEccG = Point 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc + 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca + , curveEccN = 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5 + , curveEccH = 4 + } +typeSEC_t283k1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000000000000000000000000000000010a1 +paramSEC_t283k1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000 + , curveEccB = 0x000000000000000000000000000000000000000000000000000000000000000000000001 + , curveEccG = Point 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836 + 0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259 + , curveEccN = 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61 + , curveEccH = 4 + } +typeSEC_t283r1 = CurveBinary $ CurveBinaryParam 0x0800000000000000000000000000000000000000000000000000000000000000000010a1 +paramSEC_t283r1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000001 + , curveEccB = 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5 + , curveEccG = Point 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053 + 0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4 + , curveEccN = 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 + , curveEccH = 2 + } +typeSEC_t409k1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 +paramSEC_t409k1 = CurveParameters + { curveEccA = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + , curveEccB = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 + , curveEccG = Point 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746 + 0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b + , curveEccN = 0x007ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf + , curveEccH = 4 + } +typeSEC_t409r1 = CurveBinary $ CurveBinaryParam 0x02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 +paramSEC_t409r1 = CurveParameters + { curveEccA = 0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 + , curveEccB = 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f + , curveEccG = Point 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7 + 0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706 + , curveEccN = 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 + , curveEccH = 2 + } +typeSEC_t571k1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 +paramSEC_t571k1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + , curveEccB = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 + , curveEccG = Point 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972 + 0x0349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3 + , curveEccN = 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001 + , curveEccH = 4 + } +typeSEC_t571r1 = CurveBinary $ CurveBinaryParam 0x080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 +paramSEC_t571r1 = CurveParameters + { curveEccA = 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 + , curveEccB = 0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a + , curveEccG = Point 0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19 + 0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b + , curveEccN = 0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47 + , curveEccH = 2 + } diff --git a/Crypto/Error/Types.hs b/Crypto/Error/Types.hs index dff0c8b7..4aaf4e04 100644 --- a/Crypto/Error/Types.hs +++ b/Crypto/Error/Types.hs @@ -34,6 +34,12 @@ data CryptoError = | CryptoError_SecretKeyStructureInvalid | CryptoError_PublicKeySizeInvalid | CryptoError_SharedSecretSizeInvalid + -- elliptic cryptography error + | CryptoError_EcScalarOutOfBounds + | CryptoError_PointSizeInvalid + | CryptoError_PointFormatInvalid + | CryptoError_PointFormatUnsupported + | CryptoError_PointCoordinatesInvalid -- Message authentification error | CryptoError_MacKeyInvalid | CryptoError_AuthenticationTagSizeInvalid diff --git a/Crypto/Internal/Proxy.hs b/Crypto/Internal/Proxy.hs new file mode 100644 index 00000000..1873b2b1 --- /dev/null +++ b/Crypto/Internal/Proxy.hs @@ -0,0 +1,13 @@ +-- | +-- Module : Crypto.Internal.Proxy +-- License : BSD-style +-- Maintainer : Vincent Hanquez +-- Stability : experimental +-- Portability : Good +-- +module Crypto.Internal.Proxy + ( Proxy(..) + ) where + +-- | A type witness for 'a' as phantom type +data Proxy a = Proxy diff --git a/Crypto/KDF/HKDF.hs b/Crypto/KDF/HKDF.hs index 0b956011..e9d0b4cd 100644 --- a/Crypto/KDF/HKDF.hs +++ b/Crypto/KDF/HKDF.hs @@ -18,15 +18,21 @@ module Crypto.KDF.HKDF ) where import Data.Word -import Crypto.Hash +import Crypto.Hash import Crypto.MAC.HMAC -import Crypto.Internal.ByteArray (ScrubbedBytes, Bytes, ByteArray, ByteArrayAccess) +import Crypto.Internal.ByteArray (ScrubbedBytes, ByteArray, ByteArrayAccess) import qualified Crypto.Internal.ByteArray as B -- | Pseudo Random Key data PRK a = PRK (HMAC a) | PRK_NoExpand ScrubbedBytes deriving (Eq) +instance ByteArrayAccess (PRK a) where + length (PRK hm) = B.length hm + length (PRK_NoExpand sb) = B.length sb + withByteArray (PRK hm) = B.withByteArray hm + withByteArray (PRK_NoExpand sb) = B.withByteArray sb + -- | Extract a Pseudo Random Key using the parameter and the underlaying hash mechanism extract :: (HashAlgorithm a, ByteArrayAccess salt, ByteArrayAccess ikm) => salt -- ^ Salt @@ -38,7 +44,7 @@ extract salt ikm = PRK $ hmac salt ikm -- -- Only use when guaranteed to have a good quality and random data to use directly as key. -- This effectively skip a HMAC with key=salt and data=key. -extractSkip :: (HashAlgorithm a, ByteArrayAccess ikm) +extractSkip :: ByteArrayAccess ikm => ikm -> PRK a extractSkip ikm = PRK_NoExpand $ B.convert ikm diff --git a/Crypto/PubKey/Curve25519.hs b/Crypto/PubKey/Curve25519.hs index 32163bdd..d8463eb8 100644 --- a/Crypto/PubKey/Curve25519.hs +++ b/Crypto/PubKey/Curve25519.hs @@ -9,6 +9,7 @@ -- {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE MagicHash #-} +{-# LANGUAGE ScopedTypeVariables #-} module Crypto.PubKey.Curve25519 ( SecretKey , PublicKey @@ -20,17 +21,22 @@ module Crypto.PubKey.Curve25519 -- * methods , dh , toPublic + , generateSecretKey ) where +import Data.Bits import Data.Word import Foreign.Ptr +import Foreign.Storable import GHC.Ptr import Crypto.Error import Crypto.Internal.Compat import Crypto.Internal.Imports -import Crypto.Internal.ByteArray (ByteArrayAccess, ScrubbedBytes, Bytes, withByteArray) +import Crypto.Internal.ByteArray (ByteArrayAccess, ByteArray, ScrubbedBytes, Bytes, withByteArray) import qualified Crypto.Internal.ByteArray as B +import Crypto.Error (CryptoFailable(..)) +import Crypto.Random -- | A Curve25519 Secret key newtype SecretKey = SecretKey ScrubbedBytes @@ -105,6 +111,18 @@ toPublic (SecretKey sec) = PublicKey <$> basePoint = Ptr "\x09\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"# {-# NOINLINE toPublic #-} +-- | Generate a secret key. +generateSecretKey :: MonadRandom m => m SecretKey +generateSecretKey = tweakToSecretKey <$> getRandomBytes 32 + where + tweakToSecretKey :: ScrubbedBytes -> SecretKey + tweakToSecretKey bin = SecretKey $ B.copyAndFreeze bin $ \inp -> do + modifyByte inp 0 (\e0 -> e0 .&. 0xf8) + modifyByte inp 31 (\e31 -> (e31 .&. 0x7f) .|. 0x40) + + modifyByte :: Ptr Word8 -> Int -> (Word8 -> Word8) -> IO () + modifyByte p n f = peekByteOff p n >>= pokeByteOff p n . f + foreign import ccall "cryptonite_curve25519_donna" ccryptonite_curve25519 :: Ptr Word8 -- ^ public -> Ptr Word8 -- ^ secret diff --git a/Crypto/PubKey/ECC/P256.hs b/Crypto/PubKey/ECC/P256.hs index f7048f7b..99ecbccd 100644 --- a/Crypto/PubKey/ECC/P256.hs +++ b/Crypto/PubKey/ECC/P256.hs @@ -18,6 +18,7 @@ module Crypto.PubKey.ECC.P256 , pointBase , pointAdd , pointMul + , pointDh , pointsMulVarTime , pointIsValid , toPoint @@ -48,7 +49,7 @@ import Crypto.Internal.Compat import Crypto.Internal.Imports import Crypto.Internal.ByteArray import qualified Crypto.Internal.ByteArray as B -import Data.Memory.PtrMethods (memSet) +import Data.Memory.PtrMethods (memSet, memCopy) import Crypto.Error import Crypto.Random import Crypto.Number.Serialize.Internal (os2ip, i2ospOf) @@ -56,7 +57,7 @@ import qualified Crypto.Number.Serialize as S (os2ip, i2ospOf) -- | A P256 scalar newtype Scalar = Scalar ScrubbedBytes - deriving (Eq,ByteArrayAccess) + deriving (Show,Eq,ByteArrayAccess) -- | A P256 point newtype Point = Point Bytes @@ -112,6 +113,14 @@ pointMul scalar p = withNewPoint $ \dx dy -> withScalar scalar $ \n -> withPoint p $ \px py -> withScalarZero $ \nzero -> ccryptonite_p256_points_mul_vartime nzero n px py dx dy +-- | Similar to 'pointMul', serializing the x coordinate as binary +pointDh :: ByteArray binary => Scalar -> Point -> binary +pointDh scalar p = + B.unsafeCreate scalarSize $ \dst -> withTempPoint $ \dx dy -> do + withScalar scalar $ \n -> withPoint p $ \px py -> withScalarZero $ \nzero -> + ccryptonite_p256_points_mul_vartime nzero n px py dx dy + memCopy dst (castPtr dx) scalarSize + -- | multiply the point @p with @n2 and add a lifted to curve value @n1 -- -- > n1 * G + n2 * p @@ -282,6 +291,9 @@ withNewScalarFreeze :: (Ptr P256Scalar -> IO ()) -> Scalar withNewScalarFreeze f = Scalar $ B.allocAndFreeze scalarSize f {-# NOINLINE withNewScalarFreeze #-} +withTempPoint :: (Ptr P256X -> Ptr P256Y -> IO a) -> IO a +withTempPoint f = allocTempScrubbed scalarSize (\p -> let px = castPtr p in f px (pxToPy px)) + withTempScalar :: (Ptr P256Scalar -> IO a) -> IO a withTempScalar f = allocTempScrubbed scalarSize (f . castPtr) diff --git a/Crypto/PubKey/ECC/Types.hs b/Crypto/PubKey/ECC/Types.hs index 57ea9a91..8f6a0704 100644 --- a/Crypto/PubKey/ECC/Types.hs +++ b/Crypto/PubKey/ECC/Types.hs @@ -1,6 +1,6 @@ {-# LANGUAGE DeriveDataTypeable #-} -- | --- Module : Crypto.PubKey.ECC.types +-- Module : Crypto.PubKey.ECC.Types -- License : BSD-style -- Maintainer : Vincent Hanquez -- Stability : Experimental diff --git a/Crypto/PubKey/ECIES.hs b/Crypto/PubKey/ECIES.hs new file mode 100644 index 00000000..cd3aac8b --- /dev/null +++ b/Crypto/PubKey/ECIES.hs @@ -0,0 +1,48 @@ +-- | +-- Module : Crypto.PubKey.ECIES +-- License : BSD-style +-- Maintainer : Vincent Hanquez +-- Stability : experimental +-- Portability : unknown +-- +-- IES with Elliptic curve +-- +-- This is a simple cryptographic system between 2 parties using Elliptic Curve. +-- +-- The sending party create a shared secret using the receiver public key, and use the shared secret +-- to generate cryptographic material for an symmetric encryption scheme (preferably authenticated encryption). +-- +-- The receiving party receive the temporary ephemeral public key which is combined to its secret key +-- to create the shared secret which just like on the sending is used to generate cryptographic material. +-- +-- This module doesn't provide any symmetric data encryption capability or any mean to derive +-- cryptographic key material for a symmetric key from the shared secret. +-- this is left to the user for now. +-- +module Crypto.PubKey.ECIES + ( deriveEncrypt + , deriveDecrypt + ) where + +import Crypto.ECC +import Crypto.Random +import Crypto.Internal.Proxy + +-- | Generate random a new Shared secret and the associated point +-- to do a ECIES style encryption +deriveEncrypt :: (MonadRandom randomly, EllipticCurveDH curve) + => proxy curve -- ^ representation of the curve + -> Point curve -- ^ the public key of the receiver + -> randomly (Point curve, SharedSecret) +deriveEncrypt proxy pub = do + (KeyPair rPoint rScalar) <- curveGenerateKeyPair proxy + return (rPoint, ecdh proxy rScalar pub) + +-- | Derive the shared secret with the receiver key +-- and the R point of the scheme. +deriveDecrypt :: EllipticCurveDH curve + => proxy curve -- ^ representation of the curve + -> Point curve -- ^ The received R (supposedly, randomly generated on the encrypt side) + -> Scalar curve -- ^ The secret key of the receiver + -> SharedSecret +deriveDecrypt proxy point secret = ecdh proxy secret point diff --git a/cryptonite.cabal b/cryptonite.cabal index 580e8025..ac83d56a 100644 --- a/cryptonite.cabal +++ b/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 @@ -184,6 +186,9 @@ Library Crypto.Random.Probabilistic Crypto.PubKey.Internal Crypto.PubKey.ElGamal + Crypto.ECC.Simple.Types + Crypto.ECC.Simple.Prim + Crypto.Internal.Proxy Crypto.Internal.ByteArray Crypto.Internal.Compat Crypto.Internal.CompatPrim