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Diffstat (limited to 'src')
| -rw-r--r-- | src/Ecc.hs | 274 |
1 files changed, 274 insertions, 0 deletions
diff --git a/src/Ecc.hs b/src/Ecc.hs new file mode 100644 index 0000000..7523afb --- /dev/null +++ b/src/Ecc.hs @@ -0,0 +1,274 @@ +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE KindSignatures #-} +{-# LANGUAGE OverloadedStrings #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE TypeOperators #-} + +module Ecc where + +import qualified Crypto.Hash.SHA256 as SHA256 +import Data.Bits +import qualified Data.ByteString as BS +import Data.Proxy +import GHC.TypeLits +import Text.Printf (PrintfArg, printf) + +-- FiniteFields +--https://stackoverflow.com/questions/39823408/prime-finite-field-z-pz-in-haskell-with-operator-overloading +newtype FieldElement (n :: Nat) = FieldElement Integer deriving Eq + +instance KnownNat n => Num (FieldElement n) where + FieldElement x + FieldElement y = fromInteger $ x + y + FieldElement x * FieldElement y = fromInteger $ x * y + abs x = x + signum _ = 1 + negate (FieldElement x) = fromInteger $ negate x + fromInteger a = FieldElement (mod a n) where n = natVal (Proxy :: Proxy n) + +instance KnownNat n => Fractional (FieldElement n) where + recip a = a ^ (n - 2) where n = natVal (Proxy :: Proxy n) + fromRational r = error "cant transform" -- fromInteger (numerator r) / fromInteger (denominator r) + +instance KnownNat n => Show (FieldElement n) where + show (FieldElement a) | n == (2 ^ 256 - 2 ^ 32 - 977) = printf "0x%064x" a + | otherwise = "FieldElement_" ++ show n ++ " " ++ show a + where n = natVal (Proxy :: Proxy n) + + +assert :: Bool -> Bool +assert False = error "WRONG" +assert x = x + +aa = + let a = FieldElement 2 :: FieldElement 31 + b = FieldElement 15 + in (a + b == FieldElement 17, a /= b, a - b == FieldElement 18) + +bb = + let a = FieldElement 19 :: FieldElement 31 + b = FieldElement 24 + in a * b + +-- Elliptic curve +data ECPoint a + = Infinity + | ECPoint + { x :: a + , y :: a + , a :: a + , b :: a + } + deriving (Eq) + + +instance {-# OVERLAPPABLE #-} (PrintfArg a, Num a) => Show (ECPoint a) where + show Infinity = "ECPoint(Infinity)" + show p = printf "ECPoint(%f, %f)_%f_%f" (x p) (y p) (a p) (b p) + +instance {-# OVERLAPPING #-} KnownNat n => Show (ECPoint (FieldElement n)) where + show Infinity = "ECPoint(Infinity)" + show p | n == (2 ^ 256 - 2 ^ 32 - 977) = "S256Point" ++ points + | otherwise = "ECPoint_" ++ show n ++ points ++ params + where + n = natVal (Proxy :: Proxy n) + points = "(" ++ si (x p) ++ ", " ++ si (y p) ++ ")" + params = "a_" ++ si (a p) ++ "|b_" ++ si (b p) + si (FieldElement r) | n == (2 ^ 256 - 2 ^ 32 - 977) = printf "0x%064x" r + | otherwise = show r + +validECPoint :: (Eq a, Num a) => ECPoint a -> Bool +validECPoint Infinity = True +validECPoint (ECPoint x y a b) = y ^ 2 == x ^ 3 + a * x + b + +add :: (Eq a, Fractional a) => ECPoint a -> ECPoint a -> ECPoint a +add Infinity p = p +add p Infinity = p +add p q | a p /= a q || b p /= b q = error "point not on same curve" + | x p == x q && y p /= y q = Infinity + | x p /= x q = new_point $ (y q - y p) / (x q - x p) + | x p == x q && y p == 0 = Infinity + | p == q = new_point $ (3 * x p ^ 2 + a p) / (2 * y p) + | otherwise = error "Unexpected case of points" + where + new_point slope = + let new_x = slope ^ 2 - x p - x q + new_y = slope * (x p - new_x) - y p + in ECPoint new_x new_y (a p) (b p) + + +binaryExpansion :: (Semigroup a) => Integer -> a -> a -> a +binaryExpansion m value result + | m == 0 = result + | otherwise = binaryExpansion (m `shiftR` 1) (value <> value) accumulator + where accumulator = if m .&. 1 == 1 then result <> value else result + +scalarProduct :: (Eq a, Fractional a) => Integer -> ECPoint a -> ECPoint a +scalarProduct m ec = binaryExpansion m ec Infinity + +instance (Eq a, Fractional a) => Semigroup (ECPoint a) where + (<>) = add + +instance (Eq a, Fractional a) => Monoid (ECPoint a) where + mempty = Infinity + +tre = FieldElement 3 :: FieldElement 31 +cc = + let a = ECPoint tre (-7) 5 7 + b = ECPoint 18 77 5 7 + c = ECPoint (-1) (-1) 5 7 + in ( validECPoint a + , validECPoint b + , validECPoint c + , a /= b + , a == a + , add Infinity a + , add a (ECPoint 3 7 5 7) + , add (ECPoint 3 7 5 7) c + , add c c + ) + +dd = + let a = FieldElement 0 :: FieldElement 223 + b = FieldElement 7 + x = FieldElement 192 + y = FieldElement 105 + in ECPoint x y a b +ee = ECPoint 192 105 (FieldElement 0 :: FieldElement 223) 7 +ff = ECPoint 192 105 0 7 :: ECPoint (FieldElement 223) + +aPoint = ECPoint 192 105 0 7 :: ECPoint (FieldElement 223) +total = add aPoint $ add aPoint $ add aPoint $ add aPoint aPoint + +totalfold = foldr add Infinity $ replicate 5 aPoint +totalmconcat = mconcat $ replicate 5 aPoint + +type S256Field = FieldElement (2 ^ 256- 2^ 32 - 977) +type NField + = FieldElement + 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 +type S256Point = ECPoint S256Field +s256point :: S256Field -> S256Field -> S256Point +s256point x y = + let p = ECPoint x y 0 7 + in if validECPoint p then p else error "Invalid point" +li :: S256Field +li = 12 +ll :: ECPoint (FieldElement 31) +ll = Infinity +ri = ECPoint 3 7 5 7 :: S256Point + + +ncons = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 +gcons = s256point + 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 + 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8 + +asInt :: KnownNat n => FieldElement n -> Integer +asInt (FieldElement n) = n + +-- z = 0xbc62d4b80d9e36da29c16c5d4d9f11731f36052c72401a76c23c0fb5a9b74423 +-- r = 0x37206a0610995c58074999cb9767b87af4c4978db68c06e8e6e81d282047a7c6 +-- s = 0x8ca63759c1157ebeaec0d03cecca119fc9a75bf8e6d0fa65c841c8e2738cdaec ::NField +-- px = 0x04519fac3d910ca7e7138f7013706f619fa8f033e6ec6e09370ea38cee6a7574 +-- py = 0x82b51eab8c27c66e26c858a079bcdf4f1ada34cec420cafc7eac1a42216fb6c4 +-- point = s256point px py +-- u = z / s +-- v = r / s +-- signa = scalarProduct (asInt u) gcons <> scalarProduct (asInt v) point + +pub = s256point + 0x887387e452b8eacc4acfde10d9aaf7f6d9a0f975aabb10d006e4da568744d06c + 0x61de6d95231cd89026e286df3b6ae4a894a3378e393e93a0f45b666329a0ae34 + +z1 = 0xec208baa0fc1c19f708a9ca96fdeff3ac3f230bb4a7ba4aede4942ad003c0f60 +r1 = 0xac8d1c87e51d0d441be8b3dd5b05c8795b48875dffe00b7ffcfac23010d3a395 +s1 = + 0x68342ceff8935ededd102dd876ffd6ba72d6a427a3edb13d26eb0781cb423c4 :: NField + +signa1 = + scalarProduct (asInt $ z1 / s1) gcons <> scalarProduct (asInt $ r1 / s1) pub + +z2 = + 0x7c076ff316692a3d7eb3c3bb0f8b1488cf72e1afcd929e29307032997a838a3d :: NField +r2 = 0xeff69ef2b1bd93a66ed5219add4fb51e11a840f404876325a1e8ffe0529a2c :: NField +s2 = + 0xc7207fee197d27c618aea621406f6bf5ef6fca38681d82b2f06fddbdce6feab6 :: NField + + +data Signature = Signature + { r :: S256Field + , s :: NField + } deriving (Show) + +verifySignanture :: NField -> Signature -> S256Point -> Bool +verifySignanture z (Signature r s) pub = x target == r + where + target = + scalarProduct (asInt $ z / s) gcons + <> scalarProduct (asInt $ (fromIntegral (asInt r)) / s) pub + + +fromBytes :: BS.ByteString -> Integer +fromBytes = BS.foldl' f 0 where f a b = a `shiftL` 8 .|. fromIntegral b + +integerToBytes :: Integer -> BS.ByteString +integerToBytes = BS.pack . go + where + go c = case c of + 0 -> [] + c -> go (c `div` 256) ++ [fromIntegral (c `mod` 256)] + +zeroPad :: Integer -> BS.ByteString -> BS.ByteString +zeroPad n s = BS.append padding s + where + padding = BS.pack (replicate (fromIntegral n - fromIntegral (BS.length s)) 0) + +toBytes32 :: Integer -> BS.ByteString +toBytes32 = zeroPad 32 . integerToBytes + +hash256 :: BS.ByteString -> BS.ByteString +hash256 = SHA256.hash . SHA256.hash + +sighash :: BS.ByteString -> NField +sighash = fromIntegral . fromBytes . hash256 + +-- priv = fromIntegral $ fromBytes $ hash256 "my secret" :: NField +priv = 12345 +mesg = fromIntegral $ fromBytes $ hash256 "Programming Bitcoin!" :: NField +k = 1234567890 :: NField +rm = scalarProduct (asInt k) gcons +sm = (mesg + fromIntegral (asInt (x rm)) * priv) / k +pubm = scalarProduct (asInt priv) gcons + +signMessage :: NField -> BS.ByteString -> Signature +signMessage priv mesg = + let z = sighash mesg + k = deterministicK priv z + rm = scalarProduct (asInt k) gcons + FieldElement sm = (z + fromIntegral (asInt (x rm)) * priv) / k + ss = if sm > (div ncons 2) then ncons - sm else sm + in Signature (x rm) (fromIntegral ss) + +deterministicK :: NField -> NField -> NField +deterministicK priv (FieldElement z) = fromInteger $ candidate k2 v2 + where + k = BS.pack $ replicate 32 0 + v = BS.pack $ replicate 32 1 + zbs = toBytes32 z + FieldElement sk = priv + skbs = toBytes32 sk + k1 = SHA256.hmac k $ v `BS.append` "\NUL" `BS.append` skbs `BS.append` zbs + v1 = SHA256.hmac k1 v + k2 = SHA256.hmac k1 $ v1 `BS.append` "\SOH" `BS.append` skbs `BS.append` zbs + v2 = SHA256.hmac k2 v1 + + candidate k v = + let vNew = SHA256.hmac k v + can = fromBytes vNew + in if can >= 1 && can < ncons + then can + else + let kp = SHA256.hmac k $ vNew `BS.append` "\NUL" + vp = SHA256.hmac kp vNew + in candidate kp vp |