diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +The MIT License (MIT) + +Copyright (c) 2016 Baojun Wang + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/app/Main.hs b/app/Main.hs new file mode 100644 --- /dev/null +++ b/app/Main.hs @@ -0,0 +1,8 @@ +module Main where + +import qualified Data.ByteString.Lazy as LBS +import Data.ByteString (ByteString) +import Crypto.Hash + +main :: IO () +main = LBS.getContents >>= print . (hashLazy :: LBS.ByteString -> SHA256) diff --git a/hashing.cabal b/hashing.cabal new file mode 100644 --- /dev/null +++ b/hashing.cabal @@ -0,0 +1,63 @@ +name: hashing +version: 0.1.0.0 +synopsis: Initial project template from stack +description: Please see README.md +homepage: https://github.com/wangbj/hashing/blob/master/README.md +license: BSD3 +license-file: LICENSE +author: Baojun Wang +maintainer: wangbj@gmail.com +copyright: 2016 Baojun Wang +category: Cryptography +build-type: Simple +-- extra-source-files: +cabal-version: >=1.10 + +library + hs-source-dirs: src + exposed-modules: Crypto.Hash + , Crypto.Hash.ADT + , Crypto.Hash.SHA1 + , Crypto.Hash.SHA256 + , Crypto.Hash.SHA512 + , Crypto.Hash.MD5 + , Crypto.Hash.Whirlpool + build-depends: QuickCheck >= 2.8.1 + , array >= 0.5.1.0 + , base >= 4.7 && < 5 + , bytestring >= 0.10.6.0 + , mtl >= 2.2.1 + , template-haskell >= 2.10.0.0 + default-language: Haskell2010 + +executable hashing-exe + hs-source-dirs: app + main-is: Main.hs + ghc-options: -threaded -rtsopts -Wall -with-rtsopts=-N1 + build-depends: QuickCheck >= 2.8.1 + , array >= 0.5.1.0 + , base + , bytestring >= 0.10.6.0 + , hashing + , mtl >= 2.2.1 + , template-haskell >= 2.10.0.0 + default-language: Haskell2010 + +test-suite hashing-test + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Spec.hs + build-depends: QuickCheck >= 2.8.1 + , array >= 0.5.1.0 + , base + , bytestring >= 0.10.6.0 + , hashing >= 0.1.0.0 + , mtl >= 2.2.1 + , template-haskell >= 2.10.0.0 + , cryptonite >= 0.15 + ghc-options: -threaded -rtsopts -with-rtsopts=-N1 + default-language: Haskell2010 + +source-repository head + type: git + location: https://github.com/wangbj/hashing diff --git a/src/Crypto/Hash.hs b/src/Crypto/Hash.hs new file mode 100644 --- /dev/null +++ b/src/Crypto/Hash.hs @@ -0,0 +1,45 @@ +-- | pure hash interface, supported hash algorithms: +-- +-- * SHA1 +-- +-- * SHA224/SHA256 +-- +-- * SHA384/SHA512 +-- +-- * MD5 +-- +-- * Whirlpool +-- +-- NOTE: performance is just about 1 \/ 5 - 1 \/ 15 of C/ASM implementations. +-- +module Crypto.Hash ( + HashAlgorithm(..) + , SHA1 + , SHA224 + , SHA256 + , SHA384 + , SHA512 + , MD5 + , Whirlpool + , hash + , hashLazy + ) where + +import qualified Data.ByteString.Lazy as LBS +import Data.ByteString (ByteString) + +import Crypto.Hash.ADT + +import Crypto.Hash.SHA1 +import Crypto.Hash.SHA256 +import Crypto.Hash.SHA512 +import Crypto.Hash.MD5 +import Crypto.Hash.Whirlpool + +-- | Hash strict byte string +hash :: (HashAlgorithm a) => ByteString -> a +hash = hashFinal . hashUpdate hashInit + +-- | Hash lazy byte string +hashLazy :: (HashAlgorithm a) => LBS.ByteString -> a +hashLazy = hashFinal . LBS.foldlChunks hashUpdate hashInit diff --git a/src/Crypto/Hash/ADT.hs b/src/Crypto/Hash/ADT.hs new file mode 100644 --- /dev/null +++ b/src/Crypto/Hash/ADT.hs @@ -0,0 +1,31 @@ +module Crypto.Hash.ADT ( + Context(..) + , HashAlgorithm(..) + , Digest (..) + ) where + +import Data.ByteString (ByteString) +import Data.Int + +data Context a = Context { + ctxTotalBytesRead :: {-# UNPACK #-} !Int64 + , ctxBufferRead :: {-# UNPACK #-} !Int + , ctxBuffer :: {-# UNPACK #-} !ByteString + , ctxHashValueAcc :: !a + } deriving Show + +instance Functor Context where + fmap f (Context t r b v) = Context t r b (f v) + +newtype Digest a = Digest String deriving Show + +-- | Hash algorithm interface +-- +-- provides classic init\/update\/final API. however, +-- user should call higher level API such as hash or hashLazy. +class HashAlgorithm a where + hashBlockSize :: a -> Int + hashDigestSize :: a -> Int + hashInit :: Context a + hashUpdate :: Context a -> ByteString -> Context a + hashFinal :: Context a -> a diff --git a/src/Crypto/Hash/MD5.hs b/src/Crypto/Hash/MD5.hs new file mode 100644 --- /dev/null +++ b/src/Crypto/Hash/MD5.hs @@ -0,0 +1,154 @@ +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE Safe #-} + +module Crypto.Hash.MD5 ( + MD5 + ) where + +import qualified Data.ByteString.Lazy.Char8 as LC +import qualified Data.ByteString.Lazy as LBS +import qualified Data.ByteString as B +import Data.ByteString (ByteString) +import Data.ByteString.Builder +import Data.Array.Unboxed +import Data.Int +import Data.Word +import Data.Bits +import Data.Monoid +import Data.List(foldl') + +import Crypto.Hash.ADT + +initSs :: UArray Int Int +initSs = listArray (0, 63) [ + 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22 + , 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20 + , 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23 + , 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21 ] + +initKs :: UArray Int Word32 +initKs = listArray (0, 63) [ + 0xd76aa478, 0xe8c7b756, 0x242070db, 0xc1bdceee + , 0xf57c0faf, 0x4787c62a, 0xa8304613, 0xfd469501 + , 0x698098d8, 0x8b44f7af, 0xffff5bb1, 0x895cd7be + , 0x6b901122, 0xfd987193, 0xa679438e, 0x49b40821 + , 0xf61e2562, 0xc040b340, 0x265e5a51, 0xe9b6c7aa + , 0xd62f105d, 0x02441453, 0xd8a1e681, 0xe7d3fbc8 + , 0x21e1cde6, 0xc33707d6, 0xf4d50d87, 0x455a14ed + , 0xa9e3e905, 0xfcefa3f8, 0x676f02d9, 0x8d2a4c8a + , 0xfffa3942, 0x8771f681, 0x6d9d6122, 0xfde5380c + , 0xa4beea44, 0x4bdecfa9, 0xf6bb4b60, 0xbebfbc70 + , 0x289b7ec6, 0xeaa127fa, 0xd4ef3085, 0x04881d05 + , 0xd9d4d039, 0xe6db99e5, 0x1fa27cf8, 0xc4ac5665 + , 0xf4292244, 0x432aff97, 0xab9423a7, 0xfc93a039 + , 0x655b59c3, 0x8f0ccc92, 0xffeff47d, 0x85845dd1 + , 0x6fa87e4f, 0xfe2ce6e0, 0xa3014314, 0x4e0811a1 + , 0xf7537e82, 0xbd3af235, 0x2ad7d2bb, 0xeb86d391 ] + +data MD5 = MD5 {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + deriving Eq + +instance Show MD5 where + show = LC.unpack . toLazyByteString . foldMap (word32HexFixed . byteSwap32) . toList + where toList (MD5 a b c d) = a:b:c:[d] + +initHash :: MD5 +initHash = MD5 0x67452301 0xefcdab89 0x98badcfe 0x10325476 + +encodeInt64Helper :: Int64 -> [Word8] +encodeInt64Helper x_ = [w0, w1, w2, w3, w4, w5, w6, w7] + where x = x_ * 8 + w7 = fromIntegral $ (x `shiftR` 56) .&. 0xff + w6 = fromIntegral $ (x `shiftR` 48) .&. 0xff + w5 = fromIntegral $ (x `shiftR` 40) .&. 0xff + w4 = fromIntegral $ (x `shiftR` 32) .&. 0xff + w3 = fromIntegral $ (x `shiftR` 24) .&. 0xff + w2 = fromIntegral $ (x `shiftR` 16) .&. 0xff + w1 = fromIntegral $ (x `shiftR` 8) .&. 0xff + w0 = fromIntegral $ (x `shiftR` 0) .&. 0xff + +encodeInt64 :: Int64 -> ByteString +encodeInt64 = B.pack . encodeInt64Helper + +md5BlockSize :: Int +md5BlockSize = 64 + +md5DigestSize :: Int +md5DigestSize = 16 + +lastChunk :: Int64 -> ByteString -> [ByteString] +lastChunk msglen s + | len < (md5BlockSize - 8) = [s <> B.cons 0x80 (B.replicate (md5BlockSize - 9 - len) 0x0) <> encodedLen] + | len < (2*md5BlockSize - 8) = helper (s <> B.cons 0x80 (B.replicate (2*md5BlockSize -9 - len) 0x0) <> encodedLen) + where + len = B.length s + encodedLen = encodeInt64 msglen + helper bs = [s1, s2] + where (!s1, !s2) = B.splitAt 64 bs + +readW32 :: ByteString -> Word32 +readW32 = byteSwap32 . B.foldl' acc 0 + where acc x c = x `shiftL` 8 + fromIntegral c + {-# INLINE acc #-} +{-# INLINE readW32 #-} + +prepareBlock :: ByteString -> UArray Int Word32 +prepareBlock = listArray (0, 15) . go + where go s + | B.null s = [] + | otherwise = let !s1 = B.take 4 s + !s' = B.drop 4 s + in readW32 s1 : go s' + {-# INLINE go #-} + +md5BlockUpdate :: MD5 -> UArray Int Word32 -> MD5 +md5BlockUpdate h u = foldl' blkUpdate h [0..63] + where + blkUpdate (MD5 a b c d) i = MD5 d b' b c + where + !(!f, !g) + | i < 16 = ((d `xor` (b .&. (c `xor` d))), i) + | i < 32 = ((c `xor` (d .&. (b `xor` c))), (5*i+1) .&. 0xf) + | i < 48 = (b `xor` c `xor` d, (3*i+5) .&. 0xf) + | i < 64 = ((c `xor` (b .|. (complement d))), (7*i) .&. 0xf) + !b' = b + (a+f+(initKs!i)+(u!g)) `rotateL` (initSs!i) + blkUpdate :: MD5 -> Int -> MD5 + {-# INLINE blkUpdate #-} + +{-# INLINE encodeChunk #-} +encodeChunk :: MD5 -> ByteString -> MD5 +encodeChunk hv@(MD5 a b c d) bs = MD5 (a+a') (b+b') (c+c') (d+d') + where + MD5 a' b' c' d' = md5BlockUpdate hv (prepareBlock bs) + +{-# NOINLINE md5Hash #-} +md5Hash :: LBS.ByteString -> MD5 +md5Hash = md5Final . LBS.foldlChunks md5Update md5Init + +md5Init :: Context MD5 +md5Init = Context 0 0 B.empty initHash + +md5Update :: Context MD5 -> ByteString -> Context MD5 +md5Update ctx@(Context n k w hv) s + | B.null s = ctx + | sizeRead < sizeToRead = Context (n + fromIntegral sizeRead) (k + sizeRead) (w <> s1) hv + | sizeRead >= sizeToRead = md5Update (Context (n + fromIntegral sizeToRead) 0 mempty (encodeChunk hv (w <> s1))) s' + where + !sizeToRead = md5BlockSize - k + !s1 = B.take sizeToRead s + !s' = B.drop sizeToRead s + !sizeRead = B.length s1 + +{-# NOINLINE md5Final #-} +md5Final :: Context MD5 -> MD5 +md5Final (Context n _ w hv) = foldl' encodeChunk hv (lastChunk n w) + +instance HashAlgorithm MD5 where + hashBlockSize = const md5BlockSize + hashDigestSize = const md5DigestSize + hashInit = md5Init + hashUpdate = md5Update + hashFinal = md5Final diff --git a/src/Crypto/Hash/SHA1.hs b/src/Crypto/Hash/SHA1.hs new file mode 100644 --- /dev/null +++ b/src/Crypto/Hash/SHA1.hs @@ -0,0 +1,175 @@ +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE BangPatterns #-} +{-# LANGUAGE UnboxedTuples #-} + +module Crypto.Hash.SHA1 + ( + SHA1 + ) where + +import qualified Data.ByteString.Lazy as LBS +import qualified Data.ByteString as B +import qualified Data.ByteString.Lazy.Char8 as LC +import Data.ByteString (ByteString) +import Data.ByteString.Builder +import Control.Monad.ST +import Data.Int +import Data.Word +import Data.Bits +import Data.Monoid +import Data.Array.Unboxed +import Data.Array.Unsafe +import Data.Array.ST +import Data.List(foldl') + +import Crypto.Hash.ADT + +encodeInt64Helper :: Int64 -> [Word8] +encodeInt64Helper x_ = [w7, w6, w5, w4, w3, w2, w1, w0] + where x = x_ * 8 + w7 = fromIntegral $ (x `shiftR` 56) .&. 0xff + w6 = fromIntegral $ (x `shiftR` 48) .&. 0xff + w5 = fromIntegral $ (x `shiftR` 40) .&. 0xff + w4 = fromIntegral $ (x `shiftR` 32) .&. 0xff + w3 = fromIntegral $ (x `shiftR` 24) .&. 0xff + w2 = fromIntegral $ (x `shiftR` 16) .&. 0xff + w1 = fromIntegral $ (x `shiftR` 8) .&. 0xff + w0 = fromIntegral $ (x `shiftR` 0) .&. 0xff + +encodeInt64 :: Int64 -> ByteString +encodeInt64 = B.pack . encodeInt64Helper + +sha1BlockSize :: Int +sha1BlockSize = 64 + +lastChunk :: Int64 -> ByteString -> [ByteString] +lastChunk msglen s + | len < (sha1BlockSize - 8) = [s <> B.cons 0x80 (B.replicate (sha1BlockSize - 9 - len) 0x0) <> encodedLen] + | len < (2 * sha1BlockSize - 8) = helper (s <> B.cons 0x80 (B.replicate (2 * sha1BlockSize - 9 - len) 0x0) <> encodedLen) + where + len = B.length s + encodedLen = encodeInt64 msglen + helper bs = [s1, s2] + where (s1, s2) = B.splitAt 64 bs + +data SHA1 = SHA1 {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + deriving Eq + +initHash :: SHA1 +initHash = SHA1 0x67452301 0xEFCDAB89 0x98BADCFE 0x10325476 0xC3D2E1F0 + +instance Show SHA1 where + show = LC.unpack . toLazyByteString . foldMap word32HexFixed . toList + where toList (SHA1 a b c d e) = a:b:c:d:[e] + +sha1BlockUpdate :: SHA1 -> UArray Int Word64 -> SHA1 +sha1BlockUpdate hv = foldl' acc hv . assocs + where acc (SHA1 a b c d e) (!i, !w) = SHA1 temp2 temp1 (a `rotateL` 30) (b `rotateL` 30) c + where getK i + | i < 10 = 0x5a827999 + | i < 20 = 0x6ed9eba1 + | i < 30 = 0x8f1bbcdc + | i < 40 = 0xca62c1d6 + getK :: Int -> Word32 + {-# INLINE getK #-} + getF1 i + | i < 10 = d `xor` (b .&. (c `xor` d)) + | i < 20 = b `xor` c `xor` d + | i < 30 = (b .&. c) .|. (d .&. (b `xor` c)) + | i < 40 = b `xor` c `xor` d + getF1 :: Int -> Word32 + {-# INLINE getF1 #-} + getF2 i + | i < 10 = c `xor` (a .&. ((b `rotateL` 30) `xor` c)) + | i < 20 = a `xor` (b `rotateL` 30) `xor` c + | i < 30 = (a .&. (b `rotateL` 30)) .|. (c .&. (a `xor` (b `rotateL` 30))) + | i < 40 = a `xor` (b `rotateL` 30) `xor` c + getF2 :: Int -> Word32 + {-# INLINE getF2 #-} + !f1 = getF1 i + !f2 = getF2 i + !k = getK i + !temp1 = (a `rotateL` 5) + f1 + e + k + (fromIntegral (w `shiftR` 32)) + !temp2 = (temp1 `rotateL` 5) + f2 + d + k + (fromIntegral (w .&. 0xffffffff)) + {-# INLINE acc #-} + +{-# INLINE readW64 #-} +readW64 :: ByteString -> Word64 +readW64 = B.foldl' acc 0 . B.take 8 + where acc x c = x `shiftL` 8 + fromIntegral c + acc :: Word64 -> Word8 -> Word64 + {-# INLINE acc #-} + +prepareBlock :: ByteString -> UArray Int Word64 +prepareBlock s = runST $ do + iou <- newArray (0, 39) 0 :: ST s (STUArray s Int Word64) + let + !w1 = readW64 s + !w2 = readW64 (B.drop 8 s) + !w3 = readW64 (B.drop 16 s) + !w4 = readW64 (B.drop 24 s) + !w5 = readW64 (B.drop 32 s) + !w6 = readW64 (B.drop 40 s) + !w7 = readW64 (B.drop 48 s) + !w8 = readW64 (B.drop 56 s) + writeArray iou 0 w1 + writeArray iou 1 w2 + writeArray iou 2 w3 + writeArray iou 3 w4 + writeArray iou 4 w5 + writeArray iou 5 w6 + writeArray iou 6 w7 + writeArray iou 7 w8 + let step1 i = readArray iou (i-8) >>= \x1 -> + readArray iou (i-7) >>= \x2 -> + readArray iou (i-4) >>= \x3 -> + readArray iou (i-2) >>= \x4 -> + readArray iou (i-1) >>= \x5 -> + let !wi = (x1 `xor` x2 `xor` x3 `xor` ( ((x4 .&. 0xffffffff) `shiftL` 32) .|. (x5 `shiftR` 32) )) `rotateL` 1 + !i1 = (wi `shiftR` 32) .&. 0x1 + !i2 = wi .&. 0x1 + !wj = (wi .&. 0xfffffffefffffffe) .|. i1 .|. (i2 `shiftL` 32) + in writeArray iou i wj + {-# INLINE step1 #-} + mapM_ step1 [8..39] + unsafeFreeze iou + +{-# INLINE encodeChunk #-} +encodeChunk :: SHA1 -> ByteString -> SHA1 +encodeChunk hv@(SHA1 a b c d e) bs = SHA1 (a+a') (b+b') (c+c') (d+d') (e+e') + where + SHA1 a' b' c' d' e' = sha1BlockUpdate hv (prepareBlock bs) + +sha1Init :: Context SHA1 +sha1Init = Context 0 0 B.empty initHash + +{-# NOINLINE sha1Update #-} +sha1Update :: Context SHA1 -> ByteString -> Context SHA1 +sha1Update ctx@(Context n k w hv) s + | B.null s = ctx + | sizeRead < sizeToRead = Context (n + fromIntegral sizeRead) (k + sizeRead) (w <> s1) hv + | sizeRead >= sizeToRead = sha1Update (Context (n + fromIntegral sizeToRead) 0 mempty (encodeChunk hv (w <> s1))) s' + where + !sizeToRead = sha1BlockSize - k + !s1 = B.take sizeToRead s + !s' = B.drop sizeToRead s + !sizeRead = B.length s1 + +{-# NOINLINE sha1Final #-} +sha1Final :: Context SHA1 -> SHA1 +sha1Final (Context n _ w hv) = foldl' encodeChunk hv (lastChunk n w) + +{-# NOINLINE sha1Hash #-} +sha1Hash :: LBS.ByteString -> SHA1 +sha1Hash = sha1Final . LBS.foldlChunks sha1Update sha1Init + +instance HashAlgorithm SHA1 where + hashBlockSize = const sha1BlockSize + hashDigestSize = const 20 + hashInit = sha1Init + hashUpdate = sha1Update + hashFinal = sha1Final diff --git a/src/Crypto/Hash/SHA256.hs b/src/Crypto/Hash/SHA256.hs new file mode 100644 --- /dev/null +++ b/src/Crypto/Hash/SHA256.hs @@ -0,0 +1,219 @@ +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE BangPatterns #-} + +module Crypto.Hash.SHA256 + ( + SHA256 + , SHA224 + ) where + +import qualified Data.ByteString as B +import qualified Data.ByteString.Lazy as LBS +import qualified Data.ByteString.Lazy.Char8 as LC +import Data.ByteString (ByteString) +import Data.ByteString.Builder +import Control.Monad.ST +import Data.Int +import Data.Word +import Data.Bits +import Data.Monoid +import Data.Array.Unboxed +import Data.Array.Unsafe +import Data.Array.ST +import Data.List(foldl') + +import Crypto.Hash.ADT + +initHs :: [Word32] +initHs = [ + 0x6a09e667 , 0xbb67ae85 , 0x3c6ef372 , 0xa54ff53a + , 0x510e527f , 0x9b05688c , 0x1f83d9ab , 0x5be0cd19 ] + +initKs :: [Word32] +initKs = [ + 0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5, + 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, + 0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da, + 0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967, + 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, + 0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070, + 0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3, + 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2 ] + +encodeInt64Helper :: Int64 -> [Word8] +encodeInt64Helper x_ = [w7, w6, w5, w4, w3, w2, w1, w0] + where x = x_ * 8 + w7 = fromIntegral $ (x `shiftR` 56) .&. 0xff + w6 = fromIntegral $ (x `shiftR` 48) .&. 0xff + w5 = fromIntegral $ (x `shiftR` 40) .&. 0xff + w4 = fromIntegral $ (x `shiftR` 32) .&. 0xff + w3 = fromIntegral $ (x `shiftR` 24) .&. 0xff + w2 = fromIntegral $ (x `shiftR` 16) .&. 0xff + w1 = fromIntegral $ (x `shiftR` 8) .&. 0xff + w0 = fromIntegral $ (x `shiftR` 0) .&. 0xff + +encodeInt64 :: Int64 -> ByteString +encodeInt64 = B.pack . encodeInt64Helper + +sha256BlockSize = 64 + +lastChunk :: Int64 -> ByteString -> [ByteString] +lastChunk msglen s + | len < 56 = [s <> B.cons 0x80 (B.replicate (55 - len) 0x0) <> encodedLen] + | len < 120 = helper (s <> B.cons 0x80 (B.replicate (119 - len) 0x0) <> encodedLen) + where + len = B.length s + encodedLen = encodeInt64 msglen + helper bs = [s1, s2] + where (s1, s2) = B.splitAt 64 bs + +data SHA256 = SHA256 {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + deriving Eq + +data SHA224 = SHA224 {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + {-# UNPACK #-} !Word32 + +initHash :: SHA256 +initHash = fromList initHs + where fromList (a:b:c:d:e:f:g:h:_) = SHA256 a b c d e f g h + +initHash224 :: SHA256 +initHash224 = fromList [0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939, 0xffc00b31, 0x68581511, 0x64f98fa7, 0xbefa4fa4] + where fromList (a:b:c:d:e:f:g:h:_) = SHA256 a b c d e f g h + +instance Show SHA256 where + show = LC.unpack . toLazyByteString . foldMap word32HexFixed . toList + where toList (SHA256 a b c d e f g h) = a:b:c:d:e:f:g:[h] + +instance Show SHA224 where + show = LC.unpack . toLazyByteString . foldMap word32HexFixed . toList + where toList (SHA224 a b c d e f g h) = a:b:c:d:e:f:[g] + +instance Eq SHA224 where + (SHA224 a1 b1 c1 d1 e1 f1 g1 _) == (SHA224 a2 b2 c2 d2 e2 f2 g2 _) = + a1 == a2 && b1 == b2 && c1 == c2 && d1 == d2 + && e1 == e2 && f1 == f2 && g1 == g2 + +{-# INLINABLE sha256BlockUpdate #-} +sha256BlockUpdate :: SHA256 -> Word32 -> SHA256 +sha256BlockUpdate (SHA256 a b c d e f g h) w = + let + !s1 = (e `rotateR` 6) `xor` (e `rotateR` 11) `xor` (e `rotateR` 25) + !ch = (e .&. f) `xor` (complement e .&. g) + !temp1 = h + s1 + ch + w + !s0 = (a `rotateR` 2) `xor` (a `rotateR` 13) `xor` (a `rotateR` 22) + !maj = (a .&. b) `xor` (a .&. c) `xor` (b .&. c) + !temp2 = s0 + maj + in SHA256 (temp1 + temp2) a b c (d + temp1) e f g + +{-# INLINE readW64 #-} +readW64 :: ByteString -> Word64 +readW64 = B.foldl' acc 0 . B.take 8 + where acc x c = x `shiftL` 8 + fromIntegral c + acc :: Word64 -> Word8 -> Word64 + {-# INLINE acc #-} + +prepareBlock :: ByteString -> UArray Int Word32 +prepareBlock s = runST $ do + iou <- newArray (0, 63) 0 :: ST s (STUArray s Int Word32) + let + !w1 = readW64 s + !w2 = readW64 (B.drop 8 s) + !w3 = readW64 (B.drop 16 s) + !w4 = readW64 (B.drop 24 s) + !w5 = readW64 (B.drop 32 s) + !w6 = readW64 (B.drop 40 s) + !w7 = readW64 (B.drop 48 s) + !w8 = readW64 (B.drop 56 s) + write2 k x = writeArray iou (2*k) (fromIntegral (x `shiftR` 32)) >> + writeArray iou (1+2*k) (fromIntegral (x .&. 0xffffffff)) + {-# INLINE write2 #-} + write2 0 w1 + write2 1 w2 + write2 2 w3 + write2 3 w4 + write2 4 w5 + write2 5 w6 + write2 6 w7 + write2 7 w8 + let go i = readArray iou (i-16) >>= \x1 -> + readArray iou (i-15) >>= \x2 -> + readArray iou (i- 7) >>= \x3 -> + readArray iou (i- 2) >>= \x4 -> + let !s0 = (x2 `rotateR` 7) `xor` (x2 `rotateR` 18) `xor` (x2 `shiftR` 3) + !s1 = (x4 `rotateR` 17) `xor` (x4 `rotateR` 19) `xor` (x4 `shiftR` 10) + in writeArray iou i (x1 + s0 + x3 + s1) + {-# INLINE go #-} + mapM_ go [16..63] + unsafeFreeze iou + +{-# INLINE encodeChunk #-} +encodeChunk :: SHA256 -> ByteString -> SHA256 +encodeChunk hv@(SHA256 a b c d e f g h) bs = SHA256 (a+a') (b+b') (c+c') (d+d') (e+e') (f+f') (g+g') (h+h') + where + SHA256 a' b' c' d' e' f' g' h' = foldl' sha256BlockUpdate hv (zipWith (+) (elems (prepareBlock bs)) initKs) + +{-# NOINLINE sha256Hash #-} +sha256Hash :: LBS.ByteString -> SHA256 +sha256Hash = sha256Final . LBS.foldlChunks sha256Update sha256Init + +sha256Init :: Context SHA256 +sha256Init = Context 0 0 B.empty initHash + +{-# NOINLINE sha256Update #-} +sha256Update :: Context SHA256 -> ByteString -> Context SHA256 +sha256Update ctx@(Context n k w hv) s + | B.null s = ctx + | sizeRead < sizeToRead = Context (n + fromIntegral sizeRead) (k + sizeRead) (w <> s1) hv + | sizeRead >= sizeToRead = sha256Update (Context (n + fromIntegral sizeToRead) 0 mempty (encodeChunk hv (w <> s1))) s' + where + !sizeToRead = sha256BlockSize - k + (!s1, !s') = B.splitAt sizeToRead s + !sizeRead = B.length s1 + +{-# NOINLINE sha256Final #-} +sha256Final :: Context SHA256 -> SHA256 +sha256Final (Context n _ w hv) = foldl' encodeChunk hv (lastChunk n w) + +fromSHA224 :: SHA224 -> SHA256 +fromSHA256 :: SHA256 -> SHA224 +fromSHA224 (SHA224 a b c d e f g h) = SHA256 a b c d e f g h +fromSHA256 (SHA256 a b c d e f g h) = SHA224 a b c d e f g h + +sha224Init :: Context SHA224 +sha224Init = fmap fromSHA256 (Context 0 0 B.empty initHash224) +sha224Update :: Context SHA224 -> ByteString -> Context SHA224 +sha224Update = fmap (fmap fromSHA256) . sha256Update . fmap fromSHA224 +sha224Final :: Context SHA224 -> SHA224 +sha224Final = fromSHA256 . sha256Final . fmap fromSHA224 + +--{-# NOINLINE sha224Hash #-} +sha224Hash :: LBS.ByteString -> SHA224 +sha224Hash = sha224Final . LBS.foldlChunks sha224Update sha224Init + +instance HashAlgorithm SHA256 where + hashBlockSize = const 64 + hashDigestSize = const 32 + hashInit = sha256Init + hashUpdate = sha256Update + hashFinal = sha256Final + +instance HashAlgorithm SHA224 where + hashBlockSize = const 64 + hashDigestSize = const 28 + hashInit = sha224Init + hashUpdate = sha224Update + hashFinal = sha224Final diff --git a/src/Crypto/Hash/SHA512.hs b/src/Crypto/Hash/SHA512.hs new file mode 100644 --- /dev/null +++ b/src/Crypto/Hash/SHA512.hs @@ -0,0 +1,237 @@ +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE BangPatterns #-} + +module Crypto.Hash.SHA512 + ( + SHA512 + , SHA384 + ) where + +import qualified Data.ByteString as B +import qualified Data.ByteString.Lazy as LBS +import qualified Data.ByteString.Lazy.Char8 as LC +import Data.ByteString (ByteString) +import Data.ByteString.Builder +import Control.Monad.ST +import Data.Int +import Data.Word +import Data.Bits +import Data.Monoid +import Data.Array.Unboxed +import Data.Array.Unsafe +import Data.Array.ST +import Data.List(foldl') + +import Crypto.Hash.ADT + +initHs :: [Word64] +initHs = [ + 0x6a09e667f3bcc908, 0xbb67ae8584caa73b, 0x3c6ef372fe94f82b, 0xa54ff53a5f1d36f1 + , 0x510e527fade682d1, 0x9b05688c2b3e6c1f, 0x1f83d9abfb41bd6b, 0x5be0cd19137e2179 ] + +initKs :: [Word64] +initKs = [ + 0x428a2f98d728ae22, 0x7137449123ef65cd, 0xb5c0fbcfec4d3b2f, 0xe9b5dba58189dbbc, 0x3956c25bf348b538 + , 0x59f111f1b605d019, 0x923f82a4af194f9b, 0xab1c5ed5da6d8118, 0xd807aa98a3030242, 0x12835b0145706fbe + , 0x243185be4ee4b28c, 0x550c7dc3d5ffb4e2, 0x72be5d74f27b896f, 0x80deb1fe3b1696b1, 0x9bdc06a725c71235 + , 0xc19bf174cf692694, 0xe49b69c19ef14ad2, 0xefbe4786384f25e3, 0x0fc19dc68b8cd5b5, 0x240ca1cc77ac9c65 + , 0x2de92c6f592b0275, 0x4a7484aa6ea6e483, 0x5cb0a9dcbd41fbd4, 0x76f988da831153b5, 0x983e5152ee66dfab + , 0xa831c66d2db43210, 0xb00327c898fb213f, 0xbf597fc7beef0ee4, 0xc6e00bf33da88fc2, 0xd5a79147930aa725 + , 0x06ca6351e003826f, 0x142929670a0e6e70, 0x27b70a8546d22ffc, 0x2e1b21385c26c926, 0x4d2c6dfc5ac42aed + , 0x53380d139d95b3df, 0x650a73548baf63de, 0x766a0abb3c77b2a8, 0x81c2c92e47edaee6, 0x92722c851482353b + , 0xa2bfe8a14cf10364, 0xa81a664bbc423001, 0xc24b8b70d0f89791, 0xc76c51a30654be30, 0xd192e819d6ef5218 + , 0xd69906245565a910, 0xf40e35855771202a, 0x106aa07032bbd1b8, 0x19a4c116b8d2d0c8, 0x1e376c085141ab53 + , 0x2748774cdf8eeb99, 0x34b0bcb5e19b48a8, 0x391c0cb3c5c95a63, 0x4ed8aa4ae3418acb, 0x5b9cca4f7763e373 + , 0x682e6ff3d6b2b8a3, 0x748f82ee5defb2fc, 0x78a5636f43172f60, 0x84c87814a1f0ab72, 0x8cc702081a6439ec + , 0x90befffa23631e28, 0xa4506cebde82bde9, 0xbef9a3f7b2c67915, 0xc67178f2e372532b, 0xca273eceea26619c + , 0xd186b8c721c0c207, 0xeada7dd6cde0eb1e, 0xf57d4f7fee6ed178, 0x06f067aa72176fba, 0x0a637dc5a2c898a6 + , 0x113f9804bef90dae, 0x1b710b35131c471b, 0x28db77f523047d84, 0x32caab7b40c72493, 0x3c9ebe0a15c9bebc + , 0x431d67c49c100d4c, 0x4cc5d4becb3e42b6, 0x597f299cfc657e2a, 0x5fcb6fab3ad6faec, 0x6c44198c4a475817 ] + +encodeInt64Helper :: Int64 -> [Word8] +encodeInt64Helper x_ = (replicate 8 0) <> [w7, w6, w5, w4, w3, w2, w1, w0] + where x = x_ * 8 + w7 = fromIntegral $ (x `shiftR` 56) .&. 0xff + w6 = fromIntegral $ (x `shiftR` 48) .&. 0xff + w5 = fromIntegral $ (x `shiftR` 40) .&. 0xff + w4 = fromIntegral $ (x `shiftR` 32) .&. 0xff + w3 = fromIntegral $ (x `shiftR` 24) .&. 0xff + w2 = fromIntegral $ (x `shiftR` 16) .&. 0xff + w1 = fromIntegral $ (x `shiftR` 8) .&. 0xff + w0 = fromIntegral $ (x `shiftR` 0) .&. 0xff + +encodeInt64 :: Int64 -> ByteString +encodeInt64 = B.pack . encodeInt64Helper + +sha512ChunkSize :: Int +sha512ChunkSize = 128 + +lastChunk :: Int64 -> ByteString -> [ByteString] +lastChunk msglen s + | len < 112 = [s <> B.cons 0x80 (B.replicate (111 - len) 0x0) <> encodedLen] + | len >= 112 = helper (s <> B.cons 0x80 (B.replicate (239 - len) 0x0) <> encodedLen) + where + len = B.length s + encodedLen = encodeInt64 msglen + helper bs = [s1, s2] + where (s1, s2) = B.splitAt sha512ChunkSize bs + +data SHA512 = SHA512 {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + deriving Eq + +data SHA384 = SHA384 {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + +initHash :: SHA512 +initHash = fromList initHs + where fromList (a:b:c:d:e:f:g:h:_) = SHA512 a b c d e f g h + +initHash384 :: SHA512 +initHash384 = fromList [0xcbbb9d5dc1059ed8, 0x629a292a367cd507, 0x9159015a3070dd17, 0x152fecd8f70e5939, + 0x67332667ffc00b31, 0x8eb44a8768581511, 0xdb0c2e0d64f98fa7, 0x47b5481dbefa4fa4] + where fromList (a:b:c:d:e:f:g:h:_) = SHA512 a b c d e f g h + +instance Show SHA512 where + show = LC.unpack . toLazyByteString . foldMap word64HexFixed . toList + where toList (SHA512 a b c d e f g h) = a:b:c:d:e:f:g:[h] + +instance Show SHA384 where + show = LC.unpack . toLazyByteString . foldMap word64HexFixed . toList + where toList (SHA384 a b c d e f _ _) = a:b:c:d:e:[f] + +instance Eq SHA384 where + (SHA384 a1 b1 c1 d1 e1 f1 _ _) == (SHA384 a2 b2 c2 d2 e2 f2 _ _) = + a1 == a2 && b1 == b2 && c1 == c2 && d1 == d2 && e1 == e2 && f1 == f2 + +{-# INLINABLE sha512BlockUpdate #-} +sha512BlockUpdate :: SHA512 -> Word64 -> SHA512 +sha512BlockUpdate (SHA512 a b c d e f g h) w = + let + !s1 = mkS1 e + !ch = (e .&. f) `xor` (complement e .&. g) + !temp1 = h + s1 + ch + w + !s0 = mkS0 a + !maj = (a .&. b) `xor` (a .&. c) `xor` (b .&. c) + !temp2 = s0 + maj + in SHA512 (temp1 + temp2) a b c (d + temp1) e f g + +{-# INLINE readW64 #-} +readW64 :: ByteString -> Word64 +readW64 = B.foldl' acc 0 . B.take 8 + where acc x c = x `shiftL` 8 + fromIntegral c + acc :: Word64 -> Word8 -> Word64 + {-# INLINE acc #-} + +mkS0 :: Word64 -> Word64 +mkS1 :: Word64 -> Word64 +mkS0 x = (x `rotateR` 28) `xor` (x `rotateR` 34) `xor` (x `rotateR` 39) +mkS1 x = (x `rotateR` 14) `xor` (x `rotateR` 18) `xor` (x `rotateR` 41) +{-# INLINE mkS0 #-} +{-# INLINE mkS1 #-} + +mkS00 :: Word64 -> Word64 +mkS01 :: Word64 -> Word64 +mkS00 x = (x `rotateR` 1) `xor` (x `rotateR` 8) `xor` (x `shiftR` 7) +mkS01 x = (x `rotateR` 19) `xor` (x `rotateR` 61) `xor` (x `shiftR` 6) + +prepareBlock :: ByteString -> UArray Int Word64 +prepareBlock s = runST $ do + iou <- newArray (0, 79) 0 :: ST s (STUArray s Int Word64) + let + !w1 = readW64 s + !w2 = readW64 (B.drop 8 s) + !w3 = readW64 (B.drop 16 s) + !w4 = readW64 (B.drop 24 s) + !w5 = readW64 (B.drop 32 s) + !w6 = readW64 (B.drop 40 s) + !w7 = readW64 (B.drop 48 s) + !w8 = readW64 (B.drop 56 s) + !w9 = readW64 (B.drop 64 s) + !w10 = readW64 (B.drop 72 s) + !w11 = readW64 (B.drop 80 s) + !w12 = readW64 (B.drop 88 s) + !w13 = readW64 (B.drop 96 s) + !w14 = readW64 (B.drop 104 s) + !w15 = readW64 (B.drop 112 s) + !w16 = readW64 (B.drop 120 s) + writeArray iou 0 w1 >> writeArray iou 1 w2 >> writeArray iou 2 w3 >> writeArray iou 3 w4 >> + writeArray iou 4 w5 >> writeArray iou 5 w6 >> writeArray iou 6 w7 >> writeArray iou 7 w8 >> + writeArray iou 8 w9 >> writeArray iou 9 w10 >> writeArray iou 10 w11 >> writeArray iou 11 w12 >> + writeArray iou 12 w13 >> writeArray iou 13 w14 >> writeArray iou 14 w15 >> writeArray iou 15 w16 + let go i = readArray iou (i-16) >>= \x1 -> + readArray iou (i-15) >>= \x2 -> + readArray iou (i- 7) >>= \x3 -> + readArray iou (i- 2) >>= \x4 -> + let !s0 = mkS00 x2 + !s1 = mkS01 x4 + in writeArray iou i (x1 + s0 + x3 + s1) + {-# INLINE go #-} + mapM_ go [16..79] + unsafeFreeze iou + +{-# INLINE encodeChunk #-} +encodeChunk :: SHA512 -> ByteString -> SHA512 +encodeChunk hv@(SHA512 a b c d e f g h) bs = SHA512 (a+a') (b+b') (c+c') (d+d') (e+e') (f+f') (g+g') (h+h') + where + SHA512 a' b' c' d' e' f' g' h' = foldl' sha512BlockUpdate hv (zipWith (+) (elems (prepareBlock bs)) initKs) + +{-# NOINLINE sha512Hash #-} +sha512Hash :: LBS.ByteString -> SHA512 +sha512Hash = sha512Final . LBS.foldlChunks sha512Update sha512Init + +sha512Init :: Context SHA512 +sha512Init = Context 0 0 B.empty initHash + +{-# NOINLINE sha512Update #-} +sha512Update :: Context SHA512 -> ByteString -> Context SHA512 +sha512Update ctx@(Context n k w hv) s + | B.null s = ctx + | sizeRead < sizeToRead = Context (n + fromIntegral sizeRead) (k + sizeRead) (w <> s1) hv + | sizeRead >= sizeToRead = sha512Update (Context (n + fromIntegral sizeToRead) 0 mempty (encodeChunk hv (w <> s1))) s' + where + !sizeToRead = sha512ChunkSize - k + (!s1, !s') = B.splitAt sizeToRead s + !sizeRead = B.length s1 + +{-# NOINLINE sha512Final #-} +sha512Final :: Context SHA512 -> SHA512 +sha512Final (Context n _ w hv) = foldl' encodeChunk hv (lastChunk n w) + +instance HashAlgorithm SHA512 where + hashBlockSize = const 128 + hashDigestSize = const 64 + hashInit = sha512Init + hashUpdate = sha512Update + hashFinal = sha512Final + +fromSHA384 :: SHA384 -> SHA512 +fromSHA512 :: SHA512 -> SHA384 +fromSHA384 (SHA384 a b c d e f g h) = SHA512 a b c d e f g h +fromSHA512 (SHA512 a b c d e f g h) = SHA384 a b c d e f g h + +sha384Init :: Context SHA384 +sha384Init = fmap fromSHA512 (Context 0 0 B.empty initHash384) +sha384Update :: Context SHA384 -> ByteString -> Context SHA384 +sha384Update = fmap (fmap fromSHA512) . sha512Update . fmap fromSHA384 +sha384Final :: Context SHA384 -> SHA384 +sha384Final = fromSHA512 . sha512Final . fmap fromSHA384 + +instance HashAlgorithm SHA384 where + hashBlockSize = const 128 + hashDigestSize = const 48 + hashInit = sha384Init + hashUpdate = sha384Update + hashFinal = sha384Final diff --git a/src/Crypto/Hash/Whirlpool.hs b/src/Crypto/Hash/Whirlpool.hs new file mode 100644 --- /dev/null +++ b/src/Crypto/Hash/Whirlpool.hs @@ -0,0 +1,829 @@ +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE BangPatterns #-} + +module Crypto.Hash.Whirlpool + ( + Whirlpool + ) where + +import qualified Data.ByteString.Lazy as LBS +import qualified Data.ByteString as B +import qualified Data.ByteString.Lazy.Char8 as LC +import Data.ByteString (ByteString) +import Data.ByteString.Builder +import Data.Array.Unboxed +import Data.Int +import Data.Word +import Data.Bits +import Data.Monoid +import Data.List(foldl') + +import Crypto.Hash.ADT + +_c0, _c1, _c2, _c3, _c4, _c5, _c6, _c7 :: [Word64] +_c0 = [ + 0x18186018c07830d8, 0x23238c2305af4626, 0xc6c63fc67ef991b8, 0xe8e887e8136fcdfb + , 0x878726874ca113cb, 0xb8b8dab8a9626d11, 0x0101040108050209, 0x4f4f214f426e9e0d + , 0x3636d836adee6c9b, 0xa6a6a2a6590451ff, 0xd2d26fd2debdb90c, 0xf5f5f3f5fb06f70e + , 0x7979f979ef80f296, 0x6f6fa16f5fcede30, 0x91917e91fcef3f6d, 0x52525552aa07a4f8 + , 0x60609d6027fdc047, 0xbcbccabc89766535, 0x9b9b569baccd2b37, 0x8e8e028e048c018a + , 0xa3a3b6a371155bd2, 0x0c0c300c603c186c, 0x7b7bf17bff8af684, 0x3535d435b5e16a80 + , 0x1d1d741de8693af5, 0xe0e0a7e05347ddb3, 0xd7d77bd7f6acb321, 0xc2c22fc25eed999c + , 0x2e2eb82e6d965c43, 0x4b4b314b627a9629, 0xfefedffea321e15d, 0x575741578216aed5 + , 0x15155415a8412abd, 0x7777c1779fb6eee8, 0x3737dc37a5eb6e92, 0xe5e5b3e57b56d79e + , 0x9f9f469f8cd92313, 0xf0f0e7f0d317fd23, 0x4a4a354a6a7f9420, 0xdada4fda9e95a944 + , 0x58587d58fa25b0a2, 0xc9c903c906ca8fcf, 0x2929a429558d527c, 0x0a0a280a5022145a + , 0xb1b1feb1e14f7f50, 0xa0a0baa0691a5dc9, 0x6b6bb16b7fdad614, 0x85852e855cab17d9 + , 0xbdbdcebd8173673c, 0x5d5d695dd234ba8f, 0x1010401080502090, 0xf4f4f7f4f303f507 + , 0xcbcb0bcb16c08bdd, 0x3e3ef83eedc67cd3, 0x0505140528110a2d, 0x676781671fe6ce78 + , 0xe4e4b7e47353d597, 0x27279c2725bb4e02, 0x4141194132588273, 0x8b8b168b2c9d0ba7 + , 0xa7a7a6a7510153f6, 0x7d7de97dcf94fab2, 0x95956e95dcfb3749, 0xd8d847d88e9fad56 + , 0xfbfbcbfb8b30eb70, 0xeeee9fee2371c1cd, 0x7c7ced7cc791f8bb, 0x6666856617e3cc71 + , 0xdddd53dda68ea77b, 0x17175c17b84b2eaf, 0x4747014702468e45, 0x9e9e429e84dc211a + , 0xcaca0fca1ec589d4, 0x2d2db42d75995a58, 0xbfbfc6bf9179632e, 0x07071c07381b0e3f + , 0xadad8ead012347ac, 0x5a5a755aea2fb4b0, 0x838336836cb51bef, 0x3333cc3385ff66b6 + , 0x636391633ff2c65c, 0x02020802100a0412, 0xaaaa92aa39384993, 0x7171d971afa8e2de + , 0xc8c807c80ecf8dc6, 0x19196419c87d32d1, 0x494939497270923b, 0xd9d943d9869aaf5f + , 0xf2f2eff2c31df931, 0xe3e3abe34b48dba8, 0x5b5b715be22ab6b9, 0x88881a8834920dbc + , 0x9a9a529aa4c8293e, 0x262698262dbe4c0b, 0x3232c8328dfa64bf, 0xb0b0fab0e94a7d59 + , 0xe9e983e91b6acff2, 0x0f0f3c0f78331e77, 0xd5d573d5e6a6b733, 0x80803a8074ba1df4 + , 0xbebec2be997c6127, 0xcdcd13cd26de87eb, 0x3434d034bde46889, 0x48483d487a759032 + , 0xffffdbffab24e354, 0x7a7af57af78ff48d, 0x90907a90f4ea3d64, 0x5f5f615fc23ebe9d + , 0x202080201da0403d, 0x6868bd6867d5d00f, 0x1a1a681ad07234ca, 0xaeae82ae192c41b7 + , 0xb4b4eab4c95e757d, 0x54544d549a19a8ce, 0x93937693ece53b7f, 0x222288220daa442f + , 0x64648d6407e9c863, 0xf1f1e3f1db12ff2a, 0x7373d173bfa2e6cc, 0x12124812905a2482 + , 0x40401d403a5d807a, 0x0808200840281048, 0xc3c32bc356e89b95, 0xecec97ec337bc5df + , 0xdbdb4bdb9690ab4d, 0xa1a1bea1611f5fc0, 0x8d8d0e8d1c830791, 0x3d3df43df5c97ac8 + , 0x97976697ccf1335b, 0x0000000000000000, 0xcfcf1bcf36d483f9, 0x2b2bac2b4587566e + , 0x7676c57697b3ece1, 0x8282328264b019e6, 0xd6d67fd6fea9b128, 0x1b1b6c1bd87736c3 + , 0xb5b5eeb5c15b7774, 0xafaf86af112943be, 0x6a6ab56a77dfd41d, 0x50505d50ba0da0ea + , 0x45450945124c8a57, 0xf3f3ebf3cb18fb38, 0x3030c0309df060ad, 0xefef9bef2b74c3c4 + , 0x3f3ffc3fe5c37eda, 0x55554955921caac7, 0xa2a2b2a2791059db, 0xeaea8fea0365c9e9 + , 0x656589650fecca6a, 0xbabad2bab9686903, 0x2f2fbc2f65935e4a, 0xc0c027c04ee79d8e + , 0xdede5fdebe81a160, 0x1c1c701ce06c38fc, 0xfdfdd3fdbb2ee746, 0x4d4d294d52649a1f + , 0x92927292e4e03976, 0x7575c9758fbceafa, 0x06061806301e0c36, 0x8a8a128a249809ae + , 0xb2b2f2b2f940794b, 0xe6e6bfe66359d185, 0x0e0e380e70361c7e, 0x1f1f7c1ff8633ee7 + , 0x6262956237f7c455, 0xd4d477d4eea3b53a, 0xa8a89aa829324d81, 0x96966296c4f43152 + , 0xf9f9c3f99b3aef62, 0xc5c533c566f697a3, 0x2525942535b14a10, 0x59597959f220b2ab + , 0x84842a8454ae15d0, 0x7272d572b7a7e4c5, 0x3939e439d5dd72ec, 0x4c4c2d4c5a619816 + , 0x5e5e655eca3bbc94, 0x7878fd78e785f09f, 0x3838e038ddd870e5, 0x8c8c0a8c14860598 + , 0xd1d163d1c6b2bf17, 0xa5a5aea5410b57e4, 0xe2e2afe2434dd9a1, 0x616199612ff8c24e + , 0xb3b3f6b3f1457b42, 0x2121842115a54234, 0x9c9c4a9c94d62508, 0x1e1e781ef0663cee + , 0x4343114322528661, 0xc7c73bc776fc93b1, 0xfcfcd7fcb32be54f, 0x0404100420140824 + , 0x51515951b208a2e3, 0x99995e99bcc72f25, 0x6d6da96d4fc4da22, 0x0d0d340d68391a65 + , 0xfafacffa8335e979, 0xdfdf5bdfb684a369, 0x7e7ee57ed79bfca9, 0x242490243db44819 + , 0x3b3bec3bc5d776fe, 0xabab96ab313d4b9a, 0xcece1fce3ed181f0, 0x1111441188552299 + , 0x8f8f068f0c890383, 0x4e4e254e4a6b9c04, 0xb7b7e6b7d1517366, 0xebeb8beb0b60cbe0 + , 0x3c3cf03cfdcc78c1, 0x81813e817cbf1ffd, 0x94946a94d4fe3540, 0xf7f7fbf7eb0cf31c + , 0xb9b9deb9a1676f18, 0x13134c13985f268b, 0x2c2cb02c7d9c5851, 0xd3d36bd3d6b8bb05 + , 0xe7e7bbe76b5cd38c, 0x6e6ea56e57cbdc39, 0xc4c437c46ef395aa, 0x03030c03180f061b + , 0x565645568a13acdc, 0x44440d441a49885e, 0x7f7fe17fdf9efea0, 0xa9a99ea921374f88 + , 0x2a2aa82a4d825467, 0xbbbbd6bbb16d6b0a, 0xc1c123c146e29f87, 0x53535153a202a6f1 + , 0xdcdc57dcae8ba572, 0x0b0b2c0b58271653, 0x9d9d4e9d9cd32701, 0x6c6cad6c47c1d82b + , 0x3131c43195f562a4, 0x7474cd7487b9e8f3, 0xf6f6fff6e309f115, 0x464605460a438c4c + , 0xacac8aac092645a5, 0x89891e893c970fb5, 0x14145014a04428b4, 0xe1e1a3e15b42dfba + , 0x16165816b04e2ca6, 0x3a3ae83acdd274f7, 0x6969b9696fd0d206, 0x09092409482d1241 + , 0x7070dd70a7ade0d7, 0xb6b6e2b6d954716f, 0xd0d067d0ceb7bd1e, 0xeded93ed3b7ec7d6 + , 0xcccc17cc2edb85e2, 0x424215422a578468, 0x98985a98b4c22d2c, 0xa4a4aaa4490e55ed + , 0x2828a0285d885075, 0x5c5c6d5cda31b886, 0xf8f8c7f8933fed6b, 0x8686228644a411c2 + ] + +_c1 = [ + 0xd818186018c07830, 0x2623238c2305af46, 0xb8c6c63fc67ef991, 0xfbe8e887e8136fcd + , 0xcb878726874ca113, 0x11b8b8dab8a9626d, 0x0901010401080502, 0x0d4f4f214f426e9e + , 0x9b3636d836adee6c, 0xffa6a6a2a6590451, 0x0cd2d26fd2debdb9, 0x0ef5f5f3f5fb06f7 + , 0x967979f979ef80f2, 0x306f6fa16f5fcede, 0x6d91917e91fcef3f, 0xf852525552aa07a4 + , 0x4760609d6027fdc0, 0x35bcbccabc897665, 0x379b9b569baccd2b, 0x8a8e8e028e048c01 + , 0xd2a3a3b6a371155b, 0x6c0c0c300c603c18, 0x847b7bf17bff8af6, 0x803535d435b5e16a + , 0xf51d1d741de8693a, 0xb3e0e0a7e05347dd, 0x21d7d77bd7f6acb3, 0x9cc2c22fc25eed99 + , 0x432e2eb82e6d965c, 0x294b4b314b627a96, 0x5dfefedffea321e1, 0xd5575741578216ae + , 0xbd15155415a8412a, 0xe87777c1779fb6ee, 0x923737dc37a5eb6e, 0x9ee5e5b3e57b56d7 + , 0x139f9f469f8cd923, 0x23f0f0e7f0d317fd, 0x204a4a354a6a7f94, 0x44dada4fda9e95a9 + , 0xa258587d58fa25b0, 0xcfc9c903c906ca8f, 0x7c2929a429558d52, 0x5a0a0a280a502214 + , 0x50b1b1feb1e14f7f, 0xc9a0a0baa0691a5d, 0x146b6bb16b7fdad6, 0xd985852e855cab17 + , 0x3cbdbdcebd817367, 0x8f5d5d695dd234ba, 0x9010104010805020, 0x07f4f4f7f4f303f5 + , 0xddcbcb0bcb16c08b, 0xd33e3ef83eedc67c, 0x2d0505140528110a, 0x78676781671fe6ce + , 0x97e4e4b7e47353d5, 0x0227279c2725bb4e, 0x7341411941325882, 0xa78b8b168b2c9d0b + , 0xf6a7a7a6a7510153, 0xb27d7de97dcf94fa, 0x4995956e95dcfb37, 0x56d8d847d88e9fad + , 0x70fbfbcbfb8b30eb, 0xcdeeee9fee2371c1, 0xbb7c7ced7cc791f8, 0x716666856617e3cc + , 0x7bdddd53dda68ea7, 0xaf17175c17b84b2e, 0x454747014702468e, 0x1a9e9e429e84dc21 + , 0xd4caca0fca1ec589, 0x582d2db42d75995a, 0x2ebfbfc6bf917963, 0x3f07071c07381b0e + , 0xacadad8ead012347, 0xb05a5a755aea2fb4, 0xef838336836cb51b, 0xb63333cc3385ff66 + , 0x5c636391633ff2c6, 0x1202020802100a04, 0x93aaaa92aa393849, 0xde7171d971afa8e2 + , 0xc6c8c807c80ecf8d, 0xd119196419c87d32, 0x3b49493949727092, 0x5fd9d943d9869aaf + , 0x31f2f2eff2c31df9, 0xa8e3e3abe34b48db, 0xb95b5b715be22ab6, 0xbc88881a8834920d + , 0x3e9a9a529aa4c829, 0x0b262698262dbe4c, 0xbf3232c8328dfa64, 0x59b0b0fab0e94a7d + , 0xf2e9e983e91b6acf, 0x770f0f3c0f78331e, 0x33d5d573d5e6a6b7, 0xf480803a8074ba1d + , 0x27bebec2be997c61, 0xebcdcd13cd26de87, 0x893434d034bde468, 0x3248483d487a7590 + , 0x54ffffdbffab24e3, 0x8d7a7af57af78ff4, 0x6490907a90f4ea3d, 0x9d5f5f615fc23ebe + , 0x3d202080201da040, 0x0f6868bd6867d5d0, 0xca1a1a681ad07234, 0xb7aeae82ae192c41 + , 0x7db4b4eab4c95e75, 0xce54544d549a19a8, 0x7f93937693ece53b, 0x2f222288220daa44 + , 0x6364648d6407e9c8, 0x2af1f1e3f1db12ff, 0xcc7373d173bfa2e6, 0x8212124812905a24 + , 0x7a40401d403a5d80, 0x4808082008402810, 0x95c3c32bc356e89b, 0xdfecec97ec337bc5 + , 0x4ddbdb4bdb9690ab, 0xc0a1a1bea1611f5f, 0x918d8d0e8d1c8307, 0xc83d3df43df5c97a + , 0x5b97976697ccf133, 0x0000000000000000, 0xf9cfcf1bcf36d483, 0x6e2b2bac2b458756 + , 0xe17676c57697b3ec, 0xe68282328264b019, 0x28d6d67fd6fea9b1, 0xc31b1b6c1bd87736 + , 0x74b5b5eeb5c15b77, 0xbeafaf86af112943, 0x1d6a6ab56a77dfd4, 0xea50505d50ba0da0 + , 0x5745450945124c8a, 0x38f3f3ebf3cb18fb, 0xad3030c0309df060, 0xc4efef9bef2b74c3 + , 0xda3f3ffc3fe5c37e, 0xc755554955921caa, 0xdba2a2b2a2791059, 0xe9eaea8fea0365c9 + , 0x6a656589650fecca, 0x03babad2bab96869, 0x4a2f2fbc2f65935e, 0x8ec0c027c04ee79d + , 0x60dede5fdebe81a1, 0xfc1c1c701ce06c38, 0x46fdfdd3fdbb2ee7, 0x1f4d4d294d52649a + , 0x7692927292e4e039, 0xfa7575c9758fbcea, 0x3606061806301e0c, 0xae8a8a128a249809 + , 0x4bb2b2f2b2f94079, 0x85e6e6bfe66359d1, 0x7e0e0e380e70361c, 0xe71f1f7c1ff8633e + , 0x556262956237f7c4, 0x3ad4d477d4eea3b5, 0x81a8a89aa829324d, 0x5296966296c4f431 + , 0x62f9f9c3f99b3aef, 0xa3c5c533c566f697, 0x102525942535b14a, 0xab59597959f220b2 + , 0xd084842a8454ae15, 0xc57272d572b7a7e4, 0xec3939e439d5dd72, 0x164c4c2d4c5a6198 + , 0x945e5e655eca3bbc, 0x9f7878fd78e785f0, 0xe53838e038ddd870, 0x988c8c0a8c148605 + , 0x17d1d163d1c6b2bf, 0xe4a5a5aea5410b57, 0xa1e2e2afe2434dd9, 0x4e616199612ff8c2 + , 0x42b3b3f6b3f1457b, 0x342121842115a542, 0x089c9c4a9c94d625, 0xee1e1e781ef0663c + , 0x6143431143225286, 0xb1c7c73bc776fc93, 0x4ffcfcd7fcb32be5, 0x2404041004201408 + , 0xe351515951b208a2, 0x2599995e99bcc72f, 0x226d6da96d4fc4da, 0x650d0d340d68391a + , 0x79fafacffa8335e9, 0x69dfdf5bdfb684a3, 0xa97e7ee57ed79bfc, 0x19242490243db448 + , 0xfe3b3bec3bc5d776, 0x9aabab96ab313d4b, 0xf0cece1fce3ed181, 0x9911114411885522 + , 0x838f8f068f0c8903, 0x044e4e254e4a6b9c, 0x66b7b7e6b7d15173, 0xe0ebeb8beb0b60cb + , 0xc13c3cf03cfdcc78, 0xfd81813e817cbf1f, 0x4094946a94d4fe35, 0x1cf7f7fbf7eb0cf3 + , 0x18b9b9deb9a1676f, 0x8b13134c13985f26, 0x512c2cb02c7d9c58, 0x05d3d36bd3d6b8bb + , 0x8ce7e7bbe76b5cd3, 0x396e6ea56e57cbdc, 0xaac4c437c46ef395, 0x1b03030c03180f06 + , 0xdc565645568a13ac, 0x5e44440d441a4988, 0xa07f7fe17fdf9efe, 0x88a9a99ea921374f + , 0x672a2aa82a4d8254, 0x0abbbbd6bbb16d6b, 0x87c1c123c146e29f, 0xf153535153a202a6 + , 0x72dcdc57dcae8ba5, 0x530b0b2c0b582716, 0x019d9d4e9d9cd327, 0x2b6c6cad6c47c1d8 + , 0xa43131c43195f562, 0xf37474cd7487b9e8, 0x15f6f6fff6e309f1, 0x4c464605460a438c + , 0xa5acac8aac092645, 0xb589891e893c970f, 0xb414145014a04428, 0xbae1e1a3e15b42df + , 0xa616165816b04e2c, 0xf73a3ae83acdd274, 0x066969b9696fd0d2, 0x4109092409482d12 + , 0xd77070dd70a7ade0, 0x6fb6b6e2b6d95471, 0x1ed0d067d0ceb7bd, 0xd6eded93ed3b7ec7 + , 0xe2cccc17cc2edb85, 0x68424215422a5784, 0x2c98985a98b4c22d, 0xeda4a4aaa4490e55 + , 0x752828a0285d8850, 0x865c5c6d5cda31b8, 0x6bf8f8c7f8933fed, 0xc28686228644a411 + ] + +_c2 = [ + 0x30d818186018c078, 0x462623238c2305af, 0x91b8c6c63fc67ef9, 0xcdfbe8e887e8136f + , 0x13cb878726874ca1, 0x6d11b8b8dab8a962, 0x0209010104010805, 0x9e0d4f4f214f426e + , 0x6c9b3636d836adee, 0x51ffa6a6a2a65904, 0xb90cd2d26fd2debd, 0xf70ef5f5f3f5fb06 + , 0xf2967979f979ef80, 0xde306f6fa16f5fce, 0x3f6d91917e91fcef, 0xa4f852525552aa07 + , 0xc04760609d6027fd, 0x6535bcbccabc8976, 0x2b379b9b569baccd, 0x018a8e8e028e048c + , 0x5bd2a3a3b6a37115, 0x186c0c0c300c603c, 0xf6847b7bf17bff8a, 0x6a803535d435b5e1 + , 0x3af51d1d741de869, 0xddb3e0e0a7e05347, 0xb321d7d77bd7f6ac, 0x999cc2c22fc25eed + , 0x5c432e2eb82e6d96, 0x96294b4b314b627a, 0xe15dfefedffea321, 0xaed5575741578216 + , 0x2abd15155415a841, 0xeee87777c1779fb6, 0x6e923737dc37a5eb, 0xd79ee5e5b3e57b56 + , 0x23139f9f469f8cd9, 0xfd23f0f0e7f0d317, 0x94204a4a354a6a7f, 0xa944dada4fda9e95 + , 0xb0a258587d58fa25, 0x8fcfc9c903c906ca, 0x527c2929a429558d, 0x145a0a0a280a5022 + , 0x7f50b1b1feb1e14f, 0x5dc9a0a0baa0691a, 0xd6146b6bb16b7fda, 0x17d985852e855cab + , 0x673cbdbdcebd8173, 0xba8f5d5d695dd234, 0x2090101040108050, 0xf507f4f4f7f4f303 + , 0x8bddcbcb0bcb16c0, 0x7cd33e3ef83eedc6, 0x0a2d050514052811, 0xce78676781671fe6 + , 0xd597e4e4b7e47353, 0x4e0227279c2725bb, 0x8273414119413258, 0x0ba78b8b168b2c9d + , 0x53f6a7a7a6a75101, 0xfab27d7de97dcf94, 0x374995956e95dcfb, 0xad56d8d847d88e9f + , 0xeb70fbfbcbfb8b30, 0xc1cdeeee9fee2371, 0xf8bb7c7ced7cc791, 0xcc716666856617e3 + , 0xa77bdddd53dda68e, 0x2eaf17175c17b84b, 0x8e45474701470246, 0x211a9e9e429e84dc + , 0x89d4caca0fca1ec5, 0x5a582d2db42d7599, 0x632ebfbfc6bf9179, 0x0e3f07071c07381b + , 0x47acadad8ead0123, 0xb4b05a5a755aea2f, 0x1bef838336836cb5, 0x66b63333cc3385ff + , 0xc65c636391633ff2, 0x041202020802100a, 0x4993aaaa92aa3938, 0xe2de7171d971afa8 + , 0x8dc6c8c807c80ecf, 0x32d119196419c87d, 0x923b494939497270, 0xaf5fd9d943d9869a + , 0xf931f2f2eff2c31d, 0xdba8e3e3abe34b48, 0xb6b95b5b715be22a, 0x0dbc88881a883492 + , 0x293e9a9a529aa4c8, 0x4c0b262698262dbe, 0x64bf3232c8328dfa, 0x7d59b0b0fab0e94a + , 0xcff2e9e983e91b6a, 0x1e770f0f3c0f7833, 0xb733d5d573d5e6a6, 0x1df480803a8074ba + , 0x6127bebec2be997c, 0x87ebcdcd13cd26de, 0x68893434d034bde4, 0x903248483d487a75 + , 0xe354ffffdbffab24, 0xf48d7a7af57af78f, 0x3d6490907a90f4ea, 0xbe9d5f5f615fc23e + , 0x403d202080201da0, 0xd00f6868bd6867d5, 0x34ca1a1a681ad072, 0x41b7aeae82ae192c + , 0x757db4b4eab4c95e, 0xa8ce54544d549a19, 0x3b7f93937693ece5, 0x442f222288220daa + , 0xc86364648d6407e9, 0xff2af1f1e3f1db12, 0xe6cc7373d173bfa2, 0x248212124812905a + , 0x807a40401d403a5d, 0x1048080820084028, 0x9b95c3c32bc356e8, 0xc5dfecec97ec337b + , 0xab4ddbdb4bdb9690, 0x5fc0a1a1bea1611f, 0x07918d8d0e8d1c83, 0x7ac83d3df43df5c9 + , 0x335b97976697ccf1, 0x0000000000000000, 0x83f9cfcf1bcf36d4, 0x566e2b2bac2b4587 + , 0xece17676c57697b3, 0x19e68282328264b0, 0xb128d6d67fd6fea9, 0x36c31b1b6c1bd877 + , 0x7774b5b5eeb5c15b, 0x43beafaf86af1129, 0xd41d6a6ab56a77df, 0xa0ea50505d50ba0d + , 0x8a5745450945124c, 0xfb38f3f3ebf3cb18, 0x60ad3030c0309df0, 0xc3c4efef9bef2b74 + , 0x7eda3f3ffc3fe5c3, 0xaac755554955921c, 0x59dba2a2b2a27910, 0xc9e9eaea8fea0365 + , 0xca6a656589650fec, 0x6903babad2bab968, 0x5e4a2f2fbc2f6593, 0x9d8ec0c027c04ee7 + , 0xa160dede5fdebe81, 0x38fc1c1c701ce06c, 0xe746fdfdd3fdbb2e, 0x9a1f4d4d294d5264 + , 0x397692927292e4e0, 0xeafa7575c9758fbc, 0x0c3606061806301e, 0x09ae8a8a128a2498 + , 0x794bb2b2f2b2f940, 0xd185e6e6bfe66359, 0x1c7e0e0e380e7036, 0x3ee71f1f7c1ff863 + , 0xc4556262956237f7, 0xb53ad4d477d4eea3, 0x4d81a8a89aa82932, 0x315296966296c4f4 + , 0xef62f9f9c3f99b3a, 0x97a3c5c533c566f6, 0x4a102525942535b1, 0xb2ab59597959f220 + , 0x15d084842a8454ae, 0xe4c57272d572b7a7, 0x72ec3939e439d5dd, 0x98164c4c2d4c5a61 + , 0xbc945e5e655eca3b, 0xf09f7878fd78e785, 0x70e53838e038ddd8, 0x05988c8c0a8c1486 + , 0xbf17d1d163d1c6b2, 0x57e4a5a5aea5410b, 0xd9a1e2e2afe2434d, 0xc24e616199612ff8 + , 0x7b42b3b3f6b3f145, 0x42342121842115a5, 0x25089c9c4a9c94d6, 0x3cee1e1e781ef066 + , 0x8661434311432252, 0x93b1c7c73bc776fc, 0xe54ffcfcd7fcb32b, 0x0824040410042014 + , 0xa2e351515951b208, 0x2f2599995e99bcc7, 0xda226d6da96d4fc4, 0x1a650d0d340d6839 + , 0xe979fafacffa8335, 0xa369dfdf5bdfb684, 0xfca97e7ee57ed79b, 0x4819242490243db4 + , 0x76fe3b3bec3bc5d7, 0x4b9aabab96ab313d, 0x81f0cece1fce3ed1, 0x2299111144118855 + , 0x03838f8f068f0c89, 0x9c044e4e254e4a6b, 0x7366b7b7e6b7d151, 0xcbe0ebeb8beb0b60 + , 0x78c13c3cf03cfdcc, 0x1ffd81813e817cbf, 0x354094946a94d4fe, 0xf31cf7f7fbf7eb0c + , 0x6f18b9b9deb9a167, 0x268b13134c13985f, 0x58512c2cb02c7d9c, 0xbb05d3d36bd3d6b8 + , 0xd38ce7e7bbe76b5c, 0xdc396e6ea56e57cb, 0x95aac4c437c46ef3, 0x061b03030c03180f + , 0xacdc565645568a13, 0x885e44440d441a49, 0xfea07f7fe17fdf9e, 0x4f88a9a99ea92137 + , 0x54672a2aa82a4d82, 0x6b0abbbbd6bbb16d, 0x9f87c1c123c146e2, 0xa6f153535153a202 + , 0xa572dcdc57dcae8b, 0x16530b0b2c0b5827, 0x27019d9d4e9d9cd3, 0xd82b6c6cad6c47c1 + , 0x62a43131c43195f5, 0xe8f37474cd7487b9, 0xf115f6f6fff6e309, 0x8c4c464605460a43 + , 0x45a5acac8aac0926, 0x0fb589891e893c97, 0x28b414145014a044, 0xdfbae1e1a3e15b42 + , 0x2ca616165816b04e, 0x74f73a3ae83acdd2, 0xd2066969b9696fd0, 0x124109092409482d + , 0xe0d77070dd70a7ad, 0x716fb6b6e2b6d954, 0xbd1ed0d067d0ceb7, 0xc7d6eded93ed3b7e + , 0x85e2cccc17cc2edb, 0x8468424215422a57, 0x2d2c98985a98b4c2, 0x55eda4a4aaa4490e + , 0x50752828a0285d88, 0xb8865c5c6d5cda31, 0xed6bf8f8c7f8933f, 0x11c28686228644a4 + ] + +_c3 = [ + 0x7830d818186018c0, 0xaf462623238c2305, 0xf991b8c6c63fc67e, 0x6fcdfbe8e887e813 + , 0xa113cb878726874c, 0x626d11b8b8dab8a9, 0x0502090101040108, 0x6e9e0d4f4f214f42 + , 0xee6c9b3636d836ad, 0x0451ffa6a6a2a659, 0xbdb90cd2d26fd2de, 0x06f70ef5f5f3f5fb + , 0x80f2967979f979ef, 0xcede306f6fa16f5f, 0xef3f6d91917e91fc, 0x07a4f852525552aa + , 0xfdc04760609d6027, 0x766535bcbccabc89, 0xcd2b379b9b569bac, 0x8c018a8e8e028e04 + , 0x155bd2a3a3b6a371, 0x3c186c0c0c300c60, 0x8af6847b7bf17bff, 0xe16a803535d435b5 + , 0x693af51d1d741de8, 0x47ddb3e0e0a7e053, 0xacb321d7d77bd7f6, 0xed999cc2c22fc25e + , 0x965c432e2eb82e6d, 0x7a96294b4b314b62, 0x21e15dfefedffea3, 0x16aed55757415782 + , 0x412abd15155415a8, 0xb6eee87777c1779f, 0xeb6e923737dc37a5, 0x56d79ee5e5b3e57b + , 0xd923139f9f469f8c, 0x17fd23f0f0e7f0d3, 0x7f94204a4a354a6a, 0x95a944dada4fda9e + , 0x25b0a258587d58fa, 0xca8fcfc9c903c906, 0x8d527c2929a42955, 0x22145a0a0a280a50 + , 0x4f7f50b1b1feb1e1, 0x1a5dc9a0a0baa069, 0xdad6146b6bb16b7f, 0xab17d985852e855c + , 0x73673cbdbdcebd81, 0x34ba8f5d5d695dd2, 0x5020901010401080, 0x03f507f4f4f7f4f3 + , 0xc08bddcbcb0bcb16, 0xc67cd33e3ef83eed, 0x110a2d0505140528, 0xe6ce78676781671f + , 0x53d597e4e4b7e473, 0xbb4e0227279c2725, 0x5882734141194132, 0x9d0ba78b8b168b2c + , 0x0153f6a7a7a6a751, 0x94fab27d7de97dcf, 0xfb374995956e95dc, 0x9fad56d8d847d88e + , 0x30eb70fbfbcbfb8b, 0x71c1cdeeee9fee23, 0x91f8bb7c7ced7cc7, 0xe3cc716666856617 + , 0x8ea77bdddd53dda6, 0x4b2eaf17175c17b8, 0x468e454747014702, 0xdc211a9e9e429e84 + , 0xc589d4caca0fca1e, 0x995a582d2db42d75, 0x79632ebfbfc6bf91, 0x1b0e3f07071c0738 + , 0x2347acadad8ead01, 0x2fb4b05a5a755aea, 0xb51bef838336836c, 0xff66b63333cc3385 + , 0xf2c65c636391633f, 0x0a04120202080210, 0x384993aaaa92aa39, 0xa8e2de7171d971af + , 0xcf8dc6c8c807c80e, 0x7d32d119196419c8, 0x70923b4949394972, 0x9aaf5fd9d943d986 + , 0x1df931f2f2eff2c3, 0x48dba8e3e3abe34b, 0x2ab6b95b5b715be2, 0x920dbc88881a8834 + , 0xc8293e9a9a529aa4, 0xbe4c0b262698262d, 0xfa64bf3232c8328d, 0x4a7d59b0b0fab0e9 + , 0x6acff2e9e983e91b, 0x331e770f0f3c0f78, 0xa6b733d5d573d5e6, 0xba1df480803a8074 + , 0x7c6127bebec2be99, 0xde87ebcdcd13cd26, 0xe468893434d034bd, 0x75903248483d487a + , 0x24e354ffffdbffab, 0x8ff48d7a7af57af7, 0xea3d6490907a90f4, 0x3ebe9d5f5f615fc2 + , 0xa0403d202080201d, 0xd5d00f6868bd6867, 0x7234ca1a1a681ad0, 0x2c41b7aeae82ae19 + , 0x5e757db4b4eab4c9, 0x19a8ce54544d549a, 0xe53b7f93937693ec, 0xaa442f222288220d + , 0xe9c86364648d6407, 0x12ff2af1f1e3f1db, 0xa2e6cc7373d173bf, 0x5a24821212481290 + , 0x5d807a40401d403a, 0x2810480808200840, 0xe89b95c3c32bc356, 0x7bc5dfecec97ec33 + , 0x90ab4ddbdb4bdb96, 0x1f5fc0a1a1bea161, 0x8307918d8d0e8d1c, 0xc97ac83d3df43df5 + , 0xf1335b97976697cc, 0x0000000000000000, 0xd483f9cfcf1bcf36, 0x87566e2b2bac2b45 + , 0xb3ece17676c57697, 0xb019e68282328264, 0xa9b128d6d67fd6fe, 0x7736c31b1b6c1bd8 + , 0x5b7774b5b5eeb5c1, 0x2943beafaf86af11, 0xdfd41d6a6ab56a77, 0x0da0ea50505d50ba + , 0x4c8a574545094512, 0x18fb38f3f3ebf3cb, 0xf060ad3030c0309d, 0x74c3c4efef9bef2b + , 0xc37eda3f3ffc3fe5, 0x1caac75555495592, 0x1059dba2a2b2a279, 0x65c9e9eaea8fea03 + , 0xecca6a656589650f, 0x686903babad2bab9, 0x935e4a2f2fbc2f65, 0xe79d8ec0c027c04e + , 0x81a160dede5fdebe, 0x6c38fc1c1c701ce0, 0x2ee746fdfdd3fdbb, 0x649a1f4d4d294d52 + , 0xe0397692927292e4, 0xbceafa7575c9758f, 0x1e0c360606180630, 0x9809ae8a8a128a24 + , 0x40794bb2b2f2b2f9, 0x59d185e6e6bfe663, 0x361c7e0e0e380e70, 0x633ee71f1f7c1ff8 + , 0xf7c4556262956237, 0xa3b53ad4d477d4ee, 0x324d81a8a89aa829, 0xf4315296966296c4 + , 0x3aef62f9f9c3f99b, 0xf697a3c5c533c566, 0xb14a102525942535, 0x20b2ab59597959f2 + , 0xae15d084842a8454, 0xa7e4c57272d572b7, 0xdd72ec3939e439d5, 0x6198164c4c2d4c5a + , 0x3bbc945e5e655eca, 0x85f09f7878fd78e7, 0xd870e53838e038dd, 0x8605988c8c0a8c14 + , 0xb2bf17d1d163d1c6, 0x0b57e4a5a5aea541, 0x4dd9a1e2e2afe243, 0xf8c24e616199612f + , 0x457b42b3b3f6b3f1, 0xa542342121842115, 0xd625089c9c4a9c94, 0x663cee1e1e781ef0 + , 0x5286614343114322, 0xfc93b1c7c73bc776, 0x2be54ffcfcd7fcb3, 0x1408240404100420 + , 0x08a2e351515951b2, 0xc72f2599995e99bc, 0xc4da226d6da96d4f, 0x391a650d0d340d68 + , 0x35e979fafacffa83, 0x84a369dfdf5bdfb6, 0x9bfca97e7ee57ed7, 0xb44819242490243d + , 0xd776fe3b3bec3bc5, 0x3d4b9aabab96ab31, 0xd181f0cece1fce3e, 0x5522991111441188 + , 0x8903838f8f068f0c, 0x6b9c044e4e254e4a, 0x517366b7b7e6b7d1, 0x60cbe0ebeb8beb0b + , 0xcc78c13c3cf03cfd, 0xbf1ffd81813e817c, 0xfe354094946a94d4, 0x0cf31cf7f7fbf7eb + , 0x676f18b9b9deb9a1, 0x5f268b13134c1398, 0x9c58512c2cb02c7d, 0xb8bb05d3d36bd3d6 + , 0x5cd38ce7e7bbe76b, 0xcbdc396e6ea56e57, 0xf395aac4c437c46e, 0x0f061b03030c0318 + , 0x13acdc565645568a, 0x49885e44440d441a, 0x9efea07f7fe17fdf, 0x374f88a9a99ea921 + , 0x8254672a2aa82a4d, 0x6d6b0abbbbd6bbb1, 0xe29f87c1c123c146, 0x02a6f153535153a2 + , 0x8ba572dcdc57dcae, 0x2716530b0b2c0b58, 0xd327019d9d4e9d9c, 0xc1d82b6c6cad6c47 + , 0xf562a43131c43195, 0xb9e8f37474cd7487, 0x09f115f6f6fff6e3, 0x438c4c464605460a + , 0x2645a5acac8aac09, 0x970fb589891e893c, 0x4428b414145014a0, 0x42dfbae1e1a3e15b + , 0x4e2ca616165816b0, 0xd274f73a3ae83acd, 0xd0d2066969b9696f, 0x2d12410909240948 + , 0xade0d77070dd70a7, 0x54716fb6b6e2b6d9, 0xb7bd1ed0d067d0ce, 0x7ec7d6eded93ed3b + , 0xdb85e2cccc17cc2e, 0x578468424215422a, 0xc22d2c98985a98b4, 0x0e55eda4a4aaa449 + , 0x8850752828a0285d, 0x31b8865c5c6d5cda, 0x3fed6bf8f8c7f893, 0xa411c28686228644 + ] + +_c4 = [ + 0xc07830d818186018, 0x05af462623238c23, 0x7ef991b8c6c63fc6, 0x136fcdfbe8e887e8 + , 0x4ca113cb87872687, 0xa9626d11b8b8dab8, 0x0805020901010401, 0x426e9e0d4f4f214f + , 0xadee6c9b3636d836, 0x590451ffa6a6a2a6, 0xdebdb90cd2d26fd2, 0xfb06f70ef5f5f3f5 + , 0xef80f2967979f979, 0x5fcede306f6fa16f, 0xfcef3f6d91917e91, 0xaa07a4f852525552 + , 0x27fdc04760609d60, 0x89766535bcbccabc, 0xaccd2b379b9b569b, 0x048c018a8e8e028e + , 0x71155bd2a3a3b6a3, 0x603c186c0c0c300c, 0xff8af6847b7bf17b, 0xb5e16a803535d435 + , 0xe8693af51d1d741d, 0x5347ddb3e0e0a7e0, 0xf6acb321d7d77bd7, 0x5eed999cc2c22fc2 + , 0x6d965c432e2eb82e, 0x627a96294b4b314b, 0xa321e15dfefedffe, 0x8216aed557574157 + , 0xa8412abd15155415, 0x9fb6eee87777c177, 0xa5eb6e923737dc37, 0x7b56d79ee5e5b3e5 + , 0x8cd923139f9f469f, 0xd317fd23f0f0e7f0, 0x6a7f94204a4a354a, 0x9e95a944dada4fda + , 0xfa25b0a258587d58, 0x06ca8fcfc9c903c9, 0x558d527c2929a429, 0x5022145a0a0a280a + , 0xe14f7f50b1b1feb1, 0x691a5dc9a0a0baa0, 0x7fdad6146b6bb16b, 0x5cab17d985852e85 + , 0x8173673cbdbdcebd, 0xd234ba8f5d5d695d, 0x8050209010104010, 0xf303f507f4f4f7f4 + , 0x16c08bddcbcb0bcb, 0xedc67cd33e3ef83e, 0x28110a2d05051405, 0x1fe6ce7867678167 + , 0x7353d597e4e4b7e4, 0x25bb4e0227279c27, 0x3258827341411941, 0x2c9d0ba78b8b168b + , 0x510153f6a7a7a6a7, 0xcf94fab27d7de97d, 0xdcfb374995956e95, 0x8e9fad56d8d847d8 + , 0x8b30eb70fbfbcbfb, 0x2371c1cdeeee9fee, 0xc791f8bb7c7ced7c, 0x17e3cc7166668566 + , 0xa68ea77bdddd53dd, 0xb84b2eaf17175c17, 0x02468e4547470147, 0x84dc211a9e9e429e + , 0x1ec589d4caca0fca, 0x75995a582d2db42d, 0x9179632ebfbfc6bf, 0x381b0e3f07071c07 + , 0x012347acadad8ead, 0xea2fb4b05a5a755a, 0x6cb51bef83833683, 0x85ff66b63333cc33 + , 0x3ff2c65c63639163, 0x100a041202020802, 0x39384993aaaa92aa, 0xafa8e2de7171d971 + , 0x0ecf8dc6c8c807c8, 0xc87d32d119196419, 0x7270923b49493949, 0x869aaf5fd9d943d9 + , 0xc31df931f2f2eff2, 0x4b48dba8e3e3abe3, 0xe22ab6b95b5b715b, 0x34920dbc88881a88 + , 0xa4c8293e9a9a529a, 0x2dbe4c0b26269826, 0x8dfa64bf3232c832, 0xe94a7d59b0b0fab0 + , 0x1b6acff2e9e983e9, 0x78331e770f0f3c0f, 0xe6a6b733d5d573d5, 0x74ba1df480803a80 + , 0x997c6127bebec2be, 0x26de87ebcdcd13cd, 0xbde468893434d034, 0x7a75903248483d48 + , 0xab24e354ffffdbff, 0xf78ff48d7a7af57a, 0xf4ea3d6490907a90, 0xc23ebe9d5f5f615f + , 0x1da0403d20208020, 0x67d5d00f6868bd68, 0xd07234ca1a1a681a, 0x192c41b7aeae82ae + , 0xc95e757db4b4eab4, 0x9a19a8ce54544d54, 0xece53b7f93937693, 0x0daa442f22228822 + , 0x07e9c86364648d64, 0xdb12ff2af1f1e3f1, 0xbfa2e6cc7373d173, 0x905a248212124812 + , 0x3a5d807a40401d40, 0x4028104808082008, 0x56e89b95c3c32bc3, 0x337bc5dfecec97ec + , 0x9690ab4ddbdb4bdb, 0x611f5fc0a1a1bea1, 0x1c8307918d8d0e8d, 0xf5c97ac83d3df43d + , 0xccf1335b97976697, 0x0000000000000000, 0x36d483f9cfcf1bcf, 0x4587566e2b2bac2b + , 0x97b3ece17676c576, 0x64b019e682823282, 0xfea9b128d6d67fd6, 0xd87736c31b1b6c1b + , 0xc15b7774b5b5eeb5, 0x112943beafaf86af, 0x77dfd41d6a6ab56a, 0xba0da0ea50505d50 + , 0x124c8a5745450945, 0xcb18fb38f3f3ebf3, 0x9df060ad3030c030, 0x2b74c3c4efef9bef + , 0xe5c37eda3f3ffc3f, 0x921caac755554955, 0x791059dba2a2b2a2, 0x0365c9e9eaea8fea + , 0x0fecca6a65658965, 0xb9686903babad2ba, 0x65935e4a2f2fbc2f, 0x4ee79d8ec0c027c0 + , 0xbe81a160dede5fde, 0xe06c38fc1c1c701c, 0xbb2ee746fdfdd3fd, 0x52649a1f4d4d294d + , 0xe4e0397692927292, 0x8fbceafa7575c975, 0x301e0c3606061806, 0x249809ae8a8a128a + , 0xf940794bb2b2f2b2, 0x6359d185e6e6bfe6, 0x70361c7e0e0e380e, 0xf8633ee71f1f7c1f + , 0x37f7c45562629562, 0xeea3b53ad4d477d4, 0x29324d81a8a89aa8, 0xc4f4315296966296 + , 0x9b3aef62f9f9c3f9, 0x66f697a3c5c533c5, 0x35b14a1025259425, 0xf220b2ab59597959 + , 0x54ae15d084842a84, 0xb7a7e4c57272d572, 0xd5dd72ec3939e439, 0x5a6198164c4c2d4c + , 0xca3bbc945e5e655e, 0xe785f09f7878fd78, 0xddd870e53838e038, 0x148605988c8c0a8c + , 0xc6b2bf17d1d163d1, 0x410b57e4a5a5aea5, 0x434dd9a1e2e2afe2, 0x2ff8c24e61619961 + , 0xf1457b42b3b3f6b3, 0x15a5423421218421, 0x94d625089c9c4a9c, 0xf0663cee1e1e781e + , 0x2252866143431143, 0x76fc93b1c7c73bc7, 0xb32be54ffcfcd7fc, 0x2014082404041004 + , 0xb208a2e351515951, 0xbcc72f2599995e99, 0x4fc4da226d6da96d, 0x68391a650d0d340d + , 0x8335e979fafacffa, 0xb684a369dfdf5bdf, 0xd79bfca97e7ee57e, 0x3db4481924249024 + , 0xc5d776fe3b3bec3b, 0x313d4b9aabab96ab, 0x3ed181f0cece1fce, 0x8855229911114411 + , 0x0c8903838f8f068f, 0x4a6b9c044e4e254e, 0xd1517366b7b7e6b7, 0x0b60cbe0ebeb8beb + , 0xfdcc78c13c3cf03c, 0x7cbf1ffd81813e81, 0xd4fe354094946a94, 0xeb0cf31cf7f7fbf7 + , 0xa1676f18b9b9deb9, 0x985f268b13134c13, 0x7d9c58512c2cb02c, 0xd6b8bb05d3d36bd3 + , 0x6b5cd38ce7e7bbe7, 0x57cbdc396e6ea56e, 0x6ef395aac4c437c4, 0x180f061b03030c03 + , 0x8a13acdc56564556, 0x1a49885e44440d44, 0xdf9efea07f7fe17f, 0x21374f88a9a99ea9 + , 0x4d8254672a2aa82a, 0xb16d6b0abbbbd6bb, 0x46e29f87c1c123c1, 0xa202a6f153535153 + , 0xae8ba572dcdc57dc, 0x582716530b0b2c0b, 0x9cd327019d9d4e9d, 0x47c1d82b6c6cad6c + , 0x95f562a43131c431, 0x87b9e8f37474cd74, 0xe309f115f6f6fff6, 0x0a438c4c46460546 + , 0x092645a5acac8aac, 0x3c970fb589891e89, 0xa04428b414145014, 0x5b42dfbae1e1a3e1 + , 0xb04e2ca616165816, 0xcdd274f73a3ae83a, 0x6fd0d2066969b969, 0x482d124109092409 + , 0xa7ade0d77070dd70, 0xd954716fb6b6e2b6, 0xceb7bd1ed0d067d0, 0x3b7ec7d6eded93ed + , 0x2edb85e2cccc17cc, 0x2a57846842421542, 0xb4c22d2c98985a98, 0x490e55eda4a4aaa4 + , 0x5d8850752828a028, 0xda31b8865c5c6d5c, 0x933fed6bf8f8c7f8, 0x44a411c286862286 + ] + +_c5 = [ + 0x18c07830d8181860, 0x2305af462623238c, 0xc67ef991b8c6c63f, 0xe8136fcdfbe8e887 + , 0x874ca113cb878726, 0xb8a9626d11b8b8da, 0x0108050209010104, 0x4f426e9e0d4f4f21 + , 0x36adee6c9b3636d8, 0xa6590451ffa6a6a2, 0xd2debdb90cd2d26f, 0xf5fb06f70ef5f5f3 + , 0x79ef80f2967979f9, 0x6f5fcede306f6fa1, 0x91fcef3f6d91917e, 0x52aa07a4f8525255 + , 0x6027fdc04760609d, 0xbc89766535bcbcca, 0x9baccd2b379b9b56, 0x8e048c018a8e8e02 + , 0xa371155bd2a3a3b6, 0x0c603c186c0c0c30, 0x7bff8af6847b7bf1, 0x35b5e16a803535d4 + , 0x1de8693af51d1d74, 0xe05347ddb3e0e0a7, 0xd7f6acb321d7d77b, 0xc25eed999cc2c22f + , 0x2e6d965c432e2eb8, 0x4b627a96294b4b31, 0xfea321e15dfefedf, 0x578216aed5575741 + , 0x15a8412abd151554, 0x779fb6eee87777c1, 0x37a5eb6e923737dc, 0xe57b56d79ee5e5b3 + , 0x9f8cd923139f9f46, 0xf0d317fd23f0f0e7, 0x4a6a7f94204a4a35, 0xda9e95a944dada4f + , 0x58fa25b0a258587d, 0xc906ca8fcfc9c903, 0x29558d527c2929a4, 0x0a5022145a0a0a28 + , 0xb1e14f7f50b1b1fe, 0xa0691a5dc9a0a0ba, 0x6b7fdad6146b6bb1, 0x855cab17d985852e + , 0xbd8173673cbdbdce, 0x5dd234ba8f5d5d69, 0x1080502090101040, 0xf4f303f507f4f4f7 + , 0xcb16c08bddcbcb0b, 0x3eedc67cd33e3ef8, 0x0528110a2d050514, 0x671fe6ce78676781 + , 0xe47353d597e4e4b7, 0x2725bb4e0227279c, 0x4132588273414119, 0x8b2c9d0ba78b8b16 + , 0xa7510153f6a7a7a6, 0x7dcf94fab27d7de9, 0x95dcfb374995956e, 0xd88e9fad56d8d847 + , 0xfb8b30eb70fbfbcb, 0xee2371c1cdeeee9f, 0x7cc791f8bb7c7ced, 0x6617e3cc71666685 + , 0xdda68ea77bdddd53, 0x17b84b2eaf17175c, 0x4702468e45474701, 0x9e84dc211a9e9e42 + , 0xca1ec589d4caca0f, 0x2d75995a582d2db4, 0xbf9179632ebfbfc6, 0x07381b0e3f07071c + , 0xad012347acadad8e, 0x5aea2fb4b05a5a75, 0x836cb51bef838336, 0x3385ff66b63333cc + , 0x633ff2c65c636391, 0x02100a0412020208, 0xaa39384993aaaa92, 0x71afa8e2de7171d9 + , 0xc80ecf8dc6c8c807, 0x19c87d32d1191964, 0x497270923b494939, 0xd9869aaf5fd9d943 + , 0xf2c31df931f2f2ef, 0xe34b48dba8e3e3ab, 0x5be22ab6b95b5b71, 0x8834920dbc88881a + , 0x9aa4c8293e9a9a52, 0x262dbe4c0b262698, 0x328dfa64bf3232c8, 0xb0e94a7d59b0b0fa + , 0xe91b6acff2e9e983, 0x0f78331e770f0f3c, 0xd5e6a6b733d5d573, 0x8074ba1df480803a + , 0xbe997c6127bebec2, 0xcd26de87ebcdcd13, 0x34bde468893434d0, 0x487a75903248483d + , 0xffab24e354ffffdb, 0x7af78ff48d7a7af5, 0x90f4ea3d6490907a, 0x5fc23ebe9d5f5f61 + , 0x201da0403d202080, 0x6867d5d00f6868bd, 0x1ad07234ca1a1a68, 0xae192c41b7aeae82 + , 0xb4c95e757db4b4ea, 0x549a19a8ce54544d, 0x93ece53b7f939376, 0x220daa442f222288 + , 0x6407e9c86364648d, 0xf1db12ff2af1f1e3, 0x73bfa2e6cc7373d1, 0x12905a2482121248 + , 0x403a5d807a40401d, 0x0840281048080820, 0xc356e89b95c3c32b, 0xec337bc5dfecec97 + , 0xdb9690ab4ddbdb4b, 0xa1611f5fc0a1a1be, 0x8d1c8307918d8d0e, 0x3df5c97ac83d3df4 + , 0x97ccf1335b979766, 0x0000000000000000, 0xcf36d483f9cfcf1b, 0x2b4587566e2b2bac + , 0x7697b3ece17676c5, 0x8264b019e6828232, 0xd6fea9b128d6d67f, 0x1bd87736c31b1b6c + , 0xb5c15b7774b5b5ee, 0xaf112943beafaf86, 0x6a77dfd41d6a6ab5, 0x50ba0da0ea50505d + , 0x45124c8a57454509, 0xf3cb18fb38f3f3eb, 0x309df060ad3030c0, 0xef2b74c3c4efef9b + , 0x3fe5c37eda3f3ffc, 0x55921caac7555549, 0xa2791059dba2a2b2, 0xea0365c9e9eaea8f + , 0x650fecca6a656589, 0xbab9686903babad2, 0x2f65935e4a2f2fbc, 0xc04ee79d8ec0c027 + , 0xdebe81a160dede5f, 0x1ce06c38fc1c1c70, 0xfdbb2ee746fdfdd3, 0x4d52649a1f4d4d29 + , 0x92e4e03976929272, 0x758fbceafa7575c9, 0x06301e0c36060618, 0x8a249809ae8a8a12 + , 0xb2f940794bb2b2f2, 0xe66359d185e6e6bf, 0x0e70361c7e0e0e38, 0x1ff8633ee71f1f7c + , 0x6237f7c455626295, 0xd4eea3b53ad4d477, 0xa829324d81a8a89a, 0x96c4f43152969662 + , 0xf99b3aef62f9f9c3, 0xc566f697a3c5c533, 0x2535b14a10252594, 0x59f220b2ab595979 + , 0x8454ae15d084842a, 0x72b7a7e4c57272d5, 0x39d5dd72ec3939e4, 0x4c5a6198164c4c2d + , 0x5eca3bbc945e5e65, 0x78e785f09f7878fd, 0x38ddd870e53838e0, 0x8c148605988c8c0a + , 0xd1c6b2bf17d1d163, 0xa5410b57e4a5a5ae, 0xe2434dd9a1e2e2af, 0x612ff8c24e616199 + , 0xb3f1457b42b3b3f6, 0x2115a54234212184, 0x9c94d625089c9c4a, 0x1ef0663cee1e1e78 + , 0x4322528661434311, 0xc776fc93b1c7c73b, 0xfcb32be54ffcfcd7, 0x0420140824040410 + , 0x51b208a2e3515159, 0x99bcc72f2599995e, 0x6d4fc4da226d6da9, 0x0d68391a650d0d34 + , 0xfa8335e979fafacf, 0xdfb684a369dfdf5b, 0x7ed79bfca97e7ee5, 0x243db44819242490 + , 0x3bc5d776fe3b3bec, 0xab313d4b9aabab96, 0xce3ed181f0cece1f, 0x1188552299111144 + , 0x8f0c8903838f8f06, 0x4e4a6b9c044e4e25, 0xb7d1517366b7b7e6, 0xeb0b60cbe0ebeb8b + , 0x3cfdcc78c13c3cf0, 0x817cbf1ffd81813e, 0x94d4fe354094946a, 0xf7eb0cf31cf7f7fb + , 0xb9a1676f18b9b9de, 0x13985f268b13134c, 0x2c7d9c58512c2cb0, 0xd3d6b8bb05d3d36b + , 0xe76b5cd38ce7e7bb, 0x6e57cbdc396e6ea5, 0xc46ef395aac4c437, 0x03180f061b03030c + , 0x568a13acdc565645, 0x441a49885e44440d, 0x7fdf9efea07f7fe1, 0xa921374f88a9a99e + , 0x2a4d8254672a2aa8, 0xbbb16d6b0abbbbd6, 0xc146e29f87c1c123, 0x53a202a6f1535351 + , 0xdcae8ba572dcdc57, 0x0b582716530b0b2c, 0x9d9cd327019d9d4e, 0x6c47c1d82b6c6cad + , 0x3195f562a43131c4, 0x7487b9e8f37474cd, 0xf6e309f115f6f6ff, 0x460a438c4c464605 + , 0xac092645a5acac8a, 0x893c970fb589891e, 0x14a04428b4141450, 0xe15b42dfbae1e1a3 + , 0x16b04e2ca6161658, 0x3acdd274f73a3ae8, 0x696fd0d2066969b9, 0x09482d1241090924 + , 0x70a7ade0d77070dd, 0xb6d954716fb6b6e2, 0xd0ceb7bd1ed0d067, 0xed3b7ec7d6eded93 + , 0xcc2edb85e2cccc17, 0x422a578468424215, 0x98b4c22d2c98985a, 0xa4490e55eda4a4aa + , 0x285d8850752828a0, 0x5cda31b8865c5c6d, 0xf8933fed6bf8f8c7, 0x8644a411c2868622 + ] + +_c6 = [ + 0x6018c07830d81818, 0x8c2305af46262323, 0x3fc67ef991b8c6c6, 0x87e8136fcdfbe8e8 + , 0x26874ca113cb8787, 0xdab8a9626d11b8b8, 0x0401080502090101, 0x214f426e9e0d4f4f + , 0xd836adee6c9b3636, 0xa2a6590451ffa6a6, 0x6fd2debdb90cd2d2, 0xf3f5fb06f70ef5f5 + , 0xf979ef80f2967979, 0xa16f5fcede306f6f, 0x7e91fcef3f6d9191, 0x5552aa07a4f85252 + , 0x9d6027fdc0476060, 0xcabc89766535bcbc, 0x569baccd2b379b9b, 0x028e048c018a8e8e + , 0xb6a371155bd2a3a3, 0x300c603c186c0c0c, 0xf17bff8af6847b7b, 0xd435b5e16a803535 + , 0x741de8693af51d1d, 0xa7e05347ddb3e0e0, 0x7bd7f6acb321d7d7, 0x2fc25eed999cc2c2 + , 0xb82e6d965c432e2e, 0x314b627a96294b4b, 0xdffea321e15dfefe, 0x41578216aed55757 + , 0x5415a8412abd1515, 0xc1779fb6eee87777, 0xdc37a5eb6e923737, 0xb3e57b56d79ee5e5 + , 0x469f8cd923139f9f, 0xe7f0d317fd23f0f0, 0x354a6a7f94204a4a, 0x4fda9e95a944dada + , 0x7d58fa25b0a25858, 0x03c906ca8fcfc9c9, 0xa429558d527c2929, 0x280a5022145a0a0a + , 0xfeb1e14f7f50b1b1, 0xbaa0691a5dc9a0a0, 0xb16b7fdad6146b6b, 0x2e855cab17d98585 + , 0xcebd8173673cbdbd, 0x695dd234ba8f5d5d, 0x4010805020901010, 0xf7f4f303f507f4f4 + , 0x0bcb16c08bddcbcb, 0xf83eedc67cd33e3e, 0x140528110a2d0505, 0x81671fe6ce786767 + , 0xb7e47353d597e4e4, 0x9c2725bb4e022727, 0x1941325882734141, 0x168b2c9d0ba78b8b + , 0xa6a7510153f6a7a7, 0xe97dcf94fab27d7d, 0x6e95dcfb37499595, 0x47d88e9fad56d8d8 + , 0xcbfb8b30eb70fbfb, 0x9fee2371c1cdeeee, 0xed7cc791f8bb7c7c, 0x856617e3cc716666 + , 0x53dda68ea77bdddd, 0x5c17b84b2eaf1717, 0x014702468e454747, 0x429e84dc211a9e9e + , 0x0fca1ec589d4caca, 0xb42d75995a582d2d, 0xc6bf9179632ebfbf, 0x1c07381b0e3f0707 + , 0x8ead012347acadad, 0x755aea2fb4b05a5a, 0x36836cb51bef8383, 0xcc3385ff66b63333 + , 0x91633ff2c65c6363, 0x0802100a04120202, 0x92aa39384993aaaa, 0xd971afa8e2de7171 + , 0x07c80ecf8dc6c8c8, 0x6419c87d32d11919, 0x39497270923b4949, 0x43d9869aaf5fd9d9 + , 0xeff2c31df931f2f2, 0xabe34b48dba8e3e3, 0x715be22ab6b95b5b, 0x1a8834920dbc8888 + , 0x529aa4c8293e9a9a, 0x98262dbe4c0b2626, 0xc8328dfa64bf3232, 0xfab0e94a7d59b0b0 + , 0x83e91b6acff2e9e9, 0x3c0f78331e770f0f, 0x73d5e6a6b733d5d5, 0x3a8074ba1df48080 + , 0xc2be997c6127bebe, 0x13cd26de87ebcdcd, 0xd034bde468893434, 0x3d487a7590324848 + , 0xdbffab24e354ffff, 0xf57af78ff48d7a7a, 0x7a90f4ea3d649090, 0x615fc23ebe9d5f5f + , 0x80201da0403d2020, 0xbd6867d5d00f6868, 0x681ad07234ca1a1a, 0x82ae192c41b7aeae + , 0xeab4c95e757db4b4, 0x4d549a19a8ce5454, 0x7693ece53b7f9393, 0x88220daa442f2222 + , 0x8d6407e9c8636464, 0xe3f1db12ff2af1f1, 0xd173bfa2e6cc7373, 0x4812905a24821212 + , 0x1d403a5d807a4040, 0x2008402810480808, 0x2bc356e89b95c3c3, 0x97ec337bc5dfecec + , 0x4bdb9690ab4ddbdb, 0xbea1611f5fc0a1a1, 0x0e8d1c8307918d8d, 0xf43df5c97ac83d3d + , 0x6697ccf1335b9797, 0x0000000000000000, 0x1bcf36d483f9cfcf, 0xac2b4587566e2b2b + , 0xc57697b3ece17676, 0x328264b019e68282, 0x7fd6fea9b128d6d6, 0x6c1bd87736c31b1b + , 0xeeb5c15b7774b5b5, 0x86af112943beafaf, 0xb56a77dfd41d6a6a, 0x5d50ba0da0ea5050 + , 0x0945124c8a574545, 0xebf3cb18fb38f3f3, 0xc0309df060ad3030, 0x9bef2b74c3c4efef + , 0xfc3fe5c37eda3f3f, 0x4955921caac75555, 0xb2a2791059dba2a2, 0x8fea0365c9e9eaea + , 0x89650fecca6a6565, 0xd2bab9686903baba, 0xbc2f65935e4a2f2f, 0x27c04ee79d8ec0c0 + , 0x5fdebe81a160dede, 0x701ce06c38fc1c1c, 0xd3fdbb2ee746fdfd, 0x294d52649a1f4d4d + , 0x7292e4e039769292, 0xc9758fbceafa7575, 0x1806301e0c360606, 0x128a249809ae8a8a + , 0xf2b2f940794bb2b2, 0xbfe66359d185e6e6, 0x380e70361c7e0e0e, 0x7c1ff8633ee71f1f + , 0x956237f7c4556262, 0x77d4eea3b53ad4d4, 0x9aa829324d81a8a8, 0x6296c4f431529696 + , 0xc3f99b3aef62f9f9, 0x33c566f697a3c5c5, 0x942535b14a102525, 0x7959f220b2ab5959 + , 0x2a8454ae15d08484, 0xd572b7a7e4c57272, 0xe439d5dd72ec3939, 0x2d4c5a6198164c4c + , 0x655eca3bbc945e5e, 0xfd78e785f09f7878, 0xe038ddd870e53838, 0x0a8c148605988c8c + , 0x63d1c6b2bf17d1d1, 0xaea5410b57e4a5a5, 0xafe2434dd9a1e2e2, 0x99612ff8c24e6161 + , 0xf6b3f1457b42b3b3, 0x842115a542342121, 0x4a9c94d625089c9c, 0x781ef0663cee1e1e + , 0x1143225286614343, 0x3bc776fc93b1c7c7, 0xd7fcb32be54ffcfc, 0x1004201408240404 + , 0x5951b208a2e35151, 0x5e99bcc72f259999, 0xa96d4fc4da226d6d, 0x340d68391a650d0d + , 0xcffa8335e979fafa, 0x5bdfb684a369dfdf, 0xe57ed79bfca97e7e, 0x90243db448192424 + , 0xec3bc5d776fe3b3b, 0x96ab313d4b9aabab, 0x1fce3ed181f0cece, 0x4411885522991111 + , 0x068f0c8903838f8f, 0x254e4a6b9c044e4e, 0xe6b7d1517366b7b7, 0x8beb0b60cbe0ebeb + , 0xf03cfdcc78c13c3c, 0x3e817cbf1ffd8181, 0x6a94d4fe35409494, 0xfbf7eb0cf31cf7f7 + , 0xdeb9a1676f18b9b9, 0x4c13985f268b1313, 0xb02c7d9c58512c2c, 0x6bd3d6b8bb05d3d3 + , 0xbbe76b5cd38ce7e7, 0xa56e57cbdc396e6e, 0x37c46ef395aac4c4, 0x0c03180f061b0303 + , 0x45568a13acdc5656, 0x0d441a49885e4444, 0xe17fdf9efea07f7f, 0x9ea921374f88a9a9 + , 0xa82a4d8254672a2a, 0xd6bbb16d6b0abbbb, 0x23c146e29f87c1c1, 0x5153a202a6f15353 + , 0x57dcae8ba572dcdc, 0x2c0b582716530b0b, 0x4e9d9cd327019d9d, 0xad6c47c1d82b6c6c + , 0xc43195f562a43131, 0xcd7487b9e8f37474, 0xfff6e309f115f6f6, 0x05460a438c4c4646 + , 0x8aac092645a5acac, 0x1e893c970fb58989, 0x5014a04428b41414, 0xa3e15b42dfbae1e1 + , 0x5816b04e2ca61616, 0xe83acdd274f73a3a, 0xb9696fd0d2066969, 0x2409482d12410909 + , 0xdd70a7ade0d77070, 0xe2b6d954716fb6b6, 0x67d0ceb7bd1ed0d0, 0x93ed3b7ec7d6eded + , 0x17cc2edb85e2cccc, 0x15422a5784684242, 0x5a98b4c22d2c9898, 0xaaa4490e55eda4a4 + , 0xa0285d8850752828, 0x6d5cda31b8865c5c, 0xc7f8933fed6bf8f8, 0x228644a411c28686 + ] + +_c7 = [ + 0x186018c07830d818, 0x238c2305af462623, 0xc63fc67ef991b8c6, 0xe887e8136fcdfbe8 + , 0x8726874ca113cb87, 0xb8dab8a9626d11b8, 0x0104010805020901, 0x4f214f426e9e0d4f + , 0x36d836adee6c9b36, 0xa6a2a6590451ffa6, 0xd26fd2debdb90cd2, 0xf5f3f5fb06f70ef5 + , 0x79f979ef80f29679, 0x6fa16f5fcede306f, 0x917e91fcef3f6d91, 0x525552aa07a4f852 + , 0x609d6027fdc04760, 0xbccabc89766535bc, 0x9b569baccd2b379b, 0x8e028e048c018a8e + , 0xa3b6a371155bd2a3, 0x0c300c603c186c0c, 0x7bf17bff8af6847b, 0x35d435b5e16a8035 + , 0x1d741de8693af51d, 0xe0a7e05347ddb3e0, 0xd77bd7f6acb321d7, 0xc22fc25eed999cc2 + , 0x2eb82e6d965c432e, 0x4b314b627a96294b, 0xfedffea321e15dfe, 0x5741578216aed557 + , 0x155415a8412abd15, 0x77c1779fb6eee877, 0x37dc37a5eb6e9237, 0xe5b3e57b56d79ee5 + , 0x9f469f8cd923139f, 0xf0e7f0d317fd23f0, 0x4a354a6a7f94204a, 0xda4fda9e95a944da + , 0x587d58fa25b0a258, 0xc903c906ca8fcfc9, 0x29a429558d527c29, 0x0a280a5022145a0a + , 0xb1feb1e14f7f50b1, 0xa0baa0691a5dc9a0, 0x6bb16b7fdad6146b, 0x852e855cab17d985 + , 0xbdcebd8173673cbd, 0x5d695dd234ba8f5d, 0x1040108050209010, 0xf4f7f4f303f507f4 + , 0xcb0bcb16c08bddcb, 0x3ef83eedc67cd33e, 0x05140528110a2d05, 0x6781671fe6ce7867 + , 0xe4b7e47353d597e4, 0x279c2725bb4e0227, 0x4119413258827341, 0x8b168b2c9d0ba78b + , 0xa7a6a7510153f6a7, 0x7de97dcf94fab27d, 0x956e95dcfb374995, 0xd847d88e9fad56d8 + , 0xfbcbfb8b30eb70fb, 0xee9fee2371c1cdee, 0x7ced7cc791f8bb7c, 0x66856617e3cc7166 + , 0xdd53dda68ea77bdd, 0x175c17b84b2eaf17, 0x47014702468e4547, 0x9e429e84dc211a9e + , 0xca0fca1ec589d4ca, 0x2db42d75995a582d, 0xbfc6bf9179632ebf, 0x071c07381b0e3f07 + , 0xad8ead012347acad, 0x5a755aea2fb4b05a, 0x8336836cb51bef83, 0x33cc3385ff66b633 + , 0x6391633ff2c65c63, 0x020802100a041202, 0xaa92aa39384993aa, 0x71d971afa8e2de71 + , 0xc807c80ecf8dc6c8, 0x196419c87d32d119, 0x4939497270923b49, 0xd943d9869aaf5fd9 + , 0xf2eff2c31df931f2, 0xe3abe34b48dba8e3, 0x5b715be22ab6b95b, 0x881a8834920dbc88 + , 0x9a529aa4c8293e9a, 0x2698262dbe4c0b26, 0x32c8328dfa64bf32, 0xb0fab0e94a7d59b0 + , 0xe983e91b6acff2e9, 0x0f3c0f78331e770f, 0xd573d5e6a6b733d5, 0x803a8074ba1df480 + , 0xbec2be997c6127be, 0xcd13cd26de87ebcd, 0x34d034bde4688934, 0x483d487a75903248 + , 0xffdbffab24e354ff, 0x7af57af78ff48d7a, 0x907a90f4ea3d6490, 0x5f615fc23ebe9d5f + , 0x2080201da0403d20, 0x68bd6867d5d00f68, 0x1a681ad07234ca1a, 0xae82ae192c41b7ae + , 0xb4eab4c95e757db4, 0x544d549a19a8ce54, 0x937693ece53b7f93, 0x2288220daa442f22 + , 0x648d6407e9c86364, 0xf1e3f1db12ff2af1, 0x73d173bfa2e6cc73, 0x124812905a248212 + , 0x401d403a5d807a40, 0x0820084028104808, 0xc32bc356e89b95c3, 0xec97ec337bc5dfec + , 0xdb4bdb9690ab4ddb, 0xa1bea1611f5fc0a1, 0x8d0e8d1c8307918d, 0x3df43df5c97ac83d + , 0x976697ccf1335b97, 0x0000000000000000, 0xcf1bcf36d483f9cf, 0x2bac2b4587566e2b + , 0x76c57697b3ece176, 0x82328264b019e682, 0xd67fd6fea9b128d6, 0x1b6c1bd87736c31b + , 0xb5eeb5c15b7774b5, 0xaf86af112943beaf, 0x6ab56a77dfd41d6a, 0x505d50ba0da0ea50 + , 0x450945124c8a5745, 0xf3ebf3cb18fb38f3, 0x30c0309df060ad30, 0xef9bef2b74c3c4ef + , 0x3ffc3fe5c37eda3f, 0x554955921caac755, 0xa2b2a2791059dba2, 0xea8fea0365c9e9ea + , 0x6589650fecca6a65, 0xbad2bab9686903ba, 0x2fbc2f65935e4a2f, 0xc027c04ee79d8ec0 + , 0xde5fdebe81a160de, 0x1c701ce06c38fc1c, 0xfdd3fdbb2ee746fd, 0x4d294d52649a1f4d + , 0x927292e4e0397692, 0x75c9758fbceafa75, 0x061806301e0c3606, 0x8a128a249809ae8a + , 0xb2f2b2f940794bb2, 0xe6bfe66359d185e6, 0x0e380e70361c7e0e, 0x1f7c1ff8633ee71f + , 0x62956237f7c45562, 0xd477d4eea3b53ad4, 0xa89aa829324d81a8, 0x966296c4f4315296 + , 0xf9c3f99b3aef62f9, 0xc533c566f697a3c5, 0x25942535b14a1025, 0x597959f220b2ab59 + , 0x842a8454ae15d084, 0x72d572b7a7e4c572, 0x39e439d5dd72ec39, 0x4c2d4c5a6198164c + , 0x5e655eca3bbc945e, 0x78fd78e785f09f78, 0x38e038ddd870e538, 0x8c0a8c148605988c + , 0xd163d1c6b2bf17d1, 0xa5aea5410b57e4a5, 0xe2afe2434dd9a1e2, 0x6199612ff8c24e61 + , 0xb3f6b3f1457b42b3, 0x21842115a5423421, 0x9c4a9c94d625089c, 0x1e781ef0663cee1e + , 0x4311432252866143, 0xc73bc776fc93b1c7, 0xfcd7fcb32be54ffc, 0x0410042014082404 + , 0x515951b208a2e351, 0x995e99bcc72f2599, 0x6da96d4fc4da226d, 0x0d340d68391a650d + , 0xfacffa8335e979fa, 0xdf5bdfb684a369df, 0x7ee57ed79bfca97e, 0x2490243db4481924 + , 0x3bec3bc5d776fe3b, 0xab96ab313d4b9aab, 0xce1fce3ed181f0ce, 0x1144118855229911 + , 0x8f068f0c8903838f, 0x4e254e4a6b9c044e, 0xb7e6b7d1517366b7, 0xeb8beb0b60cbe0eb + , 0x3cf03cfdcc78c13c, 0x813e817cbf1ffd81, 0x946a94d4fe354094, 0xf7fbf7eb0cf31cf7 + , 0xb9deb9a1676f18b9, 0x134c13985f268b13, 0x2cb02c7d9c58512c, 0xd36bd3d6b8bb05d3 + , 0xe7bbe76b5cd38ce7, 0x6ea56e57cbdc396e, 0xc437c46ef395aac4, 0x030c03180f061b03 + , 0x5645568a13acdc56, 0x440d441a49885e44, 0x7fe17fdf9efea07f, 0xa99ea921374f88a9 + , 0x2aa82a4d8254672a, 0xbbd6bbb16d6b0abb, 0xc123c146e29f87c1, 0x535153a202a6f153 + , 0xdc57dcae8ba572dc, 0x0b2c0b582716530b, 0x9d4e9d9cd327019d, 0x6cad6c47c1d82b6c + , 0x31c43195f562a431, 0x74cd7487b9e8f374, 0xf6fff6e309f115f6, 0x4605460a438c4c46 + , 0xac8aac092645a5ac, 0x891e893c970fb589, 0x145014a04428b414, 0xe1a3e15b42dfbae1 + , 0x165816b04e2ca616, 0x3ae83acdd274f73a, 0x69b9696fd0d20669, 0x092409482d124109 + , 0x70dd70a7ade0d770, 0xb6e2b6d954716fb6, 0xd067d0ceb7bd1ed0, 0xed93ed3b7ec7d6ed + , 0xcc17cc2edb85e2cc, 0x4215422a57846842, 0x985a98b4c22d2c98, 0xa4aaa4490e55eda4 + , 0x28a0285d88507528, 0x5c6d5cda31b8865c, 0xf8c7f8933fed6bf8, 0x86228644a411c286 + ] + +ccs :: UArray (Int, Int) Word64 +ccs = array ( (0,0), (7, 255) ) $ zip [(x, y) | x <- [0..7], y <- [0..255]] (concat [_c0, _c1, _c2, _c3, _c4, _c5, _c6, _c7]) + +rcs :: UArray Int Word64 +rcs = listArray (0, 9) [ + 0x1823c6e887b8014f + , 0x36a6d2f5796f9152 + , 0x60bc9b8ea30c7b35 + , 0x1de0d7c22e4bfe57 + , 0x157737e59ff04ada + , 0x58c9290ab1a06b85 + , 0xbd5d10f4cb3e0567 + , 0xe427418ba77d95d8 + , 0xfbee7c66dd17479e + , 0xca2dbf07ad5a8333 + ] + +encodeInt64Helper :: Int64 -> [Word8] +encodeInt64Helper x_ = [w7, w6, w5, w4, w3, w2, w1, w0] + where x = x_ * 8 + w7 = fromIntegral $ (x `shiftR` 56) .&. 0xff + w6 = fromIntegral $ (x `shiftR` 48) .&. 0xff + w5 = fromIntegral $ (x `shiftR` 40) .&. 0xff + w4 = fromIntegral $ (x `shiftR` 32) .&. 0xff + w3 = fromIntegral $ (x `shiftR` 24) .&. 0xff + w2 = fromIntegral $ (x `shiftR` 16) .&. 0xff + w1 = fromIntegral $ (x `shiftR` 8) .&. 0xff + w0 = fromIntegral $ (x `shiftR` 0) .&. 0xff + +encodeInt64 :: Int64 -> ByteString +encodeInt64 = B.pack . encodeInt64Helper + +whirlpoolBlockSize :: Int +whirlpoolBlockSize = 64 + +whirlpoolDigestSize :: Int +whirlpoolDigestSize = 64 + +lastChunk :: Int64 -> ByteString -> [ByteString] +lastChunk msglen s + | len < 32 = [s <> B.cons 0x80 (B.replicate (55 - len) 0x0) <> encodedLen] + | len < 64 = (s <> B.singleton 0x80 <> (B.replicate (63-fromIntegral len) 0)) : [(B.replicate 56 0x0) <> encodedLen] + where + len = B.length s + encodedLen = encodeInt64 msglen + +data Whirlpool = Whirlpool {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + {-# UNPACK #-} !Word64 + deriving Eq + +{-# INLINE fromList #-} +{-# INLINE toList #-} +fromList :: [Word64] -> Whirlpool +toList :: Whirlpool -> [Word64] +fromList (a:b:c:d:e:f:g:h:_) = Whirlpool a b c d e f g h +toList (Whirlpool a b c d e f g h) = a:b:c:d:e:f:g:[h] + +initHash :: Whirlpool +initHash = Whirlpool 0 0 0 0 0 0 0 0 + +instance Show Whirlpool where + show = LC.unpack . toLazyByteString . foldMap (word64HexFixed) . toList + +{-# INLINE readW64 #-} +readW64 :: ByteString -> Word64 +readW64 = B.foldl' acc 0 . B.take 8 + where acc x c = x `shiftL` 8 + fromIntegral c + acc :: Word64 -> Word8 -> Word64 + {-# INLINE acc #-} + +{-# INLINE prepareBlock #-} +prepareBlock :: ByteString -> Whirlpool +prepareBlock bs = Whirlpool w1 w2 w3 w4 w5 w6 w7 w8 + where + !w1 = readW64 bs + !w2 = readW64 (B.drop 8 bs) + !w3 = readW64 (B.drop 16 bs) + !w4 = readW64 (B.drop 24 bs) + !w5 = readW64 (B.drop 32 bs) + !w6 = readW64 (B.drop 40 bs) + !w7 = readW64 (B.drop 48 bs) + !w8 = readW64 (B.drop 56 bs) + +{-# INLINE zipW #-} +zipW :: (Word64->Word64->Word64) -> Whirlpool -> Whirlpool -> Whirlpool +zipW zf (Whirlpool a b c d e f g h) (Whirlpool a' b' c' d' e' f' g' h') = + Whirlpool (zf a a') (zf b b') (zf c c') (zf d d') + (zf e e') (zf f f') (zf g g') (zf h h') + +whirlpoolBlockUpdate :: Whirlpool -> ByteString -> Whirlpool +whirlpoolBlockUpdate h0 bs = zipW xor h0 . zipW xor block . fst . foldl' blkUpdate (zipW xor h0 block, h0) $ indices rcs + where !block = prepareBlock bs + {-# INLINE blkUpdate #-} + blkUpdate !((Whirlpool s0 s1 s2 s3 s4 s5 s6 s7), !(Whirlpool k0 k1 k2 k3 k4 k5 k6 k7)) r = (st', hv') + where + !j0 = ccs ! (0, fromIntegral ((k0 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k7 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k6 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k5 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k4 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k3 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k2 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k1 ) .&. 0xff)) + `xor` rcs ! r + !j1 = ccs ! (0, fromIntegral ((k1 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k0 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k7 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k6 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k5 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k4 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k3 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k2 ) .&. 0xff)) + !j2 = ccs ! (0, fromIntegral ((k2 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k1 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k0 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k7 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k6 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k5 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k4 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k3 ) .&. 0xff)) + !j3 = ccs ! (0, fromIntegral ((k3 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k2 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k1 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k0 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k7 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k6 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k5 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k4 ) .&. 0xff)) + !j4 = ccs ! (0, fromIntegral ((k4 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k3 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k2 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k1 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k0 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k7 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k6 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k5 ) .&. 0xff)) + !j5 = ccs ! (0, fromIntegral ((k5 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k4 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k3 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k2 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k1 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k0 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k7 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k6 ) .&. 0xff)) + !j6 = ccs ! (0, fromIntegral ((k6 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k5 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k4 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k3 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k2 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k1 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k0 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k7 ) .&. 0xff)) + !j7 = ccs ! (0, fromIntegral ((k7 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((k6 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((k5 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((k4 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((k3 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((k2 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((k1 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((k0 ) .&. 0xff)) + !hv' = Whirlpool j0 j1 j2 j3 j4 j5 j6 j7 + !l0 = ccs ! (0, fromIntegral ((s0 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s7 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s6 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s5 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s4 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s3 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s2 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s1 ) .&. 0xff)) + `xor` j0 + !l1 = ccs ! (0, fromIntegral ((s1 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s0 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s7 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s6 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s5 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s4 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s3 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s2 ) .&. 0xff)) + `xor` j1 + !l2 = ccs ! (0, fromIntegral ((s2 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s1 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s0 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s7 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s6 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s5 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s4 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s3 ) .&. 0xff)) + `xor` j2 + !l3 = ccs ! (0, fromIntegral ((s3 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s2 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s1 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s0 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s7 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s6 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s5 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s4 ) .&. 0xff)) + `xor` j3 + !l4 = ccs ! (0, fromIntegral ((s4 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s3 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s2 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s1 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s0 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s7 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s6 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s5 ) .&. 0xff)) + `xor` j4 + !l5 = ccs ! (0, fromIntegral ((s5 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s4 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s3 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s2 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s1 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s0 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s7 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s6 ) .&. 0xff)) + `xor` j5 + !l6 = ccs ! (0, fromIntegral ((s6 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s5 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s4 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s3 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s2 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s1 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s0 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s7 ) .&. 0xff)) + `xor` j6 + !l7 = ccs ! (0, fromIntegral ((s7 `shiftR` 56) )) + `xor` ccs ! (1, fromIntegral ((s6 `shiftR` 48) .&. 0xff)) + `xor` ccs ! (2, fromIntegral ((s5 `shiftR` 40) .&. 0xff)) + `xor` ccs ! (3, fromIntegral ((s4 `shiftR` 32) .&. 0xff)) + `xor` ccs ! (4, fromIntegral ((s3 `shiftR` 24) .&. 0xff)) + `xor` ccs ! (5, fromIntegral ((s2 `shiftR` 16) .&. 0xff)) + `xor` ccs ! (6, fromIntegral ((s1 `shiftR` 8 ) .&. 0xff)) + `xor` ccs ! (7, fromIntegral ((s0 ) .&. 0xff)) + `xor` j7 + !st' = Whirlpool l0 l1 l2 l3 l4 l5 l6 l7 + +whirlpoolInit :: Context Whirlpool +whirlpoolInit = Context 0 0 B.empty initHash + +{-# NOINLINE whirlpoolUpdate #-} +whirlpoolUpdate :: Context Whirlpool -> ByteString -> Context Whirlpool +whirlpoolUpdate ctx@(Context n k w hv) s + | B.null s = ctx + | sizeRead < sizeToRead = Context (n + fromIntegral sizeRead) (k + sizeRead) (w <> s1) hv + | sizeRead >= sizeToRead = whirlpoolUpdate (Context (n + fromIntegral sizeToRead) 0 mempty (whirlpoolBlockUpdate hv (w <> s1)) ) s' + where + !sizeToRead = whirlpoolBlockSize - k + !s1 = B.take sizeToRead s + !s' = B.drop sizeToRead s + !sizeRead = B.length s1 + +{-# NOINLINE whirlpoolFinal #-} +whirlpoolFinal :: Context Whirlpool -> Whirlpool +whirlpoolFinal (Context n _ w hv) = foldl' whirlpoolBlockUpdate hv (lastChunk n w) + +{-# NOINLINE whirlpoolHash #-} +whirlpoolHash :: LBS.ByteString -> Whirlpool +whirlpoolHash = whirlpoolFinal . LBS.foldlChunks whirlpoolUpdate whirlpoolInit + +instance HashAlgorithm Whirlpool where + hashBlockSize = const whirlpoolBlockSize + hashDigestSize = const whirlpoolDigestSize + hashInit = whirlpoolInit + hashUpdate = whirlpoolUpdate + hashFinal = whirlpoolFinal diff --git a/test/Spec.hs b/test/Spec.hs new file mode 100644 --- /dev/null +++ b/test/Spec.hs @@ -0,0 +1,97 @@ +{-# LANGUAGE PackageImports #-} +{-# LANGUAGE TemplateHaskell #-} + +import qualified Data.ByteString.Lazy as LBS +import qualified Data.ByteString as B +import Data.ByteString.Internal +import Test.QuickCheck +import Test.QuickCheck.Monadic +import Control.Monad +import "hashing" Crypto.Hash +import Foreign.ForeignPtr +import Foreign.Ptr + +import qualified "cryptonite" Crypto.Hash as H + +data BoxedBS = BoxedBS { + unBoxedBS :: ByteString + } deriving Show + +instance Arbitrary BoxedBS where + arbitrary = do + g <- resize (2^10) (listOf arbitrary) + return $! BoxedBS (B.pack g) + +data BoxedLBS = BoxedLBS { + unBoxedLBS :: LBS.ByteString + } deriving Show + +instance Arbitrary BoxedLBS where + arbitrary = do + g <- resize (2^10) (listOf arbitrary) + return $! BoxedLBS (LBS.pack g) + +prop_ByteStringPtrAlignedTo8Bytes :: BoxedBS -> Property +prop_ByteStringPtrAlignedTo8Bytes (BoxedBS (PS fptr _ _)) = monadicIO $ do + t <- run (withForeignPtr fptr $ \ptr -> + return $! alignPtr ptr 8 == ptr) + assert t + +prop_SHA256HashLazyEqualsHashStrict (BoxedLBS lbs) = lhs == rhs + where lhs = hashLazy lbs :: SHA256 + rhs = hashFinal . foldl hashUpdate hashInit . LBS.toChunks $ lbs + +prop_SHA224HashLazyEqualsHashStrict (BoxedLBS lbs) = lhs == rhs + where lhs = hashLazy lbs :: SHA224 + rhs = hashFinal . foldl hashUpdate hashInit . LBS.toChunks $ lbs + +prop_MD5HashIsCorrect (BoxedLBS lbs) = show lhs == show rhs + where lhs = hashLazy lbs :: MD5 + rhs = H.hashlazy lbs :: H.Digest H.MD5 + +prop_WhirlpoolHashIsCorrect (BoxedLBS lbs) = show lhs == show rhs + where lhs = hashLazy lbs :: Whirlpool + rhs = H.hashlazy lbs :: H.Digest H.Whirlpool + +prop_SHA1HashIsCorrect (BoxedLBS lbs) = show lhs == show rhs + where lhs = hashLazy lbs :: SHA1 + rhs = H.hashlazy lbs :: H.Digest H.SHA1 + +prop_SHA224HashIsCorrect (BoxedLBS lbs) = show lhs == show rhs + where lhs = hashLazy lbs :: SHA224 + rhs = H.hashlazy lbs :: H.Digest H.SHA224 + +prop_SHA256HashIsCorrect (BoxedLBS lbs) = show lhs == show rhs + where lhs = hashLazy lbs :: SHA256 + rhs = H.hashlazy lbs :: H.Digest H.SHA256 + +prop_SHA384HashIsCorrect (BoxedLBS lbs) = show lhs == show rhs + where lhs = hashLazy lbs :: SHA384 + rhs = H.hashlazy lbs :: H.Digest H.SHA384 + +prop_SHA512HashIsCorrect (BoxedLBS lbs) = show lhs == show rhs + where lhs = hashLazy lbs :: SHA512 + rhs = H.hashlazy lbs :: H.Digest H.SHA512 + +data BoxedBSUnaligned = BoxedBSUnaligned { + unBoxedBSUnaligned :: ByteString + } deriving Show + +instance Arbitrary BoxedBSUnaligned where + arbitrary = do + g <- resize (2^10) (listOf arbitrary) + i <- elements [1, 3, 5, 7, 9, 11, 13, 17] + let bs = B.pack g + j <- choose (1, min 1 (B.length bs - i)) + return $! BoxedBSUnaligned . B.take j . B.drop i $ bs + +prop_SHA512HashUnalignedIsCorrect :: BoxedBSUnaligned -> Bool +prop_SHA512HashUnalignedIsCorrect (BoxedBSUnaligned bs) = show lhs == show rhs + where lhs = hash bs :: SHA512 + rhs = H.hash bs :: H.Digest H.SHA512 + +return [] +runTests = $quickCheckAll + +main :: IO () +main = void runTests