·< - a Haskell reverse-engineering challenge on the 2020 hxpCTF

Main.hs

#!/usr/bin/env runhaskell
{-# LANGUAGE OverloadedStrings #-}
import Prelude hiding (replicate, putStrLn)
import Data.List hiding (replicate)
import Data.Tuple
import Data.Ord
import Data.Function
import Data.ByteString (replicate, ByteString)
import Data.ByteString.Char8 (putStrLn, pack)
import Control.Monad
import Control.Arrow
import Control.Applicative
import Crypto.Cipher.AES
import Crypto.Hash.SHA256
import Unsafe.Coerce

c = "\xd7\xc8\x35\x14\xc4\x27\xcd\x6f\x78\x3a\x80\x57\x76\xb0\xfd\x42\x25\xe4\x87\x5f\x99\x28\x87\x0a\x06\xef\x63\x81\x44"

-- infixr 0 $
-- infixr 1 >>>     --- flip (.)
-- infixr 1 <<<     --- (.)
-- infixr 1 ^>>     --- flip (.)
-- infixl 1 &
-- infixr 1 >>=
-- infixl 4 <$>
-- infixl 4 <*>
-- infixl 4 <**>
-- infixr 9 .

main = do
    input <- getContents
    putStrLn (calculateOutput (read input))

calculateOutput :: [Int] -> ByteString
calculateOutput input = maybe "wrong" (doAES input) (unsafeCoerce (checkInput input))

checkInput :: [Int] -> Bool
checkInput input = and [or (map (\x2 -> x2 input y x) checks)
                            | x <- [0..39], y <- [0..39]]

indexOf :: Eq a => [a] -> a -> Int
indexOf xs x = unsingle $ elemIndices x xs
    where
    unsingle [n] = n

mystery4 p x0 x1 a = (indexOf p x1) >= (indexOf p (x0 a))

checks :: [[Int] -> Int -> Int -> Bool]
checks = [
    (\ input x y -> mystery4 (nthPerm x) (input !!) y x),
    (\ input x y -> (input !! x) == y),
    (\ input x y -> mystery4 (nthPerm (40 + y)) (indexOf input) x y)]

lcg :: [Int]
lcg = tail (iterate next 44)
    where
    next x = (1337 * x + 42) `mod` 400013

lcgChunks :: [[Int]]
lcgChunks = tail $ fst <$> iterate (\(_, x) -> (take 40 x, drop 40 x)) ([], lcg)

randomPermutations :: [[Int]]
randomPermutations = (\x -> sortBy (comparing (x !!)) [0 .. 39]) <$> lcgChunks

nthPerm :: Int -> [Int]
nthPerm n = randomPermutations !! n

doAES :: [Int] -> a -> ByteString
doAES x _ = decryptCTR (initAES (hash (pack (show x)))) (replicate 16 0) c