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@L-TChen
Last active May 27, 2018
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FLOLAC'18 Exercise: A case-sensitive Caesar cipher and decipher based on frequency analysis, written in Haskell.
{-# LANGUAGE UnicodeSyntax #-}
{-# LANGUAGE TupleSections #-}
module Caesar where
import Data.Map (Map, fromList, fromListWith, unionWith)
import Data.Char
import Data.List
import Data.Function
encode Int String String
encode n str = rotate n <$> str
decode String (String, Int)
decode xs = fst $ minimumBy (compare `on` snd) $ scores xs
scores String [((String, Int), Float)]
scores xs = do
i [0..25]
let cand = encode (-i) xs in
return ((cand, i), distance refFreqTab $ mkFreqTab cand)
-- Rotate English alphabet only
rotate Int Char Char
rotate m x = case (isAsciiUpper x, isAsciiLower x) of
(True, _) chr $ ((m + ord x - ord 'A') `mod` 26) + ord 'A'
(_, True) chr $ ((m + ord x - ord 'a') `mod` 26) + ord 'a'
_ x
-- Euclidean distance
distance Map Char Float Map Char Float Float
distance xs ys = sqrt $ sum $ unionWith (\x y (x - y)^2) xs ys
-- Make a frequence table for English alphabet
mkFreqTab String Map Char Float
mkFreqTab xs = (100/total *) <$> fromListWith (+) (((,1) <$> xs') ++ ((,0) <$> ['A'..'Z']))
where xs' = filter isAsciiUpper (toUpper <$> xs)
total = fromIntegral $ length xs'
-- https://en.wikipedia.org/wiki/Letter_frequency#Relative_frequencies_of_letters_in_the_English_language
refFreqTab Map Char Float
refFreqTab = fromList
[('E', 12.702), ('T', 9.056), ('A', 8.167), ('O', 7.507), ('I', 6.966), ('N', 6.749),
('S', 6.749), ('H', 6.094), ('R', 5.987), ('D', 4.253), ('L', 4.025), ('C', 2.782),
('U', 2.758), ('M', 2.406), ('W', 2.36), ('F', 2.228), ('G', 2.015), ('Y', 1.974),
('P', 1.929), ('B', 1.492), ('V', 0.978), ('K', 0.772), ('J', 0.153), ('X', 0.15),
('Q', 0.095), ('Z', 0.074)]
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