Discussion:
Map-to-integer for ciphers?
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박신환
2018-07-29 09:44:33 UTC
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For use of ciphers (SHA-256, RSA-2048, etc.), a type must be able to be injectively mapped to integers. It seems `Enum` is currently the closest thing that does this.
But `Enum` is supposed to be for arithmetic sequences, so it seems better to define a new typeclass. (Here named `Cipherable`)
There are some types that aren't members of `Enum`. For example, `Maybe`, `[]`, etc. They seem okay to be Cipherable. Hence:


{-# LANGUAGE ScopedTypeVariables #-}

instance Cipherable a => Cipherable (Maybe a) where
toEnum 0 = Nothing
toEnum n = Just (toEnum n)
fromEnum Nothing = 0
fromEnum (Just x) = 1 + fromEnum x

instance forall a. (Cipherable a, Bounded a) => Cipherable [a] where
toEnum 0 = []
toEnum n = let
(q,r) = (n-1) `quotRem` (1 + fromEnum (maxBound :: a))
in toEnum r : toEnum q
fromEnum [] = 0
fromEnum (x:xs) = 1 + fromEnum x + (1 + fromEnum (maxBound :: a)) * fromEnum xs

instance Cipherable Void where
toEnum = errorWithoutStackTrace "Cipher.Cipherable.Void.toEnum"
fromEnum = absurd


(Besides, it is possible to re-write that of `[]` without ScopedTypeVariables? I see no way...)
박신환
2018-07-29 09:47:52 UTC
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For use of ciphers (SHA-256, RSA-2048, etc.), a type must be able to be injectively mapped to integers. It seems `Enum` is currently the closest thing that does this.

But `Enum` is supposed to be for arithmetic sequences, so it seems better to define a new typeclass. (Here named `Cipherable`)

Here, `Cipherable` has `deCipher :: Natural -> a` and `enCipher :: a -> Natural`.

There are some types that aren't members of `Enum`. For example, `Maybe`, `[]`, etc. They seem okay to be Cipherable. Hence:




{-# LANGUAGE ScopedTypeVariables #-}

instance Cipherable a => Cipherable (Maybe a) where
deCipher 0 = Nothing
deCipher n = Just (toEnum n)
enCipher Nothing = 0
enCipher (Just x) = 1 + fromEnum x

instance forall a. (Cipherable a, Bounded a) => Cipherable [a] where
deCipher 0 = []
deCipher n = let
(q,r) = (n-1) `quotRem` (1 + fromEnum (maxBound :: a))
in toEnum r : toEnum q
enCipher [] = 0
enCipher (x:xs) = 1 + fromEnum x + (1 + fromEnum (maxBound :: a)) * fromEnum xs

instance Cipherable Void where
deCipher = errorWithoutStackTrace "Cipher.Cipherable.Void.deCipher"
enCipher = absurd


(Besides, it is possible to re-write that of `[]` without ScopedTypeVariables? I see no way...)
박신환
2018-07-29 09:50:24 UTC
Permalink
For use of ciphers (SHA-256, RSA-2048, etc.), a type must be able to be injectively mapped to integers. It seems `Enum` is currently the closest thing that does this.

But `Enum` is supposed to be for arithmetic sequences, so it seems better to define a new typeclass. (Here named `Cipherable`)

Here, `Cipherable` has `deCipher :: Natural -> a` and `enCipher :: a -> Natural`.

There are some types that aren't members of `Enum`. For example, `Maybe`, `[]`, etc. They seem okay to be Cipherable. Hence:




{-# LANGUAGE ScopedTypeVariables #-}

instance Cipherable a => Cipherable (Maybe a) where
deCipher 0 = Nothing
deCipher n = Just (deCipher (n-1))
enCipher Nothing = 0
enCipher (Just x) = 1 + enCipher x

instance forall a. (Cipherable a, Bounded a) => Cipherable [a] where
deCipher 0 = []
deCipher n = let
(q,r) = (n-1) `quotRem` (1 + enCipher (maxBound :: a))
in deCipher r : deCipher q
enCipher [] = 0
enCipher (x:xs) = 1 + enCipher x + (1 + enCipher (maxBound :: a)) * fromEnum xs

instance Cipherable Void where
deCipher = errorWithoutStackTrace "Cipher.Cipherable.Void.deCipher"
enCipher = absurd


(Besides, it is possible to re-write that of `[]` without ScopedTypeVariables? I see no way...)
Henning Thielemann
2018-07-29 09:53:44 UTC
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Post by 박신환
instance forall a. (Cipherable a, Bounded a) => Cipherable [a] where
    deCipher 0 = []
    deCipher n = let
        (q,r) = (n-1) `quotRem` (1 + enCipher (maxBound :: a))
        in deCipher r : deCipher q
let (q,r) = (n-1) `quotRem` (1 + enCipher (maxBound `asTypeOf` rd))
rd = deCipher r
in rd : deCipher q
Post by 박신환
    enCipher []     = 0
    enCipher (x:xs) = 1 + enCipher x + (1 + enCipher (maxBound :: a)) * fromEnum xs
maxBound `asTypeOf` x

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