    -- |
    -- Module      : Crypto.PubKey.Rabin.Modified
    -- License     : BSD-style
    -- Maintainer  : Carlos Rodriguez-Vega <crodveg@yahoo.es>
    -- Stability   : experimental
    -- Portability : unknown
    --
    -- Modified-Rabin public-key digital signature algorithm.
    -- See algorithm 11.30 in "Handbook of Applied Cryptography" by Alfred J. Menezes et al.
    --
    {-# LANGUAGE DeriveDataTypeable #-}
    module Crypto.PubKey.Rabin.Modified
        ( PublicKey(..)
        , PrivateKey(..)
        , generate
        , sign
        , verify
        ) where

    import           Data.ByteString
    import           Data.Data

    import           Crypto.Hash
    import           Crypto.Number.ModArithmetic (expSafe, jacobi)
    import           Crypto.Number.Serialize (os2ip)
    import           Crypto.PubKey.Rabin.Types
    import           Crypto.Random.Types

    -- | Represent a Modified-Rabin public key.
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    public_n    :: Integer  -- ^ public p*q
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    -- | Represent a Modified-Rabin private key.
    data PrivateKey = PrivateKey
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    limit then Error -> Either Error Integer
    forall a b. a -> Either a b
    Left Error
    MessageTooLong
            else let h' :: Integer
    h' = Integer
    16Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    *Integer
    h Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    + Integer
    6
                  in case Integer -> Integer -> Maybe Integer
    jacobi Integer
    h' Integer
    n of
                        Just Integer
    1    -> Integer -> Either Error Integer
    forall a b. b -> Either a b
    Right (Integer -> Either Error Integer)
    -> Integer -> Either Error Integer
    forall a b. (a -> b) -> a -> b
    $ Integer -> Integer -> Integer -> Integer
    expSafe Integer
    h' Integer
    d Integer
    n
                        Just (-1) -> Integer -> Either Error Integer
    forall a b. b -> Either a b
    Right (Integer -> Either Error Integer)
    -> Integer -> Either Error Integer
    forall a b. (a -> b) -> a -> b
    $ Integer -> Integer -> Integer -> Integer
    expSafe (Integer
    h' Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    `div` Integer
    2) Integer
    d Integer
    n
                        Maybe Integer
    _         -> Error -> Either Error Integer
    forall a b. a -> Either a b
    Left Error
    InvalidParameters

    -- | Verify signature using hash algorithm and public key.
    verify :: HashAlgorithm hash
           => PublicKey     -- ^ public key
           -> hash          -- ^ hash function
           -> ByteString    -- ^ message
           -> Integer       -- ^ signature
           -> Bool
    verify :: forall hash.
    HashAlgorithm hash =>
    PublicKey -> hash -> ByteString -> PrimeCondition
    verify PublicKey
    pk hash
    hashAlg ByteString
    m Integer
    s =
        let n :: Integer
    n   = PublicKey -> Integer
    public_n PublicKey
    pk
            h :: Integer
    h   = Digest hash -> Integer
    forall ba. ByteArrayAccess ba => ba -> Integer
    os2ip (Digest hash -> Integer) -> Digest hash -> Integer
    forall a b. (a -> b) -> a -> b
    $ hash -> ByteString -> Digest hash
    forall ba alg.
    (ByteArrayAccess ba, HashAlgorithm alg) =>
    alg -> ba -> Digest alg
    hashWith hash
    hashAlg ByteString
    m
            s' :: Integer
    s'  = Integer -> Integer -> Integer -> Integer
    expSafe Integer
    s Integer
    2 Integer
    n
            s'' :: Integer
    s'' = case Integer
    s' Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    `mod` Integer
    8 of
                Integer
    6 -> Integer
    s'
                Integer
    3 -> Integer
    2Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    *Integer
    s'
                Integer
    7 -> Integer
    n Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    - Integer
    s'
                Integer
    2 -> Integer
    2Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    *(Integer
    n Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    - Integer
    s')
                Integer
    _ -> Integer
    0
         in case Integer
    s'' Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    `mod` Integer
    16 of
                Integer
    6 -> let h' :: Integer
    h' = (Integer
    s'' Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    - Integer
    6) Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    `div` Integer
    16
                      in Integer
    h' Integer -> PrimeCondition
    forall a. Eq a => a -> a -> Bool
    == Integer
    h
                Integer
    _ -> Bool
    False