    -- |
    -- Module      : Crypto.PubKey.RSA
    -- License     : BSD-style
    -- Maintainer  : Vincent Hanquez <vincent@snarc.org>
    -- Stability   : experimental
    -- Portability : Good
    --
    module Crypto.PubKey.RSA
        ( Error(..)
        , PublicKey(..)
        , PrivateKey(..)
        , Blinder(..)
        -- * generation function
        , generateWith
        , generate
        , generateBlinder
        ) where

    import Crypto.Internal.Imports
    import Crypto.Random.Types
    import Crypto.Number.ModArithmetic (inverse, inverseCoprimes)
    import Crypto.Number.Generate (generateMax)
    import Crypto.Number.Prime (generatePrime)
    import Crypto.PubKey.RSA.Types

    {-
    -- some bad implementation will not serialize ASN.1 integer properly, leading
    -- to negative modulus.
    -- TODO : Find a better place for this
    toPositive :: Integer -> Integer
    toPositive int
        | int < 0   = uintOfBytes $ bytesOfInt int
        | otherwise = int
      where uintOfBytes = foldl (\acc n -> (acc `shiftL` 8) + fromIntegral n) 0
            bytesOfInt :: Integer -> [Word8]
            bytesOfInt n = if testBit (head nints) 7 then nints else 0xff : nints
              where nints = reverse $ plusOne $ reverse $ map complement $ bytesOfUInt (abs n)
                    plusOne []     = [1]
                    plusOne (x:xs) = if x == 0xff then 0 : plusOne xs else (x+1) : xs
                    bytesOfUInt x = reverse (list x)
                      where list i = if i <= 0xff then [fromIntegral i] else (fromIntegral i .&. 0xff) : list (i `shiftR` 8)
    -}

    -- | Generate a key pair given p and q.
    --
    -- p and q need to be distinct prime numbers.
    --
    -- e need to be coprime to phi=(p-1)*(q-1). If that's not the
    -- case, the function will not return a key pair.
    -- A small hamming weight results in better performance.
    --
    -- * e=0x10001 is a popular choice
    --
    -- * e=3 is popular as well, but proven to not be as secure for some cases.
    --
    generateWith :: (Integer, Integer) -- ^ chosen distinct primes p and q
                 -> Int                -- ^ size in bytes
                 -> Integer            -- ^ RSA public exponant 'e'
                 -> Maybe (PublicKey, PrivateKey)
    generateWith (p,q) size e =
        case inverse e phi of
            Nothing -> Nothing
            Just d  -> Just (pub,priv d)
      where n   = p*q
            phi = (p-1)*(q-1)
            -- q and p should be *distinct* *prime* numbers, hence always coprime
            qinv = inverseCoprimes q p
            pub = PublicKey { public_size = size
                            , public_n    = n
                            , public_e    = e
                            }
            priv d = PrivateKey { private_pub  = pub
                                , private_d    = d
                                , private_p    = p
                                , private_q    = q
                                , private_dP   = d `mod` (p-1)
                                , private_dQ   = d `mod` (q-1)
                                , private_qinv = qinv
                                }

    -- | generate a pair of (private, public) key of size in bytes.
    generate :: MonadRandom m
             => Int     -- ^ size in bytes
             -> Integer -- ^ RSA public exponant 'e'
             -> m (PublicKey, PrivateKey)
    generate size e = loop
      where
        loop = do -- loop until we find a valid key pair given e
            pq <- generatePQ
            case generateWith pq size e of
                Nothing -> loop
                Just pp -> return pp
        generatePQ = do
            p <- generatePrime (8 * (size `div` 2))
            q <- generateQ p
            return (p,q)
        generateQ p = do
            q <- generatePrime (8 * (size - (size `div` 2)))
            if p == q then generateQ p else return q

    -- | Generate a blinder to use with decryption and signing operation
    --
    -- the unique parameter apart from the random number generator is the
    -- public key value N.
    generateBlinder :: MonadRandom m
                    => Integer -- ^ RSA public N parameter.
                    -> m Blinder
    generateBlinder n =
        (\r -> Blinder r (inverseCoprimes r n)) <$> generateMax n