    -- |
    -- 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.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 exponent 'e'
                 -> Maybe (PublicKey, PrivateKey)
    generateWith :: (Integer, Integer)
    -> Int -> Integer -> Maybe (PublicKey, PrivateKey)
    generateWith (Integer
    p,Integer
    q) Int
    size Integer
    e =
        case Integer -> Integer -> Maybe Integer
    inverse Integer
    e Integer
    phi of
            Maybe Integer
    Nothing -> Maybe (PublicKey, PrivateKey)
    forall a. Maybe a
    Nothing
            Just Integer
    d  -> (PublicKey, PrivateKey) -> Maybe (PublicKey, PrivateKey)
    forall a. a -> Maybe a
    Just (PublicKey
    pub,Integer -> PrivateKey
    priv Integer
    d)
      where n :: Integer
    n   = Integer
    pInteger -> Integer -> Integer
    forall a. Num a => a -> a -> a
    *Integer
    q
            phi :: Integer
    phi = (Integer
    pInteger -> Integer -> Integer
    forall a. Num a => a -> a -> a
    -Integer
    1)Integer -> Integer -> Integer
    forall a. Num a => a -> a -> a
    *(Integer
    qInteger -> Integer -> Integer
    forall a. Num a => a -> a -> a
    -Integer
    1)
            -- q and p should be *distinct* *prime* numbers, hence always coprime
            qinv :: Integer
    qinv = Integer -> Integer -> Integer
    inverseCoprimes Integer
    q Integer
    p
            pub :: PublicKey
    pub = PublicKey { public_size :: Int
    public_size = Int
    size
                            , public_n :: Integer
    public_n    = Integer
    n
                            , public_e :: Integer
    public_e    = Integer
    e
                            }
            priv :: Integer -> PrivateKey
    priv Integer
    d = PrivateKey { private_pub :: PublicKey
    private_pub  = PublicKey
    pub
                                , private_d :: Integer
    private_d    = Integer
    d
                                , private_p :: Integer
    private_p    = Integer
    p
                                , private_q :: Integer
    private_q    = Integer
    q
                                , private_dP :: Integer
    private_dP   = Integer
    d Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    `mod` (Integer
    pInteger -> Integer -> Integer
    forall a. Num a => a -> a -> a
    -Integer
    1)
                                , private_dQ :: Integer
    private_dQ   = Integer
    d Integer -> Integer -> Integer
    forall a. Integral a => a -> a -> a
    `mod` (Integer
    qInteger -> Integer -> Integer
    forall a. Num a => a -> a -> a
    -Integer
    1)
                                , private_qinv :: Integer
    private_qinv = Integer
    qinv
                                }

    -- | generate a pair of (private, public) key of size in bytes.
    generate :: MonadRandom m
             => Int     -- ^ size in bytes
             -> Integer -- ^ RSA public exponent 'e'
             -> m (PublicKey, PrivateKey)
    generate :: forall (m :: * -> *).
    MonadRandom m =>
    Int -> Integer -> m (PublicKey, PrivateKey)
    generate Int
    size Integer
    e = m (PublicKey, PrivateKey)
    loop
      where
        loop :: m (PublicKey, PrivateKey)
    loop = do -- loop until we find a valid key pair given e
            pq <- m (Integer, Integer)
    generatePQ
            case generateWith pq size e of
                Maybe (PublicKey, PrivateKey)
    Nothing -> m (PublicKey, PrivateKey)
    loop
                Just (PublicKey, PrivateKey)
    pp -> (PublicKey, PrivateKey) -> m (PublicKey, PrivateKey)
    forall a. a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return (PublicKey, PrivateKey)
    pp
        generatePQ :: m (Integer, Integer)
    generatePQ = do
            p <- Int -> m Integer
    forall (m :: * -> *). MonadRandom m => Int -> m Integer
    generatePrime (Int
    8 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    * (Int
    size Int -> Int -> Int
    forall a. Integral a => a -> a -> a
    `div` Int
    2))
            q <- generateQ p
            return (p,q)
        generateQ :: Integer -> m Integer
    generateQ Integer
    p = do
            q <- Int -> m Integer
    forall (m :: * -> *). MonadRandom m => Int -> m Integer
    generatePrime (Int
    8 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    * (Int
    size Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - (Int
    size Int -> Int -> Int
    forall a. Integral a => a -> a -> a
    `div` Int
    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 :: forall (m :: * -> *). MonadRandom m => Integer -> m Blinder
    generateBlinder Integer
    n =
        (\Integer
    r -> Integer -> Integer -> Blinder
    Blinder Integer
    r (Integer -> Integer -> Integer
    inverseCoprimes Integer
    r Integer
    n)) (Integer -> Blinder) -> m Integer -> m Blinder
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Integer -> m Integer
    forall {m :: * -> *}. MonadRandom m => Integer -> m Integer
    generateMax Integer
    n