-- |
-- Module      : Crypto.PubKey.Rabin.RW
-- License     : BSD-style
-- Maintainer  : Carlos Rodriguez-Vega <crodveg@yahoo.es>
-- Stability   : experimental
-- Portability : unknown
--
-- Rabin-Williams cryptosystem for public-key encryption and digital signature. 
-- See pages 323 - 324 in "Computational Number Theory and Modern Cryptography" by Song Y. Yan.
-- Also inspired by https://github.com/vanilala/vncrypt/blob/master/vncrypt/vnrw_gmp.c.
-- 
{-# LANGUAGE DeriveDataTypeable #-}
module Crypto.PubKey.Rabin.RW
    ( PublicKey(..)
    , PrivateKey(..)
    , generate
    , encrypt
    , encryptWithSeed
    , decrypt
    , sign
    , verify
    ) where

import           Data.ByteString
import           Data.Data

import           Crypto.Hash
import           Crypto.Number.Basic (numBytes)
import           Crypto.Number.ModArithmetic (expSafe, jacobi)
import           Crypto.Number.Serialize (i2osp, i2ospOf_, os2ip)
import           Crypto.PubKey.Rabin.OAEP
import           Crypto.PubKey.Rabin.Types
import           Crypto.Random.Types

-- | Represent a Rabin-Williams public key.
data PublicKey = PublicKey
    { PublicKey -> Int
public_size :: Int      -- ^ size of key in bytes
    , PublicKey -> Integer
public_n    :: Integer  -- ^ public p*q
    } deriving (Int -> PublicKey -> ShowS
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-- | Represent a Rabin-Williams private key.
data PrivateKey = PrivateKey
    { PrivateKey -> PublicKey
private_pub :: PublicKey
    , PrivateKey -> Integer
private_p   :: Integer   -- ^ p prime number
    , PrivateKey -> Integer
private_q   :: Integer   -- ^ q prime number
    , PrivateKey -> Integer
private_d   :: Integer
    } deriving (Int -> PrivateKey -> ShowS
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-- | Generate a pair of (private, public) key of size in bytes.
-- Prime p is congruent 3 mod 8 and prime q is congruent 7 mod 8.
generate :: MonadRandom m
         => Int           
         -> m (PublicKey, PrivateKey)
generate :: forall (m :: * -> *).
MonadRandom m =>
Int -> m (PublicKey, PrivateKey)
generate Int
size = do
    (Integer
p, Integer
q) <- forall (m :: * -> *).
MonadRandom m =>
Int -> PrimeCondition -> PrimeCondition -> m (Integer, Integer)
generatePrimes Int
size (\Integer
p -> Integer
p forall a. Integral a => a -> a -> a
`mod` Integer
8 forall a. Eq a => a -> a -> Bool
== Integer
3) (\Integer
q -> Integer
q forall a. Integral a => a -> a -> a
`mod` Integer
8 forall a. Eq a => a -> a -> Bool
== Integer
7) 
    forall (m :: * -> *) a. Monad m => a -> m a
return (Integer -> Integer -> (PublicKey, PrivateKey)
generateKeys Integer
p Integer
q)
  where 
    generateKeys :: Integer -> Integer -> (PublicKey, PrivateKey)
generateKeys Integer
p Integer
q =
        let n :: Integer
n = Integer
pforall a. Num a => a -> a -> a
*Integer
q   
            d :: Integer
d = ((Integer
p forall a. Num a => a -> a -> a
- Integer
1)forall a. Num a => a -> a -> a
*(Integer
q forall a. Num a => a -> a -> a
- Integer
1) forall a. Integral a => a -> a -> a
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4 forall a. Num a => a -> a -> a
+ Integer
1) forall a. Integral a => a -> a -> a
`div` Integer
2
            publicKey :: PublicKey
publicKey = PublicKey { public_size :: Int
public_size = Int
size
                                    , public_n :: Integer
public_n    = Integer
n }
            privateKey :: PrivateKey
privateKey = PrivateKey { private_pub :: PublicKey
private_pub = PublicKey
publicKey
                                    , private_p :: Integer
private_p   = Integer
p
                                    , private_q :: Integer
private_q   = Integer
q
                                    , private_d :: Integer
private_d   = Integer
d }
            in (PublicKey
publicKey, PrivateKey
privateKey)

-- | Encrypt plaintext using public key an a predefined OAEP seed.
--
-- See algorithm 8.11 in "Handbook of Applied Cryptography" by Alfred J. Menezes et al.
encryptWithSeed :: HashAlgorithm hash
                => ByteString                               -- ^ Seed
                -> OAEPParams hash ByteString ByteString    -- ^ OAEP padding
                -> PublicKey                                -- ^ public key
                -> ByteString                               -- ^ plaintext
                -> Either Error ByteString
encryptWithSeed :: forall hash.
HashAlgorithm hash =>
ByteString
-> OAEPParams hash ByteString ByteString
-> PublicKey
-> ByteString
-> Either Error ByteString
encryptWithSeed ByteString
seed OAEPParams hash ByteString ByteString
oaep PublicKey
pk ByteString
m =
    let n :: Integer
n = PublicKey -> Integer
public_n PublicKey
pk
        k :: Int
k = Integer -> Int
numBytes Integer
n
     in do
        ByteString
m'  <- forall hash.
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-> Int
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m
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m'' <- Integer -> Integer -> Either Error Integer
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n forall a b. (a -> b) -> a -> b
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ep2 Integer
n Integer
m''

-- | Encrypt plaintext using public key.
encrypt :: (HashAlgorithm hash, MonadRandom m)
        => OAEPParams hash ByteString ByteString    -- ^ OAEP padding parameters
        -> PublicKey                                -- ^ public key
        -> ByteString                               -- ^ plaintext 
        -> m (Either Error ByteString)
encrypt :: forall hash (m :: * -> *).
(HashAlgorithm hash, MonadRandom m) =>
OAEPParams hash ByteString ByteString
-> PublicKey -> ByteString -> m (Either Error ByteString)
encrypt OAEPParams hash ByteString ByteString
oaep PublicKey
pk ByteString
m = do
    ByteString
seed <- forall (m :: * -> *) byteArray.
(MonadRandom m, ByteArray byteArray) =>
Int -> m byteArray
getRandomBytes Int
hashLen
    forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ forall hash.
HashAlgorithm hash =>
ByteString
-> OAEPParams hash ByteString ByteString
-> PublicKey
-> ByteString
-> Either Error ByteString
encryptWithSeed ByteString
seed OAEPParams hash ByteString ByteString
oaep PublicKey
pk ByteString
m
  where
    hashLen :: Int
hashLen = forall a. HashAlgorithm a => a -> Int
hashDigestSize (forall hash seed output. OAEPParams hash seed output -> hash
oaepHash OAEPParams hash ByteString ByteString
oaep)   

-- | Decrypt ciphertext using private key.
decrypt :: HashAlgorithm hash
        => OAEPParams hash ByteString ByteString    -- ^ OAEP padding parameters
        -> PrivateKey                               -- ^ private key
        -> ByteString                               -- ^ ciphertext
        -> Maybe ByteString
decrypt :: forall hash.
HashAlgorithm hash =>
OAEPParams hash ByteString ByteString
-> PrivateKey -> ByteString -> Maybe ByteString
decrypt OAEPParams hash ByteString ByteString
oaep PrivateKey
pk ByteString
c =
    let d :: Integer
d  = PrivateKey -> Integer
private_d PrivateKey
pk    
        n :: Integer
n  = PublicKey -> Integer
public_n forall a b. (a -> b) -> a -> b
$ PrivateKey -> PublicKey
private_pub PrivateKey
pk
        k :: Int
k  = Integer -> Int
numBytes Integer
n
        c' :: ByteString
c' = forall ba. ByteArray ba => Int -> Integer -> ba
i2ospOf_ Int
k forall a b. (a -> b) -> a -> b
$ Integer -> Integer -> Integer
dp2 Integer
n forall a b. (a -> b) -> a -> b
$ Integer -> Integer -> Integer -> Integer
dp1 Integer
d Integer
n forall a b. (a -> b) -> a -> b
$ forall ba. ByteArrayAccess ba => ba -> Integer
os2ip ByteString
c
     in case forall hash.
HashAlgorithm hash =>
OAEPParams hash ByteString ByteString
-> Int -> ByteString -> Either Error ByteString
unpad OAEPParams hash ByteString ByteString
oaep Int
k ByteString
c' of
            Left Error
_  -> forall a. Maybe a
Nothing
            Right ByteString
p -> forall a. a -> Maybe a
Just ByteString
p   

-- | Sign message using hash algorithm and private key.
sign :: HashAlgorithm hash
     => PrivateKey  -- ^ private key
     -> hash        -- ^ hash function
     -> ByteString  -- ^ message to sign
     -> Either Error Integer
sign :: forall hash.
HashAlgorithm hash =>
PrivateKey -> hash -> ByteString -> Either Error Integer
sign PrivateKey
pk hash
hashAlg ByteString
m =
    let d :: Integer
d = PrivateKey -> Integer
private_d PrivateKey
pk
        n :: Integer
n = PublicKey -> Integer
public_n forall a b. (a -> b) -> a -> b
$ PrivateKey -> PublicKey
private_pub PrivateKey
pk
     in do
        Integer
m' <- Integer -> Integer -> Either Error Integer
ep1 Integer
n forall a b. (a -> b) -> a -> b
$ forall ba. ByteArrayAccess ba => ba -> Integer
os2ip forall a b. (a -> b) -> a -> b
$ forall ba alg.
(ByteArrayAccess ba, HashAlgorithm alg) =>
alg -> ba -> Digest alg
hashWith hash
hashAlg ByteString
m
        forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ Integer -> Integer -> Integer -> Integer
dp1 Integer
d Integer
n Integer
m' 

-- | 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  = forall ba. ByteArrayAccess ba => ba -> Integer
os2ip forall a b. (a -> b) -> a -> b
$ forall ba alg.
(ByteArrayAccess ba, HashAlgorithm alg) =>
alg -> ba -> Digest alg
hashWith hash
hashAlg ByteString
m
        h' :: Integer
h' = Integer -> Integer -> Integer
dp2 Integer
n forall a b. (a -> b) -> a -> b
$ Integer -> Integer -> Integer
ep2 Integer
n Integer
s
     in Integer
h' forall a. Eq a => a -> a -> Bool
== Integer
h

-- | Encryption primitive 1
ep1 :: Integer -> Integer -> Either Error Integer
ep1 :: Integer -> Integer -> Either Error Integer
ep1 Integer
n Integer
m =
    let m' :: Integer
m'   = Integer
2forall a. Num a => a -> a -> a
*Integer
m forall a. Num a => a -> a -> a
+ Integer
1
        m'' :: Integer
m''  = Integer
2forall a. Num a => a -> a -> a
*Integer
m'
        m''' :: Integer
m''' = Integer
2forall a. Num a => a -> a -> a
*Integer
m''
     in case Integer -> Integer -> Maybe Integer
jacobi Integer
m' Integer
n of
            Just (-1) | Integer
m'' forall a. Ord a => a -> a -> Bool
< Integer
n -> forall a b. b -> Either a b
Right Integer
m''
            Just Integer
1 | Integer
m''' forall a. Ord a => a -> a -> Bool
< Integer
n   -> forall a b. b -> Either a b
Right Integer
m'''
            Maybe Integer
_                   -> forall a b. a -> Either a b
Left Error
InvalidParameters

-- | Encryption primitive 2
ep2 :: Integer -> Integer -> Integer
ep2 :: Integer -> Integer -> Integer
ep2 Integer
n Integer
m = Integer -> Integer -> Integer -> Integer
expSafe Integer
m Integer
2 Integer
n

-- | Decryption primitive 1
dp1 :: Integer -> Integer -> Integer -> Integer
dp1 :: Integer -> Integer -> Integer -> Integer
dp1 Integer
d Integer
n Integer
c = Integer -> Integer -> Integer -> Integer
expSafe Integer
c Integer
d Integer
n

-- | Decryption primitive 2
dp2 :: Integer -> Integer -> Integer
dp2 :: Integer -> Integer -> Integer
dp2 Integer
n Integer
c = let c' :: Integer
c'  = Integer
c forall a. Integral a => a -> a -> a
`div` Integer
2
              c'' :: Integer
c'' = (Integer
n forall a. Num a => a -> a -> a
- Integer
c) forall a. Integral a => a -> a -> a
`div` Integer
2
           in case Integer
c forall a. Integral a => a -> a -> a
`mod` Integer
4 of
                Integer
0 -> ((Integer
c' forall a. Integral a => a -> a -> a
`div` Integer
2 forall a. Num a => a -> a -> a
- Integer
1) forall a. Integral a => a -> a -> a
`div` Integer
2)
                Integer
1 -> ((Integer
c'' forall a. Integral a => a -> a -> a
`div` Integer
2 forall a. Num a => a -> a -> a
- Integer
1) forall a. Integral a => a -> a -> a
`div` Integer
2)
                Integer
2 -> ((Integer
c' forall a. Num a => a -> a -> a
- Integer
1) forall a. Integral a => a -> a -> a
`div` Integer
2)
                Integer
_ -> ((Integer
c'' forall a. Num a => a -> a -> a
- Integer
1) forall a. Integral a => a -> a -> a
`div` Integer
2)