{-# 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
data PublicKey = PublicKey
{ PublicKey -> Int
public_size :: Int
, PublicKey -> Integer
public_n :: Integer
} deriving (Int -> PublicKey -> ShowS
[PublicKey] -> ShowS
PublicKey -> String
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data PrivateKey = PrivateKey
{ PrivateKey -> PublicKey
private_pub :: PublicKey
, PrivateKey -> Integer
private_p :: Integer
, PrivateKey -> Integer
private_q :: Integer
, PrivateKey -> Integer
private_d :: Integer
} deriving (Int -> PrivateKey -> ShowS
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generate :: MonadRandom m
=> Int
-> m (PublicKey, PrivateKey)
generate :: forall (m :: * -> *).
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Int -> m (PublicKey, PrivateKey)
generate Int
size = do
(Integer
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q) <- forall (m :: * -> *).
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generatePrimes Int
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7)
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ 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
n forall a. Num a => a -> a -> a
- Integer
p forall a. Num a => a -> a -> a
- Integer
q forall a. Num a => a -> a -> a
+ Integer
5) forall a. Integral a => a -> a -> a
`div` Integer
8
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)
sign :: HashAlgorithm hash
=> PrivateKey
-> hash
-> ByteString
-> Either Error Integer
sign :: forall hash.
HashAlgorithm hash =>
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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
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
limit :: Integer
limit = (Integer
n forall a. Num a => a -> a -> a
- Integer
6) forall a. Integral a => a -> a -> a
`div` Integer
16
in if Integer
h forall a. Ord a => a -> a -> Bool
> Integer
limit then forall a b. a -> Either a b
Left Error
MessageTooLong
else let h' :: Integer
h' = Integer
16forall a. Num a => a -> a -> a
*Integer
h forall a. Num a => a -> a -> a
+ Integer
6
in case Integer -> Integer -> Maybe Integer
jacobi Integer
h' Integer
n of
Just Integer
1 -> forall a b. b -> Either a b
Right forall a b. (a -> b) -> a -> b
$ Integer -> Integer -> Integer -> Integer
expSafe Integer
h' Integer
d Integer
n
Just (-1) -> forall a b. b -> Either a b
Right forall a b. (a -> b) -> a -> b
$ Integer -> Integer -> Integer -> Integer
expSafe (Integer
h' forall a. Integral a => a -> a -> a
`div` Integer
2) Integer
d Integer
n
Maybe Integer
_ -> forall a b. a -> Either a b
Left Error
InvalidParameters
verify :: HashAlgorithm hash
=> PublicKey
-> hash
-> ByteString
-> Integer
-> 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
s' :: Integer
s' = Integer -> Integer -> Integer -> Integer
expSafe Integer
s Integer
2 Integer
n
s'' :: Integer
s'' = case Integer
s' forall a. Integral a => a -> a -> a
`mod` Integer
8 of
Integer
6 -> Integer
s'
Integer
3 -> Integer
2forall a. Num a => a -> a -> a
*Integer
s'
Integer
7 -> Integer
n forall a. Num a => a -> a -> a
- Integer
s'
Integer
2 -> Integer
2forall a. Num a => a -> a -> a
*(Integer
n forall a. Num a => a -> a -> a
- Integer
s')
Integer
_ -> Integer
0
in case Integer
s'' forall a. Integral a => a -> a -> a
`mod` Integer
16 of
Integer
6 -> let h' :: Integer
h' = (Integer
s'' forall a. Num a => a -> a -> a
- Integer
6) forall a. Integral a => a -> a -> a
`div` Integer
16
in Integer
h' forall a. Eq a => a -> a -> Bool
== Integer
h
Integer
_ -> Bool
False