{-# LANGUAGE DeriveAnyClass #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE DerivingStrategies #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE UndecidableInstances #-} -- for Reifies instances
module Voting.Protocol.Tally where

import Control.DeepSeq (NFData)
import Control.Monad (Monad(..), mapM, unless)
import Control.Monad.Trans.Except (Except, ExceptT, throwE)
import Data.Aeson (ToJSON(..),FromJSON(..),(.:),(.=))
import Data.Eq (Eq(..))
import Data.Function (($), (.))
import Data.Functor ((<$>))
import Data.Maybe (maybe)
import Data.Semigroup (Semigroup(..))
import Data.Ord (Ord(..))
import Data.Reflection (Reifies(..))
import Data.Tuple (fst, snd)
import GHC.Generics (Generic)
import Numeric.Natural (Natural)
import System.Random (RandomGen)
import Text.Show (Show(..))
import qualified Data.Aeson as JSON
import qualified Data.Aeson.Types as JSON
import qualified Data.Aeson.Encoding as JSON
import qualified Control.Monad.Trans.State.Strict as S
import qualified Data.ByteString as BS
import qualified Data.List as List
import qualified Data.Map.Strict as Map

import Voting.Protocol.Utils
import Voting.Protocol.Arith
import Voting.Protocol.Credential
import Voting.Protocol.Election

-- * Type 'Tally'
data Tally crypto v c = Tally
 { tally_countMax :: !Natural
   -- ^ The maximal number of supportive 'Opinion's that a choice can get,
   -- which is here the same as the number of 'Ballot's.
   --
   -- Used in 'proveTally' to decrypt the actual
   -- count of votes obtained by a choice,
   -- by precomputing all powers of 'groupGen's up to it.
 , tally_encByChoiceByQuest :: !(EncryptedTally crypto v c)
   -- ^ 'Encryption' by 'Question' by 'Ballot'.
 , tally_decShareByTrustee :: ![DecryptionShare crypto v c]
   -- ^ 'DecryptionShare' by trustee.
 , tally_countByChoiceByQuest :: ![[Natural]]
   -- ^ The decrypted count of supportive 'Opinion's, by choice by 'Question'.
 } deriving (Generic)
deriving instance Eq (FieldElement crypto c) => Eq (Tally crypto v c)
deriving instance (Show (FieldElement crypto c), Show (G crypto c)) => Show (Tally crypto v c)
deriving instance NFData (FieldElement crypto c) => NFData (Tally crypto v c)
instance
 ( Reifies v Version
 , Reifies c crypto
 , Group crypto
 , ToJSON (FieldElement crypto c)
 ) => ToJSON (Tally crypto v c) where
        toJSON Tally{..} =
                JSON.object
                 [ "num_tallied"         .= tally_countMax
                 , "encrypted_tally"     .= tally_encByChoiceByQuest
                 , "partial_decryptions" .= tally_decShareByTrustee
                 , "result"              .= tally_countByChoiceByQuest
                 ]
        toEncoding Tally{..} =
                JSON.pairs
                 (  "num_tallied"         .= tally_countMax
                 <> "encrypted_tally"     .= tally_encByChoiceByQuest
                 <> "partial_decryptions" .= tally_decShareByTrustee
                 <> "result"              .= tally_countByChoiceByQuest
                 )
instance
 ( Reifies v Version
 , Reifies c crypto
 , Group crypto
 , FromJSON (G crypto c)
 ) => FromJSON (Tally crypto v c) where
        parseJSON = JSON.withObject "Tally" $ \o -> do
                tally_countMax             <- o .: "num_tallied"
                tally_encByChoiceByQuest   <- o .: "encrypted_tally"
                tally_decShareByTrustee    <- o .: "partial_decryptions"
                tally_countByChoiceByQuest <- o .: "result"
                return Tally{..}

-- ** Type 'EncryptedTally'
-- | 'Encryption' by choice by 'Question'.
type EncryptedTally crypto v c = [[Encryption crypto v c]]

-- | @('encryptedTally' ballots)@
-- returns the sum of the 'Encryption's of the given @ballots@,
-- along with the number of 'Ballot's.
encryptedTally ::
 Reifies c crypto =>
 Multiplicative (FieldElement crypto c) =>
 [Ballot crypto v c] -> (EncryptedTally crypto v c, Natural)
encryptedTally = List.foldr insertEncryptedTally emptyEncryptedTally

-- | The initial 'EncryptedTally' which tallies no 'Ballot'.
emptyEncryptedTally ::
 Reifies c crypto =>
 Multiplicative (FieldElement crypto c) =>
 (EncryptedTally crypto v c, Natural)
emptyEncryptedTally = (List.repeat (List.repeat zero), 0)

-- | @('insertEncryptedTally' ballot encTally)@
-- returns the 'EncryptedTally' adding the votes of the given @(ballot)@
-- to those of the given @(encTally)@.
insertEncryptedTally ::
 Reifies c crypto =>
 Multiplicative (FieldElement crypto c) =>
 Ballot crypto v c -> (EncryptedTally crypto v c, Natural) -> (EncryptedTally crypto v c, Natural)
insertEncryptedTally Ballot{..} (encTally, numBallots) =
        ( List.zipWith
                 (\Answer{..} -> List.zipWith (+) (fst <$> answer_opinions))
                 ballot_answers
                 encTally
        , numBallots+1
        )

-- ** Type 'DecryptionShareCombinator'
type DecryptionShareCombinator crypto v c =
 EncryptedTally crypto v c ->
 [DecryptionShare crypto v c] ->
 Except ErrorTally [[DecryptionFactor crypto c]]

proveTally ::
 Reifies c crypto =>
 Group crypto =>
 Multiplicative (FieldElement crypto c) =>
 Ord (FieldElement crypto c) =>
 (EncryptedTally crypto v c, Natural) -> [DecryptionShare crypto v c] ->
 DecryptionShareCombinator crypto v c ->
 Except ErrorTally (Tally crypto v c)
proveTally
 (tally_encByChoiceByQuest, tally_countMax)
 tally_decShareByTrustee
 decShareCombinator = do
        decFactorByChoiceByQuest <-
                decShareCombinator
                 tally_encByChoiceByQuest
                 tally_decShareByTrustee
        dec <- isoZipWithM (throwE ErrorTally_NumberOfQuestions)
         (maybe (throwE ErrorTally_NumberOfChoices) return `o2`
                isoZipWith (\Encryption{..} decFactor -> encryption_vault / decFactor))
         tally_encByChoiceByQuest
         decFactorByChoiceByQuest
        let logMap = Map.fromList $ List.zip groupGenPowers [0..tally_countMax]
        let log x =
                maybe (throwE ErrorTally_CannotDecryptCount) return $
                Map.lookup x logMap
        tally_countByChoiceByQuest <- (log `mapM`)`mapM`dec
        return Tally{..}

verifyTally ::
 Reifies c crypto =>
 Group crypto =>
 Multiplicative (FieldElement crypto c) =>
 Eq (FieldElement crypto c) =>
 Tally crypto v c ->
 DecryptionShareCombinator crypto v c ->
 Except ErrorTally ()
verifyTally Tally{..} decShareCombinator = do
        decFactorByChoiceByQuest <- decShareCombinator tally_encByChoiceByQuest tally_decShareByTrustee
        isoZipWith3M_ (throwE ErrorTally_NumberOfQuestions)
         (isoZipWith3M_ (throwE ErrorTally_NumberOfChoices)
                 (\Encryption{..} decFactor count -> do
                        let groupGenPowCount = encryption_vault / decFactor
                        unless (groupGenPowCount == groupGen ^ fromNatural count) $
                                throwE ErrorTally_WrongProof))
         tally_encByChoiceByQuest
         decFactorByChoiceByQuest
         tally_countByChoiceByQuest

-- ** Type 'DecryptionShare'
-- | A decryption share is a 'DecryptionFactor' and a decryption 'Proof', by choice by 'Question'.
-- Computed by a trustee in 'proveDecryptionShare'.
newtype DecryptionShare crypto v c = DecryptionShare
 { unDecryptionShare :: [[(DecryptionFactor crypto c, Proof crypto v c)]] }
 deriving (Generic)
deriving instance Eq (FieldElement crypto c) => Eq (DecryptionShare crypto v c)
deriving instance Show (G crypto c) => Show (DecryptionShare crypto v c)
deriving newtype instance NFData (FieldElement crypto c) => NFData (DecryptionShare crypto v c)
instance
 ( Group crypto
 , ToJSON (FieldElement crypto c)
 ) => ToJSON (DecryptionShare crypto v c) where
        toJSON (DecryptionShare decByChoiceByQuest) =
                JSON.object
                 [ "decryption_factors" .=
                        toJSONList (((toJSON . fst) <$>) <$> decByChoiceByQuest)
                 , "decryption_proofs" .=
                        toJSONList (((toJSON . snd) <$>) <$> decByChoiceByQuest)
                 ]
        toEncoding (DecryptionShare decByChoiceByQuest) =
                JSON.pairs $
                        JSON.pair "decryption_factors"
                         (JSON.list (JSON.list (toEncoding . fst)) decByChoiceByQuest) <>
                        JSON.pair "decryption_proofs"
                         (JSON.list (JSON.list (toEncoding . snd)) decByChoiceByQuest)
instance
 ( Reifies c crypto
 , Group crypto
 , FromJSON (G crypto c)
 ) => FromJSON (DecryptionShare crypto v c) where
        parseJSON = JSON.withObject "DecryptionShare" $ \o -> do
                decFactors <- o .: "decryption_factors"
                decProofs  <- o .: "decryption_proofs"
                let err msg = JSON.typeMismatch ("DecryptionShare: "<>msg) (JSON.Object o)
                DecryptionShare
                 <$> isoZipWithM (err "inconsistent number of questions")
                         (isoZipWithM (err "inconsistent number of choices")
                                 (\a b -> return (a, b)))
                 decFactors decProofs

-- *** Type 'DecryptionFactor'
-- | @'encryption_nonce' '^'trusteeSecKey@
type DecryptionFactor = G

-- @('proveDecryptionShare' encByChoiceByQuest trusteeSecKey)@
proveDecryptionShare ::
 Reifies v Version =>
 Reifies c crypto =>
 Group crypto =>
 Multiplicative (FieldElement crypto c) =>
 Key crypto =>
 ToNatural (FieldElement crypto c) =>
 Monad m => RandomGen r =>
 EncryptedTally crypto v c -> SecretKey crypto c -> S.StateT r m (DecryptionShare crypto v c)
proveDecryptionShare encByChoiceByQuest trusteeSecKey =
        (DecryptionShare <$>) $
        (proveDecryptionFactor trusteeSecKey `mapM`) `mapM` encByChoiceByQuest

proveDecryptionFactor ::
 Reifies v Version =>
 Reifies c crypto =>
 Group crypto =>
 Multiplicative (FieldElement crypto c) =>
 Key crypto =>
 ToNatural (FieldElement crypto c) =>
 Monad m => RandomGen r =>
 SecretKey crypto c -> Encryption crypto v c -> S.StateT r m (DecryptionFactor crypto c, Proof crypto v c)
proveDecryptionFactor trusteeSecKey Encryption{..} = do
        proof <- prove trusteeSecKey [groupGen, encryption_nonce] (hash zkp)
        return (encryption_nonce^trusteeSecKey, proof)
        where zkp = decryptionShareStatement (publicKey trusteeSecKey)

decryptionShareStatement ::
 Reifies c crypto =>
 ToNatural (FieldElement crypto c) =>
 PublicKey crypto c -> BS.ByteString
decryptionShareStatement pubKey =
        "decrypt|"<>bytesNat pubKey<>"|"

-- *** Type 'ErrorTally'
data ErrorTally
 =   ErrorTally_NumberOfQuestions
     -- ^ The number of 'Question's is not the one expected.
 |   ErrorTally_NumberOfChoices
     -- ^ The number of choices is not the one expected.
 |   ErrorTally_NumberOfTrustees
     -- ^ The number of trustees is not the one expected.
 |   ErrorTally_WrongProof
     -- ^ The 'Proof' of a 'DecryptionFactor' is wrong.
 |   ErrorTally_CannotDecryptCount
     -- ^ Raised by 'proveTally' when the discrete logarithm of @'groupGen' '^'count@
     -- cannot be computed, likely because 'tally_countMax' is wrong,
     -- or because the 'EncryptedTally' or 'DecryptionShare's have not been verified.
 deriving (Eq,Show,Generic,NFData)

-- | @('verifyDecryptionShare' encTally trusteePubKey trusteeDecShare)@
-- checks that 'trusteeDecShare'
-- (supposedly submitted by a trustee whose 'PublicKey' is 'trusteePubKey')
-- is valid with respect to the 'EncryptedTally' 'encTally'.
verifyDecryptionShare ::
 Reifies v Version =>
 Reifies c crypto =>
 Group crypto =>
 Multiplicative (FieldElement crypto c) =>
 ToNatural (FieldElement crypto c) =>
 Monad m =>
 EncryptedTally crypto v c -> PublicKey crypto c -> DecryptionShare crypto v c ->
 ExceptT ErrorTally m ()
verifyDecryptionShare encByChoiceByQuest trusteePubKey (DecryptionShare decShare) =
        let zkp = decryptionShareStatement trusteePubKey in
        isoZipWithM_ (throwE ErrorTally_NumberOfQuestions)
         (isoZipWithM_ (throwE ErrorTally_NumberOfChoices) $
         \Encryption{..} (decFactor, proof) ->
                unless (proof_challenge proof == hash zkp
                 [ commit proof groupGen trusteePubKey
                 , commit proof encryption_nonce decFactor
                 ]) $ throwE ErrorTally_WrongProof)
         encByChoiceByQuest
         decShare

verifyDecryptionShareByTrustee ::
 Reifies v Version =>
 Reifies c crypto =>
 Group crypto =>
 Multiplicative (FieldElement crypto c) =>
 ToNatural (FieldElement crypto c) =>
 Monad m =>
 EncryptedTally crypto v c -> [PublicKey crypto c] -> [DecryptionShare crypto v c] ->
 ExceptT ErrorTally m ()
verifyDecryptionShareByTrustee encTally =
        isoZipWithM_ (throwE ErrorTally_NumberOfTrustees)
         (verifyDecryptionShare encTally)