hjugement-protocol 0.0.8.20191027 → 0.0.9.20191031

raw patch · 13 files changed

+402/−622 lines, 13 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• benchmarks/Election.hs +42/−48
• hjugement-protocol.cabal +3/−2
• src/Voting/Protocol/Arith.hs +101/−109
• src/Voting/Protocol/Election.hs +78/−197
• src/Voting/Protocol/FFC.hs +49/−58
• src/Voting/Protocol/Tally.hs +23/−58
• src/Voting/Protocol/Trustee/Indispensable.hs +11/−33
• tests/HUnit/Credential.hs +5/−6
• tests/HUnit/Election.hs +23/−28
• tests/HUnit/FFC.hs +3/−4
• tests/HUnit/Trustee/Indispensable.hs +39/−41
• tests/QuickCheck/Election.hs +16/−27
• tests/QuickCheck/Trustee.hs +9/−11

@@ -13,10 +13,9 @@ makeElection ::  forall crypto v c.  Reifies v Version =>- Reifies c crypto =>- JSON.ToJSON crypto =>- JSON.ToJSON (FieldElement crypto c) =>+ GroupParams crypto c =>  Key crypto =>+ JSON.ToJSON crypto =>  Int -> Int -> Election crypto v c makeElection nQuests nChoices = elec 	where@@ -48,11 +47,7 @@  makeBallot ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Key crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c => Key crypto =>  Election crypto v c -> Ballot crypto v c makeBallot elec = 	case runExcept $ (`evalStateT` mkStdGen seed) $ do@@ -74,18 +69,13 @@  benchEncryptBallot ::  forall crypto v c.+ GroupParams crypto c =>  Reifies v Version =>- Reifies c crypto =>- JSON.ToJSON crypto =>- Group crypto =>  Key crypto =>+ JSON.ToJSON crypto =>  NFData crypto =>- NFData (FieldElement crypto c) =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>- JSON.ToJSON (FieldElement crypto c) =>  Proxy v -> Proxy c -> Int -> Int -> Benchmark-benchEncryptBallot (_v::Proxy v) (_c::Proxy c) nQuests nChoices =+benchEncryptBallot _v _c nQuests nChoices = 	let setupEnv = do 		let elec :: Election crypto v c = makeElection nQuests nChoices 		return elec in@@ -96,15 +86,10 @@ benchVerifyBallot ::  forall crypto v c.  Reifies v Version =>- Reifies c crypto =>- JSON.ToJSON crypto =>- Group crypto =>+ GroupParams crypto c =>  Key crypto =>+ JSON.ToJSON crypto =>  NFData crypto =>- NFData (FieldElement crypto c) =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>- JSON.ToJSON (FieldElement crypto c) =>  Proxy v -> Proxy c -> Int -> Int -> Benchmark benchVerifyBallot (_v::Proxy v) (_c::Proxy c) nQuests nChoices = 	let setupEnv = do@@ -117,31 +102,40 @@  benchmarks :: [Benchmark] benchmarks =- let inputs =-	 [ (nQ,nC)-	 | nQ <- [1,5,10,15,20,25]-	 , nC <- [5,7]-	 ] in- [ bgroup "stableVersion" $ reify stableVersion $ \v ->-	 [ bgroup "weakFFC" $ reify weakFFC $ \c ->-		 [ bgroup "encryptBallot"-			 [ benchEncryptBallot v c nQuests nChoices-			 | (nQuests,nChoices) <- inputs-			 ]-		 , bgroup "verifyBallot"-			 [ benchVerifyBallot v c nQuests nChoices-			 | (nQuests,nChoices) <- inputs-			 ]+ [ benchsByVersion stableVersion+ -- , benchsByVersion experimentalVersion+ ]++benchsByVersion :: Version -> Benchmark+benchsByVersion version =+	reify version $ \v ->+	bgroup ("v"<>show version)+		[ benchsByCrypto v weakFFC+		, benchsByCrypto v beleniosFFC+		]++benchsByCrypto ::+ Reifies v Version =>+ ReifyCrypto crypto =>+ Key crypto =>+ JSON.ToJSON crypto =>+ NFData crypto =>+ Proxy v -> crypto -> Benchmark+benchsByCrypto v crypto =+	reifyCrypto crypto $ \c ->+	bgroup (Text.unpack (cryptoName crypto))+	 [ bgroup "encryptBallot"+		 [ benchEncryptBallot v c nQuests nChoices+		 | (nQuests,nChoices) <- inputs 		 ]-	 , bgroup "beleniosFFC" $ reify beleniosFFC $ \c ->-		 [ bgroup "encryptBallot"-			 [ benchEncryptBallot v c nQuests nChoices-			 | (nQuests,nChoices) <- inputs-			 ]-		 , bgroup "verifyBallot"-			 [ benchVerifyBallot v c nQuests nChoices-			 | (nQuests,nChoices) <- inputs-			 ]+	 , bgroup "verifyBallot"+		 [ benchVerifyBallot v c nQuests nChoices+		 | (nQuests,nChoices) <- inputs 		 ] 	 ]- ]+	where+	inputs =+		[ (nQ,nC)+		| nQ <- [1,5,10,15,20,25]+		, nC <- [5,7]+		]

@@ -2,7 +2,7 @@ -- PVP:  +-+------- breaking API changes --       | | +----- non-breaking API additions --       | | | +--- code changes with no API change-version: 0.0.8.20191027+version: 0.0.9.20191031 category: Politic synopsis: A cryptographic protocol for the Majority Judgment. description:@@ -72,7 +72,7 @@   default-language: Haskell2010   default-extensions:     AllowAmbiguousTypes-    ConstraintKinds+    -- ConstraintKinds     DefaultSignatures     FlexibleContexts     FlexibleInstances@@ -211,6 +211,7 @@   build-depends:     base >= 4.6 && < 5     , hjugement-protocol+    , aeson >= 1.3     , containers >= 0.5     , criterion >= 1.4     , deepseq >= 1.4

@@ -2,13 +2,12 @@ {-# LANGUAGE DeriveAnyClass #-} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE DerivingStrategies #-}+{-# LANGUAGE GADTs #-} {-# LANGUAGE OverloadedStrings #-} {-# LANGUAGE Rank2Types #-} -- for ReifyCrypto {-# LANGUAGE UndecidableInstances #-} -- for Reifies instances {-# OPTIONS_GHC -fno-warn-orphans #-}--- | Finite Field Cryptography (FFC)--- is a method of implementing discrete logarithm cryptography--- using finite field mathematics.+-- | Arithmetic module Voting.Protocol.Arith where  import Control.Arrow (first)@@ -100,102 +99,72 @@  -- | @(b '^' e)@ returns the modular exponentiation of base 'b' by exponent 'e'. (^) ::+ forall crypto c.  Reifies c crypto =>- Multiplicative (FieldElement crypto c) =>+ Multiplicative (G crypto c) =>  G crypto c -> E crypto c -> G crypto c (^) b (E e)  | e == 0 = one  | otherwise = t * (b*b) ^ E (e`shiftR`1)-	where-	t | testBit e 0 = b-		| otherwise   = one+	where t | testBit e 0 = b+	        | otherwise   = one infixr 8 ^ --- | 'groupGenInverses' returns the infinite list--- of 'inv'erse powers of 'groupGen':--- @['groupGen' '^' 'neg' i | i <- [0..]]@,--- but by computing each value from the previous one.------ Used by 'intervalDisjunctions'.-groupGenInverses ::- forall crypto c.- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- [G crypto c]-groupGenInverses = go one-	where-	invGen = inv $ groupGen @crypto @c-	go g = g : go (g * invGen)--groupGenPowers ::- forall crypto c.- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- [G crypto c]-groupGenPowers = go one-	where go g = g : go (g * groupGen @crypto @c)---- | @('randomR' i)@ returns a random integer in @[0..i-1]@.-randomR ::- Monad m =>- Random.RandomGen r =>- Random.Random i =>- Negable i =>- Multiplicative i =>- i -> S.StateT r m i-randomR i = S.StateT $ return . Random.randomR (zero, i-one)---- | @('random')@ returns a random integer--- in the range determined by its type.-random ::- Monad m =>- Random.RandomGen r =>- Random.Random i =>- Negable i =>- Multiplicative i =>- S.StateT r m i-random = S.StateT $ return . Random.random--instance Random.Random Natural where-	randomR (mini,maxi) =-		first (fromIntegral::Integer -> Natural) .-		Random.randomR (fromIntegral mini, fromIntegral maxi)-	random = first (fromIntegral::Integer -> Natural) . Random.random---- * Type family 'FieldElement'-type family FieldElement crypto :: * -> *+-- * Class 'GroupParams' where+class+ ( Multiplicative (G crypto c)+ , Invertible     (G crypto c)+ , FromNatural    (G crypto c)+ , ToNatural      (G crypto c)+ , Eq             (G crypto c)+ , Ord            (G crypto c)+ , Show           (G crypto c)+ , NFData         (G crypto c)+ , FromJSON       (G crypto c)+ , ToJSON         (G crypto c)+ , Reifies c crypto+ ) => GroupParams crypto c where+	-- | A generator of the subgroup.+	groupGen   :: G crypto c+	-- | The order of the subgroup.+	groupOrder :: Proxy c -> Natural+	+	-- | 'groupGenPowers' returns the infinite list+	-- of powers of 'groupGen'.+	--+	-- NOTE: In the 'GroupParams' class to keep+	-- computed values in memory across calls to 'groupGenPowers'.+	groupGenPowers :: [G crypto c]+	groupGenPowers = go one+		where go g = g : go (g * groupGen)+	+	-- | 'groupGenInverses' returns the infinite list+	-- of 'inv'erse powers of 'groupGen':+	-- @['groupGen' '^' 'neg' i | i <- [0..]]@,+	-- but by computing each value from the previous one.+	--+	-- NOTE: In the 'GroupParams' class to keep+	-- computed values in memory across calls to 'groupGenInverses'.+	--+	-- Used by 'intervalDisjunctions'.+	groupGenInverses :: [G crypto c]+	groupGenInverses = go one+		where+		invGen = inv $ groupGen+		go g = g : go (g * invGen) --- * Class 'Group' where-class Group crypto where-	groupGen   :: Reifies c crypto => G crypto c-	groupOrder :: Reifies c crypto => Proxy c -> Natural+-- ** Class 'ReifyCrypto'+class ReifyCrypto crypto where+	-- | Like 'reify' but augmented with the 'GroupParams' constraint.+	reifyCrypto :: crypto -> (forall c. Reifies c crypto => GroupParams crypto c => Proxy c -> r) -> r  -- ** Type 'G' -- | The type of the elements of a subgroup of a field.-newtype G crypto c = G { unG :: FieldElement crypto c }-deriving newtype instance Eq     (FieldElement crypto c) => Eq     (G crypto c)-deriving newtype instance Ord    (FieldElement crypto c) => Ord    (G crypto c)-deriving newtype instance Show   (FieldElement crypto c) => Show   (G crypto c)-deriving newtype instance NFData (FieldElement crypto c) => NFData (G crypto c)-instance ToJSON (FieldElement crypto c) => ToJSON (G crypto c) where-	toJSON = JSON.toJSON . unG-instance FromNatural (FieldElement crypto c) => FromNatural (G crypto c) where-	fromNatural = G . fromNatural-instance ToNatural (FieldElement crypto c) => ToNatural (G crypto c) where-	nat = nat . unG-instance Multiplicative (FieldElement crypto c) => Multiplicative (G crypto c) where-	one = G one-	G x * G y = G (x * y)-instance- ( Reifies c crypto- , Group crypto- , Multiplicative (FieldElement crypto c)- ) => Invertible (G crypto c) where-	-- | NOTE: add 'groupOrder' so the exponent given to (^) is positive.-	inv = (^ E (fromJust $ groupOrder @crypto (Proxy @c)`minusNaturalMaybe`1))+newtype G crypto c = G { unG :: FieldElement crypto } +-- *** Type family 'FieldElement'+type family FieldElement crypto :: *+ -- ** Type 'E' -- | An exponent of a (cyclic) subgroup of a field. -- The value is always in @[0..'groupOrder'-1]@.@@ -204,43 +173,43 @@  deriving newtype NFData instance ToJSON (E crypto c) where 	toJSON = JSON.toJSON . show . unE-instance (Reifies c crypto, Group crypto) => FromJSON (E crypto c) where+instance GroupParams crypto c => FromJSON (E crypto c) where 	parseJSON (JSON.String s) 	 | Just (c0,_) <- Text.uncons s 	 , c0 /= '0' 	 , Text.all Char.isDigit s 	 , Just x <- readMaybe (Text.unpack s)-	 , x < groupOrder @crypto (Proxy @c)+	 , x < groupOrder (Proxy @c) 	 = return (E x) 	parseJSON json = JSON.typeMismatch "Exponent" json-instance (Reifies c crypto, Group crypto) => FromNatural (E crypto c) where+instance GroupParams crypto c => FromNatural (E crypto c) where 	fromNatural i =-		E $ abs $ i `mod` groupOrder @crypto (Proxy @c)+		E $ abs $ i `mod` groupOrder (Proxy @c) 		where-		abs x | x < 0 = x + groupOrder @crypto (Proxy @c)+		abs x | x < 0 = x + groupOrder (Proxy @c) 		      | otherwise = x instance ToNatural (E crypto c) where 	nat = unE-instance (Reifies c crypto, Group crypto) => Additive (E crypto c) where+instance GroupParams crypto c => Additive (E crypto c) where 	zero = E zero-	E x + E y = E $ (x + y) `mod` groupOrder @crypto (Proxy @c)-instance (Reifies c crypto, Group crypto) => Negable (E crypto c) where+	E x + E y = E $ (x + y) `mod` groupOrder (Proxy @c)+instance GroupParams crypto c => Negable (E crypto c) where 	neg (E x) 	 | x == 0 = zero-	 | otherwise = E $ fromJust $ nat (groupOrder @crypto (Proxy @c))`minusNaturalMaybe`x-instance (Reifies c crypto, Group crypto) => Multiplicative (E crypto c) where+	 | otherwise = E $ fromJust $ nat (groupOrder (Proxy @c))`minusNaturalMaybe`x+instance GroupParams crypto c => Multiplicative (E crypto c) where 	one = E one-	E x * E y = E $ (x * y) `mod` groupOrder @crypto (Proxy @c)-instance (Reifies c crypto, Group crypto) => Random.Random (E crypto c) where+	E x * E y = E $ (x * y) `mod` groupOrder (Proxy @c)+instance GroupParams crypto c => Random.Random (E crypto c) where 	randomR (E lo, E hi) = 		first (E . fromIntegral) . 		Random.randomR 		 ( 0`max`toInteger lo-		 , toInteger hi`min`(toInteger (groupOrder @crypto (Proxy @c)) - 1) )+		 , toInteger hi`min`(toInteger (groupOrder (Proxy @c)) - 1) ) 	random = 		first (E . fromIntegral) .-		Random.randomR (0, toInteger (groupOrder @crypto (Proxy @c)) - 1)-instance (Reifies c crypto, Group crypto) => Enum (E crypto c) where+		Random.randomR (0, toInteger (groupOrder (Proxy @c)) - 1)+instance GroupParams crypto c => Enum (E crypto c) where 	toEnum = fromNatural . fromIntegral 	fromEnum = fromIntegral . nat 	enumFromTo lo hi = List.unfoldr@@ -275,13 +244,7 @@ -- Used by 'proveEncryption' and 'verifyEncryption', -- where the 'bs' usually contains the 'statement' to be proven, -- and the 'gs' contains the 'commitments'.-hash ::- Reifies c crypto =>- Group crypto =>- ToNatural (FieldElement crypto c) =>- BS.ByteString ->- [G crypto c] ->- E crypto c+hash :: GroupParams crypto c => BS.ByteString -> [G crypto c] -> E crypto c hash bs gs = do 	let s = bs <> BS.intercalate (fromString ",") (bytesNat <$> gs) 	let h = Crypto.hashWith Crypto.SHA256 s@@ -333,3 +296,32 @@ 	TL.toStrict $ 	TL.tail $ TLB.toLazyText $ TLB.hexadecimal $ 	setBit n 256++-- * Random++-- | @('randomR' i)@ returns a random integer in @[0..i-1]@.+randomR ::+ Monad m =>+ Random.RandomGen r =>+ Random.Random i =>+ Negable i =>+ Multiplicative i =>+ i -> S.StateT r m i+randomR i = S.StateT $ return . Random.randomR (zero, i-one)++-- | @('random')@ returns a random integer+-- in the range determined by its type.+random ::+ Monad m =>+ Random.RandomGen r =>+ Random.Random i =>+ Negable i =>+ Multiplicative i =>+ S.StateT r m i+random = S.StateT $ return . Random.random++instance Random.Random Natural where+	randomR (mini,maxi) =+		first (fromIntegral::Integer -> Natural) .+		Random.randomR (fromIntegral mini, fromIntegral maxi)+	random = first (fromIntegral::Integer -> Natural) . Random.random

@@ -53,7 +53,6 @@ import Voting.Protocol.Utils import Voting.Protocol.Arith import Voting.Protocol.Credential-import Voting.Protocol.FFC (FFC)  -- * Type 'Encryption' -- | ElGamal-like encryption.@@ -75,13 +74,12 @@    -- ^ Encrypted 'clear' text,    -- equal to @('pubKey' '^'encNone '*' 'groupGen' '^'clear)@  } deriving (Generic)-deriving instance Eq (FieldElement crypto c) => Eq (Encryption crypto v c)-deriving instance (Show (FieldElement crypto c), Show (G crypto c)) => Show (Encryption crypto v c)-deriving instance NFData (FieldElement crypto c) => NFData (Encryption crypto v c)+deriving instance Eq (G crypto c) => Eq (Encryption crypto v c)+deriving instance (Show (G crypto c), Show (G crypto c)) => Show (Encryption crypto v c)+deriving instance NFData (G crypto c) => NFData (Encryption crypto v c) instance  ( Reifies v Version- , Reifies c crypto- , ToJSON (FieldElement crypto c)+ , GroupParams crypto c  ) => ToJSON (Encryption crypto v c) where 	toJSON Encryption{..} = 		JSON.object@@ -95,8 +93,7 @@ 		 ) instance  ( Reifies v Version- , Reifies c crypto- , FromJSON (G crypto c)+ , GroupParams crypto c  ) => FromJSON (Encryption crypto v c) where 	parseJSON = JSON.withObject "Encryption" $ \o -> do 		encryption_nonce <- o .: "alpha"@@ -105,10 +102,7 @@  -- | Additive homomorphism. -- Using the fact that: @'groupGen' '^'x '*' 'groupGen' '^'y '==' 'groupGen' '^'(x'+'y)@.-instance- ( Reifies c crypto- , Multiplicative (FieldElement crypto c)- ) => Additive (Encryption crypto v c) where+instance GroupParams crypto c => Additive (Encryption crypto v c) where 	zero = Encryption one one 	x+y = Encryption 	 (encryption_nonce x * encryption_nonce y)@@ -127,9 +121,7 @@ -- without the 'SecretKey' associated with 'pubKey'. encrypt ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m => RandomGen r =>  PublicKey crypto c -> E crypto c ->  S.StateT r m (EncryptionNonce crypto c, Encryption crypto v c)@@ -177,7 +169,7 @@    -- to ensure that each 'prove' does not reveal any information    -- about its secret.  } deriving (Eq,Show,NFData,Generic)-instance Group crypto => ToJSON (Proof crypto v c) where+instance ToJSON (Proof crypto v c) where 	toJSON Proof{..} = 		JSON.object 		 [ "challenge" .= proof_challenge@@ -188,7 +180,7 @@ 		 (  "challenge" .= proof_challenge 		 <> "response"  .= proof_response 		 )-instance (Reifies c crypto, Group crypto) => FromJSON (Proof crypto v c) where+instance GroupParams crypto c => FromJSON (Proof crypto v c) where 	parseJSON = JSON.withObject "TrusteePublicKey" $ \o -> do 		proof_challenge <- o .: "challenge" 		proof_response  <- o .: "response"@@ -241,10 +233,8 @@ -- can be used to deduce @sec@ (using the special-soundness). prove ::  forall crypto v c list m r.- Reifies c crypto =>  Reifies v Version =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m => RandomGen r => Functor list =>  E crypto c ->  list (G crypto c) ->@@ -268,10 +258,8 @@ -- | Like 'prove' but quicker. It chould replace 'prove' entirely -- when Helios-C specifications will be fixed. proveQuicker ::- Reifies c crypto =>  Reifies v Version =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m => RandomGen r => Functor list =>  E crypto c ->  list (G crypto c) ->@@ -295,8 +283,7 @@ -- Used in 'proveEncryption' to fill the returned 'DisjProof' -- with fake 'Proof's for all 'Disjunction's but the encrypted one. fakeProof ::- Reifies c crypto =>- Group crypto =>+ GroupParams crypto c =>  Monad m => RandomGen r =>  S.StateT r m (Proof crypto v c) fakeProof = do@@ -315,9 +302,7 @@ commit ::  forall crypto v c.  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Proof crypto v c ->  G crypto c ->  G crypto c ->@@ -339,8 +324,7 @@ -- | Like 'commit' but quicker. It chould replace 'commit' entirely -- when Helios-C specifications will be fixed. commitQuicker ::- Reifies c crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Proof crypto v c ->  G crypto c ->  G crypto c ->@@ -357,17 +341,13 @@  booleanDisjunctions ::  forall crypto c.- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  [Disjunction crypto c] booleanDisjunctions = List.take 2 $ groupGenInverses @crypto  intervalDisjunctions ::  forall crypto c.- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Natural -> Natural -> [Disjunction crypto c] intervalDisjunctions mini maxi = 	List.genericTake (fromJust $ (nat maxi + 1)`minusNaturalMaybe`nat mini) $@@ -386,19 +366,6 @@ newtype DisjProof crypto v c = DisjProof [Proof crypto v c]  deriving (Eq,Show,Generic)  deriving newtype (NFData,ToJSON,FromJSON)-{--deriving instance Eq (GroupExponent crypto c) => Eq (DisjProof crypto v c)-deriving instance Show (GroupExponent crypto c) => Show (DisjProof crypto v c)-deriving newtype instance NFData (GroupExponent crypto c) => NFData (DisjProof crypto v c)-deriving newtype instance- ( Reifies c crypto- , ToJSON (GroupExponent crypto c)- ) => ToJSON (DisjProof crypto v c)-deriving newtype instance- ( Reifies c crypto- , FromJSON (GroupExponent crypto c)- ) => FromJSON (DisjProof crypto v c)--}  -- | @('proveEncryption' elecPubKey voterZKP (prevDisjs,nextDisjs) (encNonce,enc))@ -- returns a 'DisjProof' that 'enc' 'encrypt's@@ -412,10 +379,7 @@ -- DOC: Pierrick Gaudry. <https://hal.inria.fr/hal-01576379 Some ZK security proofs for Belenios>, 2017. proveEncryption ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- ToNatural (FieldElement crypto c) =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m => RandomGen r =>  PublicKey crypto c -> ZKP ->  ([Disjunction crypto c],[Disjunction crypto c]) ->@@ -445,10 +409,7 @@  verifyEncryption ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- ToNatural (FieldElement crypto c) =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m =>  PublicKey crypto c -> ZKP ->  [Disjunction crypto c] -> (Encryption crypto v c, DisjProof crypto v c) ->@@ -467,8 +428,7 @@  -- ** Hashing encryptionStatement ::- Reifies c crypto =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  ZKP -> Encryption crypto v c -> BS.ByteString encryptionStatement (ZKP voterZKP) Encryption{..} = 	"prove|"<>voterZKP<>"|"@@ -482,9 +442,7 @@ -- and for the verifier the 'Proof' comes from the prover. encryptionCommitments ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  PublicKey crypto c -> Encryption crypto v c ->  Disjunction crypto c -> Proof crypto v c -> [G crypto c] encryptionCommitments elecPubKey Encryption{..} disj proof =@@ -546,14 +504,12 @@    -- is an element of @[mini..maxi]@.  -- , answer_blankProof ::  } deriving (Generic)-deriving instance Eq (FieldElement crypto c) => Eq (Answer crypto v c)-deriving instance (Show (FieldElement crypto c), Show (G crypto c)) => Show (Answer crypto v c)-deriving instance NFData (FieldElement crypto c) => NFData (Answer crypto v c)+deriving instance Eq (G crypto c) => Eq (Answer crypto v c)+deriving instance (Show (G crypto c), Show (G crypto c)) => Show (Answer crypto v c)+deriving instance NFData (G crypto c) => NFData (Answer crypto v c) instance  ( Reifies v Version- , Reifies c crypto- , ToJSON (FieldElement crypto c)- , Group crypto+ , GroupParams crypto c  ) => ToJSON (Answer crypto v c) where 	toJSON Answer{..} = 		let (answer_choices, answer_individual_proofs) =@@ -573,9 +529,7 @@ 		 ) instance  ( Reifies v Version- , Reifies c crypto- , FromJSON (G crypto c)- , Group crypto+ , GroupParams crypto c  ) => FromJSON (Answer crypto v c) where 	parseJSON = JSON.withObject "Answer" $ \o -> do 		answer_choices <- o .: "choices"@@ -589,15 +543,12 @@ -- unless an 'ErrorAnswer' is returned. encryptAnswer ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m => RandomGen r =>  PublicKey crypto c -> ZKP ->  Question v -> [Bool] ->  S.StateT r (ExceptT ErrorAnswer m) (Answer crypto v c)-encryptAnswer elecPubKey zkp Question{..} opinionByChoice+encryptAnswer (elecPubKey::PublicKey crypto c) zkp Question{..} opinionByChoice  | not (question_mini <= opinionsSum && opinionsSum <= question_maxi) = 	lift $ throwE $ 		ErrorAnswer_WrongSumOfOpinions opinionsSum question_mini question_maxi@@ -633,23 +584,21 @@  verifyAnswer ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  PublicKey crypto c -> ZKP ->  Question v -> Answer crypto v c -> Bool-verifyAnswer elecPubKey zkp Question{..} Answer{..}+verifyAnswer (elecPubKey::PublicKey crypto c) zkp Question{..} Answer{..}  | List.length question_choices /= List.length answer_opinions = False- | otherwise = either (const False) id $ runExcept $ do-	validOpinions <--		verifyEncryption elecPubKey zkp booleanDisjunctions-		 `traverse` answer_opinions-	validSum <- verifyEncryption elecPubKey zkp-	 (intervalDisjunctions question_mini question_maxi)-	 ( sum (fst <$> answer_opinions)-	 , answer_sumProof )-	return (and validOpinions && validSum)+ | otherwise = do+	either (const False) id $ runExcept $ do+		validOpinions <-+			verifyEncryption elecPubKey zkp booleanDisjunctions+			 `traverse` answer_opinions+		validSum <- verifyEncryption elecPubKey zkp+		 (intervalDisjunctions question_mini question_maxi)+		 ( sum (fst <$> answer_opinions)+		 , answer_sumProof )+		return (and validOpinions && validSum)  -- ** Type 'ErrorAnswer' -- | Error raised by 'encryptAnswer'.@@ -673,14 +622,13 @@  , election_version     :: !(Maybe Version)  , election_public_key  :: !(PublicKey crypto c)  } deriving (Generic)-deriving instance (Eq crypto, Eq (FieldElement crypto c)) => Eq (Election crypto v c)-deriving instance (Show crypto, Show (FieldElement crypto c)) => Show (Election crypto v c)-deriving instance (NFData crypto, NFData (FieldElement crypto c)) => NFData (Election crypto v c)+deriving instance (Eq crypto, Eq (G crypto c)) => Eq (Election crypto v c)+deriving instance (Show crypto, Show (G crypto c)) => Show (Election crypto v c)+deriving instance (NFData crypto, NFData (G crypto c)) => NFData (Election crypto v c) instance- ( ToJSON crypto- , ToJSON (FieldElement crypto c)- , Reifies v Version- , Reifies c crypto+ ( Reifies v Version+ , GroupParams crypto c+ , ToJSON crypto  ) => ToJSON (Election crypto v c) where 	toJSON Election{..} = 		JSON.object $@@ -707,15 +655,22 @@ 		 ) <> 		 maybe mempty ("version" .=) election_version +hashElection ::+ Reifies v Version =>+ GroupParams crypto c =>+ ToJSON crypto =>+ Election crypto v c -> Base64SHA256+hashElection = base64SHA256 . BSL.toStrict . JSON.encode+ readElection ::- ReifyCrypto crypto =>+ forall crypto r.  FromJSON crypto =>+ ReifyCrypto crypto =>  FilePath ->  (forall v c.-  Reifies v Version =>-  Reifies c crypto =>-  FieldElementConstraints crypto c =>-  Election crypto v c -> r) ->+	Reifies v Version =>+	GroupParams crypto c =>+	Election crypto v c -> r) ->  ExceptT String IO r readElection filePath k = do 	fileData <- lift $ BS.readFile filePath@@ -748,61 +703,6 @@ 				 , .. 				 } -hashElection ::- ToJSON crypto =>- Reifies c crypto =>- Reifies v Version =>- ToJSON (FieldElement crypto c) =>- Election crypto v c -> Base64SHA256-hashElection = base64SHA256 . BSL.toStrict . JSON.encode---- ** Class 'ReifyCrypto'--- | @('reifyCrypto' crypto k)@ is like @('reify' crypto k)@--- but gives to @(k)@ more constraints than just @('Reifies' c crypto)@,--- which is used when defining classes on @(crypto)@--- where @(c)@ (the type variable guarantying the same--- @crypto@graphic parameters are used throughout)--- is not yet in scope and thus where one cannot--- add those constraints requiring to have @(c)@ in scope.--- See for instance the 'QuickcheckElection' class, in the tests.------ For convenience, the 'ReifyCrypto' class also implies the pervasive--- constraint 'Group'.-class- ( Group crypto- , Key crypto- , Show crypto- , NFData crypto- , JSON.ToJSON crypto- , JSON.FromJSON crypto- ) => ReifyCrypto crypto where-	reifyCrypto ::-	 crypto -> (forall c.-	  Reifies c crypto =>-	  FieldElementConstraints crypto c =>-	  Proxy c -> r) -> r-instance ReifyCrypto FFC where-	reifyCrypto = reify---- ** Class 'FieldElementConstraints'--- | List the 'Constraint's on the element of the field--- when the @(crypto)@ has not been instantiated to a specific type yet.--- It concerns only 'Constraint's whose method act on @(a)@,--- not @(x c)@ (eg. 'Group').-type FieldElementConstraints crypto c =- ( Multiplicative (FieldElement crypto c)- , FromNatural    (FieldElement crypto c)- , ToNatural      (FieldElement crypto c)- , Eq             (FieldElement crypto c)- , Ord            (FieldElement crypto c)- , Show           (FieldElement crypto c)- , NFData         (FieldElement crypto c)- , FromJSON       (FieldElement crypto c)- , ToJSON         (FieldElement crypto c)- , FromJSON       (G crypto c)- , ToJSON         (G crypto c)- )- -- * Type 'Ballot' data Ballot crypto v c = Ballot  { ballot_answers       :: ![Answer crypto v c]@@ -810,12 +710,11 @@  , ballot_election_uuid :: !UUID  , ballot_election_hash :: !Base64SHA256  } deriving (Generic)-deriving instance (NFData (FieldElement crypto c), NFData crypto) => NFData (Ballot crypto v c)+deriving instance (NFData (G crypto c), NFData crypto) => NFData (Ballot crypto v c) instance  ( Reifies v Version- , Reifies c crypto- , Group crypto- , ToJSON (FieldElement crypto c)+ , GroupParams crypto c+ , ToJSON (G crypto c)  ) => ToJSON (Ballot crypto v c) where 	toJSON Ballot{..} = 		JSON.object $@@ -833,9 +732,7 @@ 		 maybe mempty ("signature" .=) ballot_signature instance  ( Reifies v Version- , Reifies c crypto- , Group crypto- , FromJSON (G crypto c)+ , GroupParams crypto c  ) => FromJSON (Ballot crypto v c) where 	parseJSON = JSON.withObject "Ballot" $ \o -> do 		ballot_answers       <- o .: "answers"@@ -849,18 +746,13 @@ -- where 'opinionsByQuest' is a list of 'Opinion's -- on each 'question_choices' of each 'election_questions'. encryptBallot ::- forall crypto m v c r.- Reifies c crypto =>  Reifies v Version =>- Group crypto =>- Key crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c => Key crypto =>  Monad m => RandomGen r =>  Election crypto v c ->  Maybe (SecretKey crypto c) -> [[Bool]] ->  S.StateT r (ExceptT ErrorBallot m) (Ballot crypto v c)-encryptBallot Election{..} ballotSecKeyMay opinionsByQuest+encryptBallot (Election{..}::Election crypto v c) ballotSecKeyMay opinionsByQuest  | List.length election_questions /= List.length opinionsByQuest = 	lift $ throwE $ 		ErrorBallot_WrongNumberOfAnswers@@ -884,12 +776,12 @@ 		signature_proof <- 			proveQuicker ballotSecKey (Identity groupGen) $ 			 \(Identity commitment) ->-				hash @_ @crypto+				hash @crypto 				 -- NOTE: the order is unusual, the commitments are first 				 -- then comes the statement. Best guess is that 				 -- this is easier to code due to their respective types.-				 (signatureCommitments @_ @crypto voterZKP commitment)-				 (signatureStatement @_ @crypto ballot_answers)+				 (signatureCommitments @crypto voterZKP commitment)+				 (signatureStatement @crypto ballot_answers) 		return $ Just Signature{..} 	return Ballot 	 { ballot_answers@@ -899,16 +791,11 @@ 	 }  verifyBallot ::- forall crypto v c.  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>- ToNatural (PublicKey crypto c) =>+ GroupParams crypto c =>  Election crypto v c ->  Ballot crypto v c -> Bool-verifyBallot Election{..} Ballot{..} =+verifyBallot (Election{..}::Election crypto v c) Ballot{..} = 	ballot_election_uuid == election_uuid && 	ballot_election_hash == election_hash && 	List.length election_questions == List.length ballot_answers &&@@ -919,8 +806,8 @@ 			let zkp = ZKP (bytesNat signature_publicKey) in 			(, zkp) $ 				proof_challenge signature_proof == hash-				 (signatureCommitments @_ @crypto zkp (commitQuicker signature_proof groupGen signature_publicKey))-				 (signatureStatement @_ @crypto ballot_answers)+				 (signatureCommitments @crypto zkp (commitQuicker signature_proof groupGen signature_publicKey))+				 (signatureStatement @crypto ballot_answers) 	in 	and $ isValidSign : 		List.zipWith (verifyAnswer election_public_key zkpSign)@@ -937,14 +824,10 @@    -- ^ Verification key.  , signature_proof     :: !(Proof crypto v c)  } deriving (Generic)-deriving instance- ( NFData crypto- , NFData (FieldElement crypto c)- ) => NFData (Signature crypto v c)+deriving instance (NFData crypto, NFData (G crypto c)) => NFData (Signature crypto v c) instance- ( Reifies c crypto- , Reifies v Version- , ToJSON (FieldElement crypto c)+ ( Reifies v Version+ , GroupParams crypto c  ) => ToJSON (Signature crypto v c) where 	toJSON (Signature pubKey Proof{..}) = 		JSON.object@@ -959,10 +842,8 @@ 		 <> "response"   .= proof_response 		 ) instance- ( Reifies c crypto- , Reifies v Version- , Group crypto- , FromJSON (PublicKey crypto c)+ ( Reifies v Version+ , GroupParams crypto c  ) => FromJSON (Signature crypto v c) where 	parseJSON = JSON.withObject "Signature" $ \o -> do 		signature_publicKey <- o .: "public_key"@@ -976,7 +857,7 @@ -- | @('signatureStatement' answers)@ -- returns the encrypted material to be signed: -- all the 'encryption_nonce's and 'encryption_vault's of the given @answers@.-signatureStatement :: Reifies c crypto => Foldable f => f (Answer crypto v c) -> [G crypto c]+signatureStatement :: GroupParams crypto c => Foldable f => f (Answer crypto v c) -> [G crypto c] signatureStatement = 	foldMap $ \Answer{..} -> 		(`foldMap` answer_opinions) $ \(Encryption{..}, _proof) ->@@ -984,8 +865,8 @@  -- | @('signatureCommitments' voterZKP commitment)@ signatureCommitments ::- Reifies c crypto =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>+ ToNatural (G crypto c) =>  ZKP -> Commitment crypto c -> BS.ByteString signatureCommitments (ZKP voterZKP) commitment = 	"sig|"<>voterZKP<>"|" -- NOTE: this is actually part of the statement

@@ -24,7 +24,7 @@ import Data.Monoid (Monoid(..)) import Data.Ord (Ord(..)) import Data.Proxy (Proxy(..))-import Data.Reflection (Reifies(..))+import Data.Reflection (Reifies(..), reify) import Data.Semigroup (Semigroup(..)) import Data.Text (Text) import GHC.Generics (Generic)@@ -45,7 +45,7 @@ import Voting.Protocol.Credential  -- * Type 'FFC'--- | Mutiplicative Sub-Group of a Finite Prime Field.+-- | Mutiplicative subgroup of a Finite Prime Field. -- -- NOTE: an 'FFC' term-value is brought into the context of many functions -- through a type-variable @c@ whose 'Reifies' constraint enables to 'reflect'@@ -57,7 +57,7 @@ -- is encoded at the type-level by including @c@ -- as a phantom type of 'F', 'G' and 'E'. data FFC = FFC- {   ffc_name :: Text+ {   ffc_name :: !Text  ,   ffc_fieldCharac :: !Natural      -- ^ The prime number characteristic of a Finite Prime Field.      --@@ -116,11 +116,25 @@ 		unless (fromJust (ffc_fieldCharac`minusNaturalMaybe`one) `rem` ffc_groupOrder == 0) $ 			JSON.typeMismatch "FFC: groupOrder does not divide fieldCharac-1" (JSON.Object o) 		return FFC{..}-instance Group FFC where-	groupGen :: forall c. Reifies c FFC => G FFC c-	groupGen = G $ F $ ffc_groupGen $ reflect (Proxy::Proxy c)-	groupOrder :: forall c. Reifies c FFC => Proxy c -> Natural+instance Reifies c FFC => GroupParams FFC c where+	groupGen = G $ ffc_groupGen $ reflect (Proxy::Proxy c) 	groupOrder c = ffc_groupOrder $ reflect c+instance ReifyCrypto FFC where+	reifyCrypto = reify+instance Key FFC where+	cryptoType _ = "FFC"+	cryptoName = ffc_name+	randomSecretKey = random+	credentialSecretKey (UUID uuid) (Credential cred) =+		fromNatural $ decodeBigEndian $+		Crypto.fastPBKDF2_SHA256+		 Crypto.Parameters+		 { Crypto.iterCounts   = 1000+		 , Crypto.outputLength = 32 -- bytes, ie. 256 bits+		 }+		 (Text.encodeUtf8 cred)+		 (Text.encodeUtf8 uuid)+	publicKey = (groupGen @FFC ^)  fieldCharac :: forall c. Reifies c FFC => Natural fieldCharac = ffc_fieldCharac $ reflect (Proxy::Proxy c)@@ -147,7 +161,6 @@  , ffc_groupOrder  = 78571733251071885079927659812671450121821421258408794611510081919805623223441  } --- * Type 'F' -- | The type of the elements of a Finite Prime Field. -- -- A field must satisfy the following properties:@@ -171,19 +184,11 @@ --   @(a'+'b)'*'c == (a'*'c) '+' (b'*'c)@ -- -- The 'Natural' is always within @[0..'fieldCharac'-1]@.-newtype F c = F { unF :: Natural }- deriving (Eq,Ord,Show)- deriving newtype NFData-type instance FieldElement FFC = F-instance Reifies c FFC => FromJSON (F c) where-	parseJSON (JSON.String s)-	 | Just (c0,_) <- Text.uncons s-	 , c0 /= '0'-	 , Text.all Char.isDigit s-	 , Just x <- readMaybe (Text.unpack s)-	 , x < fieldCharac @c-	 = return (F x)-	parseJSON json = JSON.typeMismatch "FieldElement FFC" json+type instance FieldElement FFC = Natural+deriving newtype instance Eq     (G FFC c)+deriving newtype instance Ord    (G FFC c)+deriving newtype instance NFData (G FFC c)+deriving newtype instance Show   (G FFC c) instance Reifies c FFC => FromJSON (G FFC c) where 	parseJSON (JSON.String s) 	 | Just (c0,_) <- Text.uncons s@@ -191,52 +196,38 @@ 	 , Text.all Char.isDigit s 	 , Just x <- readMaybe (Text.unpack s) 	 , x < fieldCharac @c-	 , r <- G (F x)+	 , r <- G x 	 , r ^ E (groupOrder @FFC (Proxy @c)) == one 	 = return r 	parseJSON json = JSON.typeMismatch "GroupElement" json-instance ToJSON (F c) where-	toJSON (F x) = JSON.toJSON (show x)-instance Reifies c FFC => FromNatural (F c) where-	fromNatural i = F $ abs $ i `mod` fieldCharac @c+instance ToJSON (G FFC c) where+	toJSON (G x) = JSON.toJSON (show x)+instance Reifies c FFC => FromNatural (G FFC c) where+	fromNatural i = G $ abs $ i `mod` fieldCharac @c 		where 		abs x | x < 0 = x + fieldCharac @c 		      | otherwise = x-instance ToNatural (F c) where-	nat = unF-instance Reifies c FFC => Additive (F c) where-	zero = F 0-	F x + F y = F $ (x + y) `mod` fieldCharac @c-instance Reifies c FFC => Negable (F c) where-	neg (F x)+instance ToNatural (G FFC c) where+	nat = unG+instance Reifies c FFC => Additive (G FFC c) where+	zero = G 0+	G x + G y = G $ (x + y) `mod` fieldCharac @c+instance Reifies c FFC => Negable (G FFC c) where+	neg (G x) 	 | x == 0 = zero-	 | otherwise = F $ fromJust $ nat (fieldCharac @c)`minusNaturalMaybe`x-instance Reifies c FFC => Multiplicative (F c) where-	one = F 1-	F x * F y = F $ (x * y) `mod` fieldCharac @c-instance Reifies c FFC => Random.Random (F c) where-	randomR (F lo, F hi) =-		first (F . fromIntegral) .+	 | otherwise = G $ fromJust $ nat (fieldCharac @c)`minusNaturalMaybe`x+instance Reifies c FFC => Multiplicative (G FFC c) where+	one = G 1+	G x * G y = G $ (x * y) `mod` fieldCharac @c+instance Reifies c FFC => Random.Random (G FFC c) where+	randomR (G lo, G hi) =+		first (G . fromIntegral) . 		Random.randomR 		 ( 0`max`toInteger lo 		 , toInteger hi`min`(toInteger (fieldCharac @c) - 1) ) 	random =-		first (F . fromIntegral) .+		first (G . fromIntegral) . 		Random.randomR (0, toInteger (fieldCharac @c) - 1)---- * Conversions--instance Key FFC where-	cryptoType _ = "FFC"-	cryptoName = ffc_name-	randomSecretKey = random-	credentialSecretKey (UUID uuid) (Credential cred) =-		fromNatural $ decodeBigEndian $-		Crypto.fastPBKDF2_SHA256-		 Crypto.Parameters-		 { Crypto.iterCounts   = 1000-		 , Crypto.outputLength = 32 -- bytes, ie. 256 bits-		 }-		 (Text.encodeUtf8 cred)-		 (Text.encodeUtf8 uuid)-	publicKey = (groupGen @FFC ^)+instance Reifies c FFC => Invertible (G FFC c) where+	-- | NOTE: add 'groupOrder' so the exponent given to (^) is positive.+	inv = (^ E (fromJust $ groupOrder @FFC (Proxy @c)`minusNaturalMaybe`1))

@@ -14,7 +14,6 @@ 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)@@ -50,14 +49,12 @@  , 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)+deriving instance Eq (G crypto c) => Eq (Tally crypto v c)+deriving instance (Show (G crypto c), Show (G crypto c)) => Show (Tally crypto v c)+deriving instance NFData (G crypto c) => NFData (Tally crypto v c) instance  ( Reifies v Version- , Reifies c crypto- , Group crypto- , ToJSON (FieldElement crypto c)+ , GroupParams crypto c  ) => ToJSON (Tally crypto v c) where 	toJSON Tally{..} = 		JSON.object@@ -75,9 +72,7 @@ 		 ) instance  ( Reifies v Version- , Reifies c crypto- , Group crypto- , FromJSON (G crypto c)+ , GroupParams crypto c  ) => FromJSON (Tally crypto v c) where 	parseJSON = JSON.withObject "Tally" $ \o -> do 		tally_countMax             <- o .: "num_tallied"@@ -94,15 +89,13 @@ -- 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) =>+ GroupParams 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) =>+ GroupParams crypto c =>  (EncryptedTally crypto v c, Natural) emptyEncryptedTally = (List.repeat (List.repeat zero), 0) @@ -110,9 +103,10 @@ -- 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)+ GroupParams 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))@@ -128,13 +122,9 @@  Except ErrorTally [[DecryptionFactor crypto c]]  proveTally ::- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- Ord (FieldElement crypto c) =>+ GroupParams crypto c =>  (EncryptedTally crypto v c, Natural) -> [DecryptionShare crypto v c] ->- DecryptionShareCombinator crypto v c ->- Except ErrorTally (Tally crypto v c)+ DecryptionShareCombinator crypto v c -> Except ErrorTally (Tally crypto v c) proveTally  (tally_encByChoiceByQuest, tally_countMax)  tally_decShareByTrustee@@ -156,10 +146,7 @@ 	return Tally{..}  verifyTally ::- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- Eq (FieldElement crypto c) =>+ GroupParams crypto c =>  Tally crypto v c ->  DecryptionShareCombinator crypto v c ->  Except ErrorTally ()@@ -181,13 +168,10 @@ 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 Eq (G 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+deriving newtype instance NFData (G crypto c) => NFData (DecryptionShare crypto v c)+instance ToJSON (G crypto c) => ToJSON (DecryptionShare crypto v c) where 	toJSON (DecryptionShare decByChoiceByQuest) = 		JSON.object 		 [ "decryption_factors" .=@@ -201,11 +185,7 @@ 			 (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+instance GroupParams crypto c => FromJSON (DecryptionShare crypto v c) where 	parseJSON = JSON.withObject "DecryptionShare" $ \o -> do 		decFactors <- o .: "decryption_factors" 		decProofs  <- o .: "decryption_proofs"@@ -223,11 +203,8 @@ -- @('proveDecryptionShare' encByChoiceByQuest trusteeSecKey)@ proveDecryptionShare ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams 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 =@@ -236,11 +213,8 @@  proveDecryptionFactor ::  Reifies v Version => - Reifies c crypto => - Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams 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@@ -248,10 +222,7 @@ 	return (encryption_nonce^trusteeSecKey, proof) 	where zkp = decryptionShareStatement (publicKey trusteeSecKey) -decryptionShareStatement ::- Reifies c crypto =>- ToNatural (FieldElement crypto c) =>- PublicKey crypto c -> BS.ByteString+decryptionShareStatement :: GroupParams crypto c => PublicKey crypto c -> BS.ByteString decryptionShareStatement pubKey = 	"decrypt|"<>bytesNat pubKey<>"|" @@ -277,10 +248,7 @@ -- 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) =>+ GroupParams crypto c =>  Monad m =>  EncryptedTally crypto v c -> PublicKey crypto c -> DecryptionShare crypto v c ->  ExceptT ErrorTally m ()@@ -298,10 +266,7 @@  verifyDecryptionShareByTrustee ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m =>  EncryptedTally crypto v c -> [PublicKey crypto c] -> [DecryptionShare crypto v c] ->  ExceptT ErrorTally m ()

@@ -47,13 +47,10 @@ 	-- Which is done in 'proveIndispensableTrusteePublicKey' 	-- and 'verifyIndispensableTrusteePublicKey'.  } deriving (Generic)-deriving instance Eq (FieldElement crypto c) => Eq (TrusteePublicKey crypto v c)-deriving instance (Show (FieldElement crypto c), Show (PublicKey crypto c)) => Show (TrusteePublicKey crypto v c)-deriving instance NFData (FieldElement crypto c) => NFData (TrusteePublicKey crypto v c)-instance- ( Group crypto- , ToJSON (FieldElement crypto c)- ) => ToJSON (TrusteePublicKey crypto v c) where+deriving instance Eq (G crypto c) => Eq (TrusteePublicKey crypto v c)+deriving instance (Show (G crypto c), Show (PublicKey crypto c)) => Show (TrusteePublicKey crypto v c)+deriving instance NFData (G crypto c) => NFData (TrusteePublicKey crypto v c)+instance ToJSON (G crypto c) => ToJSON (TrusteePublicKey crypto v c) where 	toJSON TrusteePublicKey{..} = 		JSON.object 		 [ "pok"        .= trustee_SecretKeyProof@@ -64,11 +61,7 @@ 		 (  "pok"        .= trustee_SecretKeyProof 		 <> "public_key" .= trustee_PublicKey 		 )-instance- ( Reifies c crypto- , Group crypto- , FromJSON (PublicKey crypto c)- ) => FromJSON (TrusteePublicKey crypto v c) where+instance GroupParams crypto c => FromJSON (TrusteePublicKey crypto v c) where 	parseJSON = JSON.withObject "TrusteePublicKey" $ \o -> do 		trustee_PublicKey <- o .: "public_key" 		trustee_SecretKeyProof <- o .: "pok"@@ -81,11 +74,8 @@ -- and a 'Proof' of its knowledge. proveIndispensableTrusteePublicKey ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>+ GroupParams crypto c =>  Key crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>  Monad m => RandomGen r =>  SecretKey crypto c -> S.StateT r m (TrusteePublicKey crypto v c) proveIndispensableTrusteePublicKey trustSecKey = do@@ -103,10 +93,7 @@ -- the given 'trustee_PublicKey' is known by the trustee. verifyIndispensableTrusteePublicKey ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m =>  TrusteePublicKey crypto v c ->  ExceptT ErrorTrusteePublicKey m ()@@ -126,8 +113,7 @@  -- ** Hashing indispensableTrusteePublicKeyStatement ::- Reifies c crypto =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  PublicKey crypto c -> BS.ByteString indispensableTrusteePublicKeyStatement trustPubKey = 	"pok|"<>bytesNat trustPubKey<>"|"@@ -137,9 +123,7 @@ -- ** Generating an 'Election''s 'PublicKey' from multiple 'TrusteePublicKey's.  combineIndispensableTrusteePublicKeys ::- Reifies c crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  [TrusteePublicKey crypto v c] -> PublicKey crypto c combineIndispensableTrusteePublicKeys = 	List.foldr (\TrusteePublicKey{..} -> (trustee_PublicKey *)) one@@ -148,10 +132,7 @@  verifyIndispensableDecryptionShareByTrustee ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m =>  EncryptedTally crypto v c -> [PublicKey crypto c] -> [DecryptionShare crypto v c] ->  ExceptT ErrorTally m ()@@ -165,10 +146,7 @@ -- returns the 'DecryptionFactor's by choice by 'Question' combineIndispensableDecryptionShares ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>- ToNatural (FieldElement crypto c) =>+ GroupParams crypto c =>  [PublicKey crypto c] -> DecryptionShareCombinator crypto v c combineIndispensableDecryptionShares  pubKeyByTrustee

@@ -35,7 +35,7 @@ 	 , "xLcs7ev6Jy6FHHE"  ==> Right (Credential "xLcs7ev6Jy6FHHE") 	 ]  , testGroup "credentialSecretKey" $-	 [ testSecretKey beleniosFFC+	 [  testSecretKey beleniosFFC 		 (UUID "xLcs7ev6Jy6FHH") 		 (Credential "xLcs7ev6Jy6FHHE") 		 24202898752499029126606335829564687069186982035759723128887013101942425902424@@ -43,10 +43,9 @@  ]  testSecretKey ::- ReifyCrypto crypto =>- Key crypto =>+ ReifyCrypto crypto => Key crypto =>  crypto -> UUID -> Credential -> Natural -> TestTree testSecretKey crypto uuid cred exp =-	reifyCrypto crypto $ \(Proxy::Proxy c) ->-	testCase (show (uuid,cred)) $-		credentialSecretKey @_ @c uuid cred @?= E exp+	reifyCrypto crypto $ \(_c::Proxy c) ->+		testCase (show (uuid,cred)) $+			credentialSecretKey @_ @c uuid cred @?= E exp

@@ -32,11 +32,9 @@  ]  hunitsEncryptBallot ::- ReifyCrypto crypto =>- JSON.ToJSON crypto =>- Key crypto =>- Reifies v Version => Proxy v ->- crypto -> TestTree+ Reifies v Version =>+ ReifyCrypto crypto => Key crypto => JSON.ToJSON crypto =>+ Proxy v -> crypto -> TestTree hunitsEncryptBallot v crypto = 	testGroup (Text.unpack $ cryptoName crypto) 	 [ hunitEncryptBallot v crypto 0@@ -81,31 +79,28 @@ 	 ]  hunitEncryptBallot ::- ReifyCrypto crypto =>- JSON.ToJSON crypto =>- Key crypto =>- Reifies v Version => Proxy v ->- crypto -> Int -> [Question v] -> [[Bool]] ->- Either ErrorBallot Bool ->- TestTree+ Reifies v Version =>+ ReifyCrypto crypto => Key crypto => JSON.ToJSON crypto =>+ Proxy v -> crypto -> Int -> [Question v] -> [[Bool]] ->+ Either ErrorBallot Bool -> TestTree hunitEncryptBallot v election_crypto seed election_questions opins exp = 	let got =-		reifyCrypto election_crypto $ \(Proxy::Proxy c) ->-		runExcept $-		(`evalStateT` Random.mkStdGen seed) $ do-			election_uuid <- randomUUID-			cred <- randomCredential-			let ballotSecKey = credentialSecretKey @_ @c election_uuid cred-			election_public_key <- publicKey <$> randomSecretKey-			let elec = Election-				 { election_name        = "election"-				 , election_description = "description"-				 , election_hash        = hashElection elec-				 , election_version     = Just (reflect v)-				 , ..-				 }-			verifyBallot elec-			 <$> encryptBallot elec (Just ballotSecKey) opins+		reifyCrypto election_crypto $ \(_c::Proxy c) ->+			runExcept $+			(`evalStateT` Random.mkStdGen seed) $ do+				election_uuid <- randomUUID+				cred <- randomCredential+				let ballotSecKey = credentialSecretKey @_ @c election_uuid cred+				election_public_key <- publicKey <$> randomSecretKey+				let elec = Election+					 { election_name        = "election"+					 , election_description = "description"+					 , election_hash        = hashElection elec+					 , election_version     = Just (reflect v)+					 , ..+					 }+				verifyBallot elec+				 <$> encryptBallot elec (Just ballotSecKey) opins 	in 	testCase (show opins) $ 		got @?= exp

@@ -38,13 +38,12 @@  hunitInv ::  forall crypto.- ReifyCrypto crypto =>- Key crypto =>+ ReifyCrypto crypto => Key crypto =>  crypto -> TestTree hunitInv crypto = 	testGroup (Text.unpack $ cryptoName crypto) 	 [ testCase "groupGen" $ 			reifyCrypto crypto $ \(_c::Proxy c) ->-			inv (groupGen :: G crypto c) @?=-				groupGen ^ E (fromJust $ groupOrder (Proxy @c) `minusNaturalMaybe` one)+				inv (groupGen :: G crypto c) @?=+					groupGen ^ E (fromJust $ groupOrder (Proxy @c) `minusNaturalMaybe` one) 	 ]

@@ -24,9 +24,9 @@  ]  testsVerifyIndispensableTrusteePublicKey ::- ReifyCrypto crypto =>- Reifies v Version => Proxy v ->- crypto -> TestTree+ Reifies v Version =>+ ReifyCrypto crypto => Key crypto =>+ Proxy v -> crypto -> TestTree testsVerifyIndispensableTrusteePublicKey v crypto = 	testGroup (Text.unpack $ cryptoName crypto) 	 [ testVerifyIndispensableTrusteePublicKey v crypto 0 (Right ())@@ -34,23 +34,23 @@  testVerifyIndispensableTrusteePublicKey ::  forall crypto v.- ReifyCrypto crypto =>+ ReifyCrypto crypto => Key crypto =>  Reifies v Version => Proxy v ->  crypto -> Int -> Either ErrorTrusteePublicKey () -> TestTree testVerifyIndispensableTrusteePublicKey (_v::Proxy v) crypto seed exp =-	reifyCrypto crypto $ \(Proxy::Proxy c) ->-	let got =-		runExcept $-		(`evalStateT` Random.mkStdGen seed) $ do-			trusteeSecKey :: SecretKey crypto c <- randomSecretKey-			trusteePubKey :: TrusteePublicKey crypto v c <- proveIndispensableTrusteePublicKey trusteeSecKey-			lift $ verifyIndispensableTrusteePublicKey trusteePubKey-	in-	testCase (Text.unpack $ cryptoName crypto) $-		got @?= exp+	reifyCrypto crypto $ \(_c::Proxy c) ->+		let got =+			runExcept $+			(`evalStateT` Random.mkStdGen seed) $ do+				trusteeSecKey :: SecretKey crypto c <- randomSecretKey+				trusteePubKey :: TrusteePublicKey crypto v c <- proveIndispensableTrusteePublicKey trusteeSecKey+				lift $ verifyIndispensableTrusteePublicKey trusteePubKey+		in+		testCase (Text.unpack $ cryptoName @crypto crypto) $+			got @?= exp  testsVerifyTally ::- ReifyCrypto crypto =>+ ReifyCrypto crypto => Key crypto =>  Reifies v Version => Proxy v ->  crypto -> TestTree testsVerifyTally v crypto =@@ -63,33 +63,33 @@ 	 ]  testVerifyTally ::- ReifyCrypto crypto =>- Reifies v Version => Proxy v ->- crypto -> Int -> Natural -> Natural -> Natural -> TestTree+ Reifies v Version =>+ ReifyCrypto crypto => Key crypto =>+ Proxy v -> crypto -> Int -> Natural -> Natural -> Natural -> TestTree testVerifyTally (_v::Proxy v) crypto seed nTrustees nQuests nChoices = 	let clearTallyResult = dummyTallyResult nQuests nChoices in 	let decryptedTallyResult :: Either ErrorTally [[Natural]] =-		reifyCrypto crypto $ \(Proxy::Proxy c) ->-		runExcept $-		(`evalStateT` Random.mkStdGen seed) $ do-			secKeyByTrustee :: [SecretKey crypto c] <--				replicateM (fromIntegral nTrustees) $ randomSecretKey-			trusteePubKeys-			 :: [TrusteePublicKey crypto v c]-			 <- forM secKeyByTrustee $ proveIndispensableTrusteePublicKey-			let pubKeyByTrustee = trustee_PublicKey <$> trusteePubKeys-			let elecPubKey = combineIndispensableTrusteePublicKeys trusteePubKeys-			(encTally, countMax) <- encryptTallyResult elecPubKey clearTallyResult-			decShareByTrustee-			 :: [DecryptionShare crypto v c]-			 <- forM secKeyByTrustee $ proveDecryptionShare encTally-			lift $ verifyDecryptionShareByTrustee encTally pubKeyByTrustee decShareByTrustee-			tally@Tally{..} <- lift $-				proveTally (encTally, countMax) decShareByTrustee $+		reifyCrypto crypto $ \(_c::Proxy c) ->+			runExcept $+			(`evalStateT` Random.mkStdGen seed) $ do+				secKeyByTrustee :: [SecretKey crypto c] <-+					replicateM (fromIntegral nTrustees) $ randomSecretKey+				trusteePubKeys+				 :: [TrusteePublicKey crypto v c]+				 <- forM secKeyByTrustee $ proveIndispensableTrusteePublicKey+				let pubKeyByTrustee = trustee_PublicKey <$> trusteePubKeys+				let elecPubKey = combineIndispensableTrusteePublicKeys trusteePubKeys+				(encTally, countMax) <- encryptTallyResult elecPubKey clearTallyResult+				decShareByTrustee+				 :: [DecryptionShare crypto v c]+				 <- forM secKeyByTrustee $ proveDecryptionShare encTally+				lift $ verifyDecryptionShareByTrustee encTally pubKeyByTrustee decShareByTrustee+				tally@Tally{..} <- lift $+					proveTally (encTally, countMax) decShareByTrustee $+						combineIndispensableDecryptionShares pubKeyByTrustee+				lift $ verifyTally tally $ 					combineIndispensableDecryptionShares pubKeyByTrustee-			lift $ verifyTally tally $-				combineIndispensableDecryptionShares pubKeyByTrustee-			return tally_countByChoiceByQuest+				return tally_countByChoiceByQuest 	in 	testCase (Printf.printf "#T=%i,#Q=%i,#C=%i (%i maxCount)" 	 nTrustees nQuests nChoices@@ -107,9 +107,7 @@  encryptTallyResult ::  Reifies v Version =>- Reifies c crypto =>- Group crypto =>- Multiplicative (FieldElement crypto c) =>+ GroupParams crypto c =>  Monad m => RandomGen r =>  PublicKey crypto c -> [[Natural]] -> StateT r m (EncryptedTally crypto v c, Natural) encryptTallyResult pubKey countByChoiceByQuest =

@@ -27,19 +27,19 @@ quickcheck :: Reifies v Version => Proxy v -> TestTree quickcheck v = 	testGroup "Election"-	 [ testGroup "verifyBallot" $-		 [ quickcheckElection v weakFFC-		 , quickcheckElection v beleniosFFC+	 [ testGroup "verifyBallot" $ +		 [ reify weakFFC $ quickcheckElection v+		 , reify beleniosFFC $ quickcheckElection v 		 ] 	 ]  quickcheckElection ::- ReifyCrypto crypto =>- Reifies v Version => Proxy v ->- crypto -> TestTree-quickcheckElection (_v::Proxy v) crypto =-	reifyCrypto crypto $ \(Proxy::Proxy c) ->-	testGroup (Text.unpack $ cryptoName crypto)+ Reifies v Version => + GroupParams crypto c =>+ Key crypto => JSON.ToJSON crypto => Show crypto =>+ Proxy v -> Proxy c -> TestTree+quickcheckElection (_v::Proxy v) (c::Proxy c) =+	testGroup (Text.unpack $ cryptoName (reflect c)) 	 [ testProperty "verifyBallot" $ \(seed, (elec::Election crypto v c) :> votes) -> 		isRight $ runExcept $ 			(`evalStateT` mkStdGen seed) $ do@@ -49,20 +49,15 @@ 					lift $ throwE $ ErrorBallot_Wrong 	 ] +{- instance Reifies c FFC => Arbitrary (F c) where 	arbitrary = F <$> choose (zero, fromJust $ fieldCharac @c `minusNaturalMaybe` one)-instance- ( Reifies c crypto- , Group crypto- , Multiplicative (FieldElement crypto c)- ) => Arbitrary (G crypto c) where+-}+instance GroupParams crypto c => Arbitrary (G crypto c) where 	arbitrary = do 		m <- arbitrary 		return (groupGen ^ m)-instance- ( Reifies c crypto- , Group crypto- ) => Arbitrary (E crypto c) where+instance GroupParams crypto c => Arbitrary (E crypto c) where 	arbitrary = E <$> choose (zero, fromJust $ groupOrder @crypto (Proxy @c) `minusNaturalMaybe` one) instance Arbitrary UUID where 	arbitrary = do@@ -71,7 +66,7 @@ 			randomUUID instance  ( Reifies v Version- , Reifies c crypto+ , GroupParams crypto c  , Arbitrary (E crypto c)  ) => Arbitrary (Proof crypto v c) where 	arbitrary = do@@ -95,12 +90,9 @@ 		] instance  ( Reifies v Version- , Reifies c crypto- , Group crypto+ , GroupParams crypto c  , Key crypto- , Multiplicative (FieldElement crypto c)  , JSON.ToJSON crypto- , JSON.ToJSON (FieldElement crypto c)  ) => Arbitrary (Election crypto v c) where 	arbitrary = do 		let election_name = "election"@@ -146,12 +138,9 @@ 		] instance  ( Reifies v Version- , Reifies c crypto- , Group crypto+ , GroupParams crypto c  , Key crypto  , JSON.ToJSON crypto- , JSON.ToJSON (FieldElement crypto c)- , Multiplicative (FieldElement crypto c)  ) => Arbitrary (Election crypto v c :> [[Bool]]) where 	arbitrary = do 		elec@Election{..} <- arbitrary

@@ -15,18 +15,18 @@ quickcheck v = 	testGroup "Trustee" $ 	 [ testGroup "verifyIndispensableTrusteePublicKey" $-		 [ testIndispensableTrusteePublicKey v weakFFC-		 , testIndispensableTrusteePublicKey v beleniosFFC+		 [ reify weakFFC $ testIndispensableTrusteePublicKey v+		 , reify beleniosFFC $ testIndispensableTrusteePublicKey v 		 ] 	 ]  testIndispensableTrusteePublicKey ::- ReifyCrypto crypto =>- Reifies v Version => Proxy v ->- crypto -> TestTree-testIndispensableTrusteePublicKey (_v::Proxy v) crypto =-	reifyCrypto crypto $ \(Proxy::Proxy c) ->-	testGroup (Text.unpack $ cryptoName crypto)+ Reifies v Version =>+ GroupParams crypto c =>+ Key crypto =>+ Proxy v -> Proxy c -> TestTree+testIndispensableTrusteePublicKey (_v::Proxy v) (c::Proxy c) =+	testGroup (Text.unpack $ cryptoName (reflect c)) 	 [ testProperty "Right" $ \seed -> 		isRight $ runExcept $ 			(`evalStateT` mkStdGen seed) $ do@@ -38,9 +38,7 @@  instance  ( Reifies v Version- , Reifies c crypto- , Group crypto- , Multiplicative (FieldElement crypto c)+ , GroupParams crypto c  ) => Arbitrary (TrusteePublicKey crypto v c) where 	arbitrary = do 		trustee_PublicKey <- arbitrary