Voting.Protocol.Arith

Finite Field Cryptography (FFC) is a method of implementing discrete logarithm cryptography using finite field mathematics.

Class Additive

class Additive a where

Minimal complete definition

zero, (+)

Methods

zero :: a

(+) :: a -> a -> a infixl 6

sum :: Foldable f => f a -> a

Instances

Additive Int

Defined in Voting.Protocol.Arith

Methods

zero :: Int

(+) :: Int -> Int -> Int

sum :: Foldable f => f Int -> Int

Additive Integer

Defined in Voting.Protocol.Arith

Methods

zero :: Integer

(+) :: Integer -> Integer -> Integer

sum :: Foldable f => f Integer -> Integer

Additive Natural

Defined in Voting.Protocol.Arith

Methods

zero :: Natural

(+) :: Natural -> Natural -> Natural

sum :: Foldable f => f Natural -> Natural

Reifies c FFC => Additive (F c)

Defined in Voting.Protocol.FFC

Methods

zero :: F c

(+) :: F c -> F c -> F c

sum :: Foldable f => f (F c) -> F c

(Reifies c crypto, Group crypto) => Additive (E crypto c)

Defined in Voting.Protocol.Arith

Methods

zero :: E crypto c

(+) :: E crypto c -> E crypto c -> E crypto c

sum :: Foldable f => f (E crypto c) -> E crypto c

(Reifies c crypto, Multiplicative (FieldElement crypto c)) => Additive (Encryption crypto v c)

Additive homomorphism. Using the fact that: groupGen ^x * groupGen ^y == groupGen ^(x+y).

Defined in Voting.Protocol.Election

Methods

zero :: Encryption crypto v c

(+) :: Encryption crypto v c -> Encryption crypto v c -> Encryption crypto v c

sum :: Foldable f => f (Encryption crypto v c) -> Encryption crypto v c

Class Negable

class Additive a => Negable a where

Minimal complete definition

neg

Methods

neg :: a -> a

(-) :: a -> a -> a infixl 6

Instances

Negable Int

Defined in Voting.Protocol.Arith

Methods

neg :: Int -> Int

(-) :: Int -> Int -> Int

Negable Integer

Defined in Voting.Protocol.Arith

Methods

neg :: Integer -> Integer

(-) :: Integer -> Integer -> Integer

Reifies c FFC => Negable (F c)

Defined in Voting.Protocol.FFC

Methods

neg :: F c -> F c

(-) :: F c -> F c -> F c

(Reifies c crypto, Group crypto) => Negable (E crypto c)

Defined in Voting.Protocol.Arith

Methods

neg :: E crypto c -> E crypto c

(-) :: E crypto c -> E crypto c -> E crypto c

Class Multiplicative

class Multiplicative a where

Methods

one :: a

(*) :: a -> a -> a infixl 7

Instances

Multiplicative Int

Defined in Voting.Protocol.Arith

Methods

one :: Int

(*) :: Int -> Int -> Int

Multiplicative Integer

Defined in Voting.Protocol.Arith

Methods

one :: Integer

(*) :: Integer -> Integer -> Integer

Multiplicative Natural

Defined in Voting.Protocol.Arith

Methods

one :: Natural

(*) :: Natural -> Natural -> Natural

Reifies c FFC => Multiplicative (F c)

Defined in Voting.Protocol.FFC

Methods

one :: F c

(*) :: F c -> F c -> F c

(Reifies c crypto, Group crypto) => Multiplicative (E crypto c)

Defined in Voting.Protocol.Arith

Methods

one :: E crypto c

(*) :: E crypto c -> E crypto c -> E crypto c

Multiplicative (FieldElement crypto c) => Multiplicative (G crypto c)

Defined in Voting.Protocol.Arith

Methods

one :: G crypto c

(*) :: G crypto c -> G crypto c -> G crypto c

Class Invertible

class Multiplicative a => Invertible a where

Minimal complete definition

inv

Methods

inv :: a -> a

(/) :: a -> a -> a infixl 7

Instances

(Reifies c crypto, Group crypto, Multiplicative (FieldElement crypto c)) => Invertible (G crypto c)

Defined in Voting.Protocol.Arith

Methods

inv :: G crypto c -> G crypto c

(/) :: G crypto c -> G crypto c -> G crypto c

(^) :: Reifies c crypto => Multiplicative (FieldElement crypto c) => G crypto c -> E crypto c -> G crypto c infixr 8

(b ^ e) returns the modular exponentiation of base b by exponent e.

groupGenInverses :: forall crypto c. Reifies c crypto => Group crypto => Multiplicative (FieldElement crypto c) => [G crypto c]

groupGenInverses returns the infinite list of inverse powers of groupGen: [groupGen ^ neg i | i <- [0..]], but by computing each value from the previous one.

Used by intervalDisjunctions.

groupGenPowers :: forall crypto c. Reifies c crypto => Group crypto => Multiplicative (FieldElement crypto c) => [G crypto c]

randomR :: Monad m => RandomGen r => Random i => Negable i => Multiplicative i => i -> StateT r m i

(randomR i) returns a random integer in [0..i-1].

random :: Monad m => RandomGen r => Random i => Negable i => Multiplicative i => StateT r m i

(random) returns a random integer in the range determined by its type.

Type family FieldElement

type family FieldElement crypto :: * -> *

Instances

type FieldElement FFC

Defined in Voting.Protocol.FFC

type FieldElement FFC = F

Class Group where

class Group crypto where

Methods

groupGen :: Reifies c crypto => G crypto c

groupOrder :: Reifies c crypto => Proxy c -> Natural

Instances

Group FFC

Defined in Voting.Protocol.FFC

Methods

groupGen :: Reifies c FFC => G FFC c

groupOrder :: Reifies c FFC => Proxy c -> Natural

Type G

newtype G crypto c

The type of the elements of a subgroup of a field.

Constructors

G

Fields

• unG :: FieldElement crypto c

Instances

Eq (FieldElement crypto c) => Eq (G crypto c)

Defined in Voting.Protocol.Arith

Methods

(==) :: G crypto c -> G crypto c -> Bool

(/=) :: G crypto c -> G crypto c -> Bool

Ord (FieldElement crypto c) => Ord (G crypto c)

Defined in Voting.Protocol.Arith

Methods

compare :: G crypto c -> G crypto c -> Ordering

(<) :: G crypto c -> G crypto c -> Bool

(<=) :: G crypto c -> G crypto c -> Bool

(>) :: G crypto c -> G crypto c -> Bool

(>=) :: G crypto c -> G crypto c -> Bool

max :: G crypto c -> G crypto c -> G crypto c

min :: G crypto c -> G crypto c -> G crypto c

Show (FieldElement crypto c) => Show (G crypto c)

Defined in Voting.Protocol.Arith

Methods

showsPrec :: Int -> G crypto c -> ShowS

show :: G crypto c -> String

showList :: [G crypto c] -> ShowS

ToJSON (FieldElement crypto c) => ToJSON (G crypto c)

Defined in Voting.Protocol.Arith

Methods

toJSON :: G crypto c -> Value

toEncoding :: G crypto c -> Encoding

toJSONList :: [G crypto c] -> Value

toEncodingList :: [G crypto c] -> Encoding

Reifies c FFC => FromJSON (G FFC c)

Defined in Voting.Protocol.FFC

Methods

parseJSON :: Value -> Parser (G FFC c)

parseJSONList :: Value -> Parser [G FFC c]

NFData (FieldElement crypto c) => NFData (G crypto c)

Defined in Voting.Protocol.Arith

Methods

rnf :: G crypto c -> ()

ToNatural (FieldElement crypto c) => ToNatural (G crypto c)

Defined in Voting.Protocol.Arith

Methods

nat :: G crypto c -> Natural

FromNatural (FieldElement crypto c) => FromNatural (G crypto c)

Defined in Voting.Protocol.Arith

Methods

fromNatural :: Natural -> G crypto c

(Reifies c crypto, Group crypto, Multiplicative (FieldElement crypto c)) => Invertible (G crypto c)

Defined in Voting.Protocol.Arith

Methods

inv :: G crypto c -> G crypto c

(/) :: G crypto c -> G crypto c -> G crypto c

Multiplicative (FieldElement crypto c) => Multiplicative (G crypto c)

Defined in Voting.Protocol.Arith

Methods

one :: G crypto c

(*) :: G crypto c -> G crypto c -> G crypto c

Type E

newtype E crypto c

An exponent of a (cyclic) subgroup of a field. The value is always in [0..groupOrder-1].

Constructors

E

Fields

• unE :: Natural

Instances

(Reifies c crypto, Group crypto) => Enum (E crypto c)

Defined in Voting.Protocol.Arith

Methods

succ :: E crypto c -> E crypto c

pred :: E crypto c -> E crypto c

toEnum :: Int -> E crypto c

fromEnum :: E crypto c -> Int

enumFrom :: E crypto c -> [E crypto c]

enumFromThen :: E crypto c -> E crypto c -> [E crypto c]

enumFromTo :: E crypto c -> E crypto c -> [E crypto c]

enumFromThenTo :: E crypto c -> E crypto c -> E crypto c -> [E crypto c]

Eq (E crypto c)

Defined in Voting.Protocol.Arith

Methods

(==) :: E crypto c -> E crypto c -> Bool

(/=) :: E crypto c -> E crypto c -> Bool

Ord (E crypto c)

Defined in Voting.Protocol.Arith

Methods

compare :: E crypto c -> E crypto c -> Ordering

(<) :: E crypto c -> E crypto c -> Bool

(<=) :: E crypto c -> E crypto c -> Bool

(>) :: E crypto c -> E crypto c -> Bool

(>=) :: E crypto c -> E crypto c -> Bool

max :: E crypto c -> E crypto c -> E crypto c

min :: E crypto c -> E crypto c -> E crypto c

Show (E crypto c)

Defined in Voting.Protocol.Arith

Methods

showsPrec :: Int -> E crypto c -> ShowS

show :: E crypto c -> String

showList :: [E crypto c] -> ShowS

ToJSON (E crypto c)

Defined in Voting.Protocol.Arith

Methods

toJSON :: E crypto c -> Value

toEncoding :: E crypto c -> Encoding

toJSONList :: [E crypto c] -> Value

toEncodingList :: [E crypto c] -> Encoding

(Reifies c crypto, Group crypto) => FromJSON (E crypto c)

Defined in Voting.Protocol.Arith

Methods

parseJSON :: Value -> Parser (E crypto c)

parseJSONList :: Value -> Parser [E crypto c]

NFData (E crypto c)

Defined in Voting.Protocol.Arith

Methods

rnf :: E crypto c -> ()

(Reifies c crypto, Group crypto) => Random (E crypto c)

Defined in Voting.Protocol.Arith

Methods

randomR :: RandomGen g => (E crypto c, E crypto c) -> g -> (E crypto c, g)

random :: RandomGen g => g -> (E crypto c, g)

randomRs :: RandomGen g => (E crypto c, E crypto c) -> g -> [E crypto c]

randoms :: RandomGen g => g -> [E crypto c]

randomRIO :: (E crypto c, E crypto c) -> IO (E crypto c)

randomIO :: IO (E crypto c)

ToNatural (E crypto c)

Defined in Voting.Protocol.Arith

Methods

nat :: E crypto c -> Natural

(Reifies c crypto, Group crypto) => FromNatural (E crypto c)

Defined in Voting.Protocol.Arith

Methods

fromNatural :: Natural -> E crypto c

(Reifies c crypto, Group crypto) => Multiplicative (E crypto c)

Defined in Voting.Protocol.Arith

Methods

one :: E crypto c

(*) :: E crypto c -> E crypto c -> E crypto c

(Reifies c crypto, Group crypto) => Negable (E crypto c)

Defined in Voting.Protocol.Arith

Methods

neg :: E crypto c -> E crypto c

(-) :: E crypto c -> E crypto c -> E crypto c

(Reifies c crypto, Group crypto) => Additive (E crypto c)

Defined in Voting.Protocol.Arith

Methods

zero :: E crypto c

(+) :: E crypto c -> E crypto c -> E crypto c

sum :: Foldable f => f (E crypto c) -> E crypto c

Class FromNatural

class FromNatural a where

Methods

fromNatural :: Natural -> a

Instances

Reifies c FFC => FromNatural (F c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> F c

(Reifies c crypto, Group crypto) => FromNatural (E crypto c)

Defined in Voting.Protocol.Arith

Methods

fromNatural :: Natural -> E crypto c

FromNatural (FieldElement crypto c) => FromNatural (G crypto c)

Defined in Voting.Protocol.Arith

Methods

fromNatural :: Natural -> G crypto c

Class ToNatural

class ToNatural a where

Methods

nat :: a -> Natural

Instances

ToNatural Natural

Defined in Voting.Protocol.Arith

Methods

nat :: Natural -> Natural

ToNatural (F c)

Defined in Voting.Protocol.FFC

Methods

nat :: F c -> Natural

ToNatural (E crypto c)

Defined in Voting.Protocol.Arith

Methods

nat :: E crypto c -> Natural

ToNatural (FieldElement crypto c) => ToNatural (G crypto c)

Defined in Voting.Protocol.Arith

Methods

nat :: G crypto c -> Natural

bytesNat :: ToNatural n => n -> ByteString

(bytesNat x) returns the serialization of x.

Type Hash

newtype Hash crypto c

Constructors

Hash (E crypto c)

Instances

Eq (Hash crypto c)

Defined in Voting.Protocol.Arith

Methods

(==) :: Hash crypto c -> Hash crypto c -> Bool

(/=) :: Hash crypto c -> Hash crypto c -> Bool

Ord (Hash crypto c)

Defined in Voting.Protocol.Arith

Methods

compare :: Hash crypto c -> Hash crypto c -> Ordering

(<) :: Hash crypto c -> Hash crypto c -> Bool

(<=) :: Hash crypto c -> Hash crypto c -> Bool

(>) :: Hash crypto c -> Hash crypto c -> Bool

(>=) :: Hash crypto c -> Hash crypto c -> Bool

max :: Hash crypto c -> Hash crypto c -> Hash crypto c

min :: Hash crypto c -> Hash crypto c -> Hash crypto c

Show (Hash crypto c)

Defined in Voting.Protocol.Arith

Methods

showsPrec :: Int -> Hash crypto c -> ShowS

show :: Hash crypto c -> String

showList :: [Hash crypto c] -> ShowS

NFData (Hash crypto c)

Defined in Voting.Protocol.Arith

Methods

rnf :: Hash crypto c -> ()

hash :: Reifies c crypto => Group crypto => ToNatural (FieldElement crypto c) => ByteString -> [G crypto c] -> E crypto c

(hash bs gs) returns as a number in GroupExponent the SHA256 hash of the given ByteString bs prefixing the decimal representation of given subgroup elements gs, with a comma (",") intercalated between them.

NOTE: to avoid any collision when the hash function is used in different contexts, a message gs is actually prefixed by a bs indicating the context.

Used by proveEncryption and verifyEncryption, where the bs usually contains the statement to be proven, and the gs contains the commitments.

decodeBigEndian :: ByteString -> Natural

(decodeBigEndian bs) interpret bs as big-endian number.

Type Base64SHA256

newtype Base64SHA256

Constructors

Base64SHA256 Text

Instances

Eq Base64SHA256

Defined in Voting.Protocol.Arith

Methods

(==) :: Base64SHA256 -> Base64SHA256 -> Bool

(/=) :: Base64SHA256 -> Base64SHA256 -> Bool

Ord Base64SHA256

Defined in Voting.Protocol.Arith

Methods

compare :: Base64SHA256 -> Base64SHA256 -> Ordering

(<) :: Base64SHA256 -> Base64SHA256 -> Bool

(<=) :: Base64SHA256 -> Base64SHA256 -> Bool

(>) :: Base64SHA256 -> Base64SHA256 -> Bool

(>=) :: Base64SHA256 -> Base64SHA256 -> Bool

max :: Base64SHA256 -> Base64SHA256 -> Base64SHA256

min :: Base64SHA256 -> Base64SHA256 -> Base64SHA256

Show Base64SHA256

Defined in Voting.Protocol.Arith

Methods

showsPrec :: Int -> Base64SHA256 -> ShowS

show :: Base64SHA256 -> String

showList :: [Base64SHA256] -> ShowS

Generic Base64SHA256

Defined in Voting.Protocol.Arith

Associated Types

type Rep Base64SHA256 :: Type -> Type

Methods

from :: Base64SHA256 -> Rep Base64SHA256 x

to :: Rep Base64SHA256 x -> Base64SHA256

ToJSON Base64SHA256

Defined in Voting.Protocol.Arith

Methods

toJSON :: Base64SHA256 -> Value

toEncoding :: Base64SHA256 -> Encoding

toJSONList :: [Base64SHA256] -> Value

toEncodingList :: [Base64SHA256] -> Encoding

FromJSON Base64SHA256

Defined in Voting.Protocol.Arith

Methods

parseJSON :: Value -> Parser Base64SHA256

parseJSONList :: Value -> Parser [Base64SHA256]

NFData Base64SHA256

Defined in Voting.Protocol.Arith

Methods

rnf :: Base64SHA256 -> ()

type Rep Base64SHA256

Defined in Voting.Protocol.Arith

type Rep Base64SHA256 = D1 (MetaData "Base64SHA256" "Voting.Protocol.Arith" "hjugement-protocol-0.0.8.20191027-9HiW8HrEuPGHgxG7ahMSfc" True) (C1 (MetaCons "Base64SHA256" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Text)))

base64SHA256 :: ByteString -> Base64SHA256

(base64SHA256 bs) returns the SHA256 hash of the given ByteString bs, as a Text escaped in base64 encoding (RFC 4648).

Type HexSHA256

newtype HexSHA256

Constructors

HexSHA256 Text

Instances

Eq HexSHA256

Defined in Voting.Protocol.Arith

Methods

(==) :: HexSHA256 -> HexSHA256 -> Bool

(/=) :: HexSHA256 -> HexSHA256 -> Bool

Ord HexSHA256

Defined in Voting.Protocol.Arith

Methods

compare :: HexSHA256 -> HexSHA256 -> Ordering

(<) :: HexSHA256 -> HexSHA256 -> Bool

(<=) :: HexSHA256 -> HexSHA256 -> Bool

(>) :: HexSHA256 -> HexSHA256 -> Bool

(>=) :: HexSHA256 -> HexSHA256 -> Bool

max :: HexSHA256 -> HexSHA256 -> HexSHA256

min :: HexSHA256 -> HexSHA256 -> HexSHA256

Show HexSHA256

Defined in Voting.Protocol.Arith

Methods

showsPrec :: Int -> HexSHA256 -> ShowS

show :: HexSHA256 -> String

showList :: [HexSHA256] -> ShowS

Generic HexSHA256

Defined in Voting.Protocol.Arith

Associated Types

type Rep HexSHA256 :: Type -> Type

Methods

from :: HexSHA256 -> Rep HexSHA256 x

to :: Rep HexSHA256 x -> HexSHA256

ToJSON HexSHA256

Defined in Voting.Protocol.Arith

Methods

toJSON :: HexSHA256 -> Value

toEncoding :: HexSHA256 -> Encoding

toJSONList :: [HexSHA256] -> Value

toEncodingList :: [HexSHA256] -> Encoding

FromJSON HexSHA256

Defined in Voting.Protocol.Arith

Methods

parseJSON :: Value -> Parser HexSHA256

parseJSONList :: Value -> Parser [HexSHA256]

NFData HexSHA256

Defined in Voting.Protocol.Arith

Methods

rnf :: HexSHA256 -> ()

type Rep HexSHA256

Defined in Voting.Protocol.Arith

type Rep HexSHA256 = D1 (MetaData "HexSHA256" "Voting.Protocol.Arith" "hjugement-protocol-0.0.8.20191027-9HiW8HrEuPGHgxG7ahMSfc" True) (C1 (MetaCons "HexSHA256" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Text)))

hexSHA256 :: ByteString -> Text

(hexSHA256 bs) returns the SHA256 hash of the given ByteString bs, escaped in hexadecimal into a Text of 32 lowercase characters.

Used (in retro-dependencies of this library) to hash the PublicKey of a voter or a trustee.

Orphan instances

Random Natural

Methods

randomR :: RandomGen g => (Natural, Natural) -> g -> (Natural, g)

random :: RandomGen g => g -> (Natural, g)

randomRs :: RandomGen g => (Natural, Natural) -> g -> [Natural]

randoms :: RandomGen g => g -> [Natural]

randomRIO :: (Natural, Natural) -> IO Natural

randomIO :: IO Natural