Voting.Protocol.Arith

Arithmetic

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

GroupParams crypto c => 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 FFC => Additive (G FFC c)

Defined in Voting.Protocol.FFC

Methods

zero :: G FFC c

(+) :: G FFC c -> G FFC c -> G FFC c

sum :: Foldable f => f (G FFC c) -> G FFC c

GroupParams 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

GroupParams crypto c => 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 FFC => Negable (G FFC c)

Defined in Voting.Protocol.FFC

Methods

neg :: G FFC c -> G FFC c

(-) :: G FFC c -> G FFC c -> G FFC 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

GroupParams crypto c => 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 FFC => Multiplicative (G FFC c)

Defined in Voting.Protocol.FFC

Methods

one :: G FFC c

(*) :: G FFC c -> G FFC c -> G FFC 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 FFC => Invertible (G FFC c)

Defined in Voting.Protocol.FFC

Methods

inv :: G FFC c -> G FFC c

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

(^) :: forall crypto c. Reifies c crypto => Multiplicative (G 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.

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

Minimal complete definition

groupGen, groupOrder

Methods

groupGen :: G crypto c

A generator of the subgroup.

groupOrder :: Proxy c -> Natural

The order of the subgroup.

groupGenPowers :: [G crypto c]

groupGenPowers returns the infinite list of powers of groupGen.

NOTE: In the GroupParams class to keep computed values in memory across calls to groupGenPowers.

groupGenInverses :: [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.

NOTE: In the GroupParams class to keep computed values in memory across calls to groupGenInverses.

Used by intervalDisjunctions.

Instances

Reifies c FFC => GroupParams FFC c

Defined in Voting.Protocol.FFC

Methods

groupGen :: G FFC c

groupOrder :: Proxy c -> Natural

groupGenPowers :: [G FFC c]

groupGenInverses :: [G FFC c]

Class ReifyCrypto

class ReifyCrypto crypto where

Methods

reifyCrypto :: crypto -> (forall c. Reifies c crypto => GroupParams crypto c => Proxy c -> r) -> r

Like reify but augmented with the GroupParams constraint.

Instances

ReifyCrypto FFC

Defined in Voting.Protocol.FFC

Methods

reifyCrypto :: FFC -> (forall c. (Reifies c FFC, GroupParams FFC c) => Proxy c -> r) -> r

Type G

newtype G crypto c

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

Constructors

G

Fields

• unG :: FieldElement crypto

Instances

Eq (G FFC c)

Defined in Voting.Protocol.FFC

Methods

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

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

Ord (G FFC c)

Defined in Voting.Protocol.FFC

Methods

compare :: G FFC c -> G FFC c -> Ordering

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

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

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

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

max :: G FFC c -> G FFC c -> G FFC c

min :: G FFC c -> G FFC c -> G FFC c

Show (G FFC c)

Defined in Voting.Protocol.FFC

Methods

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

show :: G FFC c -> String

showList :: [G FFC c] -> ShowS

ToJSON (G FFC c)

Defined in Voting.Protocol.FFC

Methods

toJSON :: G FFC c -> Value

toEncoding :: G FFC c -> Encoding

toJSONList :: [G FFC c] -> Value

toEncodingList :: [G FFC 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 (G FFC c)

Defined in Voting.Protocol.FFC

Methods

rnf :: G FFC c -> ()

Reifies c FFC => Random (G FFC c)

Defined in Voting.Protocol.FFC

Methods

randomR :: RandomGen g => (G FFC c, G FFC c) -> g -> (G FFC c, g)

random :: RandomGen g => g -> (G FFC c, g)

randomRs :: RandomGen g => (G FFC c, G FFC c) -> g -> [G FFC c]

randoms :: RandomGen g => g -> [G FFC c]

randomRIO :: (G FFC c, G FFC c) -> IO (G FFC c)

randomIO :: IO (G FFC c)

ToNatural (G FFC c)

Defined in Voting.Protocol.FFC

Methods

nat :: G FFC c -> Natural

Reifies c FFC => FromNatural (G FFC c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> G FFC c

Reifies c FFC => Invertible (G FFC c)

Defined in Voting.Protocol.FFC

Methods

inv :: G FFC c -> G FFC c

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

Reifies c FFC => Multiplicative (G FFC c)

Defined in Voting.Protocol.FFC

Methods

one :: G FFC c

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

Reifies c FFC => Negable (G FFC c)

Defined in Voting.Protocol.FFC

Methods

neg :: G FFC c -> G FFC c

(-) :: G FFC c -> G FFC c -> G FFC c

Reifies c FFC => Additive (G FFC c)

Defined in Voting.Protocol.FFC

Methods

zero :: G FFC c

(+) :: G FFC c -> G FFC c -> G FFC c

sum :: Foldable f => f (G FFC c) -> G FFC c

Type family FieldElement

type family FieldElement crypto :: *

Instances

type FieldElement FFC

The type of the elements of a Finite Prime Field.

A field must satisfy the following properties:

• (f, (+), zero) forms an abelian group, called the Additive group of f.
• (NonNull f, (*), one) forms an abelian group, called the Multiplicative group of f.
• (*) is associative: (a*b)*c == a*(b*c) and a*(b*c) == (a*b)*c.
• (*) and (+) are both commutative: a*b == b*a and a+b == b+a
• (*) and (+) are both left and right distributive: a*(b+c) == (a*b) + (a*c) and (a+b)*c == (a*c) + (b*c)

The Natural is always within [0..fieldCharac-1].

Defined in Voting.Protocol.FFC

type FieldElement FFC = Natural

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

GroupParams crypto c => 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

GroupParams crypto c => 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 -> ()

GroupParams crypto c => 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

GroupParams crypto c => FromNatural (E crypto c)

Defined in Voting.Protocol.Arith

Methods

fromNatural :: Natural -> E crypto c

GroupParams crypto c => Multiplicative (E crypto c)

Defined in Voting.Protocol.Arith

Methods

one :: E crypto c

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

GroupParams crypto c => 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

GroupParams crypto c => 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

GroupParams crypto c => FromNatural (E crypto c)

Defined in Voting.Protocol.Arith

Methods

fromNatural :: Natural -> E crypto c

Reifies c FFC => FromNatural (G FFC c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> G FFC c

Class ToNatural

class ToNatural a where

Methods

nat :: a -> Natural

Instances

ToNatural Natural

Defined in Voting.Protocol.Arith

Methods

nat :: Natural -> Natural

ToNatural (E crypto c)

Defined in Voting.Protocol.Arith

Methods

nat :: E crypto c -> Natural

ToNatural (G FFC c)

Defined in Voting.Protocol.FFC

Methods

nat :: G FFC 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 :: GroupParams 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-0.0.9.20191031-G4czrbu2qOeHMRyb9R422Q" 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-0.0.9.20191031-G4czrbu2qOeHMRyb9R422Q" 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.

Random

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.

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