Voting.Protocol.Arithmetic

Class CryptoParams where

class (EuclideanRing (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) => CryptoParams 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 CryptoParams 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 ^ negate i | i <- [0..]], but by computing each value from the previous one.

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

Used by intervalDisjunctions.

Instances

Reifies c FFC => CryptoParams 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 => CryptoParams crypto c => Proxy c -> r) -> r

Like reify but augmented with the CryptoParams constraint.

Instances

ReifyCrypto FFC

Defined in Voting.Protocol.FFC

Methods

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

Class Additive

class Additive a where

An additive semigroup.

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.Arithmetic

Methods

zero :: Int

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

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

Additive Integer

Defined in Voting.Protocol.Arithmetic

Methods

zero :: Integer

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

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

Additive Natural

Defined in Voting.Protocol.Arithmetic

Methods

zero :: Natural

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

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

CryptoParams crypto c => Additive (E crypto c)

Defined in Voting.Protocol.Arithmetic

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

CryptoParams crypto c => Additive (Encryption crypto v c)

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

Defined in Voting.Protocol.Cryptography

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 Semiring

class Additive a => Semiring a where

A multiplicative semigroup, with an additive semigroup (aka. a semiring).

Methods

one :: a

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

Instances

Semiring Int

Defined in Voting.Protocol.Arithmetic

Methods

one :: Int

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

Semiring Integer

Defined in Voting.Protocol.Arithmetic

Methods

one :: Integer

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

Semiring Natural

Defined in Voting.Protocol.Arithmetic

Methods

one :: Natural

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

CryptoParams crypto c => Semiring (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

one :: E crypto c

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

Reifies c FFC => Semiring (G FFC c)

Defined in Voting.Protocol.FFC

Methods

one :: G FFC c

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

(^) :: forall crypto c. Reifies c crypto => Semiring (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 Ring

class Semiring a => Ring a where

A semiring that support substraction (aka. a ring).

Minimal complete definition

negate

Methods

negate :: a -> a

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

Instances

Ring Int

Defined in Voting.Protocol.Arithmetic

Methods

negate :: Int -> Int

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

Ring Integer

Defined in Voting.Protocol.Arithmetic

Methods

negate :: Integer -> Integer

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

CryptoParams crypto c => Ring (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

negate :: E crypto c -> E crypto c

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

Reifies c FFC => Ring (G FFC c)

Defined in Voting.Protocol.FFC

Methods

negate :: G FFC c -> G FFC c

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

Class EuclideanRing

class Ring a => EuclideanRing a where

A commutative ring that support division (aka. an euclidean ring).

Minimal complete definition

inverse

Methods

inverse :: a -> a

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

Instances

Reifies c FFC => EuclideanRing (G FFC c)

Defined in Voting.Protocol.FFC

Methods

inverse :: G FFC c -> G FFC c

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

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 => EuclideanRing (G FFC c)

Defined in Voting.Protocol.FFC

Methods

inverse :: G FFC c -> G FFC c

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

Reifies c FFC => Ring (G FFC c)

Defined in Voting.Protocol.FFC

Methods

negate :: G FFC c -> G FFC c

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

Reifies c FFC => Semiring (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 => 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

CryptoParams crypto c => Bounded (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

minBound :: E crypto c

maxBound :: E crypto c

CryptoParams crypto c => Enum (E crypto c)

Defined in Voting.Protocol.Arithmetic

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.Arithmetic

Methods

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

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

Ord (E crypto c)

Defined in Voting.Protocol.Arithmetic

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.Arithmetic

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.Arithmetic

Methods

toJSON :: E crypto c -> Value

toEncoding :: E crypto c -> Encoding

toJSONList :: [E crypto c] -> Value

toEncodingList :: [E crypto c] -> Encoding

CryptoParams crypto c => FromJSON (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

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

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

NFData (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

rnf :: E crypto c -> ()

CryptoParams crypto c => Random (E crypto c)

Defined in Voting.Protocol.Arithmetic

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.Arithmetic

Methods

nat :: E crypto c -> Natural

CryptoParams crypto c => FromNatural (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

fromNatural :: Natural -> E crypto c

CryptoParams crypto c => Ring (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

negate :: E crypto c -> E crypto c

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

CryptoParams crypto c => Semiring (E crypto c)

Defined in Voting.Protocol.Arithmetic

Methods

one :: E crypto c

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

CryptoParams crypto c => Additive (E crypto c)

Defined in Voting.Protocol.Arithmetic

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

FromNatural Natural

Defined in Voting.Protocol.Arithmetic

Methods

fromNatural :: Natural -> Natural

CryptoParams crypto c => FromNatural (E crypto c)

Defined in Voting.Protocol.Arithmetic

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.Arithmetic

Methods

nat :: Natural -> Natural

ToNatural (E crypto c)

Defined in Voting.Protocol.Arithmetic

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.