Safe Haskell	None
Language	Haskell2010

Voting.Protocol.Arithmetic

Contents

Class CryptoParams where
- Class ReifyCrypto
Class Additive
Class Semiring
Class FromNatural
Class ToNatural

Synopsis

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
- groupGen :: G crypto c
- groupOrder :: Proxy c -> Natural
- groupGenPowers :: [G crypto c]
- groupGenInverses :: [G crypto c]
class ReifyCrypto crypto where
- reifyCrypto :: crypto -> (forall c. Reifies c crypto => CryptoParams crypto c => Proxy c -> r) -> r
class Additive a where
- zero :: a
- (+) :: a -> a -> a
- sum :: Foldable f => f a -> a
class Additive a => Semiring a where
- one :: a
- (*) :: a -> a -> a
(^) :: forall crypto c. Reifies c crypto => Semiring (G crypto c) => G crypto c -> E crypto c -> G crypto c
class Semiring a => Ring a where
- negate :: a -> a
- (-) :: a -> a -> a
class Ring a => EuclideanRing a where
- inverse :: a -> a
- (/) :: a -> a -> a
newtype G crypto c = G {
- unG :: FieldElement crypto
}
type family FieldElement crypto :: *
newtype E crypto c = E {
- unE :: Natural
}
class FromNatural a where
- fromNatural :: Natural -> a
class ToNatural a where
- nat :: a -> Natural
bytesNat :: ToNatural n => n -> ByteString

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 Source #

Minimal complete definition

groupGen, groupOrder

Methods

groupGen :: G crypto c Source #

A generator of the subgroup.

groupOrder :: Proxy c -> Natural Source #

The order of the subgroup.

groupGenPowers :: [G crypto c] Source #

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] Source #

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

Instances details

Reifies c FFC => CryptoParams FFC c Source #
Instance details Defined in Voting.Protocol.FFC Methods groupGen :: G FFC c Source # groupOrder :: Proxy c -> Natural Source # groupGenPowers :: [G FFC c] Source # groupGenInverses :: [G FFC c] Source #

Class `ReifyCrypto`

class ReifyCrypto crypto where Source #

Methods

reifyCrypto :: crypto -> (forall c. Reifies c crypto => CryptoParams crypto c => Proxy c -> r) -> r Source #

Like reify but augmented with the CryptoParams constraint.

Instances

Instances details

ReifyCrypto FFC Source #
Instance details Defined in Voting.Protocol.FFC Methods reifyCrypto :: FFC -> (forall c. (Reifies c FFC, CryptoParams FFC c) => Proxy c -> r) -> r Source #

Class `Additive`

class Additive a where Source #

An additive semigroup.

Minimal complete definition

zero, (+)

Methods

zero :: a Source #

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

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

Instances

Instances details

Additive Int Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods zero :: Int Source # (+) :: Int -> Int -> Int Source # sum :: Foldable f => f Int -> Int Source #
Additive Integer Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods zero :: Integer Source # (+) :: Integer -> Integer -> Integer Source # sum :: Foldable f => f Integer -> Integer Source #
Additive Natural Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods zero :: Natural Source # (+) :: Natural -> Natural -> Natural Source # sum :: Foldable f => f Natural -> Natural Source #
CryptoParams crypto c => Additive (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods zero :: E crypto c Source # (+) :: E crypto c -> E crypto c -> E crypto c Source # sum :: Foldable f => f (E crypto c) -> E crypto c Source #
Reifies c FFC => Additive (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods zero :: G FFC c Source # (+) :: G FFC c -> G FFC c -> G FFC c Source # sum :: Foldable f => f (G FFC c) -> G FFC c Source #
CryptoParams crypto c => Additive (Encryption crypto v c) Source #	Additive homomorphism. Using the fact that: `groupGen ^x * groupGen ^y == groupGen ^(x+y)`.
Instance details Defined in Voting.Protocol.Cryptography Methods zero :: Encryption crypto v c Source # (+) :: Encryption crypto v c -> Encryption crypto v c -> Encryption crypto v c Source # sum :: Foldable f => f (Encryption crypto v c) -> Encryption crypto v c Source #

Class `Semiring`

class Additive a => Semiring a where Source #

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

Methods

one :: a Source #

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

Instances

Instances details

Semiring Int Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods one :: Int Source # (*) :: Int -> Int -> Int Source #
Semiring Integer Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods one :: Integer Source # (*) :: Integer -> Integer -> Integer Source #
Semiring Natural Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods one :: Natural Source # (*) :: Natural -> Natural -> Natural Source #
CryptoParams crypto c => Semiring (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods one :: E crypto c Source # (*) :: E crypto c -> E crypto c -> E crypto c Source #
Reifies c FFC => Semiring (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods one :: G FFC c Source # (*) :: G FFC c -> G FFC c -> G FFC c Source #

(^) :: forall crypto c. Reifies c crypto => Semiring (G crypto c) => G crypto c -> E crypto c -> G crypto c infixr 8 Source #

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

Class `Ring`

class Semiring a => Ring a where Source #

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

Minimal complete definition

negate

Methods

negate :: a -> a Source #

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

Instances

Instances details

Ring Int Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods negate :: Int -> Int Source # (-) :: Int -> Int -> Int Source #
Ring Integer Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods negate :: Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source #
CryptoParams crypto c => Ring (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods negate :: E crypto c -> E crypto c Source # (-) :: E crypto c -> E crypto c -> E crypto c Source #
Reifies c FFC => Ring (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods negate :: G FFC c -> G FFC c Source # (-) :: G FFC c -> G FFC c -> G FFC c Source #

Class `EuclideanRing`

class Ring a => EuclideanRing a where Source #

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

Minimal complete definition

inverse

Methods

inverse :: a -> a Source #

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

Instances

Instances details

Reifies c FFC => EuclideanRing (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods inverse :: G FFC c -> G FFC c Source # (/) :: G FFC c -> G FFC c -> G FFC c Source #

Type `G`

newtype G crypto c Source #

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

Constructors

G
Fields unG :: FieldElement crypto

Instances

Instances details

Eq (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods (==) :: G FFC c -> G FFC c -> Bool # (/=) :: G FFC c -> G FFC c -> Bool #
Ord (G FFC c) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Voting.Protocol.FFC Methods parseJSON :: Value -> Parser (G FFC c) # parseJSONList :: Value -> Parser [G FFC c] #
NFData (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods rnf :: G FFC c -> () #
Reifies c FFC => Random (G FFC c) Source #
Instance details 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] #
ToNatural (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods nat :: G FFC c -> Natural Source #
Reifies c FFC => FromNatural (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods fromNatural :: Natural -> G FFC c Source #
Reifies c FFC => EuclideanRing (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods inverse :: G FFC c -> G FFC c Source # (/) :: G FFC c -> G FFC c -> G FFC c Source #
Reifies c FFC => Ring (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods negate :: G FFC c -> G FFC c Source # (-) :: G FFC c -> G FFC c -> G FFC c Source #
Reifies c FFC => Semiring (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods one :: G FFC c Source # (*) :: G FFC c -> G FFC c -> G FFC c Source #
Reifies c FFC => Additive (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods zero :: G FFC c Source # (+) :: G FFC c -> G FFC c -> G FFC c Source # sum :: Foldable f => f (G FFC c) -> G FFC c Source #

Type family `FieldElement`

type family FieldElement crypto :: * Source #

Instances

Instances details

type FieldElement FFC Source #

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].

Instance details

Defined in Voting.Protocol.FFC

type FieldElement FFC = Natural

Type `E`

newtype E crypto c Source #

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

Constructors

E
Fields unE :: Natural

Instances

Instances details

CryptoParams crypto c => Bounded (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods minBound :: E crypto c # maxBound :: E crypto c #
Eq (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods (==) :: E crypto c -> E crypto c -> Bool # (/=) :: E crypto c -> E crypto c -> Bool #
Ord (E crypto c) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods parseJSON :: Value -> Parser (E crypto c) # parseJSONList :: Value -> Parser [E crypto c] #
NFData (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods rnf :: E crypto c -> () #
CryptoParams crypto c => Random (E crypto c) Source #
Instance details 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] #
ToNatural (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods nat :: E crypto c -> Natural Source #
CryptoParams crypto c => FromNatural (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods fromNatural :: Natural -> E crypto c Source #
CryptoParams crypto c => Ring (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods negate :: E crypto c -> E crypto c Source # (-) :: E crypto c -> E crypto c -> E crypto c Source #
CryptoParams crypto c => Semiring (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods one :: E crypto c Source # (*) :: E crypto c -> E crypto c -> E crypto c Source #
CryptoParams crypto c => Additive (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods zero :: E crypto c Source # (+) :: E crypto c -> E crypto c -> E crypto c Source # sum :: Foldable f => f (E crypto c) -> E crypto c Source #

Class `FromNatural`

class FromNatural a where Source #

Methods

fromNatural :: Natural -> a Source #

Instances

Instances details

FromNatural Natural Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods fromNatural :: Natural -> Natural Source #
CryptoParams crypto c => FromNatural (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods fromNatural :: Natural -> E crypto c Source #
Reifies c FFC => FromNatural (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods fromNatural :: Natural -> G FFC c Source #

Class `ToNatural`

class ToNatural a where Source #

Methods

nat :: a -> Natural Source #

Instances

Instances details

ToNatural Natural Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods nat :: Natural -> Natural Source #
ToNatural (E crypto c) Source #
Instance details Defined in Voting.Protocol.Arithmetic Methods nat :: E crypto c -> Natural Source #
ToNatural (G FFC c) Source #
Instance details Defined in Voting.Protocol.FFC Methods nat :: G FFC c -> Natural Source #

bytesNat :: ToNatural n => n -> ByteString Source #

(bytesNat x) returns the serialization of x.

Class CryptoParams where

Instances

Class ReifyCrypto

Instances

Class Additive

Instances

Class Semiring

Instances

Class Ring

Instances

Class EuclideanRing

Instances

Type G

Instances

Type family FieldElement

Instances

Type E

Instances

Class FromNatural

Instances

Class ToNatural

Instances

Class `CryptoParams` where

Class `ReifyCrypto`

Class `Additive`

Class `Semiring`

Class `Ring`

Class `EuclideanRing`

Type `G`

Type family `FieldElement`

Type `E`

Class `FromNatural`

Class `ToNatural`