Pairing.Group

Definitions of the groups the pairing is defined on

Documentation

class Monoid g => CyclicGroup g where

Methods

generator :: g

order :: Proxy g -> Integer

expn :: AsInteger e => g -> e -> g

inverse :: g -> g

Instances

CyclicGroup GT

Defined in Pairing.Group

Methods

generator :: GT

order :: Proxy GT -> Integer

expn :: AsInteger e => GT -> e -> GT

inverse :: GT -> GT

CyclicGroup G2

Defined in Pairing.Group

Methods

generator :: G2

order :: Proxy G2 -> Integer

expn :: AsInteger e => G2 -> e -> G2

inverse :: G2 -> G2

CyclicGroup G1

Defined in Pairing.Group

Methods

generator :: G1

order :: Proxy G1 -> Integer

expn :: AsInteger e => G1 -> e -> G1

inverse :: G1 -> G1

type G1 = Point Fq

G1 is E(Fq) defined by y^2 = x^3 + b

type G2 = Point Fq2

G2 is E'(Fq2) defined by y^2 = x^3 + b / xi

type GT = Fq12

GT is subgroup of _r-th roots of unity of the multiplicative group of Fq12

isOnCurveG1 :: G1 -> Bool

Test whether a value in G1 satisfies the corresponding curve equation

isOnCurveG2 :: G2 -> Bool

Test whether a value in G2 satisfies the corresponding curve equation

isInGT :: GT -> Bool

Test whether a value is an _r-th root of unity

g1 :: G1

Generator for G1

g2 :: G2

Generator for G2

b1 :: Fq

Parameter for curve on Fq

b2 :: Fq2

Parameter for twisted curve over Fq2

Orphan instances

Semigroup GT

Methods

(<>) :: GT -> GT -> GT

sconcat :: NonEmpty GT -> GT

stimes :: Integral b => b -> GT -> GT

Semigroup G2

Methods

(<>) :: G2 -> G2 -> G2

sconcat :: NonEmpty G2 -> G2

stimes :: Integral b => b -> G2 -> G2

Semigroup G1

Methods

(<>) :: G1 -> G1 -> G1

sconcat :: NonEmpty G1 -> G1

stimes :: Integral b => b -> G1 -> G1

Monoid GT

Methods

mempty :: GT

mappend :: GT -> GT -> GT

mconcat :: [GT] -> GT

Monoid G2

Methods

mempty :: G2

mappend :: G2 -> G2 -> G2

mconcat :: [G2] -> G2

Monoid G1

Methods

mempty :: G1

mappend :: G1 -> G1 -> G1

mconcat :: [G1] -> G1

CyclicGroup GT

Methods

generator :: GT

order :: Proxy GT -> Integer

expn :: AsInteger e => GT -> e -> GT

inverse :: GT -> GT

CyclicGroup G2

Methods

generator :: G2

order :: Proxy G2 -> Integer

expn :: AsInteger e => G2 -> e -> G2

inverse :: G2 -> G2

CyclicGroup G1

Methods

generator :: G1

order :: Proxy G1 -> Integer

expn :: AsInteger e => G1 -> e -> G1

inverse :: G1 -> G1

Arbitrary (Point Fq)

Methods

arbitrary :: Gen (Point Fq)

shrink :: Point Fq -> [Point Fq]

Arbitrary (Point Fq2)

Methods

arbitrary :: Gen (Point Fq2)

shrink :: Point Fq2 -> [Point Fq2]