Safe Haskell	None
Language	Haskell2010

Pairing.Group

Contents

Orphan instances

Description

Definitions of the groups the pairing is defined on

Synopsis

class Monoid g => CyclicGroup g where
- generator :: g
- order :: Proxy g -> Integer
- expn :: AsInteger e => g -> e -> g
- inverse :: g -> g
type G1 = Point Fq
type G2 = Point Fq2
type GT = Fq12
isOnCurveG1 :: G1 -> Bool
isOnCurveG2 :: G2 -> Bool
isInGT :: GT -> Bool
g1 :: G1
g2 :: G2
b1 :: Fq
b2 :: Fq2
hashToG1 :: (MonadIO m, MonadRandom m) => ByteString -> m G1
randomG1 :: (MonadIO m, MonadRandom m) => m G1
randomG2 :: (MonadIO m, MonadRandom m) => m G2

Documentation

class Monoid g => CyclicGroup g where Source #

Methods

generator :: g Source #

order :: Proxy g -> Integer Source #

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

inverse :: g -> g Source #

Instances

CyclicGroup GT Source #
Instance details Defined in Pairing.Group Methods generator :: GT Source # order :: Proxy GT -> Integer Source # expn :: AsInteger e => GT -> e -> GT Source # inverse :: GT -> GT Source #
CyclicGroup G2 Source #
Instance details Defined in Pairing.Group Methods generator :: G2 Source # order :: Proxy G2 -> Integer Source # expn :: AsInteger e => G2 -> e -> G2 Source # inverse :: G2 -> G2 Source #
CyclicGroup G1 Source #
Instance details Defined in Pairing.Group Methods generator :: G1 Source # order :: Proxy G1 -> Integer Source # expn :: AsInteger e => G1 -> e -> G1 Source # inverse :: G1 -> G1 Source #

type G1 = Point Fq Source #

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

type G2 = Point Fq2 Source #

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

type GT = Fq12 Source #

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

isOnCurveG1 :: G1 -> Bool Source #

Test whether a value in G1 satisfies the corresponding curve equation

isOnCurveG2 :: G2 -> Bool Source #

Test whether a value in G2 satisfies the corresponding curve equation

isInGT :: GT -> Bool Source #

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

g1 :: G1 Source #

Generator for G1

g2 :: G2 Source #

Generator for G2

b1 :: Fq Source #

Parameter for curve on Fq

b2 :: Fq2 Source #

Parameter for twisted curve over Fq2

hashToG1 :: (MonadIO m, MonadRandom m) => ByteString -> m G1 Source #

randomG1 :: (MonadIO m, MonadRandom m) => m G1 Source #

randomG2 :: (MonadIO m, MonadRandom m) => m G2 Source #

Orphan instances

Semigroup GT Source #
Instance details Methods (<>) :: GT -> GT -> GT # sconcat :: NonEmpty GT -> GT # stimes :: Integral b => b -> GT -> GT #
Semigroup G2 Source #
Instance details Methods (<>) :: G2 -> G2 -> G2 # sconcat :: NonEmpty G2 -> G2 # stimes :: Integral b => b -> G2 -> G2 #
Semigroup G1 Source #
Instance details Methods (<>) :: G1 -> G1 -> G1 # sconcat :: NonEmpty G1 -> G1 # stimes :: Integral b => b -> G1 -> G1 #
Monoid GT Source #
Instance details Methods mempty :: GT # mappend :: GT -> GT -> GT # mconcat :: [GT] -> GT #
Monoid G2 Source #
Instance details Methods mempty :: G2 # mappend :: G2 -> G2 -> G2 # mconcat :: [G2] -> G2 #
Monoid G1 Source #
Instance details Methods mempty :: G1 # mappend :: G1 -> G1 -> G1 # mconcat :: [G1] -> G1 #
CyclicGroup GT Source #
Instance details Methods generator :: GT Source # order :: Proxy GT -> Integer Source # expn :: AsInteger e => GT -> e -> GT Source # inverse :: GT -> GT Source #
CyclicGroup G2 Source #
Instance details Methods generator :: G2 Source # order :: Proxy G2 -> Integer Source # expn :: AsInteger e => G2 -> e -> G2 Source # inverse :: G2 -> G2 Source #
CyclicGroup G1 Source #
Instance details Methods generator :: G1 Source # order :: Proxy G1 -> Integer Source # expn :: AsInteger e => G1 -> e -> G1 Source # inverse :: G1 -> G1 Source #
Arbitrary (Point Fq) Source #
Instance details Methods arbitrary :: Gen (Point Fq) # shrink :: Point Fq -> [Point Fq] #
Arbitrary (Point Fq2) Source #
Instance details Methods arbitrary :: Gen (Point Fq2) # shrink :: Point Fq2 -> [Point Fq2] #