Safe Haskell	None
Language	Haskell2010

Data.Pairing.BN254D

Contents

BN254D curve
Orphan instances

Synopsis

module Data.Pairing
module Data.Pairing.Ate
data BN254D
parameterBin :: [Int8]
parameterHex :: Integer
type Fq = Prime Q
type Fq2 = Extension U Fq
type Fq6 = Extension V Fq2
type Fq12 = Extension W Fq6
type Fr = Prime R
type G1' = PA
type G2' = PA
type GT' = RootsOfUnity R Fq12
getRootOfUnity :: Int -> Fr

Documentation

module Data.Pairing

module Data.Pairing.Ate

BN254D curve

data BN254D #

BN254D curve.

Instances

Pairing BN254D Source #
Instance details Defined in Data.Pairing.BN254D Associated Types type G1 BN254D = (g :: Type) Source # type G2 BN254D = (g :: Type) Source # type GT BN254D = (g :: Type) Source # Methods pairing :: G1 BN254D -> G2 BN254D -> GT BN254D Source #
WACurve BN254D Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254DT Methods gA_ :: WAPoint BN254D Fq2 Fr #
WACurve BN254D Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254D Methods gA_ :: WAPoint BN254D Fq Fr #
WJCurve BN254D Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254DT Methods gJ_ :: WJPoint BN254D Fq2 Fr #
WJCurve BN254D Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254D Methods gJ_ :: WJPoint BN254D Fq Fr #
WPCurve BN254D Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254DT Methods gP_ :: WPPoint BN254D Fq2 Fr #
WPCurve BN254D Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254D Methods gP_ :: WPPoint BN254D Fq Fr #
Curve Weierstrass c BN254D Fq2 Fr => WCurve c BN254D Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254DT Methods a_ :: WPoint c BN254D Fq2 Fr -> Fq2 # b_ :: WPoint c BN254D Fq2 Fr -> Fq2 # h_ :: WPoint c BN254D Fq2 Fr -> Natural # q_ :: WPoint c BN254D Fq2 Fr -> Natural # r_ :: WPoint c BN254D Fq2 Fr -> Natural #
Curve Weierstrass c BN254D Fq Fr => WCurve c BN254D Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254D Methods a_ :: WPoint c BN254D Fq Fr -> Fq # b_ :: WPoint c BN254D Fq Fr -> Fq # h_ :: WPoint c BN254D Fq Fr -> Natural # q_ :: WPoint c BN254D Fq Fr -> Natural # r_ :: WPoint c BN254D Fq Fr -> Natural #
type G1 BN254D Source #
Instance details Defined in Data.Pairing.BN254D type G1 BN254D = G1'
type G2 BN254D Source #
Instance details Defined in Data.Pairing.BN254D type G2 BN254D = G2'
type GT BN254D Source #
Instance details Defined in Data.Pairing.BN254D type GT BN254D = GT'

parameterBin :: [Int8] Source #

BN254D curve parameter s = 6t + 2 in signed binary.

parameterHex :: Integer Source #

BN254D curve parameter t in hexadecimal.

Fields

type Fq = Prime Q #

Field of points of BN254D curve.

type Fq2 = Extension U Fq #

Field of points of BN254D curve over Fq2.

type Fq6 = Extension V Fq2 Source #

Field of points of BN254D curve over Fq6.

type Fq12 = Extension W Fq6 Source #

Field of points of BN254D curve over Fq12.

type Fr = Prime R #

Field of coefficients of BN254D curve.

Groups

type G1' = PA Source #

BN254D curve left group G1 = E(Fq).

type G2' = PA Source #

BN254D curve right group G2 = E'(Fq2).

type GT' = RootsOfUnity R Fq12 Source #

Fq12 multiplicative target group GT.

Roots of unity

getRootOfUnity :: Int -> Fr Source #

Precompute primitive roots of unity for binary powers that divide r - 1.

Orphan instances

Pairing BN254D Source #
Instance details Associated Types type G1 BN254D = (g :: Type) Source # type G2 BN254D = (g :: Type) Source # type GT BN254D = (g :: Type) Source # Methods pairing :: G1 BN254D -> G2 BN254D -> GT BN254D Source #