Safe Haskell	None
Language	Haskell2010

Data.Pairing.BN254A

Contents

BN254A curve
Orphan instances

Synopsis

module Data.Pairing
module Data.Pairing.Ate
data BN254A
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

BN254A curve

data BN254A #

BN254A curve.

Instances

Pairing BN254A Source #
Instance details Defined in Data.Pairing.BN254A Associated Types type G1 BN254A = (g :: Type) Source # type G2 BN254A = (g :: Type) Source # type GT BN254A = (g :: Type) Source # Methods pairing :: G1 BN254A -> G2 BN254A -> GT BN254A Source #
WACurve BN254A Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254AT Methods gA_ :: WAPoint BN254A Fq2 Fr #
WACurve BN254A Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254A Methods gA_ :: WAPoint BN254A Fq Fr #
WJCurve BN254A Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254AT Methods gJ_ :: WJPoint BN254A Fq2 Fr #
WJCurve BN254A Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254A Methods gJ_ :: WJPoint BN254A Fq Fr #
WPCurve BN254A Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254AT Methods gP_ :: WPPoint BN254A Fq2 Fr #
WPCurve BN254A Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254A Methods gP_ :: WPPoint BN254A Fq Fr #
Curve Weierstrass c BN254A Fq2 Fr => WCurve c BN254A Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254AT Methods a_ :: WPoint c BN254A Fq2 Fr -> Fq2 # b_ :: WPoint c BN254A Fq2 Fr -> Fq2 # h_ :: WPoint c BN254A Fq2 Fr -> Natural # q_ :: WPoint c BN254A Fq2 Fr -> Natural # r_ :: WPoint c BN254A Fq2 Fr -> Natural #
Curve Weierstrass c BN254A Fq Fr => WCurve c BN254A Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254A Methods a_ :: WPoint c BN254A Fq Fr -> Fq # b_ :: WPoint c BN254A Fq Fr -> Fq # h_ :: WPoint c BN254A Fq Fr -> Natural # q_ :: WPoint c BN254A Fq Fr -> Natural # r_ :: WPoint c BN254A Fq Fr -> Natural #
type G1 BN254A Source #
Instance details Defined in Data.Pairing.BN254A type G1 BN254A = G1'
type G2 BN254A Source #
Instance details Defined in Data.Pairing.BN254A type G2 BN254A = G2'
type GT BN254A Source #
Instance details Defined in Data.Pairing.BN254A type GT BN254A = GT'

parameterBin :: [Int8] Source #

BN254A curve parameter s = 6t + 2 in signed binary.

parameterHex :: Integer Source #

BN254A curve parameter t in hexadecimal.

Fields

type Fq = Prime Q #

Field of points of BN254A curve.

type Fq2 = Extension U Fq #

Field of points of BN254A curve over Fq2.

type Fq6 = Extension V Fq2 Source #

Field of points of BN254A curve over Fq6.

type Fq12 = Extension W Fq6 Source #

Field of points of BN254A curve over Fq12.

type Fr = Prime R #

Field of coefficients of BN254A curve.

Groups

type G1' = PA Source #

BN254A curve left group G1 = E(Fq).

type G2' = PA Source #

BN254A 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 BN254A Source #
Instance details Associated Types type G1 BN254A = (g :: Type) Source # type G2 BN254A = (g :: Type) Source # type GT BN254A = (g :: Type) Source # Methods pairing :: G1 BN254A -> G2 BN254A -> GT BN254A Source #