Safe Haskell	None
Language	Haskell2010

Data.Pairing.BN254

Contents

BN254 curve
Orphan instances

Synopsis

module Data.Pairing
module Data.Pairing.Ate
data BN254
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

BN254 curve

data BN254 #

BN254 curve.

Instances

Pairing BN254 Source #
Instance details Defined in Data.Pairing.BN254 Associated Types type G1 BN254 = (g :: Type) Source # type G2 BN254 = (g :: Type) Source # type GT BN254 = (g :: Type) Source # Methods pairing :: G1 BN254 -> G2 BN254 -> GT BN254 Source #
WACurve BN254 Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254T Methods gA_ :: WAPoint BN254 Fq2 Fr #
WACurve BN254 Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254 Methods gA_ :: WAPoint BN254 Fq Fr #
WJCurve BN254 Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254T Methods gJ_ :: WJPoint BN254 Fq2 Fr #
WJCurve BN254 Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254 Methods gJ_ :: WJPoint BN254 Fq Fr #
WPCurve BN254 Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254T Methods gP_ :: WPPoint BN254 Fq2 Fr #
WPCurve BN254 Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254 Methods gP_ :: WPPoint BN254 Fq Fr #
Curve Weierstrass c BN254 Fq2 Fr => WCurve c BN254 Fq2 Fr
Instance details Defined in Data.Curve.Weierstrass.BN254T Methods a_ :: WPoint c BN254 Fq2 Fr -> Fq2 # b_ :: WPoint c BN254 Fq2 Fr -> Fq2 # h_ :: WPoint c BN254 Fq2 Fr -> Natural # q_ :: WPoint c BN254 Fq2 Fr -> Natural # r_ :: WPoint c BN254 Fq2 Fr -> Natural #
Curve Weierstrass c BN254 Fq Fr => WCurve c BN254 Fq Fr
Instance details Defined in Data.Curve.Weierstrass.BN254 Methods a_ :: WPoint c BN254 Fq Fr -> Fq # b_ :: WPoint c BN254 Fq Fr -> Fq # h_ :: WPoint c BN254 Fq Fr -> Natural # q_ :: WPoint c BN254 Fq Fr -> Natural # r_ :: WPoint c BN254 Fq Fr -> Natural #
type G1 BN254 Source #
Instance details Defined in Data.Pairing.BN254 type G1 BN254 = G1'
type G2 BN254 Source #
Instance details Defined in Data.Pairing.BN254 type G2 BN254 = G2'
type GT BN254 Source #
Instance details Defined in Data.Pairing.BN254 type GT BN254 = GT'

parameterBin :: [Int8] Source #

BN254 curve parameter s = 6t + 2 in signed binary.

parameterHex :: Integer Source #

BN254 curve parameter t in hexadecimal.

Fields

type Fq = Prime Q #

Field of points of BN254 curve.

type Fq2 = Extension U Fq #

Field of points of BN254 curve over Fq2.

type Fq6 = Extension V Fq2 Source #

Field of points of BN254 curve over Fq6.

type Fq12 = Extension W Fq6 Source #

Field of points of BN254 curve over Fq12.

type Fr = Prime R #

Field of coefficients of BN254 curve.

Groups

type G1' = PA Source #

BN254 curve left group G1 = E(Fq).

type G2' = PA Source #

BN254 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 BN254 Source #
Instance details Associated Types type G1 BN254 = (g :: Type) Source # type G2 BN254 = (g :: Type) Source # type GT BN254 = (g :: Type) Source # Methods pairing :: G1 BN254 -> G2 BN254 -> GT BN254 Source #