Curve.Weierstrass

Documentation

class GaloisField k => PrimeField' k

Minimal complete definition

toInt'

Instances

KnownNat p => PrimeField' (PrimeField p)

Defined in Curve

Methods

toInt' :: PrimeField p -> Integer

data Coordinates

Curve coordinates.

Constructors

Affine

Jacobian

Projective

data Form

Curve forms.

Constructors

Binary

Edwards

Montgomery

Weierstrass

class (GaloisField q, PrimeField' r, Group (Point f c e q r)) => Curve (f :: Form) (c :: Coordinates) e q r where

Elliptic curves.

Minimal complete definition

char, cof, disc, fromA, point, pointX, toA, yX

Associated Types

data Point f c e q r :: *

Curve point.

Methods

char :: Point f c e q r -> Integer

Curve characteristic.

cof :: Point f c e q r -> Integer

Curve cofactor.

disc :: Point f c e q r -> q

Curve discriminant.

mul :: Point f c e q r -> r -> Point f c e q r

Curve point multiplication.

point :: q -> q -> Maybe (Point f c e q r)

Get point from X and Y coordinates.

pointX :: q -> Maybe (Point f c e q r)

Get point from X coordinate.

yX :: Point f c e q r -> q -> Maybe q

Get Y coordinate from X coordinate.

fromA :: Point f Affine e q r -> Point f c e q r

Transform from affine coordinates.

toA :: Point f c e q r -> Point f Affine e q r

Transform to affine coordinates.

Instances

WACurve e q r => Curve Weierstrass Affine (e :: k) q r

Defined in Curve.Weierstrass

Associated Types

data Point Weierstrass Affine e q r :: Type

Methods

char :: Point Weierstrass Affine e q r -> Integer

cof :: Point Weierstrass Affine e q r -> Integer

disc :: Point Weierstrass Affine e q r -> q

mul :: Point Weierstrass Affine e q r -> r -> Point Weierstrass Affine e q r

point :: q -> q -> Maybe (Point Weierstrass Affine e q r)

pointX :: q -> Maybe (Point Weierstrass Affine e q r)

yX :: Point Weierstrass Affine e q r -> q -> Maybe q

fromA :: Point Weierstrass Affine e q r -> Point Weierstrass Affine e q r

toA :: Point Weierstrass Affine e q r -> Point Weierstrass Affine e q r

WJCurve e q r => Curve Weierstrass Jacobian (e :: k) q r

Defined in Curve.Weierstrass

Associated Types

data Point Weierstrass Jacobian e q r :: Type

Methods

char :: Point Weierstrass Jacobian e q r -> Integer

cof :: Point Weierstrass Jacobian e q r -> Integer

disc :: Point Weierstrass Jacobian e q r -> q

mul :: Point Weierstrass Jacobian e q r -> r -> Point Weierstrass Jacobian e q r

point :: q -> q -> Maybe (Point Weierstrass Jacobian e q r)

pointX :: q -> Maybe (Point Weierstrass Jacobian e q r)

yX :: Point Weierstrass Jacobian e q r -> q -> Maybe q

fromA :: Point Weierstrass Affine e q r -> Point Weierstrass Jacobian e q r

toA :: Point Weierstrass Jacobian e q r -> Point Weierstrass Affine e q r

WPCurve e q r => Curve Weierstrass Projective (e :: k) q r

Defined in Curve.Weierstrass

Associated Types

data Point Weierstrass Projective e q r :: Type

Methods

char :: Point Weierstrass Projective e q r -> Integer

cof :: Point Weierstrass Projective e q r -> Integer

disc :: Point Weierstrass Projective e q r -> q

mul :: Point Weierstrass Projective e q r -> r -> Point Weierstrass Projective e q r

point :: q -> q -> Maybe (Point Weierstrass Projective e q r)

pointX :: q -> Maybe (Point Weierstrass Projective e q r)

yX :: Point Weierstrass Projective e q r -> q -> Maybe q

fromA :: Point Weierstrass Affine e q r -> Point Weierstrass Projective e q r

toA :: Point Weierstrass Projective e q r -> Point Weierstrass Affine e q r

MACurve e q r => Curve Montgomery Affine (e :: k) q r

Defined in Curve.Montgomery

Associated Types

data Point Montgomery Affine e q r :: Type

Methods

char :: Point Montgomery Affine e q r -> Integer

cof :: Point Montgomery Affine e q r -> Integer

disc :: Point Montgomery Affine e q r -> q

mul :: Point Montgomery Affine e q r -> r -> Point Montgomery Affine e q r

point :: q -> q -> Maybe (Point Montgomery Affine e q r)

pointX :: q -> Maybe (Point Montgomery Affine e q r)

yX :: Point Montgomery Affine e q r -> q -> Maybe q

fromA :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r

toA :: Point Montgomery Affine e q r -> Point Montgomery Affine e q r

EACurve e q r => Curve Edwards Affine (e :: k) q r

Defined in Curve.Edwards

Associated Types

data Point Edwards Affine e q r :: Type

Methods

char :: Point Edwards Affine e q r -> Integer

cof :: Point Edwards Affine e q r -> Integer

disc :: Point Edwards Affine e q r -> q

mul :: Point Edwards Affine e q r -> r -> Point Edwards Affine e q r

point :: q -> q -> Maybe (Point Edwards Affine e q r)

pointX :: q -> Maybe (Point Edwards Affine e q r)

yX :: Point Edwards Affine e q r -> q -> Maybe q

fromA :: Point Edwards Affine e q r -> Point Edwards Affine e q r

toA :: Point Edwards Affine e q r -> Point Edwards Affine e q r

EPCurve e q r => Curve Edwards Projective (e :: k) q r

Defined in Curve.Edwards

Associated Types

data Point Edwards Projective e q r :: Type

Methods

char :: Point Edwards Projective e q r -> Integer

cof :: Point Edwards Projective e q r -> Integer

disc :: Point Edwards Projective e q r -> q

mul :: Point Edwards Projective e q r -> r -> Point Edwards Projective e q r

point :: q -> q -> Maybe (Point Edwards Projective e q r)

pointX :: q -> Maybe (Point Edwards Projective e q r)

yX :: Point Edwards Projective e q r -> q -> Maybe q

fromA :: Point Edwards Affine e q r -> Point Edwards Projective e q r

toA :: Point Edwards Projective e q r -> Point Edwards Affine e q r

BACurve e q r => Curve Binary Affine (e :: k) q r

Defined in Curve.Binary

Associated Types

data Point Binary Affine e q r :: Type

Methods

char :: Point Binary Affine e q r -> Integer

cof :: Point Binary Affine e q r -> Integer

disc :: Point Binary Affine e q r -> q

mul :: Point Binary Affine e q r -> r -> Point Binary Affine e q r

point :: q -> q -> Maybe (Point Binary Affine e q r)

pointX :: q -> Maybe (Point Binary Affine e q r)

yX :: Point Binary Affine e q r -> q -> Maybe q

fromA :: Point Binary Affine e q r -> Point Binary Affine e q r

toA :: Point Binary Affine e q r -> Point Binary Affine e q r

BPCurve e q r => Curve Binary Projective (e :: k) q r

Defined in Curve.Binary

Associated Types

data Point Binary Projective e q r :: Type

Methods

char :: Point Binary Projective e q r -> Integer

cof :: Point Binary Projective e q r -> Integer

disc :: Point Binary Projective e q r -> q

mul :: Point Binary Projective e q r -> r -> Point Binary Projective e q r

point :: q -> q -> Maybe (Point Binary Projective e q r)

pointX :: q -> Maybe (Point Binary Projective e q r)

yX :: Point Binary Projective e q r -> q -> Maybe q

fromA :: Point Binary Affine e q r -> Point Binary Projective e q r

toA :: Point Binary Projective e q r -> Point Binary Affine e q r

class WCurve Projective e q r => WPCurve e q r where

Weierstrass projective curves y^2 = x^3 + Ax + B.

Methods

gP_

Arguments

:: WPPoint e q r

Curve generator.

Instances

WPCurve SECP521R1 Fq Fr

Projective SECP521R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP521R1

Methods

gP_ :: WPPoint SECP521R1 Fq Fr

WPCurve SECP384R1 Fq Fr

Projective SECP384R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP384R1

Methods

gP_ :: WPPoint SECP384R1 Fq Fr

WPCurve SECP256R1 Fq Fr

Projective SECP256R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP256R1

Methods

gP_ :: WPPoint SECP256R1 Fq Fr

WPCurve SECP256K1 Fq Fr

Projective SECP256K1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP256K1

Methods

gP_ :: WPPoint SECP256K1 Fq Fr

WPCurve SECP224R1 Fq Fr

Projective SECP224R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP224R1

Methods

gP_ :: WPPoint SECP224R1 Fq Fr

WPCurve SECP224K1 Fq Fr

Projective SECP224K1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP224K1

Methods

gP_ :: WPPoint SECP224K1 Fq Fr

WPCurve SECP192R1 Fq Fr

Projective SECP192R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP192R1

Methods

gP_ :: WPPoint SECP192R1 Fq Fr

WPCurve SECP192K1 Fq Fr

Projective SECP192K1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP192K1

Methods

gP_ :: WPPoint SECP192K1 Fq Fr

WPCurve SECP160R2 Fq Fr

Projective SECP160R2 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP160R2

Methods

gP_ :: WPPoint SECP160R2 Fq Fr

WPCurve SECP160R1 Fq Fr

Projective SECP160R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP160R1

Methods

gP_ :: WPPoint SECP160R1 Fq Fr

WPCurve SECP160K1 Fq Fr

Projective SECP160K1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP160K1

Methods

gP_ :: WPPoint SECP160K1 Fq Fr

WPCurve SECP128R2 Fq Fr

Projective SECP128R2 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP128R2

Methods

gP_ :: WPPoint SECP128R2 Fq Fr

WPCurve SECP128R1 Fq Fr

Projective SECP128R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP128R1

Methods

gP_ :: WPPoint SECP128R1 Fq Fr

WPCurve SECP112R2 Fq Fr

Projective SECP112R2 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP112R2

Methods

gP_ :: WPPoint SECP112R2 Fq Fr

WPCurve SECP112R1 Fq Fr

Projective SECP112R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.SECP112R1

Methods

gP_ :: WPPoint SECP112R1 Fq Fr

WPCurve BrainpoolP512T1 Fq Fr

Projective BrainpoolP512T1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP512T1

Methods

gP_ :: WPPoint BrainpoolP512T1 Fq Fr

WPCurve BrainpoolP512R1 Fq Fr

Projective BrainpoolP512R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP512R1

Methods

gP_ :: WPPoint BrainpoolP512R1 Fq Fr

WPCurve BrainpoolP384T1 Fq Fr

Projective BrainpoolP384T1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP384T1

Methods

gP_ :: WPPoint BrainpoolP384T1 Fq Fr

WPCurve BrainpoolP384R1 Fq Fr

Projective BrainpoolP384R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP384R1

Methods

gP_ :: WPPoint BrainpoolP384R1 Fq Fr

WPCurve BrainpoolP320T1 Fq Fr

Projective BrainpoolP320T1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP320T1

Methods

gP_ :: WPPoint BrainpoolP320T1 Fq Fr

WPCurve BrainpoolP320R1 Fq Fr

Projective BrainpoolP320R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP320R1

Methods

gP_ :: WPPoint BrainpoolP320R1 Fq Fr

WPCurve BrainpoolP256T1 Fq Fr

Projective BrainpoolP256T1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP256T1

Methods

gP_ :: WPPoint BrainpoolP256T1 Fq Fr

WPCurve BrainpoolP256R1 Fq Fr

Projective BrainpoolP256R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP256R1

Methods

gP_ :: WPPoint BrainpoolP256R1 Fq Fr

WPCurve BrainpoolP224T1 Fq Fr

Projective BrainpoolP224T1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP224T1

Methods

gP_ :: WPPoint BrainpoolP224T1 Fq Fr

WPCurve BrainpoolP224R1 Fq Fr

Projective BrainpoolP224R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP224R1

Methods

gP_ :: WPPoint BrainpoolP224R1 Fq Fr

WPCurve BrainpoolP192T1 Fq Fr

Projective BrainpoolP192T1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP192T1

Methods

gP_ :: WPPoint BrainpoolP192T1 Fq Fr

WPCurve BrainpoolP192R1 Fq Fr

Projective BrainpoolP192R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP192R1

Methods

gP_ :: WPPoint BrainpoolP192R1 Fq Fr

WPCurve BrainpoolP160T1 Fq Fr

Projective BrainpoolP160T1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP160T1

Methods

gP_ :: WPPoint BrainpoolP160T1 Fq Fr

WPCurve BrainpoolP160R1 Fq Fr

Projective BrainpoolP160R1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BrainpoolP160R1

Methods

gP_ :: WPPoint BrainpoolP160R1 Fq Fr

WPCurve BN512 Fq Fr

Projective BN512 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN512

Methods

gP_ :: WPPoint BN512 Fq Fr

WPCurve BN462 Fq Fr

Projective BN462 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN462

Methods

gP_ :: WPPoint BN462 Fq Fr

WPCurve BN462T Fq2 Fr

Projective BN462T curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN462T

Methods

gP_ :: WPPoint BN462T Fq2 Fr

WPCurve BN384 Fq Fr

Projective BN384 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN384

Methods

gP_ :: WPPoint BN384 Fq Fr

WPCurve BN256 Fq Fr

Projective BN256 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN256

Methods

gP_ :: WPPoint BN256 Fq Fr

WPCurve BN254B Fq Fr

Projective BN254B curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN254B

Methods

gP_ :: WPPoint BN254B Fq Fr

WPCurve BN254BT Fq2 Fr

Projective BN254BT curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN254BT

Methods

gP_ :: WPPoint BN254BT Fq2 Fr

WPCurve BN254A Fq Fr

Projective BN254A curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN254A

Methods

gP_ :: WPPoint BN254A Fq Fr

WPCurve BN254AT Fq2 Fr

Projective BN254AT curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN254AT

Methods

gP_ :: WPPoint BN254AT Fq2 Fr

WPCurve BN254 Fq Fr

Projective BN254 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN254

Methods

gP_ :: WPPoint BN254 Fq Fr

WPCurve BN254T Fq2 Fr

Projective BN254T curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN254T

Methods

gP_ :: WPPoint BN254T Fq2 Fr

WPCurve BN224 Fq Fr

Projective BN224 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BN224

Methods

gP_ :: WPPoint BN224 Fq Fr

WPCurve BLS48581 Fq Fr

Projective BLS48581 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BLS48581

Methods

gP_ :: WPPoint BLS48581 Fq Fr

WPCurve BLS48581T Fq8 Fr

Projective BLS48581T curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BLS48581T

Methods

gP_ :: WPPoint BLS48581T Fq8 Fr

WPCurve BLS12381 Fq Fr

Projective BLS12381 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BLS12381

Methods

gP_ :: WPPoint BLS12381 Fq Fr

WPCurve BLS12381T Fq2 Fr

Projective BLS12381T curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.BLS12381T

Methods

gP_ :: WPPoint BLS12381T Fq2 Fr

WPCurve Anomalous Fq Fr

Projective Anomalous curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.Anomalous

Methods

gP_ :: WPPoint Anomalous Fq Fr

WPCurve ANSSIFRP256V1 Fq Fr

Projective ANSSIFRP256V1 curve is a Weierstrass projective curve.

Defined in Curve.Weierstrass.ANSSIFRP256V1

Methods

gP_ :: WPPoint ANSSIFRP256V1 Fq Fr

type WPPoint = WPoint Projective

Weierstrass projective points.

class WCurve Jacobian e q r => WJCurve e q r where

Weierstrass Jacobian curves y^2 = x^3 + Ax + B.

Methods

gJ_

Arguments

:: WJPoint e q r

Curve generator.

Instances

WJCurve SECP521R1 Fq Fr

Jacobian SECP521R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP521R1

Methods

gJ_ :: WJPoint SECP521R1 Fq Fr

WJCurve SECP384R1 Fq Fr

Jacobian SECP384R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP384R1

Methods

gJ_ :: WJPoint SECP384R1 Fq Fr

WJCurve SECP256R1 Fq Fr

Jacobian SECP256R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP256R1

Methods

gJ_ :: WJPoint SECP256R1 Fq Fr

WJCurve SECP256K1 Fq Fr

Jacobian SECP256K1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP256K1

Methods

gJ_ :: WJPoint SECP256K1 Fq Fr

WJCurve SECP224R1 Fq Fr

Jacobian SECP224R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP224R1

Methods

gJ_ :: WJPoint SECP224R1 Fq Fr

WJCurve SECP224K1 Fq Fr

Jacobian SECP224K1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP224K1

Methods

gJ_ :: WJPoint SECP224K1 Fq Fr

WJCurve SECP192R1 Fq Fr

Jacobian SECP192R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP192R1

Methods

gJ_ :: WJPoint SECP192R1 Fq Fr

WJCurve SECP192K1 Fq Fr

Jacobian SECP192K1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP192K1

Methods

gJ_ :: WJPoint SECP192K1 Fq Fr

WJCurve SECP160R2 Fq Fr

Jacobian SECP160R2 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP160R2

Methods

gJ_ :: WJPoint SECP160R2 Fq Fr

WJCurve SECP160R1 Fq Fr

Jacobian SECP160R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP160R1

Methods

gJ_ :: WJPoint SECP160R1 Fq Fr

WJCurve SECP160K1 Fq Fr

Jacobian SECP160K1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP160K1

Methods

gJ_ :: WJPoint SECP160K1 Fq Fr

WJCurve SECP128R2 Fq Fr

Jacobian SECP128R2 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP128R2

Methods

gJ_ :: WJPoint SECP128R2 Fq Fr

WJCurve SECP128R1 Fq Fr

Jacobian SECP128R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP128R1

Methods

gJ_ :: WJPoint SECP128R1 Fq Fr

WJCurve SECP112R2 Fq Fr

Jacobian SECP112R2 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP112R2

Methods

gJ_ :: WJPoint SECP112R2 Fq Fr

WJCurve SECP112R1 Fq Fr

Jacobian SECP112R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.SECP112R1

Methods

gJ_ :: WJPoint SECP112R1 Fq Fr

WJCurve BrainpoolP512T1 Fq Fr

Jacobian BrainpoolP512T1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP512T1

Methods

gJ_ :: WJPoint BrainpoolP512T1 Fq Fr

WJCurve BrainpoolP512R1 Fq Fr

Jacobian BrainpoolP512R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP512R1

Methods

gJ_ :: WJPoint BrainpoolP512R1 Fq Fr

WJCurve BrainpoolP384T1 Fq Fr

Jacobian BrainpoolP384T1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP384T1

Methods

gJ_ :: WJPoint BrainpoolP384T1 Fq Fr

WJCurve BrainpoolP384R1 Fq Fr

Jacobian BrainpoolP384R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP384R1

Methods

gJ_ :: WJPoint BrainpoolP384R1 Fq Fr

WJCurve BrainpoolP320T1 Fq Fr

Jacobian BrainpoolP320T1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP320T1

Methods

gJ_ :: WJPoint BrainpoolP320T1 Fq Fr

WJCurve BrainpoolP320R1 Fq Fr

Jacobian BrainpoolP320R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP320R1

Methods

gJ_ :: WJPoint BrainpoolP320R1 Fq Fr

WJCurve BrainpoolP256T1 Fq Fr

Jacobian BrainpoolP256T1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP256T1

Methods

gJ_ :: WJPoint BrainpoolP256T1 Fq Fr

WJCurve BrainpoolP256R1 Fq Fr

Jacobian BrainpoolP256R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP256R1

Methods

gJ_ :: WJPoint BrainpoolP256R1 Fq Fr

WJCurve BrainpoolP224T1 Fq Fr

Jacobian BrainpoolP224T1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP224T1

Methods

gJ_ :: WJPoint BrainpoolP224T1 Fq Fr

WJCurve BrainpoolP224R1 Fq Fr

Jacobian BrainpoolP224R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP224R1

Methods

gJ_ :: WJPoint BrainpoolP224R1 Fq Fr

WJCurve BrainpoolP192T1 Fq Fr

Jacobian BrainpoolP192T1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP192T1

Methods

gJ_ :: WJPoint BrainpoolP192T1 Fq Fr

WJCurve BrainpoolP192R1 Fq Fr

Jacobian BrainpoolP192R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP192R1

Methods

gJ_ :: WJPoint BrainpoolP192R1 Fq Fr

WJCurve BrainpoolP160T1 Fq Fr

Jacobian BrainpoolP160T1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP160T1

Methods

gJ_ :: WJPoint BrainpoolP160T1 Fq Fr

WJCurve BrainpoolP160R1 Fq Fr

Jacobian BrainpoolP160R1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BrainpoolP160R1

Methods

gJ_ :: WJPoint BrainpoolP160R1 Fq Fr

WJCurve BN512 Fq Fr

Jacobian BN512 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN512

Methods

gJ_ :: WJPoint BN512 Fq Fr

WJCurve BN462 Fq Fr

Jacobian BN462 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN462

Methods

gJ_ :: WJPoint BN462 Fq Fr

WJCurve BN462T Fq2 Fr

Jacobian BN462T curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN462T

Methods

gJ_ :: WJPoint BN462T Fq2 Fr

WJCurve BN384 Fq Fr

Jacobian BN384 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN384

Methods

gJ_ :: WJPoint BN384 Fq Fr

WJCurve BN256 Fq Fr

Jacobian BN256 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN256

Methods

gJ_ :: WJPoint BN256 Fq Fr

WJCurve BN254B Fq Fr

Jacobian BN254B curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN254B

Methods

gJ_ :: WJPoint BN254B Fq Fr

WJCurve BN254BT Fq2 Fr

Jacobian BN254BT curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN254BT

Methods

gJ_ :: WJPoint BN254BT Fq2 Fr

WJCurve BN254A Fq Fr

Jacobian BN254A curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN254A

Methods

gJ_ :: WJPoint BN254A Fq Fr

WJCurve BN254AT Fq2 Fr

Jacobian BN254AT curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN254AT

Methods

gJ_ :: WJPoint BN254AT Fq2 Fr

WJCurve BN254 Fq Fr

Jacobian BN254 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN254

Methods

gJ_ :: WJPoint BN254 Fq Fr

WJCurve BN254T Fq2 Fr

Jacobian BN254T curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN254T

Methods

gJ_ :: WJPoint BN254T Fq2 Fr

WJCurve BN224 Fq Fr

Jacobian BN224 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BN224

Methods

gJ_ :: WJPoint BN224 Fq Fr

WJCurve BLS48581 Fq Fr

Jacobian BLS48581 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BLS48581

Methods

gJ_ :: WJPoint BLS48581 Fq Fr

WJCurve BLS48581T Fq8 Fr

Jacobian BLS48581T curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BLS48581T

Methods

gJ_ :: WJPoint BLS48581T Fq8 Fr

WJCurve BLS12381 Fq Fr

Jacobian BLS12381 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BLS12381

Methods

gJ_ :: WJPoint BLS12381 Fq Fr

WJCurve BLS12381T Fq2 Fr

Jacobian BLS12381T curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.BLS12381T

Methods

gJ_ :: WJPoint BLS12381T Fq2 Fr

WJCurve Anomalous Fq Fr

Jacobian Anomalous curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.Anomalous

Methods

gJ_ :: WJPoint Anomalous Fq Fr

WJCurve ANSSIFRP256V1 Fq Fr

Jacobian ANSSIFRP256V1 curve is a Weierstrass Jacobian curve.

Defined in Curve.Weierstrass.ANSSIFRP256V1

Methods

gJ_ :: WJPoint ANSSIFRP256V1 Fq Fr

type WJPoint = WPoint Jacobian

Weierstrass Jacobian points.

class WCurve Affine e q r => WACurve e q r where

Weierstrass affine curves y^2 = x^3 + Ax + B.

Methods

gA_

Arguments

:: WAPoint e q r

Curve generator.

Instances

WACurve SECP521R1 Fq Fr

Affine SECP521R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP521R1

Methods

gA_ :: WAPoint SECP521R1 Fq Fr

WACurve SECP384R1 Fq Fr

Affine SECP384R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP384R1

Methods

gA_ :: WAPoint SECP384R1 Fq Fr

WACurve SECP256R1 Fq Fr

Affine SECP256R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP256R1

Methods

gA_ :: WAPoint SECP256R1 Fq Fr

WACurve SECP256K1 Fq Fr

Affine SECP256K1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP256K1

Methods

gA_ :: WAPoint SECP256K1 Fq Fr

WACurve SECP224R1 Fq Fr

Affine SECP224R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP224R1

Methods

gA_ :: WAPoint SECP224R1 Fq Fr

WACurve SECP224K1 Fq Fr

Affine SECP224K1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP224K1

Methods

gA_ :: WAPoint SECP224K1 Fq Fr

WACurve SECP192R1 Fq Fr

Affine SECP192R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP192R1

Methods

gA_ :: WAPoint SECP192R1 Fq Fr

WACurve SECP192K1 Fq Fr

Affine SECP192K1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP192K1

Methods

gA_ :: WAPoint SECP192K1 Fq Fr

WACurve SECP160R2 Fq Fr

Affine SECP160R2 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP160R2

Methods

gA_ :: WAPoint SECP160R2 Fq Fr

WACurve SECP160R1 Fq Fr

Affine SECP160R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP160R1

Methods

gA_ :: WAPoint SECP160R1 Fq Fr

WACurve SECP160K1 Fq Fr

Affine SECP160K1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP160K1

Methods

gA_ :: WAPoint SECP160K1 Fq Fr

WACurve SECP128R2 Fq Fr

Affine SECP128R2 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP128R2

Methods

gA_ :: WAPoint SECP128R2 Fq Fr

WACurve SECP128R1 Fq Fr

Affine SECP128R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP128R1

Methods

gA_ :: WAPoint SECP128R1 Fq Fr

WACurve SECP112R2 Fq Fr

Affine SECP112R2 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP112R2

Methods

gA_ :: WAPoint SECP112R2 Fq Fr

WACurve SECP112R1 Fq Fr

Affine SECP112R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.SECP112R1

Methods

gA_ :: WAPoint SECP112R1 Fq Fr

WACurve BrainpoolP512T1 Fq Fr

Affine BrainpoolP512T1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP512T1

Methods

gA_ :: WAPoint BrainpoolP512T1 Fq Fr

WACurve BrainpoolP512R1 Fq Fr

Affine BrainpoolP512R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP512R1

Methods

gA_ :: WAPoint BrainpoolP512R1 Fq Fr

WACurve BrainpoolP384T1 Fq Fr

Affine BrainpoolP384T1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP384T1

Methods

gA_ :: WAPoint BrainpoolP384T1 Fq Fr

WACurve BrainpoolP384R1 Fq Fr

Affine BrainpoolP384R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP384R1

Methods

gA_ :: WAPoint BrainpoolP384R1 Fq Fr

WACurve BrainpoolP320T1 Fq Fr

Affine BrainpoolP320T1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP320T1

Methods

gA_ :: WAPoint BrainpoolP320T1 Fq Fr

WACurve BrainpoolP320R1 Fq Fr

Affine BrainpoolP320R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP320R1

Methods

gA_ :: WAPoint BrainpoolP320R1 Fq Fr

WACurve BrainpoolP256T1 Fq Fr

Affine BrainpoolP256T1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP256T1

Methods

gA_ :: WAPoint BrainpoolP256T1 Fq Fr

WACurve BrainpoolP256R1 Fq Fr

Affine BrainpoolP256R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP256R1

Methods

gA_ :: WAPoint BrainpoolP256R1 Fq Fr

WACurve BrainpoolP224T1 Fq Fr

Affine BrainpoolP224T1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP224T1

Methods

gA_ :: WAPoint BrainpoolP224T1 Fq Fr

WACurve BrainpoolP224R1 Fq Fr

Affine BrainpoolP224R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP224R1

Methods

gA_ :: WAPoint BrainpoolP224R1 Fq Fr

WACurve BrainpoolP192T1 Fq Fr

Affine BrainpoolP192T1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP192T1

Methods

gA_ :: WAPoint BrainpoolP192T1 Fq Fr

WACurve BrainpoolP192R1 Fq Fr

Affine BrainpoolP192R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP192R1

Methods

gA_ :: WAPoint BrainpoolP192R1 Fq Fr

WACurve BrainpoolP160T1 Fq Fr

Affine BrainpoolP160T1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP160T1

Methods

gA_ :: WAPoint BrainpoolP160T1 Fq Fr

WACurve BrainpoolP160R1 Fq Fr

Affine BrainpoolP160R1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BrainpoolP160R1

Methods

gA_ :: WAPoint BrainpoolP160R1 Fq Fr

WACurve BN512 Fq Fr

Affine BN512 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN512

Methods

gA_ :: WAPoint BN512 Fq Fr

WACurve BN462 Fq Fr

Affine BN462 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN462

Methods

gA_ :: WAPoint BN462 Fq Fr

WACurve BN462T Fq2 Fr

Affine BN462T curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN462T

Methods

gA_ :: WAPoint BN462T Fq2 Fr

WACurve BN384 Fq Fr

Affine BN384 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN384

Methods

gA_ :: WAPoint BN384 Fq Fr

WACurve BN256 Fq Fr

Affine BN256 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN256

Methods

gA_ :: WAPoint BN256 Fq Fr

WACurve BN254B Fq Fr

Affine BN254B curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN254B

Methods

gA_ :: WAPoint BN254B Fq Fr

WACurve BN254BT Fq2 Fr

Affine BN254BT curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN254BT

Methods

gA_ :: WAPoint BN254BT Fq2 Fr

WACurve BN254A Fq Fr

Affine BN254A curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN254A

Methods

gA_ :: WAPoint BN254A Fq Fr

WACurve BN254AT Fq2 Fr

Affine BN254AT curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN254AT

Methods

gA_ :: WAPoint BN254AT Fq2 Fr

WACurve BN254 Fq Fr

Affine BN254 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN254

Methods

gA_ :: WAPoint BN254 Fq Fr

WACurve BN254T Fq2 Fr

Affine BN254T curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN254T

Methods

gA_ :: WAPoint BN254T Fq2 Fr

WACurve BN224 Fq Fr

Affine BN224 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BN224

Methods

gA_ :: WAPoint BN224 Fq Fr

WACurve BLS48581 Fq Fr

Affine BLS48581 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BLS48581

Methods

gA_ :: WAPoint BLS48581 Fq Fr

WACurve BLS48581T Fq8 Fr

Affine BLS48581T curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BLS48581T

Methods

gA_ :: WAPoint BLS48581T Fq8 Fr

WACurve BLS12381 Fq Fr

Affine BLS12381 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BLS12381

Methods

gA_ :: WAPoint BLS12381 Fq Fr

WACurve BLS12381T Fq2 Fr

Affine BLS12381T curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.BLS12381T

Methods

gA_ :: WAPoint BLS12381T Fq2 Fr

WACurve Anomalous Fq Fr

Affine Anomalous curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.Anomalous

Methods

gA_ :: WAPoint Anomalous Fq Fr

WACurve ANSSIFRP256V1 Fq Fr

Affine ANSSIFRP256V1 curve is a Weierstrass affine curve.

Defined in Curve.Weierstrass.ANSSIFRP256V1

Methods

gA_ :: WAPoint ANSSIFRP256V1 Fq Fr

type WAPoint = WPoint Affine

Weierstrass affine points.

class (GaloisField q, PrimeField' r, Curve Weierstrass c e q r) => WCurve c e q r where

Weierstrass curves.

Methods

a_

Arguments

:: WPoint c e q r

-> q

Coefficient A.

b_

Arguments

:: WPoint c e q r

-> q

Coefficient B.

h_

Arguments

:: WPoint c e q r

-> Integer

Curve cofactor.

q_

Arguments

:: WPoint c e q r

-> Integer

Curve characteristic.

r_

Arguments

:: WPoint c e q r

-> Integer

Curve order.

x_

Arguments

:: WPoint c e q r

-> q

Coordinate X.

y_

Arguments

:: WPoint c e q r

-> q

Coordinate Y.

Instances

Curve Weierstrass c SECP521R1 Fq Fr => WCurve c SECP521R1 Fq Fr

SECP521R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP521R1

Methods

a_ :: WPoint c SECP521R1 Fq Fr -> Fq

b_ :: WPoint c SECP521R1 Fq Fr -> Fq

h_ :: WPoint c SECP521R1 Fq Fr -> Integer

q_ :: WPoint c SECP521R1 Fq Fr -> Integer

r_ :: WPoint c SECP521R1 Fq Fr -> Integer

x_ :: WPoint c SECP521R1 Fq Fr -> Fq

y_ :: WPoint c SECP521R1 Fq Fr -> Fq

Curve Weierstrass c SECP384R1 Fq Fr => WCurve c SECP384R1 Fq Fr

SECP384R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP384R1

Methods

a_ :: WPoint c SECP384R1 Fq Fr -> Fq

b_ :: WPoint c SECP384R1 Fq Fr -> Fq

h_ :: WPoint c SECP384R1 Fq Fr -> Integer

q_ :: WPoint c SECP384R1 Fq Fr -> Integer

r_ :: WPoint c SECP384R1 Fq Fr -> Integer

x_ :: WPoint c SECP384R1 Fq Fr -> Fq

y_ :: WPoint c SECP384R1 Fq Fr -> Fq

Curve Weierstrass c SECP256R1 Fq Fr => WCurve c SECP256R1 Fq Fr

SECP256R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP256R1

Methods

a_ :: WPoint c SECP256R1 Fq Fr -> Fq

b_ :: WPoint c SECP256R1 Fq Fr -> Fq

h_ :: WPoint c SECP256R1 Fq Fr -> Integer

q_ :: WPoint c SECP256R1 Fq Fr -> Integer

r_ :: WPoint c SECP256R1 Fq Fr -> Integer

x_ :: WPoint c SECP256R1 Fq Fr -> Fq

y_ :: WPoint c SECP256R1 Fq Fr -> Fq

Curve Weierstrass c SECP256K1 Fq Fr => WCurve c SECP256K1 Fq Fr

SECP256K1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP256K1

Methods

a_ :: WPoint c SECP256K1 Fq Fr -> Fq

b_ :: WPoint c SECP256K1 Fq Fr -> Fq

h_ :: WPoint c SECP256K1 Fq Fr -> Integer

q_ :: WPoint c SECP256K1 Fq Fr -> Integer

r_ :: WPoint c SECP256K1 Fq Fr -> Integer

x_ :: WPoint c SECP256K1 Fq Fr -> Fq

y_ :: WPoint c SECP256K1 Fq Fr -> Fq

Curve Weierstrass c SECP224R1 Fq Fr => WCurve c SECP224R1 Fq Fr

SECP224R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP224R1

Methods

a_ :: WPoint c SECP224R1 Fq Fr -> Fq

b_ :: WPoint c SECP224R1 Fq Fr -> Fq

h_ :: WPoint c SECP224R1 Fq Fr -> Integer

q_ :: WPoint c SECP224R1 Fq Fr -> Integer

r_ :: WPoint c SECP224R1 Fq Fr -> Integer

x_ :: WPoint c SECP224R1 Fq Fr -> Fq

y_ :: WPoint c SECP224R1 Fq Fr -> Fq

Curve Weierstrass c SECP224K1 Fq Fr => WCurve c SECP224K1 Fq Fr

SECP224K1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP224K1

Methods

a_ :: WPoint c SECP224K1 Fq Fr -> Fq

b_ :: WPoint c SECP224K1 Fq Fr -> Fq

h_ :: WPoint c SECP224K1 Fq Fr -> Integer

q_ :: WPoint c SECP224K1 Fq Fr -> Integer

r_ :: WPoint c SECP224K1 Fq Fr -> Integer

x_ :: WPoint c SECP224K1 Fq Fr -> Fq

y_ :: WPoint c SECP224K1 Fq Fr -> Fq

Curve Weierstrass c SECP192R1 Fq Fr => WCurve c SECP192R1 Fq Fr

SECP192R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP192R1

Methods

a_ :: WPoint c SECP192R1 Fq Fr -> Fq

b_ :: WPoint c SECP192R1 Fq Fr -> Fq

h_ :: WPoint c SECP192R1 Fq Fr -> Integer

q_ :: WPoint c SECP192R1 Fq Fr -> Integer

r_ :: WPoint c SECP192R1 Fq Fr -> Integer

x_ :: WPoint c SECP192R1 Fq Fr -> Fq

y_ :: WPoint c SECP192R1 Fq Fr -> Fq

Curve Weierstrass c SECP192K1 Fq Fr => WCurve c SECP192K1 Fq Fr

SECP192K1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP192K1

Methods

a_ :: WPoint c SECP192K1 Fq Fr -> Fq

b_ :: WPoint c SECP192K1 Fq Fr -> Fq

h_ :: WPoint c SECP192K1 Fq Fr -> Integer

q_ :: WPoint c SECP192K1 Fq Fr -> Integer

r_ :: WPoint c SECP192K1 Fq Fr -> Integer

x_ :: WPoint c SECP192K1 Fq Fr -> Fq

y_ :: WPoint c SECP192K1 Fq Fr -> Fq

Curve Weierstrass c SECP160R2 Fq Fr => WCurve c SECP160R2 Fq Fr

SECP160R2 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP160R2

Methods

a_ :: WPoint c SECP160R2 Fq Fr -> Fq

b_ :: WPoint c SECP160R2 Fq Fr -> Fq

h_ :: WPoint c SECP160R2 Fq Fr -> Integer

q_ :: WPoint c SECP160R2 Fq Fr -> Integer

r_ :: WPoint c SECP160R2 Fq Fr -> Integer

x_ :: WPoint c SECP160R2 Fq Fr -> Fq

y_ :: WPoint c SECP160R2 Fq Fr -> Fq

Curve Weierstrass c SECP160R1 Fq Fr => WCurve c SECP160R1 Fq Fr

SECP160R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP160R1

Methods

a_ :: WPoint c SECP160R1 Fq Fr -> Fq

b_ :: WPoint c SECP160R1 Fq Fr -> Fq

h_ :: WPoint c SECP160R1 Fq Fr -> Integer

q_ :: WPoint c SECP160R1 Fq Fr -> Integer

r_ :: WPoint c SECP160R1 Fq Fr -> Integer

x_ :: WPoint c SECP160R1 Fq Fr -> Fq

y_ :: WPoint c SECP160R1 Fq Fr -> Fq

Curve Weierstrass c SECP160K1 Fq Fr => WCurve c SECP160K1 Fq Fr

SECP160K1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP160K1

Methods

a_ :: WPoint c SECP160K1 Fq Fr -> Fq

b_ :: WPoint c SECP160K1 Fq Fr -> Fq

h_ :: WPoint c SECP160K1 Fq Fr -> Integer

q_ :: WPoint c SECP160K1 Fq Fr -> Integer

r_ :: WPoint c SECP160K1 Fq Fr -> Integer

x_ :: WPoint c SECP160K1 Fq Fr -> Fq

y_ :: WPoint c SECP160K1 Fq Fr -> Fq

Curve Weierstrass c SECP128R2 Fq Fr => WCurve c SECP128R2 Fq Fr

SECP128R2 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP128R2

Methods

a_ :: WPoint c SECP128R2 Fq Fr -> Fq

b_ :: WPoint c SECP128R2 Fq Fr -> Fq

h_ :: WPoint c SECP128R2 Fq Fr -> Integer

q_ :: WPoint c SECP128R2 Fq Fr -> Integer

r_ :: WPoint c SECP128R2 Fq Fr -> Integer

x_ :: WPoint c SECP128R2 Fq Fr -> Fq

y_ :: WPoint c SECP128R2 Fq Fr -> Fq

Curve Weierstrass c SECP128R1 Fq Fr => WCurve c SECP128R1 Fq Fr

SECP128R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP128R1

Methods

a_ :: WPoint c SECP128R1 Fq Fr -> Fq

b_ :: WPoint c SECP128R1 Fq Fr -> Fq

h_ :: WPoint c SECP128R1 Fq Fr -> Integer

q_ :: WPoint c SECP128R1 Fq Fr -> Integer

r_ :: WPoint c SECP128R1 Fq Fr -> Integer

x_ :: WPoint c SECP128R1 Fq Fr -> Fq

y_ :: WPoint c SECP128R1 Fq Fr -> Fq

Curve Weierstrass c SECP112R2 Fq Fr => WCurve c SECP112R2 Fq Fr

SECP112R2 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP112R2

Methods

a_ :: WPoint c SECP112R2 Fq Fr -> Fq

b_ :: WPoint c SECP112R2 Fq Fr -> Fq

h_ :: WPoint c SECP112R2 Fq Fr -> Integer

q_ :: WPoint c SECP112R2 Fq Fr -> Integer

r_ :: WPoint c SECP112R2 Fq Fr -> Integer

x_ :: WPoint c SECP112R2 Fq Fr -> Fq

y_ :: WPoint c SECP112R2 Fq Fr -> Fq

Curve Weierstrass c SECP112R1 Fq Fr => WCurve c SECP112R1 Fq Fr

SECP112R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.SECP112R1

Methods

a_ :: WPoint c SECP112R1 Fq Fr -> Fq

b_ :: WPoint c SECP112R1 Fq Fr -> Fq

h_ :: WPoint c SECP112R1 Fq Fr -> Integer

q_ :: WPoint c SECP112R1 Fq Fr -> Integer

r_ :: WPoint c SECP112R1 Fq Fr -> Integer

x_ :: WPoint c SECP112R1 Fq Fr -> Fq

y_ :: WPoint c SECP112R1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP512T1 Fq Fr => WCurve c BrainpoolP512T1 Fq Fr

BrainpoolP512T1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP512T1

Methods

a_ :: WPoint c BrainpoolP512T1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP512T1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP512T1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP512T1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP512T1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP512T1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP512T1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP512R1 Fq Fr => WCurve c BrainpoolP512R1 Fq Fr

BrainpoolP512R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP512R1

Methods

a_ :: WPoint c BrainpoolP512R1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP512R1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP512R1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP512R1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP512R1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP512R1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP512R1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP384T1 Fq Fr => WCurve c BrainpoolP384T1 Fq Fr

BrainpoolP384T1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP384T1

Methods

a_ :: WPoint c BrainpoolP384T1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP384T1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP384T1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP384T1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP384T1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP384T1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP384T1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP384R1 Fq Fr => WCurve c BrainpoolP384R1 Fq Fr

BrainpoolP384R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP384R1

Methods

a_ :: WPoint c BrainpoolP384R1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP384R1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP384R1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP384R1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP384R1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP384R1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP384R1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP320T1 Fq Fr => WCurve c BrainpoolP320T1 Fq Fr

BrainpoolP320T1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP320T1

Methods

a_ :: WPoint c BrainpoolP320T1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP320T1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP320T1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP320T1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP320T1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP320T1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP320T1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP320R1 Fq Fr => WCurve c BrainpoolP320R1 Fq Fr

BrainpoolP320R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP320R1

Methods

a_ :: WPoint c BrainpoolP320R1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP320R1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP320R1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP320R1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP320R1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP320R1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP320R1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP256T1 Fq Fr => WCurve c BrainpoolP256T1 Fq Fr

BrainpoolP256T1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP256T1

Methods

a_ :: WPoint c BrainpoolP256T1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP256T1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP256T1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP256T1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP256T1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP256T1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP256T1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP256R1 Fq Fr => WCurve c BrainpoolP256R1 Fq Fr

BrainpoolP256R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP256R1

Methods

a_ :: WPoint c BrainpoolP256R1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP256R1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP256R1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP256R1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP256R1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP256R1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP256R1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP224T1 Fq Fr => WCurve c BrainpoolP224T1 Fq Fr

BrainpoolP224T1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP224T1

Methods

a_ :: WPoint c BrainpoolP224T1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP224T1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP224T1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP224T1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP224T1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP224T1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP224T1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP224R1 Fq Fr => WCurve c BrainpoolP224R1 Fq Fr

BrainpoolP224R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP224R1

Methods

a_ :: WPoint c BrainpoolP224R1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP224R1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP224R1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP224R1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP224R1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP224R1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP224R1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP192T1 Fq Fr => WCurve c BrainpoolP192T1 Fq Fr

BrainpoolP192T1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP192T1

Methods

a_ :: WPoint c BrainpoolP192T1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP192T1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP192T1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP192T1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP192T1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP192T1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP192T1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP192R1 Fq Fr => WCurve c BrainpoolP192R1 Fq Fr

BrainpoolP192R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP192R1

Methods

a_ :: WPoint c BrainpoolP192R1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP192R1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP192R1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP192R1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP192R1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP192R1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP192R1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP160T1 Fq Fr => WCurve c BrainpoolP160T1 Fq Fr

BrainpoolP160T1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP160T1

Methods

a_ :: WPoint c BrainpoolP160T1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP160T1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP160T1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP160T1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP160T1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP160T1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP160T1 Fq Fr -> Fq

Curve Weierstrass c BrainpoolP160R1 Fq Fr => WCurve c BrainpoolP160R1 Fq Fr

BrainpoolP160R1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BrainpoolP160R1

Methods

a_ :: WPoint c BrainpoolP160R1 Fq Fr -> Fq

b_ :: WPoint c BrainpoolP160R1 Fq Fr -> Fq

h_ :: WPoint c BrainpoolP160R1 Fq Fr -> Integer

q_ :: WPoint c BrainpoolP160R1 Fq Fr -> Integer

r_ :: WPoint c BrainpoolP160R1 Fq Fr -> Integer

x_ :: WPoint c BrainpoolP160R1 Fq Fr -> Fq

y_ :: WPoint c BrainpoolP160R1 Fq Fr -> Fq

Curve Weierstrass c BN512 Fq Fr => WCurve c BN512 Fq Fr

BN512 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN512

Methods

a_ :: WPoint c BN512 Fq Fr -> Fq

b_ :: WPoint c BN512 Fq Fr -> Fq

h_ :: WPoint c BN512 Fq Fr -> Integer

q_ :: WPoint c BN512 Fq Fr -> Integer

r_ :: WPoint c BN512 Fq Fr -> Integer

x_ :: WPoint c BN512 Fq Fr -> Fq

y_ :: WPoint c BN512 Fq Fr -> Fq

Curve Weierstrass c BN462 Fq Fr => WCurve c BN462 Fq Fr

BN462 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN462

Methods

a_ :: WPoint c BN462 Fq Fr -> Fq

b_ :: WPoint c BN462 Fq Fr -> Fq

h_ :: WPoint c BN462 Fq Fr -> Integer

q_ :: WPoint c BN462 Fq Fr -> Integer

r_ :: WPoint c BN462 Fq Fr -> Integer

x_ :: WPoint c BN462 Fq Fr -> Fq

y_ :: WPoint c BN462 Fq Fr -> Fq

Curve Weierstrass c BN462T Fq2 Fr => WCurve c BN462T Fq2 Fr

BN462T curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN462T

Methods

a_ :: WPoint c BN462T Fq2 Fr -> Fq2

b_ :: WPoint c BN462T Fq2 Fr -> Fq2

h_ :: WPoint c BN462T Fq2 Fr -> Integer

q_ :: WPoint c BN462T Fq2 Fr -> Integer

r_ :: WPoint c BN462T Fq2 Fr -> Integer

x_ :: WPoint c BN462T Fq2 Fr -> Fq2

y_ :: WPoint c BN462T Fq2 Fr -> Fq2

Curve Weierstrass c BN384 Fq Fr => WCurve c BN384 Fq Fr

BN384 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN384

Methods

a_ :: WPoint c BN384 Fq Fr -> Fq

b_ :: WPoint c BN384 Fq Fr -> Fq

h_ :: WPoint c BN384 Fq Fr -> Integer

q_ :: WPoint c BN384 Fq Fr -> Integer

r_ :: WPoint c BN384 Fq Fr -> Integer

x_ :: WPoint c BN384 Fq Fr -> Fq

y_ :: WPoint c BN384 Fq Fr -> Fq

Curve Weierstrass c BN256 Fq Fr => WCurve c BN256 Fq Fr

BN256 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN256

Methods

a_ :: WPoint c BN256 Fq Fr -> Fq

b_ :: WPoint c BN256 Fq Fr -> Fq

h_ :: WPoint c BN256 Fq Fr -> Integer

q_ :: WPoint c BN256 Fq Fr -> Integer

r_ :: WPoint c BN256 Fq Fr -> Integer

x_ :: WPoint c BN256 Fq Fr -> Fq

y_ :: WPoint c BN256 Fq Fr -> Fq

Curve Weierstrass c BN254B Fq Fr => WCurve c BN254B Fq Fr

BN254B curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN254B

Methods

a_ :: WPoint c BN254B Fq Fr -> Fq

b_ :: WPoint c BN254B Fq Fr -> Fq

h_ :: WPoint c BN254B Fq Fr -> Integer

q_ :: WPoint c BN254B Fq Fr -> Integer

r_ :: WPoint c BN254B Fq Fr -> Integer

x_ :: WPoint c BN254B Fq Fr -> Fq

y_ :: WPoint c BN254B Fq Fr -> Fq

Curve Weierstrass c BN254BT Fq2 Fr => WCurve c BN254BT Fq2 Fr

BN254BT curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN254BT

Methods

a_ :: WPoint c BN254BT Fq2 Fr -> Fq2

b_ :: WPoint c BN254BT Fq2 Fr -> Fq2

h_ :: WPoint c BN254BT Fq2 Fr -> Integer

q_ :: WPoint c BN254BT Fq2 Fr -> Integer

r_ :: WPoint c BN254BT Fq2 Fr -> Integer

x_ :: WPoint c BN254BT Fq2 Fr -> Fq2

y_ :: WPoint c BN254BT Fq2 Fr -> Fq2

Curve Weierstrass c BN254A Fq Fr => WCurve c BN254A Fq Fr

BN254A curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN254A

Methods

a_ :: WPoint c BN254A Fq Fr -> Fq

b_ :: WPoint c BN254A Fq Fr -> Fq

h_ :: WPoint c BN254A Fq Fr -> Integer

q_ :: WPoint c BN254A Fq Fr -> Integer

r_ :: WPoint c BN254A Fq Fr -> Integer

x_ :: WPoint c BN254A Fq Fr -> Fq

y_ :: WPoint c BN254A Fq Fr -> Fq

Curve Weierstrass c BN254AT Fq2 Fr => WCurve c BN254AT Fq2 Fr

BN254AT curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN254AT

Methods

a_ :: WPoint c BN254AT Fq2 Fr -> Fq2

b_ :: WPoint c BN254AT Fq2 Fr -> Fq2

h_ :: WPoint c BN254AT Fq2 Fr -> Integer

q_ :: WPoint c BN254AT Fq2 Fr -> Integer

r_ :: WPoint c BN254AT Fq2 Fr -> Integer

x_ :: WPoint c BN254AT Fq2 Fr -> Fq2

y_ :: WPoint c BN254AT Fq2 Fr -> Fq2

Curve Weierstrass c BN254 Fq Fr => WCurve c BN254 Fq Fr

BN254 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN254

Methods

a_ :: WPoint c BN254 Fq Fr -> Fq

b_ :: WPoint c BN254 Fq Fr -> Fq

h_ :: WPoint c BN254 Fq Fr -> Integer

q_ :: WPoint c BN254 Fq Fr -> Integer

r_ :: WPoint c BN254 Fq Fr -> Integer

x_ :: WPoint c BN254 Fq Fr -> Fq

y_ :: WPoint c BN254 Fq Fr -> Fq

Curve Weierstrass c BN254T Fq2 Fr => WCurve c BN254T Fq2 Fr

BN254T curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN254T

Methods

a_ :: WPoint c BN254T Fq2 Fr -> Fq2

b_ :: WPoint c BN254T Fq2 Fr -> Fq2

h_ :: WPoint c BN254T Fq2 Fr -> Integer

q_ :: WPoint c BN254T Fq2 Fr -> Integer

r_ :: WPoint c BN254T Fq2 Fr -> Integer

x_ :: WPoint c BN254T Fq2 Fr -> Fq2

y_ :: WPoint c BN254T Fq2 Fr -> Fq2

Curve Weierstrass c BN224 Fq Fr => WCurve c BN224 Fq Fr

BN224 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BN224

Methods

a_ :: WPoint c BN224 Fq Fr -> Fq

b_ :: WPoint c BN224 Fq Fr -> Fq

h_ :: WPoint c BN224 Fq Fr -> Integer

q_ :: WPoint c BN224 Fq Fr -> Integer

r_ :: WPoint c BN224 Fq Fr -> Integer

x_ :: WPoint c BN224 Fq Fr -> Fq

y_ :: WPoint c BN224 Fq Fr -> Fq

Curve Weierstrass c BLS48581 Fq Fr => WCurve c BLS48581 Fq Fr

BLS48581 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BLS48581

Methods

a_ :: WPoint c BLS48581 Fq Fr -> Fq

b_ :: WPoint c BLS48581 Fq Fr -> Fq

h_ :: WPoint c BLS48581 Fq Fr -> Integer

q_ :: WPoint c BLS48581 Fq Fr -> Integer

r_ :: WPoint c BLS48581 Fq Fr -> Integer

x_ :: WPoint c BLS48581 Fq Fr -> Fq

y_ :: WPoint c BLS48581 Fq Fr -> Fq

Curve Weierstrass c BLS48581T Fq8 Fr => WCurve c BLS48581T Fq8 Fr

BLS48581T curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BLS48581T

Methods

a_ :: WPoint c BLS48581T Fq8 Fr -> Fq8

b_ :: WPoint c BLS48581T Fq8 Fr -> Fq8

h_ :: WPoint c BLS48581T Fq8 Fr -> Integer

q_ :: WPoint c BLS48581T Fq8 Fr -> Integer

r_ :: WPoint c BLS48581T Fq8 Fr -> Integer

x_ :: WPoint c BLS48581T Fq8 Fr -> Fq8

y_ :: WPoint c BLS48581T Fq8 Fr -> Fq8

Curve Weierstrass c BLS12381 Fq Fr => WCurve c BLS12381 Fq Fr

BLS12381 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BLS12381

Methods

a_ :: WPoint c BLS12381 Fq Fr -> Fq

b_ :: WPoint c BLS12381 Fq Fr -> Fq

h_ :: WPoint c BLS12381 Fq Fr -> Integer

q_ :: WPoint c BLS12381 Fq Fr -> Integer

r_ :: WPoint c BLS12381 Fq Fr -> Integer

x_ :: WPoint c BLS12381 Fq Fr -> Fq

y_ :: WPoint c BLS12381 Fq Fr -> Fq

Curve Weierstrass c BLS12381T Fq2 Fr => WCurve c BLS12381T Fq2 Fr

BLS12381T curve is a Weierstrass curve.

Defined in Curve.Weierstrass.BLS12381T

Methods

a_ :: WPoint c BLS12381T Fq2 Fr -> Fq2

b_ :: WPoint c BLS12381T Fq2 Fr -> Fq2

h_ :: WPoint c BLS12381T Fq2 Fr -> Integer

q_ :: WPoint c BLS12381T Fq2 Fr -> Integer

r_ :: WPoint c BLS12381T Fq2 Fr -> Integer

x_ :: WPoint c BLS12381T Fq2 Fr -> Fq2

y_ :: WPoint c BLS12381T Fq2 Fr -> Fq2

Curve Weierstrass c Anomalous Fq Fr => WCurve c Anomalous Fq Fr

Anomalous curve is a Weierstrass curve.

Defined in Curve.Weierstrass.Anomalous

Methods

a_ :: WPoint c Anomalous Fq Fr -> Fq

b_ :: WPoint c Anomalous Fq Fr -> Fq

h_ :: WPoint c Anomalous Fq Fr -> Integer

q_ :: WPoint c Anomalous Fq Fr -> Integer

r_ :: WPoint c Anomalous Fq Fr -> Integer

x_ :: WPoint c Anomalous Fq Fr -> Fq

y_ :: WPoint c Anomalous Fq Fr -> Fq

Curve Weierstrass c ANSSIFRP256V1 Fq Fr => WCurve c ANSSIFRP256V1 Fq Fr

ANSSIFRP256V1 curve is a Weierstrass curve.

Defined in Curve.Weierstrass.ANSSIFRP256V1

Methods

a_ :: WPoint c ANSSIFRP256V1 Fq Fr -> Fq

b_ :: WPoint c ANSSIFRP256V1 Fq Fr -> Fq

h_ :: WPoint c ANSSIFRP256V1 Fq Fr -> Integer

q_ :: WPoint c ANSSIFRP256V1 Fq Fr -> Integer

r_ :: WPoint c ANSSIFRP256V1 Fq Fr -> Integer

x_ :: WPoint c ANSSIFRP256V1 Fq Fr -> Fq

y_ :: WPoint c ANSSIFRP256V1 Fq Fr -> Fq

type WPoint = Point Weierstrass

Weierstrass points.

class (Arbitrary g, Eq g, Generic g, Monoid g, Pretty g, Random g, Show g) => Group g where

Groups.

Minimal complete definition

add, dbl, def, gen, id, inv, order

Methods

add :: g -> g -> g

Element addition.

dbl :: g -> g

Element doubling.

def :: g -> Bool

Check well-defined.

gen :: g

Group generator.

id :: g

Identity element.

inv :: g -> g

Element inversion.

mul' :: g -> Integer -> g

Element multiplication.

order :: g -> Integer

Curve order.

rnd :: MonadRandom m => m g

Random element.

Instances

FGroup r q => Group (Element r q)

Defined in Group.Field

Methods

add :: Element r q -> Element r q -> Element r q

dbl :: Element r q -> Element r q

def :: Element r q -> Bool

gen :: Element r q

id :: Element r q

inv :: Element r q -> Element r q

mul' :: Element r q -> Integer -> Element r q

order :: Element r q -> Integer

rnd :: MonadRandom m => m (Element r q)

WPCurve e q r => Group (WPPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WPPoint e q r -> WPPoint e q r -> WPPoint e q r

dbl :: WPPoint e q r -> WPPoint e q r

def :: WPPoint e q r -> Bool

gen :: WPPoint e q r

id :: WPPoint e q r

inv :: WPPoint e q r -> WPPoint e q r

mul' :: WPPoint e q r -> Integer -> WPPoint e q r

order :: WPPoint e q r -> Integer

rnd :: MonadRandom m => m (WPPoint e q r)

WJCurve e q r => Group (WJPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WJPoint e q r -> WJPoint e q r -> WJPoint e q r

dbl :: WJPoint e q r -> WJPoint e q r

def :: WJPoint e q r -> Bool

gen :: WJPoint e q r

id :: WJPoint e q r

inv :: WJPoint e q r -> WJPoint e q r

mul' :: WJPoint e q r -> Integer -> WJPoint e q r

order :: WJPoint e q r -> Integer

rnd :: MonadRandom m => m (WJPoint e q r)

WACurve e q r => Group (WAPoint e q r)

Defined in Curve.Weierstrass

Methods

add :: WAPoint e q r -> WAPoint e q r -> WAPoint e q r

dbl :: WAPoint e q r -> WAPoint e q r

def :: WAPoint e q r -> Bool

gen :: WAPoint e q r

id :: WAPoint e q r

inv :: WAPoint e q r -> WAPoint e q r

mul' :: WAPoint e q r -> Integer -> WAPoint e q r

order :: WAPoint e q r -> Integer

rnd :: MonadRandom m => m (WAPoint e q r)

MACurve e q r => Group (MAPoint e q r)

Defined in Curve.Montgomery

Methods

add :: MAPoint e q r -> MAPoint e q r -> MAPoint e q r

dbl :: MAPoint e q r -> MAPoint e q r

def :: MAPoint e q r -> Bool

gen :: MAPoint e q r

id :: MAPoint e q r

inv :: MAPoint e q r -> MAPoint e q r

mul' :: MAPoint e q r -> Integer -> MAPoint e q r

order :: MAPoint e q r -> Integer

rnd :: MonadRandom m => m (MAPoint e q r)

EPCurve e q r => Group (EPPoint e q r)

Defined in Curve.Edwards

Methods

add :: EPPoint e q r -> EPPoint e q r -> EPPoint e q r

dbl :: EPPoint e q r -> EPPoint e q r

def :: EPPoint e q r -> Bool

gen :: EPPoint e q r

id :: EPPoint e q r

inv :: EPPoint e q r -> EPPoint e q r

mul' :: EPPoint e q r -> Integer -> EPPoint e q r

order :: EPPoint e q r -> Integer

rnd :: MonadRandom m => m (EPPoint e q r)

EACurve e q r => Group (EAPoint e q r)

Defined in Curve.Edwards

Methods

add :: EAPoint e q r -> EAPoint e q r -> EAPoint e q r

dbl :: EAPoint e q r -> EAPoint e q r

def :: EAPoint e q r -> Bool

gen :: EAPoint e q r

id :: EAPoint e q r

inv :: EAPoint e q r -> EAPoint e q r

mul' :: EAPoint e q r -> Integer -> EAPoint e q r

order :: EAPoint e q r -> Integer

rnd :: MonadRandom m => m (EAPoint e q r)

BPCurve e q r => Group (BPPoint e q r)

Defined in Curve.Binary

Methods

add :: BPPoint e q r -> BPPoint e q r -> BPPoint e q r

dbl :: BPPoint e q r -> BPPoint e q r

def :: BPPoint e q r -> Bool

gen :: BPPoint e q r

id :: BPPoint e q r

inv :: BPPoint e q r -> BPPoint e q r

mul' :: BPPoint e q r -> Integer -> BPPoint e q r

order :: BPPoint e q r -> Integer

rnd :: MonadRandom m => m (BPPoint e q r)

BACurve e q r => Group (BAPoint e q r)

Defined in Curve.Binary

Methods

add :: BAPoint e q r -> BAPoint e q r -> BAPoint e q r

dbl :: BAPoint e q r -> BAPoint e q r

def :: BAPoint e q r -> Bool

gen :: BAPoint e q r

id :: BAPoint e q r

inv :: BAPoint e q r -> BAPoint e q r

mul' :: BAPoint e q r -> Integer -> BAPoint e q r

order :: BAPoint e q r -> Integer

rnd :: MonadRandom m => m (BAPoint e q r)

Orphan instances

WACurve e q r => Curve Weierstrass Affine (e :: k) q r

Associated Types

data Point Weierstrass Affine e q r :: Type

Methods

char :: Point Weierstrass Affine e q r -> Integer

cof :: Point Weierstrass Affine e q r -> Integer

disc :: Point Weierstrass Affine e q r -> q

mul :: Point Weierstrass Affine e q r -> r -> Point Weierstrass Affine e q r

point :: q -> q -> Maybe (Point Weierstrass Affine e q r)

pointX :: q -> Maybe (Point Weierstrass Affine e q r)

yX :: Point Weierstrass Affine e q r -> q -> Maybe q

fromA :: Point Weierstrass Affine e q r -> Point Weierstrass Affine e q r

toA :: Point Weierstrass Affine e q r -> Point Weierstrass Affine e q r

WJCurve e q r => Curve Weierstrass Jacobian (e :: k) q r

Associated Types

data Point Weierstrass Jacobian e q r :: Type

Methods

char :: Point Weierstrass Jacobian e q r -> Integer

cof :: Point Weierstrass Jacobian e q r -> Integer

disc :: Point Weierstrass Jacobian e q r -> q

mul :: Point Weierstrass Jacobian e q r -> r -> Point Weierstrass Jacobian e q r

point :: q -> q -> Maybe (Point Weierstrass Jacobian e q r)

pointX :: q -> Maybe (Point Weierstrass Jacobian e q r)

yX :: Point Weierstrass Jacobian e q r -> q -> Maybe q

fromA :: Point Weierstrass Affine e q r -> Point Weierstrass Jacobian e q r

toA :: Point Weierstrass Jacobian e q r -> Point Weierstrass Affine e q r

WPCurve e q r => Curve Weierstrass Projective (e :: k) q r

Associated Types

data Point Weierstrass Projective e q r :: Type

Methods

char :: Point Weierstrass Projective e q r -> Integer

cof :: Point Weierstrass Projective e q r -> Integer

disc :: Point Weierstrass Projective e q r -> q

mul :: Point Weierstrass Projective e q r -> r -> Point Weierstrass Projective e q r

point :: q -> q -> Maybe (Point Weierstrass Projective e q r)

pointX :: q -> Maybe (Point Weierstrass Projective e q r)

yX :: Point Weierstrass Projective e q r -> q -> Maybe q

fromA :: Point Weierstrass Affine e q r -> Point Weierstrass Projective e q r

toA :: Point Weierstrass Projective e q r -> Point Weierstrass Affine e q r

WPCurve e q r => Eq (WPPoint e q r)

Methods

(==) :: WPPoint e q r -> WPPoint e q r -> Bool

(/=) :: WPPoint e q r -> WPPoint e q r -> Bool

WJCurve e q r => Eq (WJPoint e q r)

Methods

(==) :: WJPoint e q r -> WJPoint e q r -> Bool

(/=) :: WJPoint e q r -> WJPoint e q r -> Bool

WPCurve e q r => Pretty (WPPoint e q r)

Methods

pretty :: WPPoint e q r -> Doc

prettyList :: [WPPoint e q r] -> Doc

WJCurve e q r => Pretty (WJPoint e q r)

Methods

pretty :: WJPoint e q r -> Doc

prettyList :: [WJPoint e q r] -> Doc

WACurve e q r => Pretty (WAPoint e q r)

Methods

pretty :: WAPoint e q r -> Doc

prettyList :: [WAPoint e q r] -> Doc

WPCurve e q r => Group (WPPoint e q r)

Methods

add :: WPPoint e q r -> WPPoint e q r -> WPPoint e q r

dbl :: WPPoint e q r -> WPPoint e q r

def :: WPPoint e q r -> Bool

gen :: WPPoint e q r

id :: WPPoint e q r

inv :: WPPoint e q r -> WPPoint e q r

mul' :: WPPoint e q r -> Integer -> WPPoint e q r

order :: WPPoint e q r -> Integer

rnd :: MonadRandom m => m (WPPoint e q r)

WJCurve e q r => Group (WJPoint e q r)

Methods

add :: WJPoint e q r -> WJPoint e q r -> WJPoint e q r

dbl :: WJPoint e q r -> WJPoint e q r

def :: WJPoint e q r -> Bool

gen :: WJPoint e q r

id :: WJPoint e q r

inv :: WJPoint e q r -> WJPoint e q r

mul' :: WJPoint e q r -> Integer -> WJPoint e q r

order :: WJPoint e q r -> Integer

rnd :: MonadRandom m => m (WJPoint e q r)

WACurve e q r => Group (WAPoint e q r)

Methods

add :: WAPoint e q r -> WAPoint e q r -> WAPoint e q r

dbl :: WAPoint e q r -> WAPoint e q r

def :: WAPoint e q r -> Bool

gen :: WAPoint e q r

id :: WAPoint e q r

inv :: WAPoint e q r -> WAPoint e q r

mul' :: WAPoint e q r -> Integer -> WAPoint e q r

order :: WAPoint e q r -> Integer

rnd :: MonadRandom m => m (WAPoint e q r)

Eq q => Eq (Point Weierstrass Affine e q r)

Methods

(==) :: Point Weierstrass Affine e q r -> Point Weierstrass Affine e q r -> Bool

(/=) :: Point Weierstrass Affine e q r -> Point Weierstrass Affine e q r -> Bool

Read q => Read (Point Weierstrass Affine e q r)

Methods

readsPrec :: Int -> ReadS (Point Weierstrass Affine e q r)

readList :: ReadS [Point Weierstrass Affine e q r]

readPrec :: ReadPrec (Point Weierstrass Affine e q r)

readListPrec :: ReadPrec [Point Weierstrass Affine e q r]

Read q => Read (Point Weierstrass Jacobian e q r)

Methods

readsPrec :: Int -> ReadS (Point Weierstrass Jacobian e q r)

readList :: ReadS [Point Weierstrass Jacobian e q r]

readPrec :: ReadPrec (Point Weierstrass Jacobian e q r)

readListPrec :: ReadPrec [Point Weierstrass Jacobian e q r]

Read q => Read (Point Weierstrass Projective e q r)

Methods

readsPrec :: Int -> ReadS (Point Weierstrass Projective e q r)

readList :: ReadS [Point Weierstrass Projective e q r]

readPrec :: ReadPrec (Point Weierstrass Projective e q r)

readListPrec :: ReadPrec [Point Weierstrass Projective e q r]

Show q => Show (Point Weierstrass Affine e q r)

Methods

showsPrec :: Int -> Point Weierstrass Affine e q r -> ShowS

show :: Point Weierstrass Affine e q r -> String

showList :: [Point Weierstrass Affine e q r] -> ShowS

Show q => Show (Point Weierstrass Jacobian e q r)

Methods

showsPrec :: Int -> Point Weierstrass Jacobian e q r -> ShowS

show :: Point Weierstrass Jacobian e q r -> String

showList :: [Point Weierstrass Jacobian e q r] -> ShowS

Show q => Show (Point Weierstrass Projective e q r)

Methods

showsPrec :: Int -> Point Weierstrass Projective e q r -> ShowS

show :: Point Weierstrass Projective e q r -> String

showList :: [Point Weierstrass Projective e q r] -> ShowS

Generic (Point Weierstrass Affine e q r)

Associated Types

type Rep (Point Weierstrass Affine e q r) :: Type -> Type

Methods

from :: Point Weierstrass Affine e q r -> Rep (Point Weierstrass Affine e q r) x

to :: Rep (Point Weierstrass Affine e q r) x -> Point Weierstrass Affine e q r

Generic (Point Weierstrass Jacobian e q r)

Associated Types

type Rep (Point Weierstrass Jacobian e q r) :: Type -> Type

Methods

from :: Point Weierstrass Jacobian e q r -> Rep (Point Weierstrass Jacobian e q r) x

to :: Rep (Point Weierstrass Jacobian e q r) x -> Point Weierstrass Jacobian e q r

Generic (Point Weierstrass Projective e q r)

Associated Types

type Rep (Point Weierstrass Projective e q r) :: Type -> Type

Methods

from :: Point Weierstrass Projective e q r -> Rep (Point Weierstrass Projective e q r) x

to :: Rep (Point Weierstrass Projective e q r) x -> Point Weierstrass Projective e q r

NFData q => NFData (Point Weierstrass Affine e q r)

Methods

rnf :: Point Weierstrass Affine e q r -> ()

NFData q => NFData (Point Weierstrass Jacobian e q r)

Methods

rnf :: Point Weierstrass Jacobian e q r -> ()

NFData q => NFData (Point Weierstrass Projective e q r)

Methods

rnf :: Point Weierstrass Projective e q r -> ()