Curve.Binary

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 BCurve Projective e q r => BPCurve e q r where

Binary projective curves y^2z + xyz = x^3 + Ax^2z + Bz.

Methods

gP_

Arguments

:: BPPoint e q r

Curve generator.

Instances

BPCurve SECT571R1 F2m Fr

Projective SECT571R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT571R1

Methods

gP_ :: BPPoint SECT571R1 F2m Fr

BPCurve SECT571K1 F2m Fr

Projective SECT571K1 curve is a binary projective curve.

Defined in Curve.Binary.SECT571K1

Methods

gP_ :: BPPoint SECT571K1 F2m Fr

BPCurve SECT409R1 F2m Fr

Projective SECT409R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT409R1

Methods

gP_ :: BPPoint SECT409R1 F2m Fr

BPCurve SECT409K1 F2m Fr

Projective SECT409K1 curve is a binary projective curve.

Defined in Curve.Binary.SECT409K1

Methods

gP_ :: BPPoint SECT409K1 F2m Fr

BPCurve SECT283R1 F2m Fr

Projective SECT283R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT283R1

Methods

gP_ :: BPPoint SECT283R1 F2m Fr

BPCurve SECT283K1 F2m Fr

Projective SECT283K1 curve is a binary projective curve.

Defined in Curve.Binary.SECT283K1

Methods

gP_ :: BPPoint SECT283K1 F2m Fr

BPCurve SECT239K1 F2m Fr

Projective SECT239K1 curve is a binary projective curve.

Defined in Curve.Binary.SECT239K1

Methods

gP_ :: BPPoint SECT239K1 F2m Fr

BPCurve SECT233R1 F2m Fr

Projective SECT233R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT233R1

Methods

gP_ :: BPPoint SECT233R1 F2m Fr

BPCurve SECT233K1 F2m Fr

Projective SECT233K1 curve is a binary projective curve.

Defined in Curve.Binary.SECT233K1

Methods

gP_ :: BPPoint SECT233K1 F2m Fr

BPCurve SECT193R2 F2m Fr

Projective SECT193R2 curve is a binary projective curve.

Defined in Curve.Binary.SECT193R2

Methods

gP_ :: BPPoint SECT193R2 F2m Fr

BPCurve SECT193R1 F2m Fr

Projective SECT193R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT193R1

Methods

gP_ :: BPPoint SECT193R1 F2m Fr

BPCurve SECT163R2 F2m Fr

Projective SECT163R2 curve is a binary projective curve.

Defined in Curve.Binary.SECT163R2

Methods

gP_ :: BPPoint SECT163R2 F2m Fr

BPCurve SECT163R1 F2m Fr

Projective SECT163R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT163R1

Methods

gP_ :: BPPoint SECT163R1 F2m Fr

BPCurve SECT163K1 F2m Fr

Projective SECT163K1 curve is a binary projective curve.

Defined in Curve.Binary.SECT163K1

Methods

gP_ :: BPPoint SECT163K1 F2m Fr

BPCurve SECT131R2 F2m Fr

Projective SECT131R2 curve is a binary projective curve.

Defined in Curve.Binary.SECT131R2

Methods

gP_ :: BPPoint SECT131R2 F2m Fr

BPCurve SECT131R1 F2m Fr

Projective SECT131R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT131R1

Methods

gP_ :: BPPoint SECT131R1 F2m Fr

BPCurve SECT113R2 F2m Fr

Projective SECT113R2 curve is a binary projective curve.

Defined in Curve.Binary.SECT113R2

Methods

gP_ :: BPPoint SECT113R2 F2m Fr

BPCurve SECT113R1 F2m Fr

Projective SECT113R1 curve is a binary projective curve.

Defined in Curve.Binary.SECT113R1

Methods

gP_ :: BPPoint SECT113R1 F2m Fr

type BPPoint = BPoint Projective

Binary projective points.

class BCurve Affine e q r => BACurve e q r where

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

Methods

gA_

Arguments

:: BAPoint e q r

Curve generator.

Instances

BACurve SECT571R1 F2m Fr

Affine SECT571R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT571R1

Methods

gA_ :: BAPoint SECT571R1 F2m Fr

BACurve SECT571K1 F2m Fr

Affine SECT571K1 curve is a binary affine curve.

Defined in Curve.Binary.SECT571K1

Methods

gA_ :: BAPoint SECT571K1 F2m Fr

BACurve SECT409R1 F2m Fr

Affine SECT409R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT409R1

Methods

gA_ :: BAPoint SECT409R1 F2m Fr

BACurve SECT409K1 F2m Fr

Affine SECT409K1 curve is a binary affine curve.

Defined in Curve.Binary.SECT409K1

Methods

gA_ :: BAPoint SECT409K1 F2m Fr

BACurve SECT283R1 F2m Fr

Affine SECT283R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT283R1

Methods

gA_ :: BAPoint SECT283R1 F2m Fr

BACurve SECT283K1 F2m Fr

Affine SECT283K1 curve is a binary affine curve.

Defined in Curve.Binary.SECT283K1

Methods

gA_ :: BAPoint SECT283K1 F2m Fr

BACurve SECT239K1 F2m Fr

Affine SECT239K1 curve is a binary affine curve.

Defined in Curve.Binary.SECT239K1

Methods

gA_ :: BAPoint SECT239K1 F2m Fr

BACurve SECT233R1 F2m Fr

Affine SECT233R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT233R1

Methods

gA_ :: BAPoint SECT233R1 F2m Fr

BACurve SECT233K1 F2m Fr

Affine SECT233K1 curve is a binary affine curve.

Defined in Curve.Binary.SECT233K1

Methods

gA_ :: BAPoint SECT233K1 F2m Fr

BACurve SECT193R2 F2m Fr

Affine SECT193R2 curve is a binary affine curve.

Defined in Curve.Binary.SECT193R2

Methods

gA_ :: BAPoint SECT193R2 F2m Fr

BACurve SECT193R1 F2m Fr

Affine SECT193R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT193R1

Methods

gA_ :: BAPoint SECT193R1 F2m Fr

BACurve SECT163R2 F2m Fr

Affine SECT163R2 curve is a binary affine curve.

Defined in Curve.Binary.SECT163R2

Methods

gA_ :: BAPoint SECT163R2 F2m Fr

BACurve SECT163R1 F2m Fr

Affine SECT163R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT163R1

Methods

gA_ :: BAPoint SECT163R1 F2m Fr

BACurve SECT163K1 F2m Fr

Affine SECT163K1 curve is a binary affine curve.

Defined in Curve.Binary.SECT163K1

Methods

gA_ :: BAPoint SECT163K1 F2m Fr

BACurve SECT131R2 F2m Fr

Affine SECT131R2 curve is a binary affine curve.

Defined in Curve.Binary.SECT131R2

Methods

gA_ :: BAPoint SECT131R2 F2m Fr

BACurve SECT131R1 F2m Fr

Affine SECT131R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT131R1

Methods

gA_ :: BAPoint SECT131R1 F2m Fr

BACurve SECT113R2 F2m Fr

Affine SECT113R2 curve is a binary affine curve.

Defined in Curve.Binary.SECT113R2

Methods

gA_ :: BAPoint SECT113R2 F2m Fr

BACurve SECT113R1 F2m Fr

Affine SECT113R1 curve is a binary affine curve.

Defined in Curve.Binary.SECT113R1

Methods

gA_ :: BAPoint SECT113R1 F2m Fr

type BAPoint = BPoint Affine

Binary affine points.

class (GaloisField q, PrimeField' r, Curve Binary c e q r) => BCurve c e q r where

Binary curves.

Methods

a_

Arguments

:: BPoint c e q r

-> q

Coefficient A.

b_

Arguments

:: BPoint c e q r

-> q

Coefficient B.

h_

Arguments

:: BPoint c e q r

-> Integer

Curve cofactor.

p_

Arguments

:: BPoint c e q r

-> Integer

Curve polynomial.

r_

Arguments

:: BPoint c e q r

-> Integer

Curve order.

x_

Arguments

:: BPoint c e q r

-> q

Coordinate X.

y_

Arguments

:: BPoint c e q r

-> q

Coordinate Y.

Instances

Curve Binary c SECT571R1 F2m Fr => BCurve c SECT571R1 F2m Fr

SECT571R1 curve is a binary curve.

Defined in Curve.Binary.SECT571R1

Methods

a_ :: BPoint c SECT571R1 F2m Fr -> F2m

b_ :: BPoint c SECT571R1 F2m Fr -> F2m

h_ :: BPoint c SECT571R1 F2m Fr -> Integer

p_ :: BPoint c SECT571R1 F2m Fr -> Integer

r_ :: BPoint c SECT571R1 F2m Fr -> Integer

x_ :: BPoint c SECT571R1 F2m Fr -> F2m

y_ :: BPoint c SECT571R1 F2m Fr -> F2m

Curve Binary c SECT571K1 F2m Fr => BCurve c SECT571K1 F2m Fr

SECT571K1 curve is a binary curve.

Defined in Curve.Binary.SECT571K1

Methods

a_ :: BPoint c SECT571K1 F2m Fr -> F2m

b_ :: BPoint c SECT571K1 F2m Fr -> F2m

h_ :: BPoint c SECT571K1 F2m Fr -> Integer

p_ :: BPoint c SECT571K1 F2m Fr -> Integer

r_ :: BPoint c SECT571K1 F2m Fr -> Integer

x_ :: BPoint c SECT571K1 F2m Fr -> F2m

y_ :: BPoint c SECT571K1 F2m Fr -> F2m

Curve Binary c SECT409R1 F2m Fr => BCurve c SECT409R1 F2m Fr

SECT409R1 curve is a binary curve.

Defined in Curve.Binary.SECT409R1

Methods

a_ :: BPoint c SECT409R1 F2m Fr -> F2m

b_ :: BPoint c SECT409R1 F2m Fr -> F2m

h_ :: BPoint c SECT409R1 F2m Fr -> Integer

p_ :: BPoint c SECT409R1 F2m Fr -> Integer

r_ :: BPoint c SECT409R1 F2m Fr -> Integer

x_ :: BPoint c SECT409R1 F2m Fr -> F2m

y_ :: BPoint c SECT409R1 F2m Fr -> F2m

Curve Binary c SECT409K1 F2m Fr => BCurve c SECT409K1 F2m Fr

SECT409K1 curve is a binary curve.

Defined in Curve.Binary.SECT409K1

Methods

a_ :: BPoint c SECT409K1 F2m Fr -> F2m

b_ :: BPoint c SECT409K1 F2m Fr -> F2m

h_ :: BPoint c SECT409K1 F2m Fr -> Integer

p_ :: BPoint c SECT409K1 F2m Fr -> Integer

r_ :: BPoint c SECT409K1 F2m Fr -> Integer

x_ :: BPoint c SECT409K1 F2m Fr -> F2m

y_ :: BPoint c SECT409K1 F2m Fr -> F2m

Curve Binary c SECT283R1 F2m Fr => BCurve c SECT283R1 F2m Fr

SECT283R1 curve is a binary curve.

Defined in Curve.Binary.SECT283R1

Methods

a_ :: BPoint c SECT283R1 F2m Fr -> F2m

b_ :: BPoint c SECT283R1 F2m Fr -> F2m

h_ :: BPoint c SECT283R1 F2m Fr -> Integer

p_ :: BPoint c SECT283R1 F2m Fr -> Integer

r_ :: BPoint c SECT283R1 F2m Fr -> Integer

x_ :: BPoint c SECT283R1 F2m Fr -> F2m

y_ :: BPoint c SECT283R1 F2m Fr -> F2m

Curve Binary c SECT283K1 F2m Fr => BCurve c SECT283K1 F2m Fr

SECT283K1 curve is a binary curve.

Defined in Curve.Binary.SECT283K1

Methods

a_ :: BPoint c SECT283K1 F2m Fr -> F2m

b_ :: BPoint c SECT283K1 F2m Fr -> F2m

h_ :: BPoint c SECT283K1 F2m Fr -> Integer

p_ :: BPoint c SECT283K1 F2m Fr -> Integer

r_ :: BPoint c SECT283K1 F2m Fr -> Integer

x_ :: BPoint c SECT283K1 F2m Fr -> F2m

y_ :: BPoint c SECT283K1 F2m Fr -> F2m

Curve Binary c SECT239K1 F2m Fr => BCurve c SECT239K1 F2m Fr

SECT239K1 curve is a binary curve.

Defined in Curve.Binary.SECT239K1

Methods

a_ :: BPoint c SECT239K1 F2m Fr -> F2m

b_ :: BPoint c SECT239K1 F2m Fr -> F2m

h_ :: BPoint c SECT239K1 F2m Fr -> Integer

p_ :: BPoint c SECT239K1 F2m Fr -> Integer

r_ :: BPoint c SECT239K1 F2m Fr -> Integer

x_ :: BPoint c SECT239K1 F2m Fr -> F2m

y_ :: BPoint c SECT239K1 F2m Fr -> F2m

Curve Binary c SECT233R1 F2m Fr => BCurve c SECT233R1 F2m Fr

SECT233R1 curve is a binary curve.

Defined in Curve.Binary.SECT233R1

Methods

a_ :: BPoint c SECT233R1 F2m Fr -> F2m

b_ :: BPoint c SECT233R1 F2m Fr -> F2m

h_ :: BPoint c SECT233R1 F2m Fr -> Integer

p_ :: BPoint c SECT233R1 F2m Fr -> Integer

r_ :: BPoint c SECT233R1 F2m Fr -> Integer

x_ :: BPoint c SECT233R1 F2m Fr -> F2m

y_ :: BPoint c SECT233R1 F2m Fr -> F2m

Curve Binary c SECT233K1 F2m Fr => BCurve c SECT233K1 F2m Fr

SECT233K1 curve is a binary curve.

Defined in Curve.Binary.SECT233K1

Methods

a_ :: BPoint c SECT233K1 F2m Fr -> F2m

b_ :: BPoint c SECT233K1 F2m Fr -> F2m

h_ :: BPoint c SECT233K1 F2m Fr -> Integer

p_ :: BPoint c SECT233K1 F2m Fr -> Integer

r_ :: BPoint c SECT233K1 F2m Fr -> Integer

x_ :: BPoint c SECT233K1 F2m Fr -> F2m

y_ :: BPoint c SECT233K1 F2m Fr -> F2m

Curve Binary c SECT193R2 F2m Fr => BCurve c SECT193R2 F2m Fr

SECT193R2 curve is a binary curve.

Defined in Curve.Binary.SECT193R2

Methods

a_ :: BPoint c SECT193R2 F2m Fr -> F2m

b_ :: BPoint c SECT193R2 F2m Fr -> F2m

h_ :: BPoint c SECT193R2 F2m Fr -> Integer

p_ :: BPoint c SECT193R2 F2m Fr -> Integer

r_ :: BPoint c SECT193R2 F2m Fr -> Integer

x_ :: BPoint c SECT193R2 F2m Fr -> F2m

y_ :: BPoint c SECT193R2 F2m Fr -> F2m

Curve Binary c SECT193R1 F2m Fr => BCurve c SECT193R1 F2m Fr

SECT193R1 curve is a binary curve.

Defined in Curve.Binary.SECT193R1

Methods

a_ :: BPoint c SECT193R1 F2m Fr -> F2m

b_ :: BPoint c SECT193R1 F2m Fr -> F2m

h_ :: BPoint c SECT193R1 F2m Fr -> Integer

p_ :: BPoint c SECT193R1 F2m Fr -> Integer

r_ :: BPoint c SECT193R1 F2m Fr -> Integer

x_ :: BPoint c SECT193R1 F2m Fr -> F2m

y_ :: BPoint c SECT193R1 F2m Fr -> F2m

Curve Binary c SECT163R2 F2m Fr => BCurve c SECT163R2 F2m Fr

SECT163R2 curve is a binary curve.

Defined in Curve.Binary.SECT163R2

Methods

a_ :: BPoint c SECT163R2 F2m Fr -> F2m

b_ :: BPoint c SECT163R2 F2m Fr -> F2m

h_ :: BPoint c SECT163R2 F2m Fr -> Integer

p_ :: BPoint c SECT163R2 F2m Fr -> Integer

r_ :: BPoint c SECT163R2 F2m Fr -> Integer

x_ :: BPoint c SECT163R2 F2m Fr -> F2m

y_ :: BPoint c SECT163R2 F2m Fr -> F2m

Curve Binary c SECT163R1 F2m Fr => BCurve c SECT163R1 F2m Fr

SECT163R1 curve is a binary curve.

Defined in Curve.Binary.SECT163R1

Methods

a_ :: BPoint c SECT163R1 F2m Fr -> F2m

b_ :: BPoint c SECT163R1 F2m Fr -> F2m

h_ :: BPoint c SECT163R1 F2m Fr -> Integer

p_ :: BPoint c SECT163R1 F2m Fr -> Integer

r_ :: BPoint c SECT163R1 F2m Fr -> Integer

x_ :: BPoint c SECT163R1 F2m Fr -> F2m

y_ :: BPoint c SECT163R1 F2m Fr -> F2m

Curve Binary c SECT163K1 F2m Fr => BCurve c SECT163K1 F2m Fr

SECT163K1 curve is a binary curve.

Defined in Curve.Binary.SECT163K1

Methods

a_ :: BPoint c SECT163K1 F2m Fr -> F2m

b_ :: BPoint c SECT163K1 F2m Fr -> F2m

h_ :: BPoint c SECT163K1 F2m Fr -> Integer

p_ :: BPoint c SECT163K1 F2m Fr -> Integer

r_ :: BPoint c SECT163K1 F2m Fr -> Integer

x_ :: BPoint c SECT163K1 F2m Fr -> F2m

y_ :: BPoint c SECT163K1 F2m Fr -> F2m

Curve Binary c SECT131R2 F2m Fr => BCurve c SECT131R2 F2m Fr

SECT131R2 curve is a binary curve.

Defined in Curve.Binary.SECT131R2

Methods

a_ :: BPoint c SECT131R2 F2m Fr -> F2m

b_ :: BPoint c SECT131R2 F2m Fr -> F2m

h_ :: BPoint c SECT131R2 F2m Fr -> Integer

p_ :: BPoint c SECT131R2 F2m Fr -> Integer

r_ :: BPoint c SECT131R2 F2m Fr -> Integer

x_ :: BPoint c SECT131R2 F2m Fr -> F2m

y_ :: BPoint c SECT131R2 F2m Fr -> F2m

Curve Binary c SECT131R1 F2m Fr => BCurve c SECT131R1 F2m Fr

SECT131R1 curve is a binary curve.

Defined in Curve.Binary.SECT131R1

Methods

a_ :: BPoint c SECT131R1 F2m Fr -> F2m

b_ :: BPoint c SECT131R1 F2m Fr -> F2m

h_ :: BPoint c SECT131R1 F2m Fr -> Integer

p_ :: BPoint c SECT131R1 F2m Fr -> Integer

r_ :: BPoint c SECT131R1 F2m Fr -> Integer

x_ :: BPoint c SECT131R1 F2m Fr -> F2m

y_ :: BPoint c SECT131R1 F2m Fr -> F2m

Curve Binary c SECT113R2 F2m Fr => BCurve c SECT113R2 F2m Fr

SECT113R2 curve is a binary curve.

Defined in Curve.Binary.SECT113R2

Methods

a_ :: BPoint c SECT113R2 F2m Fr -> F2m

b_ :: BPoint c SECT113R2 F2m Fr -> F2m

h_ :: BPoint c SECT113R2 F2m Fr -> Integer

p_ :: BPoint c SECT113R2 F2m Fr -> Integer

r_ :: BPoint c SECT113R2 F2m Fr -> Integer

x_ :: BPoint c SECT113R2 F2m Fr -> F2m

y_ :: BPoint c SECT113R2 F2m Fr -> F2m

Curve Binary c SECT113R1 F2m Fr => BCurve c SECT113R1 F2m Fr

SECT113R1 curve is a binary curve.

Defined in Curve.Binary.SECT113R1

Methods

a_ :: BPoint c SECT113R1 F2m Fr -> F2m

b_ :: BPoint c SECT113R1 F2m Fr -> F2m

h_ :: BPoint c SECT113R1 F2m Fr -> Integer

p_ :: BPoint c SECT113R1 F2m Fr -> Integer

r_ :: BPoint c SECT113R1 F2m Fr -> Integer

x_ :: BPoint c SECT113R1 F2m Fr -> F2m

y_ :: BPoint c SECT113R1 F2m Fr -> F2m

type BPoint = Point Binary

Binary 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

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

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

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

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

Methods

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

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

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

Methods

pretty :: BPPoint e q r -> Doc

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

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

Methods

pretty :: BAPoint e q r -> Doc

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

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

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)

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)

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

Methods

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

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

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

Methods

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

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

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

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

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

Methods

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

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

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

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

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

Methods

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

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

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

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

Methods

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

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

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

Generic (Point Binary Affine e q r)

Associated Types

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

Methods

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

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

Generic (Point Binary Projective e q r)

Associated Types

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

Methods

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

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

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

Methods

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

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

Methods

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