org.cryptimeleon.math.structures.groups.elliptic

Interface WeierstrassCurve

All Superinterfaces:

EllipticCurve, GroupImpl, Representable, RepresentationRestorer, StandaloneRepresentable

All Known Implementing Classes:

PairingSourceGroupImpl, Secp256k1

public interface WeierstrassCurve
extends EllipticCurve

An elliptic curve defined by the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).

Contains the set of points \((x,y)\) that fulfill the weierstrass equation. In short form, the equation reduces to \(y^2 = x^3 + A4 \cdot x + A6\).

Method Summary

Modifier and Type	Method and Description
FieldElement	getA1() Returns \(A1\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
FieldElement	getA2() Returns \(A2\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
FieldElement	getA3() Returns \(A3\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
FieldElement	getA4() Returns \(A4\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
FieldElement	getA6() Returns \(A6\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).
EllipticCurvePoint	getElement(FieldElement x, FieldElement y) Construct an point on this curve given the x- and y-coordinates.
default boolean	isShortForm()

Methods inherited from interface org.cryptimeleon.math.structures.groups.elliptic.EllipticCurve

getFieldOfDefinition, isCommutative

Methods inherited from interface org.cryptimeleon.math.structures.groups.GroupImpl

estimateCostInvPerOp, exp, getGenerator, getNeutralElement, getUniformlyRandomElement, getUniformlyRandomNonNeutral, getUniqueByteLength, hasPrimeSize, implementsOwnExp, implementsOwnMultiExp, multiexp, restoreElement, restoreFromRepresentation, size

Methods inherited from interface org.cryptimeleon.math.serialization.Representable

getRepresentation

Method Detail

getA6

FieldElement getA6()

Returns \(A6\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).

getA4

FieldElement getA4()

Returns \(A4\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).

getA3

FieldElement getA3()

Returns \(A3\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).

Is zero if the curve is given by a weierstrass equation in short form.

getA2

FieldElement getA2()

Returns \(A2\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).

Is zero if the curve is given by a weierstrass equation in short form.

getA1

FieldElement getA1()

Returns \(A1\) from the weierstrass equation \(y^2 + A1 \cdot xy + A3 \cdot y = x^3 + A2 \cdot x^2 + A4 \cdot x + A6\).

Is zero if the curve is given by a weierstrass equation in short form.

getElement

EllipticCurvePoint getElement(FieldElement x,
                              FieldElement y)

Construct an point on this curve given the x- and y-coordinates.

Parameters:

x - the x-coordinate

y - the y-coordinate

Returns:

the corresponding elliptic curve point

isShortForm

default boolean isShortForm()