org.cryptimeleon.math.structures.groups.elliptic

Class AffineEllipticCurvePoint

java.lang.Object

org.cryptimeleon.math.structures.groups.elliptic.AbstractEllipticCurvePoint

org.cryptimeleon.math.structures.groups.elliptic.AffineEllipticCurvePoint

All Implemented Interfaces:

UniqueByteRepresentable, Representable, EllipticCurvePoint, GroupElementImpl

Direct Known Subclasses:

PairingSourceGroupElement

public class AffineEllipticCurvePoint
extends AbstractEllipticCurvePoint

Constructor Summary

Constructors

Constructor and Description
AffineEllipticCurvePoint(WeierstrassCurve curve)
AffineEllipticCurvePoint(WeierstrassCurve curve, FieldElement x, FieldElement y)
AffineEllipticCurvePoint(WeierstrassCurve curve, Representation repr)

Method Summary

Modifier and Type	Method and Description
AffineEllipticCurvePoint	add(EllipticCurvePoint P, FieldElement[] line) Add this to P with the help of line where line is the result of this.computeLine(P).
FieldElement[]	computeLine(EllipticCurvePoint Q) Computes a parameterization of the line through this and Q.
boolean	equals(java.lang.Object element)
GroupElementImpl	inv() Calculates the inverse of this group element.
boolean	isNormalized() Checks whether this point is normalized.
AffineEllipticCurvePoint	normalize() Normalizes this elliptic curve point.
ByteAccumulator	updateAccumulator(ByteAccumulator accumulator) Updates the ByteAccumulator with the unique byte representation of this object.

Methods inherited from class org.cryptimeleon.math.structures.groups.elliptic.AbstractEllipticCurvePoint

getFieldOfDefinition, getRepresentation, getStructure, getX, getY, getZ, hashCode, isNeutralElement, toString

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

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

op

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

pow, square

Methods inherited from interface org.cryptimeleon.math.hash.UniqueByteRepresentable

getUniqueByteRepresentation

Constructor Detail

AffineEllipticCurvePoint

public AffineEllipticCurvePoint(WeierstrassCurve curve,
                                FieldElement x,
                                FieldElement y)

AffineEllipticCurvePoint

public AffineEllipticCurvePoint(WeierstrassCurve curve)

AffineEllipticCurvePoint

public AffineEllipticCurvePoint(WeierstrassCurve curve,
                                Representation repr)

Method Detail

normalize

public AffineEllipticCurvePoint normalize()

Description copied from interface: EllipticCurvePoint

Normalizes this elliptic curve point.

Returns:

the normalized point

inv

public GroupElementImpl inv()

Description copied from interface: GroupElementImpl

Calculates the inverse of this group element.

Returns:

an element x such that x.op(this).equals(getStructure().getNeutralElement())

add

public AffineEllipticCurvePoint add(EllipticCurvePoint P,
                                    FieldElement[] line)

Description copied from interface: EllipticCurvePoint

Add this to P with the help of line where line is the result of this.computeLine(P).

The contract is that this.op(P).equals(this.add(P,this.computeLine(P))).

Parameters:

P - the point to add

line - the line to use for the addition

Returns:

the resulting curve point

computeLine

public FieldElement[] computeLine(EllipticCurvePoint Q)

Description copied from interface: EllipticCurvePoint

Computes a parameterization of the line through this and Q.

The result of this function should parameterize the line through this and Q. For example for affine points, a line through P is parameterized by \(a_0, a_1\) with \(a_0(y-yP)-a_1(x-xP)\). For Jacobian points, a line through P is parameterized by \(a_0, a_1\) with \(a_0(yZp^3-Yp)-a_1(xZp^2-Xp)\).

This function is useful to assess the line as an intermediate result of point addition for a an efficient pairing computation.

Parameters:

Q - the second point on the line

Returns:

parameterization of line through this and Q

equals

public boolean equals(java.lang.Object element)

Overrides:

equals in class java.lang.Object

isNormalized

public boolean isNormalized()

Description copied from interface: EllipticCurvePoint

Checks whether this point is normalized.

Returns:

true if this point is normalized, else false

updateAccumulator

public ByteAccumulator updateAccumulator(ByteAccumulator accumulator)

Description copied from interface: UniqueByteRepresentable

Updates the ByteAccumulator with the unique byte representation of this object.

The input to the accumulators update function is an injective (with respect to a given domain) byte encoding of this object.

For many use-cases, the AnnotatedUbrUtil can be used to quickly implement this method.

Returns:

the same accumulator as was input