org.cryptimeleon.math.structures.groups.elliptic

Interface EllipticCurvePoint

All Superinterfaces:

GroupElementImpl, Representable, UniqueByteRepresentable

All Known Implementing Classes:

AbstractEllipticCurvePoint, AffineEllipticCurvePoint, PairingSourceGroupElement

public interface EllipticCurvePoint
extends GroupElementImpl

A point on an elliptic curve.

Method Summary

Modifier and Type	Method and Description
EllipticCurvePoint	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.
Field	getFieldOfDefinition() Returns the base field over which the elliptic curve this point belongs to is defined.
boolean	isNormalized() Checks whether this point is normalized.
EllipticCurvePoint	normalize() Normalizes this elliptic curve point.
default GroupElementImpl	op(GroupElementImpl e) Calculates the result of this op e.

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

getStructure, inv, isNeutralElement, pow, square

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

getRepresentation

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

getUniqueByteRepresentation, updateAccumulator

Method Detail

normalize

EllipticCurvePoint normalize()

Normalizes this elliptic curve point.

Returns:

the normalized point

isNormalized

boolean isNormalized()

Checks whether this point is normalized.

Returns:

true if this point is normalized, else false

getFieldOfDefinition

Field getFieldOfDefinition()

Returns the base field over which the elliptic curve this point belongs to is defined.

computeLine

FieldElement[] computeLine(EllipticCurvePoint Q)

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

add

EllipticCurvePoint add(EllipticCurvePoint P,
                       FieldElement[] line)

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

op

default GroupElementImpl op(GroupElementImpl e)
                     throws java.lang.IllegalArgumentException

Description copied from interface: GroupElementImpl

Calculates the result of this op e.

Specified by:

op in interface GroupElementImpl

Parameters:

e - right hand side of the operation

Returns:

the element resulting from the group operation

Throws:

java.lang.IllegalArgumentException - if e is of the wrong type