org.cryptimeleon.math.structures.groups.elliptic

Class AbstractPairing

java.lang.Object

org.cryptimeleon.math.structures.groups.elliptic.AbstractPairing

All Implemented Interfaces:

java.util.function.BiFunction<GroupElementImpl,GroupElementImpl,GroupElementImpl>, BilinearMapImpl

public abstract class AbstractPairing
extends java.lang.Object
implements BilinearMapImpl

Base class for pairings such as Tate Pairing, Ate Pairing and Optimal Ate Pairing.

Field Summary

Fields

Modifier and Type	Field and Description
protected PairingSourceGroupImpl	g1
protected PairingSourceGroupImpl	g2
protected PairingTargetGroupImpl	gT

Constructor Summary

Constructors

Constructor and Description
AbstractPairing(PairingSourceGroupImpl g1, PairingSourceGroupImpl g2, PairingTargetGroupImpl gT)

Method Summary

Modifier and Type	Method and Description
PairingTargetGroupElementImpl	apply(GroupElementImpl g, GroupElementImpl h, java.math.BigInteger exponent) Computes \(e(g1,g2)^\text{exponent}\).
boolean	equals(java.lang.Object other)
protected abstract ExtensionFieldElement	evaluateLine(FieldElement[] line, PairingSourceGroupElement P, PairingSourceGroupElement Q) Abstract class that evaluates a line through a given point at another point.
PairingTargetGroupElementImpl	exponentiate(FieldElement f) Implements final exponentiation.
int	hashCode()
protected void	init(PairingSourceGroupImpl g1, PairingSourceGroupImpl g2, PairingTargetGroupImpl gT)
protected ExtensionFieldElement	miller(PairingSourceGroupElement P, PairingSourceGroupElement Q, java.math.BigInteger n) Implementation of Miller algorithm to be used as part of the function pair.
protected abstract ExtensionFieldElement	pair(PairingSourceGroupElement P, PairingSourceGroupElement Q) Computes the first step of the pairing.

Methods inherited from class java.lang.Object

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

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

apply, isSymmetric

Methods inherited from interface java.util.function.BiFunction

andThen

Field Detail

g1

protected PairingSourceGroupImpl g1

g2

protected PairingSourceGroupImpl g2

gT

protected PairingTargetGroupImpl gT

Constructor Detail

AbstractPairing

public AbstractPairing(PairingSourceGroupImpl g1,
                       PairingSourceGroupImpl g2,
                       PairingTargetGroupImpl gT)

Method Detail

init

protected void init(PairingSourceGroupImpl g1,
                    PairingSourceGroupImpl g2,
                    PairingTargetGroupImpl gT)

apply

public PairingTargetGroupElementImpl apply(GroupElementImpl g,
                                           GroupElementImpl h,
                                           java.math.BigInteger exponent)

Description copied from interface: BilinearMapImpl

Computes \(e(g1,g2)^\text{exponent}\).

Depending on the bilinear map and the involved groups, this may be more efficiently implemented than computing it directly via apply(g1,g2).pow(exponent). For example, implementations should do exponentiation in the group with the cheapest group operation.

Specified by:

apply in interface BilinearMapImpl

Parameters:

g - left hand side argument for the pairing function

h - right hand side argument for the pairing function

exponent - the exponent to apply to the result of the pairing

exponentiate

public PairingTargetGroupElementImpl exponentiate(FieldElement f)

Implements final exponentiation.

Exponentiation of f to the power of e=(q^k-1)/r where r is the size of groups G1, G2, and GT, respectively.

Parameters:

f - the element to exponentiate

Returns:

f^e

evaluateLine

protected abstract ExtensionFieldElement evaluateLine(FieldElement[] line,
                                                      PairingSourceGroupElement P,
                                                      PairingSourceGroupElement Q)

Abstract class that evaluates a line through a given point at another point.

The line is parameterized by the point P and the argument line. Here, line is the result of the function EllipticCurvePoint.computeLine. The line is evaluated at the point Q.

Parameters:

line - - parameterization of the line

P - - point on the line

Q - - point where line es evaluated

Returns:

l_P(Q)

pair

protected abstract ExtensionFieldElement pair(PairingSourceGroupElement P,
                                              PairingSourceGroupElement Q)

Computes the first step of the pairing.

A pairing is computed in several steps, where the first step includes miller Algorithm and the second step is the final exponentiation. This functions computes the first step of the pairing computation that depends on the concrete pairing.

Parameters:

P - - first argument of pairing

Q - - second argument of pairing

Returns:

- result of first step

miller

protected ExtensionFieldElement miller(PairingSourceGroupElement P,
                                       PairingSourceGroupElement Q,
                                       java.math.BigInteger n)

Implementation of Miller algorithm to be used as part of the function pair.

This algorithm evaluates a function with divisor [n](P-O) at Q and applies denominator elimination.

Parameters:

P - - first argument

Q - - second argument

n - - loop bound

Returns:

f_n(P, Q)

equals

public boolean equals(java.lang.Object other)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object