org.cryptimeleon.math.structures.groups.elliptic.type3.bn

Class BarretoNaehrigTatePairing

java.lang.Object

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

org.cryptimeleon.math.structures.groups.elliptic.type3.bn.BarretoNaehrigTatePairing

All Implemented Interfaces:

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

public class BarretoNaehrigTatePairing
extends AbstractPairing

Tate-pairing specific implementation of BN based pairings.

Field Summary

Fields inherited from class org.cryptimeleon.math.structures.groups.elliptic.AbstractPairing

g1, g2, gT

Constructor Summary

Constructors

Constructor and Description
BarretoNaehrigTatePairing(BarretoNaehrigGroup1Impl g1, BarretoNaehrigGroup2Impl g2, BarretoNaehrigTargetGroupImpl gT, java.math.BigInteger u) Construct Tate pairing \(\mathbb{G}_1 \times \mathbb{G}_2 \rightarrow \mathbb{G}_T\).

Method Summary

Modifier and Type	Method and Description
protected ExtensionFieldElement	evaluateLine(FieldElement[] line, PairingSourceGroupElement P, PairingSourceGroupElement Q) TODO (rh): Write javadoc for this.
PairingTargetGroupElementImpl	exponentiate(FieldElement f) Implements final exponentiation.
boolean	isSymmetric() Returns true if \(e(g,h) = e(h,g)\) for all g in G1, h in G2.
protected ExtensionFieldElement	pair(PairingSourceGroupElement P, PairingSourceGroupElement Q) Computes the first step of the pairing.
java.lang.String	toString()

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

apply, equals, hashCode, init, miller

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.BilinearMapImpl

apply

Methods inherited from interface java.util.function.BiFunction

andThen

Constructor Detail

BarretoNaehrigTatePairing

public BarretoNaehrigTatePairing(BarretoNaehrigGroup1Impl g1,
                                 BarretoNaehrigGroup2Impl g2,
                                 BarretoNaehrigTargetGroupImpl gT,
                                 java.math.BigInteger u)

Construct Tate pairing \(\mathbb{G}_1 \times \mathbb{G}_2 \rightarrow \mathbb{G}_T\).

Method Detail

evaluateLine

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

TODO (rh): Write javadoc for this. I had some notes somewhere about how exactly this works and especially the line parameterization format.

Specified by:

evaluateLine in class AbstractPairing

Parameters:

line - parameterization of the line

P - - point on the line

Q - - point where line es evaluated

Returns:

l_P(Q)

pair

protected ExtensionFieldElement pair(PairingSourceGroupElement P,
                                     PairingSourceGroupElement Q)

Description copied from class: AbstractPairing

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.

Specified by:

pair in class AbstractPairing

Parameters:

P - - first argument of pairing

Q - - second argument of pairing

Returns:

- result of first step

exponentiate

public PairingTargetGroupElementImpl exponentiate(FieldElement f)

Description copied from class: AbstractPairing

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.

Overrides:

exponentiate in class AbstractPairing

Parameters:

f - the element to exponentiate

Returns:

f^e

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

isSymmetric

public boolean isSymmetric()

Description copied from interface: BilinearMapImpl

Returns true if \(e(g,h) = e(h,g)\) for all g in G1, h in G2.