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

Class BarretoNaehrigGroup2Impl

java.lang.Object

org.cryptimeleon.math.structures.groups.elliptic.PairingSourceGroupImpl

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

org.cryptimeleon.math.structures.groups.elliptic.type3.bn.BarretoNaehrigGroup2Impl

All Implemented Interfaces:

RepresentationRestorer, Representable, StandaloneRepresentable, EllipticCurve, WeierstrassCurve, GroupImpl

public class BarretoNaehrigGroup2Impl
extends BarretoNaehrigSourceGroupImpl

G2 in the Barreto-Naehrig bilinear group.

Field Summary

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

cofactor, field, generator, size

Constructor Summary

Constructors

Constructor and Description
BarretoNaehrigGroup2Impl(java.math.BigInteger size, java.math.BigInteger traceFrobenius, ExtensionFieldElement a6) Construct subgroup of E:y^2=x^3+a6 using given parameters.
BarretoNaehrigGroup2Impl(Representation r) Recreates a group from the given representation.

Method Summary

Modifier and Type	Method and Description
double	estimateCostInvPerOp() Estimates the number of inversions that can be done per group operation for the same cost.
BarretoNaehrigGroup2ElementImpl	getElement(FieldElement x, FieldElement y) Construct an point on this curve given the x- and y-coordinates.
GroupElementImpl	getNeutralElement() Returns the neutral element of this group.

Methods inherited from class org.cryptimeleon.math.structures.groups.elliptic.type3.bn.BarretoNaehrigSourceGroupImpl

decompressX, getUniformlyRandomElement, getUniformlyRandomElementOblivious, hasPrimeSize, isShortForm, mapToPoint, mapToSubgroup, superGetUniformlyRandomElement, toString

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

cofactorMultiplication, equals, getA1, getA2, getA3, getA4, getA6, getCofactor, getFieldOfDefinition, getGenerator, getRepresentation, getSize, getUniqueByteLength, hashCode, isMember, isOnCurve, restoreElement, setGenerator, size

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.EllipticCurve

isCommutative

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

exp, getUniformlyRandomNonNeutral, implementsOwnExp, implementsOwnMultiExp, multiexp, restoreFromRepresentation

Constructor Detail

BarretoNaehrigGroup2Impl

public BarretoNaehrigGroup2Impl(java.math.BigInteger size,
                                java.math.BigInteger traceFrobenius,
                                ExtensionFieldElement a6)

Construct subgroup of E:y^2=x^3+a6 using given parameters.

Parameters:

size - size of the subgroup

traceFrobenius - used to calculate the cofactor for the resulting group

a6 - curve parameter for weierstrass equation

BarretoNaehrigGroup2Impl

public BarretoNaehrigGroup2Impl(Representation r)

Recreates a group from the given representation.

Parameters:

r - the representation to use for reconstruction

Method Detail

getElement

public BarretoNaehrigGroup2ElementImpl getElement(FieldElement x,
                                                  FieldElement y)

Description copied from interface: WeierstrassCurve

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

Specified by:

getElement in interface WeierstrassCurve

Specified by:

getElement in class PairingSourceGroupImpl

Parameters:

x - the x-coordinate

y - the y-coordinate

Returns:

the corresponding elliptic curve point

getNeutralElement

public GroupElementImpl getNeutralElement()

Description copied from interface: GroupImpl

Returns the neutral element of this group.

estimateCostInvPerOp

public double estimateCostInvPerOp()

Description copied from interface: GroupImpl

Estimates the number of inversions that can be done per group operation for the same cost. For example, 2 would mean that an inversion costs half as much as a group operation, on average.

Returns:

Estimated number of inversions that can be done per group operation for the same cost