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

Class BarretoNaehrigSourceGroupImpl

java.lang.Object

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

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

All Implemented Interfaces:

RepresentationRestorer, Representable, StandaloneRepresentable, EllipticCurve, WeierstrassCurve, GroupImpl

Direct Known Subclasses:

BarretoNaehrigGroup1Impl, BarretoNaehrigGroup2Impl

public abstract class BarretoNaehrigSourceGroupImpl
extends PairingSourceGroupImpl

Abstract class underlying both G1 and G2.

This class implements a subgroup of \(E:y^2=x^3+b\).

Field Summary

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

cofactor, field, generator, size

Constructor Summary

Constructors

Constructor and Description
BarretoNaehrigSourceGroupImpl(java.math.BigInteger size, java.math.BigInteger cofactor, ExtensionFieldElement a6)
BarretoNaehrigSourceGroupImpl(Representation r)

Method Summary

Modifier and Type	Method and Description
FieldElement	decompressX(FieldElement y, int sel) Retrieves the x-coordinate from the compressed point and its corresponding y-coordinate.
BarretoNaehrigSourceGroupElementImpl	getUniformlyRandomElement() Generates a uniformly random element of this group.
protected PairingSourceGroupElement	getUniformlyRandomElementOblivious()
boolean	hasPrimeSize() Returns true if the size of this structure is known and prime.
boolean	isShortForm()
PairingSourceGroupElement	mapToPoint(FieldElement y, int sel) Decompresses a point by mapping y coordinate of point (x,y) back to curve.
PairingSourceGroupElement	mapToSubgroup(FieldElement y, int sel) Maps a given y coordinate to a point in this subgroup.
protected PairingSourceGroupElement	superGetUniformlyRandomElement()
java.lang.String	toString()

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

cofactorMultiplication, equals, getA1, getA2, getA3, getA4, getA6, getCofactor, getElement, 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

estimateCostInvPerOp, exp, getNeutralElement, getUniformlyRandomNonNeutral, implementsOwnExp, implementsOwnMultiExp, multiexp, restoreFromRepresentation

Constructor Detail

BarretoNaehrigSourceGroupImpl

public BarretoNaehrigSourceGroupImpl(java.math.BigInteger size,
                                     java.math.BigInteger cofactor,
                                     ExtensionFieldElement a6)

BarretoNaehrigSourceGroupImpl

public BarretoNaehrigSourceGroupImpl(Representation r)

Method Detail

getUniformlyRandomElementOblivious

protected PairingSourceGroupElement getUniformlyRandomElementOblivious()
                                                                throws java.lang.UnsupportedOperationException

Throws:

java.lang.UnsupportedOperationException

mapToSubgroup

public PairingSourceGroupElement mapToSubgroup(FieldElement y,
                                               int sel)

Maps a given y coordinate to a point in this subgroup.

As opposed to mapToPoint(FieldElement, int), this function includes cofactor multiplication.

Parameters:

y - y coordinate of point

sel - selection of x coordinate

mapToPoint

public PairingSourceGroupElement mapToPoint(FieldElement y,
                                            int sel)

Decompresses a point by mapping y coordinate of point (x,y) back to curve.

This function takes the y-coordinate of a point and maps it to a point on this curve. It solves the Weierstrass equation for a matching x-coordinate. For a given field F, for each element y in F, there exist either 0 or 3 solutions over F, i.e. x-coordinates in F.

• If y is not a y-coordinate of a point on this curve (no matching x exists over the field of definition), an IllegalArgumentException is thrown.
• If 3 solutions exists, the returned solution is selected with the parameter sel mod 3.

It is important to note that this function does not map the result to the subgroup represented by this class. A cofactor multiplication is still required. We do not include cofactor multiplication into this function to assert the following contract:

     mapToPoint(P.getY(),0).equals(P);
 

Parameters:

y - y-coordinate of point

sel - selector for x-coordinate

Returns:

point (x,y) on curve

Throws:

java.lang.IllegalArgumentException - if the y-coordinate does not correspond to any curve point

decompressX

public FieldElement decompressX(FieldElement y,
                                int sel)

Retrieves the x-coordinate from the compressed point and its corresponding y-coordinate.

For more information on how this is done, consult the documentation for mapToPoint(FieldElement, int).

Parameters:

y - y-coordinate of point

sel - selector for x-coordinate

Returns:

x-coordinate of the decompressed point

Throws:

java.lang.IllegalArgumentException - if the y-coordinate does not correspond to any curve point

getUniformlyRandomElement

public BarretoNaehrigSourceGroupElementImpl getUniformlyRandomElement()
                                                               throws java.lang.UnsupportedOperationException

Description copied from interface: GroupImpl

Generates a uniformly random element of this group.

Specified by:

getUniformlyRandomElement in interface GroupImpl

Overrides:

getUniformlyRandomElement in class PairingSourceGroupImpl

Throws:

java.lang.UnsupportedOperationException - if the random generation cannot be done

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

isShortForm

public boolean isShortForm()

hasPrimeSize

public boolean hasPrimeSize()
                     throws java.lang.UnsupportedOperationException

Description copied from interface: GroupImpl

Returns true if the size of this structure is known and prime.

Throws:

java.lang.UnsupportedOperationException

superGetUniformlyRandomElement

protected PairingSourceGroupElement superGetUniformlyRandomElement()