org.cryptimeleon.math.structures.groups.elliptic

Class PairingTargetGroupImpl

java.lang.Object

org.cryptimeleon.math.structures.groups.elliptic.PairingTargetGroupImpl

All Implemented Interfaces:

RepresentationRestorer, Representable, StandaloneRepresentable, GroupImpl

Direct Known Subclasses:

BarretoNaehrigTargetGroupImpl, SupersingularTargetGroupImpl

public abstract class PairingTargetGroupImpl
extends java.lang.Object
implements GroupImpl, Representable

A multiplicative subgroup of an ExtensionField.

When initialized with (finite) ExtensionField f and prime number "size", it represents the unique subgroup of the unit group of f of size "size".

Field Summary

Fields

Modifier and Type	Field and Description
protected ExtensionField	fieldOfDefinition
protected java.math.BigInteger	size

Constructor Summary

Constructors

Constructor and Description
PairingTargetGroupImpl(ExtensionField f, java.math.BigInteger size) Construct target group as subgroup of field f of given size.
PairingTargetGroupImpl(Representation r)

Method Summary

Modifier and Type	Method and Description
boolean	equals(java.lang.Object o)
java.math.BigInteger	getCofactor()
abstract PairingTargetGroupElementImpl	getElement(ExtensionFieldElement fe) Concrete implementations should wrap the extension field element into their subclass.
ExtensionField	getFieldOfDefinition()
PairingTargetGroupElementImpl	getGenerator() Returns any generator of this group if the group is cyclic and it's feasible to compute a generator.
PairingTargetGroupElementImpl	getNeutralElement() Returns the neutral element of this group.
Representation	getRepresentation() The representation of this object.
PairingTargetGroupElementImpl	getUniformlyRandomElement() Generates a uniformly random element of this group.
java.util.Optional<java.lang.Integer>	getUniqueByteLength() Returns the number of bytes returned by this structure's UniqueByteRepresentable.getUniqueByteRepresentation(), or an empty Optional if this structure's elements do not guarantee a fixed length.
int	hashCode()
protected void	init(Representation r)
boolean	isCommutative() Returns true if this group is known to be commutative.
PairingTargetGroupElementImpl	restoreElement(Representation repr) Restores a group element from its representation.
java.math.BigInteger	size() Retrieves number of elements in the group if possible.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

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

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

Field Detail

fieldOfDefinition

protected ExtensionField fieldOfDefinition

size

protected java.math.BigInteger size

Constructor Detail

PairingTargetGroupImpl

public PairingTargetGroupImpl(ExtensionField f,
                              java.math.BigInteger size)

Construct target group as subgroup of field f of given size. If size does not divide size of the multiplicative group of f, an exception is thrown.

Parameters:

f - - field for embedding to new group

size - - size of new group

PairingTargetGroupImpl

public PairingTargetGroupImpl(Representation r)

Method Detail

getFieldOfDefinition

public ExtensionField getFieldOfDefinition()

getCofactor

public java.math.BigInteger getCofactor()

size

public java.math.BigInteger size()
                          throws java.lang.UnsupportedOperationException

Description copied from interface: GroupImpl

Retrieves number of elements in the group if possible.

Specified by:

size in interface GroupImpl

Returns:

size of this group (number of group elements in it) or null if infinite

Throws:

java.lang.UnsupportedOperationException - if the number of elements is unknown or is too expensive to compute

getRepresentation

public Representation getRepresentation()

Description copied from interface: Representable

The representation of this object. Used for serialization. A convenient way to implement this is using @link ReprUtil

Specified by:

getRepresentation in interface Representable

Returns:

a Representation or null if an equal object can be recreated without any information.

See Also:

Representation

init

protected void init(Representation r)

getNeutralElement

public PairingTargetGroupElementImpl getNeutralElement()

Description copied from interface: GroupImpl

Returns the neutral element of this group.

Specified by:

getNeutralElement in interface GroupImpl

getUniformlyRandomElement

public PairingTargetGroupElementImpl getUniformlyRandomElement()
                                                        throws java.lang.UnsupportedOperationException

Description copied from interface: GroupImpl

Generates a uniformly random element of this group.

Specified by:

getUniformlyRandomElement in interface GroupImpl

Throws:

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

getGenerator

public PairingTargetGroupElementImpl getGenerator()

Description copied from interface: GroupImpl

Returns any generator of this group if the group is cyclic and it's feasible to compute a generator.

Repeated calls may or may not always supply the same generator again (i.e. the output is not guaranteed to be random)!

Specified by:

getGenerator in interface GroupImpl

restoreElement

public PairingTargetGroupElementImpl restoreElement(Representation repr)

Description copied from interface: GroupImpl

Restores a group element from its representation.

Specified by:

restoreElement in interface GroupImpl

getElement

public abstract PairingTargetGroupElementImpl getElement(ExtensionFieldElement fe)

Concrete implementations should wrap the extension field element into their subclass.

equals

public boolean equals(java.lang.Object o)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

getUniqueByteLength

public java.util.Optional<java.lang.Integer> getUniqueByteLength()

Description copied from interface: GroupImpl

Returns the number of bytes returned by this structure's UniqueByteRepresentable.getUniqueByteRepresentation(), or an empty Optional if this structure's elements do not guarantee a fixed length.

For example, elements of Zp will always be represented by ceil(ceil(log(p))/8) bytes, hence getUniqueByteLength() would return ceil(ceil(log(p))/8).

A polynomial ring would return an empty Optional since a polynomial's unique byte representation length depends on its degree.

Specified by:

getUniqueByteLength in interface GroupImpl

Returns:

the guaranteed fixed length of getUniqueByteRepresentation(), or an empty Optional, if no guarantee

isCommutative

public boolean isCommutative()

Description copied from interface: GroupImpl

Returns true if this group is known to be commutative.

Specified by:

isCommutative in interface GroupImpl