org.cryptimeleon.math.structures.groups.sn

Class Sn

java.lang.Object

org.cryptimeleon.math.structures.groups.sn.Sn

All Implemented Interfaces:

RepresentationRestorer, Representable, StandaloneRepresentable, GroupImpl

public class Sn
extends java.lang.Object
implements GroupImpl

The group Sn for a natural number n is the set of permutations \(\pi : \{1,...,n\} \rightarrow \{1,...,n\}\) where the group operation is function composition.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	Sn.SnElementImpl A permutation on \(\{1,...,n\}\).

Field Summary

Fields

Modifier and Type	Field and Description
protected int	n

Constructor Summary

Constructors

Constructor and Description
Sn(int n) Constructs Sn for n.
Sn(Representation repr)

Method Summary

Modifier and Type	Method and Description
static Sn.SnElementImpl	createElementFromString(java.lang.String str) Creates a permutation from a string of images, each of which is separated by an empty space.
boolean	equals(java.lang.Object obj)
double	estimateCostInvPerOp() Estimates the number of inversions that can be done per group operation for the same cost.
GroupElementImpl	getGenerator() Returns any generator of this group if the group is cyclic and it's feasible to compute a generator.
int	getN() Returns the integer n of this group, such that its permutation map from and onto \(\{1,...,n\}\).
Sn.SnElementImpl	getNeutralElement() Returns the neutral element of this group.
Representation	getRepresentation() The representation of this object.
Sn.SnElementImpl	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()
boolean	hasPrimeSize() Returns true if the size of this structure is known and prime.
boolean	isCommutative() Returns true if this group is known to be commutative.
Sn.SnElementImpl	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

exp, getUniformlyRandomNonNeutral, implementsOwnExp, implementsOwnMultiExp, multiexp, restoreFromRepresentation

Field Detail

n

protected int n

Constructor Detail

Sn

public Sn(int n)

Constructs Sn for n.

Sn

public Sn(Representation repr)

Method Detail

getN

public int getN()

Returns the integer n of this group, such that its permutation map from and onto \(\{1,...,n\}\).

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

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.

Specified by:

hasPrimeSize in interface GroupImpl

Throws:

java.lang.UnsupportedOperationException

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.

Specified by:

estimateCostInvPerOp in interface GroupImpl

Returns:

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

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

getNeutralElement

public Sn.SnElementImpl getNeutralElement()

Description copied from interface: GroupImpl

Returns the neutral element of this group.

Specified by:

getNeutralElement in interface GroupImpl

getUniformlyRandomElement

public Sn.SnElementImpl 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

restoreElement

public Sn.SnElementImpl restoreElement(Representation repr)

Description copied from interface: GroupImpl

Restores a group element from its representation.

Specified by:

restoreElement in interface GroupImpl

getGenerator

public GroupElementImpl getGenerator()
                              throws java.lang.UnsupportedOperationException

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

Throws:

java.lang.UnsupportedOperationException - if group is not cyclic or it's too hard to compute a generator

createElementFromString

public static Sn.SnElementImpl createElementFromString(java.lang.String str)

Creates a permutation from a string of images, each of which is separated by an empty space.

Specifically, the format is "[image1 image2 image3]".

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals 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