org.cryptimeleon.math.structures.groups.basic

Class BasicGroupElement

java.lang.Object

org.cryptimeleon.math.structures.groups.basic.BasicGroupElement

All Implemented Interfaces:

UniqueByteRepresentable, Representable, Element, GroupElement

Direct Known Subclasses:

RingGroup.RingGroupElement

public class BasicGroupElement
extends java.lang.Object
implements GroupElement

A basic GroupElementImpl wrapper where operations are evaluated naively, i.e. operation by operation.

Field Summary

Fields

Modifier and Type	Field and Description
protected BasicGroup	group
protected GroupElementImpl	impl
protected SmallExponentPrecomputation	precomputedSmallExponents

Constructor Summary

Constructors

Constructor and Description
BasicGroupElement(BasicGroup group, GroupElementImpl impl)

Method Summary

Modifier and Type	Method and Description
GroupElement	compute() Hint that the concrete value of this GroupElement will be accessed soon (e.g., via getRepresentation() or equals()).
GroupElement	computeSync() Will compute stuff synchronously (this call blocks) so that the next call requiring the concrete value of this group element can immediately retrieve it.
boolean	equals(java.lang.Object o)
GroupElementImpl	getConcreteGroupElement()
SmallExponentPrecomputation	getPrecomputedSmallExponents()
Representation	getRepresentation() The representation of this object.
Group	getStructure() Returns the Structure that this Element belongs to.
int	hashCode()
GroupElement	inv() Calculates the inverse of this group element.
boolean	isComputed() Returns true if a concrete value has already been computed.
boolean	isNeutralElement() Returns true iff this is the neutral element of the group.
GroupElement	op(Element e) Calculates the result of this.op(e).
GroupElement	pow(java.math.BigInteger exponent) Calculates the result of applying the group operation k times.
GroupElement	precomputePow() Advises the GroupElement to prepare it for later pow() calls.
GroupElement	precomputePow(int windowSize) Advises the GroupElement to prepare it for later pow() calls.
GroupElement	square() Computes this.op(this).
java.lang.String	toString()
ByteAccumulator	updateAccumulator(ByteAccumulator accumulator) Updates the ByteAccumulator with the unique byte representation of this object.

Methods inherited from class java.lang.Object

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

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

expr, isEqualTo, isEqualTo, isEqualTo, op, op, pow, pow, pow, pow, pow, pow

Methods inherited from interface org.cryptimeleon.math.hash.UniqueByteRepresentable

getUniqueByteRepresentation

Field Detail

group

protected BasicGroup group

impl

protected GroupElementImpl impl

precomputedSmallExponents

protected SmallExponentPrecomputation precomputedSmallExponents

Constructor Detail

BasicGroupElement

public BasicGroupElement(BasicGroup group,
                         GroupElementImpl impl)

Method Detail

getStructure

public Group getStructure()

Description copied from interface: Element

Returns the Structure that this Element belongs to.

Specified by:

getStructure in interface Element

Specified by:

getStructure in interface GroupElement

inv

public GroupElement inv()

Description copied from interface: GroupElement

Calculates the inverse of this group element.

Specified by:

inv in interface GroupElement

Returns:

an element x such that x.op(this).equals(getStructure().getNeutralElement())

op

public GroupElement op(Element e)
                throws java.lang.IllegalArgumentException

Description copied from interface: GroupElement

Calculates the result of this.op(e).

Specified by:

op in interface GroupElement

Parameters:

e - right hand side of the operation

Returns:

the element resulting from the group operation

Throws:

java.lang.IllegalArgumentException - if e is of the wrong type

square

public GroupElement square()

Description copied from interface: GroupElement

Computes this.op(this).

Useful if this group allows squaring to be more efficiently implemented than general exponentiation as is the case for elliptic curves.

Specified by:

square in interface GroupElement

pow

public GroupElement pow(java.math.BigInteger exponent)

Description copied from interface: GroupElement

Calculates the result of applying the group operation k times. i.e. it computes k*this (additive group) or this^k (multiplicative group). For negative exponents k, computes this.inv().pow(-k).

Specified by:

pow in interface GroupElement

isNeutralElement

public boolean isNeutralElement()

Description copied from interface: GroupElement

Returns true iff this is the neutral element of the group.

Specified by:

isNeutralElement in interface GroupElement

precomputePow

public GroupElement precomputePow()

Description copied from interface: GroupElement

Advises the GroupElement to prepare it for later pow() calls. This will take some time and should only be done ahead of time. That is, the usual usage pattern should be:

 //Setting up your encryption scheme (or whatever)
 GroupElement g = group.getUniformlyRandomElement().precomputePow();
 //Then (maybe even multiple) future calls of
 GroupElement encrypt(GroupElement m) {
     return m.op(g.pow(sk)).compute();
 }
 

Don't use g.precomputePow().pow(x).compute(); unless you're planning to do more exponentiations of g in the future. Uses a reasonable default for the memory consumed by this. Use GroupElement.precomputePow(int) to customize.

Specified by:

precomputePow in interface GroupElement

Returns:

the same object (for chaining calls)

precomputePow

public GroupElement precomputePow(int windowSize)

Description copied from interface: GroupElement

Advises the GroupElement to prepare it for later pow() calls. This will take some time and should only be done ahead of time. That is, the usual usage pattern should be:

 //Setting up your encryption scheme (or whatever)
 GroupElement g = group.getUniformlyRandomElement().precomputePow();
 //Then (maybe even multiple) future calls of
 GroupElement encrypt(GroupElement m) {
     return m.op(g.pow(sk)).compute();
 }
 

Don't use g.precomputePow().pow(x).compute(); unless you're planning to do more exponentiations of g in the future.

Specified by:

precomputePow in interface GroupElement

Parameters:

windowSize - an indicator for how much memory you're willing to invest. Precomputation will take up space of roughly 2^(windowSize) group elements.

Returns:

the same object (for chaining calls)

getPrecomputedSmallExponents

public SmallExponentPrecomputation getPrecomputedSmallExponents()

compute

public GroupElement compute()

Description copied from interface: GroupElement

Hint that the concrete value of this GroupElement will be accessed soon (e.g., via getRepresentation() or equals()). Will start computing stuff in the background.

Specified by:

compute in interface GroupElement

Returns:

the same object (for chaining calls)

computeSync

public GroupElement computeSync()

Description copied from interface: GroupElement

Will compute stuff synchronously (this call blocks) so that the next call requiring the concrete value of this group element can immediately retrieve it. For designers of cryptographic schemes, were should be no reason to call this. Instead, use compute() which does the same, but asynchronously (i.e. concurrently).

Specified by:

computeSync in interface GroupElement

Returns:

the same object (for chaining calls)

getConcreteGroupElement

public GroupElementImpl getConcreteGroupElement()

isComputed

public boolean isComputed()

Description copied from interface: GroupElement

Returns true if a concrete value has already been computed. No need to call this outside of upb.crypto.math, it's meant to allow for optimizations.

Specified by:

isComputed in interface GroupElement

equals

public boolean equals(java.lang.Object o)

Specified by:

equals in interface Element

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Specified by:

hashCode in interface Element

Overrides:

hashCode in class java.lang.Object

updateAccumulator

public ByteAccumulator updateAccumulator(ByteAccumulator accumulator)

Description copied from interface: UniqueByteRepresentable

Updates the ByteAccumulator with the unique byte representation of this object.

The input to the accumulators update function is an injective (with respect to a given domain) byte encoding of this object.

For many use-cases, the AnnotatedUbrUtil can be used to quickly implement this method.

Specified by:

updateAccumulator in interface UniqueByteRepresentable

Returns:

the same accumulator as was input

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

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object