org.cryptimeleon.math.structures.groups

Interface GroupImpl

All Superinterfaces:

Representable, RepresentationRestorer, StandaloneRepresentable

All Known Subinterfaces:

EllipticCurve, WeierstrassCurve

All Known Implementing Classes:

BarretoNaehrigGroup1Impl, BarretoNaehrigGroup2Impl, BarretoNaehrigSourceGroupImpl, BarretoNaehrigTargetGroupImpl, CountingGroupImpl, PairingSourceGroupImpl, PairingTargetGroupImpl, RingAdditiveGroupImpl, RingGroupImpl, RingUnitGroupImpl, Secp256k1, Sn, SupersingularSourceGroupImpl, SupersingularTargetGroupImpl

public interface GroupImpl
extends StandaloneRepresentable, RepresentationRestorer

A Group. Operations are defined on its elements.

Usually wrapped by a Group to offer additional evaluation capabilities.

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.
default GroupElementImpl	exp(GroupElementImpl base, java.math.BigInteger exponent, SmallExponentPrecomputation precomputation) Can be overwritten to implement a custom exponentiation algorithm for the group.
GroupElementImpl	getGenerator() Returns any generator of this group if the group is cyclic and it's feasible to compute a generator.
GroupElementImpl	getNeutralElement() Returns the neutral element of this group.
GroupElementImpl	getUniformlyRandomElement() Generates a uniformly random element of this group.
default GroupElementImpl	getUniformlyRandomNonNeutral() Generates a uniformly random non-neutral 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.
boolean	hasPrimeSize() Returns true if the size of this structure is known and prime.
default boolean	implementsOwnExp() Indicates whether this group implements its own custom exponentiation algorithm by overwriting exp(org.cryptimeleon.math.structures.groups.GroupElementImpl, java.math.BigInteger, org.cryptimeleon.math.structures.groups.exp.SmallExponentPrecomputation).
default boolean	implementsOwnMultiExp() Indicates whether this group implements its own multi-exponentiation algorithm by overwriting multiexp(Multiexponentiation).
boolean	isCommutative() Returns true if this group is known to be commutative.
default GroupElementImpl	multiexp(Multiexponentiation mexp) Can be overwritten to implement a custom multi-exponentiation algorithm for the group.
GroupElementImpl	restoreElement(Representation repr) Restores a group element from its representation.
default GroupElementImpl	restoreFromRepresentation(java.lang.reflect.Type type, Representation repr) Takes a representation and creates an object of the given type from it if the type is supported by the restorer.
java.math.BigInteger	size() Retrieves number of elements in the group if possible.

Methods inherited from interface org.cryptimeleon.math.serialization.Representable

getRepresentation

Method Detail

getNeutralElement

GroupElementImpl getNeutralElement()

Returns the neutral element of this group.

getUniformlyRandomElement

GroupElementImpl getUniformlyRandomElement()
                                    throws java.lang.UnsupportedOperationException

Generates a uniformly random element of this group.

Throws:

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

getUniformlyRandomNonNeutral

default GroupElementImpl getUniformlyRandomNonNeutral()
                                               throws java.lang.UnsupportedOperationException

Generates a uniformly random non-neutral element of this group.

Throws:

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

restoreElement

GroupElementImpl restoreElement(Representation repr)

Restores a group element from its representation.

getGenerator

GroupElementImpl getGenerator()
                       throws java.lang.UnsupportedOperationException

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)!

Throws:

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

isCommutative

boolean isCommutative()

Returns true if this group is known to be commutative.

size

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

Retrieves number of elements in the group if possible.

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

boolean hasPrimeSize()

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

implementsOwnExp

default boolean implementsOwnExp()

Indicates whether this group implements its own custom exponentiation algorithm by overwriting exp(org.cryptimeleon.math.structures.groups.GroupElementImpl, java.math.BigInteger, org.cryptimeleon.math.structures.groups.exp.SmallExponentPrecomputation).

Returns:

true if the group overwrites exp(org.cryptimeleon.math.structures.groups.GroupElementImpl, java.math.BigInteger, org.cryptimeleon.math.structures.groups.exp.SmallExponentPrecomputation), else false

exp

default GroupElementImpl exp(GroupElementImpl base,
                             java.math.BigInteger exponent,
                             SmallExponentPrecomputation precomputation)

Can be overwritten to implement a custom exponentiation algorithm for the group.

Parameters:

base - the base of the exponentiation

exponent - the exponent of the exponentiation

precomputation - a set of precomputations that can be used to speed up the exponentiation

Returns:

the result of base base to the power of exponent

implementsOwnMultiExp

default boolean implementsOwnMultiExp()

Indicates whether this group implements its own multi-exponentiation algorithm by overwriting multiexp(Multiexponentiation).

Returns:

true if the group implements its own multi-exponentiation algorithm, else false

multiexp

default GroupElementImpl multiexp(Multiexponentiation mexp)

Can be overwritten to implement a custom multi-exponentiation algorithm for the group.

Parameters:

mexp - contains the multi-exponentiation terms

Returns:

result of computing the multi-exponentiation

estimateCostInvPerOp

double estimateCostInvPerOp()

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

restoreFromRepresentation

default GroupElementImpl restoreFromRepresentation(java.lang.reflect.Type type,
                                                   Representation repr)

Description copied from interface: RepresentationRestorer

Takes a representation and creates an object of the given type from it if the type is supported by the restorer.

Specified by:

restoreFromRepresentation in interface RepresentationRestorer

Parameters:

type - tells the restorer which type the restored object should have

repr - the representation to restore the object from

Returns:

the restored object

getUniqueByteLength

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.

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.

Returns:

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