org.cryptimeleon.math.structures.groups.elliptic

Interface BilinearMapImpl

All Superinterfaces:

java.util.function.BiFunction<GroupElementImpl,GroupElementImpl,GroupElementImpl>

All Known Implementing Classes:

AbstractPairing, DebugBilinearMapImpl

public interface BilinearMapImpl
extends java.util.function.BiFunction<GroupElementImpl,GroupElementImpl,GroupElementImpl>

Interface for implementing of a bilinear map e : G1 x G2 -> GT.

Bilinearity means that the map e is linear in both the first and second component. G1, G2 and GT are groups.

Usually wrapped by a BilinearMap for actual use.

Method Summary

Modifier and Type	Method and Description
default GroupElementImpl	apply(GroupElementImpl g1, GroupElementImpl g2) Corresponds to this.apply(g1, g2, 1).
GroupElementImpl	apply(GroupElementImpl g1, GroupElementImpl g2, java.math.BigInteger exponent) Computes \(e(g1,g2)^\text{exponent}\).
boolean	isSymmetric() Returns true if \(e(g,h) = e(h,g)\) for all g in G1, h in G2.

Methods inherited from interface java.util.function.BiFunction

andThen

Method Detail

apply

GroupElementImpl apply(GroupElementImpl g1,
                       GroupElementImpl g2,
                       java.math.BigInteger exponent)

Computes \(e(g1,g2)^\text{exponent}\).

Depending on the bilinear map and the involved groups, this may be more efficiently implemented than computing it directly via apply(g1,g2).pow(exponent). For example, implementations should do exponentiation in the group with the cheapest group operation.

Parameters:

g1 - left hand side argument for the pairing function

g2 - right hand side argument for the pairing function

exponent - the exponent to apply to the result of the pairing

apply

default GroupElementImpl apply(GroupElementImpl g1,
                               GroupElementImpl g2)

Corresponds to this.apply(g1, g2, 1).

Specified by:

apply in interface java.util.function.BiFunction<GroupElementImpl,GroupElementImpl,GroupElementImpl>

Parameters:

g1 - left hand side argument for the pairing function

g2 - right hand side argument for the pairing function

isSymmetric

boolean isSymmetric()

Returns true if \(e(g,h) = e(h,g)\) for all g in G1, h in G2.