Package dk.jonaslindstrom.ruffini.elliptic.algorithms

Class OptimalAtePairing<E1,E2,ET>

java.lang.Object

dk.jonaslindstrom.ruffini.elliptic.algorithms.OptimalAtePairing<E1,E2,ET>

public class OptimalAtePairing<E1,E2,ET>
extends Object

Compute the optimal Ate pairing. Methodology is taken from Appendix A in draft-irtf-cfrg-pairing-friendly-curves-11.

Constructor Summary

Constructors

Constructor	Description
OptimalAtePairing(java.util.function.Function<E1,E2> g1embedding, ShortWeierstrassCurveAffine<E2,?> curve2, java.util.function.Function<E2,ET> g2embedding, Field<ET> ft, java.util.function.Function<AffinePoint<E1>,SamePair<ET>> twist, BigInteger p, BigInteger r, int k)

Method Summary

Modifier and Type	Method	Description
ET	lineFunction(AffinePoint<E2> Q1, AffinePoint<E2> Q2, AffinePoint<E1> P)
ET	pairing(AffinePoint<E1> P, AffinePoint<E2> Q, List<Integer> ci)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

OptimalAtePairing

public OptimalAtePairing(java.util.function.Function<E1,E2> g1embedding,
 ShortWeierstrassCurveAffine<E2,?> curve2,
 java.util.function.Function<E2,ET> g2embedding,
 Field<ET> ft,
 java.util.function.Function<AffinePoint<E1>,SamePair<ET>> twist,
 BigInteger p,
 BigInteger r,
 int k)

Parameters:

g1embedding - Embedding from F1 to F2.

curve2 - Elliptic curve over F2.

g2embedding - Embedding from F2 to FT.

ft - The field extension FT = F1^k. Note that the target group GT is the multiplicative group of FT.

twist - A function computing the isomorphism from E1 to the twist E' over FT.

p - The characteristic of the fields.

r - The order of the groups G1, G2 and GT.

k - The embedding degree of the elliptic curve E1 over F1, eg. the smallest k such that r | p^k-1.

Method Details

lineFunction

public ET lineFunction(AffinePoint<E2> Q1,
 AffinePoint<E2> Q2,
 AffinePoint<E1> P)

pairing

public ET pairing(AffinePoint<E1> P,
 AffinePoint<E2> Q,
 List<Integer> ci)