Generators for the l-Torsion Subgroup of Jacobians of Genus Two Curves

Authors:
Christian Robenhagen Ravnshøj
Affiliations:
Department of Mathematical Sciences, University of Aarhus, Aarhus C DK-8000
Venue:
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Year:
2008

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Abstract

We give an explicit description of the matrix representation ofthe Frobenius endomorphism on the Jacobian of a genus two curve onthe subgroup of l-torsion points. By using thisdescription, we can describe the matrix representation of theWeil-pairing on the subgroup of l-torsion pointsexplicitly. Finally, the explicit description of the Weil-pairingprovides us with an efficient, probabilistic algorithm to findgenerators of the subgroup of l-torsion points on theJacobian of a genus two curve.