Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
arXiv:1204.0222 · doi:10.1016/j.jnt.2013.04.023
Abstract
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the -Tate pairing in terms of the action of the Frobenius on the -torsion of the Jacobian of a genus 2 curve. We apply similar techniques to study the non-degeneracy of the -Tate pairing restrained to subgroups of the -torsion which are maximal isotropic with respect to the Weil pairing. First, we deduce a criterion to verify whether the jacobian of a genus 2 curve has maximal endomorphism ring. Secondly, we derive a method to construct horizontal -isogenies starting from a jacobian with maximal endomorphism ring.