Pairing-based methods for Jacobians of genus 2 curves with maximal endomorphism ring
Résumé
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.