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Pairing-based methods for genus 2 jacobians with maximal endomorphism ring
Authors: Sorina IonicaAbstract:
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial self-pairings of the \ell-Tate pairing in terms of the action of the Frobenius on the \ell-torsion of the Jacobian of a genus 2 curve. We apply similar techniques to study the non-degeneracy of the \ell-Tate pairing restrained to subgroups of the \ell-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 (\ell,\ell)-isogenies starting from a jacobian with maximal endomorphism ring.
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