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hal-00675045, version 3

## Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring

Sorina Ionica () 1

Résumé : 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.

• 1 :  CARAMEL (INRIA Nancy - Grand Est / LORIA)
• INRIA – CNRS : UMR7503 – Université de Lorraine

• hal-00675045, version 3
• oai:hal.archives-ouvertes.fr:hal-00675045
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• Soumis le : Vendredi 20 Avril 2012, 18:15:54
• Dernière modification le : Vendredi 20 Avril 2012, 21:55:23