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| HAL : hal-00675045, version 4 |
| arXiv : 1204.0222 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (29-02-2012) | v2 (29-03-2012) | v3 (20-04-2012) | v4 (02-05-2013) |
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| Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring |
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| Sorina Ionica 1 |
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| (29/02/2012) |
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| 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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| 1 : | CARAMEL (INRIA Nancy - Grand Est / LORIA) |
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INRIA – CNRS : UMR7503 – Université de Lorraine |
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| Caramel |
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| Domaine | : | Mathématiques/Mathématiques générales |
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| abelian variety – Tate pairing – Galois cohomology |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00675045, version 4 | |
| http://hal.archives-ouvertes.fr/hal-00675045 | |
| oai:hal.archives-ouvertes.fr:hal-00675045 | |
| Contributeur : Sorina Ionica | |
| Soumis le : Jeudi 2 Mai 2013, 16:26:00 | |
| Dernière modification le : Jeudi 2 Mai 2013, 22:14:27 | |
