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| HAL : inria-00598029, version 1 |
| arXiv : 1106.0661 |
| DOI : 10.1007/978-3-642-25385-0_27 |
| Voir la fiche détaillée |  BibTeX,EndNote,... |
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| ASIACRYPT 2011, Seoul : Corée, République De (2011) |
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| Counting Points on Genus 2 Curves with Real Multiplication |
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| Pierrick Gaudry 1David Kohel 2 |
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| (14/11/2011) |
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| We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite field \(\F_{q}\) of large characteristic from \(\widetilde{O}(\log^8 q)\) to \(\widetilde{O}(\log^5 q)\). Using our algorithm we compute a 256-bit prime-order Jacobian, suitable for cryptographic applications, and also the order of a 1024-bit Jacobian. |
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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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| 2 : | Institut de mathématiques de Luminy (IML) |
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CNRS : UMR6206 – Université de la Méditerranée - Aix-Marseille II |
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| 3 : | TANC (INRIA Saclay - Ile de France) |
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INRIA – Polytechnique - X – CNRS : UMR7161 |
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| Domaine | : | Mathématiques/Théorie des nombres |
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| inria-00598029, version 1 | |
| http://hal.inria.fr/inria-00598029 | |
| oai:hal.inria.fr:inria-00598029 | |
| Contributeur : Benjamin Smith | |
| Soumis le : Vendredi 3 Juin 2011, 13:35:25 | |
| Dernière modification le : Vendredi 9 Décembre 2011, 01:28:53 | |
