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Communication Dans Un Congrès Année : 2011

Counting Points on Genus 2 Curves with Real Multiplication

David Kohel
Benjamin Smith

Résumé

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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Dates et versions

inria-00598029 , version 1 (03-06-2011)

Identifiants

Citer

Pierrick Gaudry, David Kohel, Benjamin Smith. Counting Points on Genus 2 Curves with Real Multiplication. ASIACRYPT 2011, International Association for Cryptologic Research, Dec 2011, Seoul, South Korea. pp.504-519, ⟨10.1007/978-3-642-25385-0_27⟩. ⟨inria-00598029⟩
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