Counting Points on Genus 2 Curves with Real Multiplication
Identifieur interne : 002726 ( Main/Curation ); précédent : 002725; suivant : 002727Counting Points on Genus 2 Curves with Real Multiplication
Auteurs : Pierrick Gaudry [France] ; David Kohel [France] ; Benjamin Smith [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: 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 $\mathbb{F}_{q}$ 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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DOI: 10.1007/978-3-642-25385-0_27
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