2011 | OriginalPaper | Buchkapitel
Counting Points on Genus 2 Curves with Real Multiplication
verfasst von : Pierrick Gaudry, David Kohel, Benjamin Smith
Erschienen in: Advances in Cryptology – ASIACRYPT 2011
Verlag: Springer Berlin Heidelberg
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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
$\mathbb{F}_{q}$
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.