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 Fqof large characteristic from Õ(log 8 q) to Õ (log5 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. © 2011 International Association for Cryptologic Research.
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CITATION STYLE
Gaudry, P., Kohel, D., & Smith, B. (2011). Counting points on genus 2 curves with real multiplication. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7073 LNCS, pp. 504–519). https://doi.org/10.1007/978-3-642-25385-0_27
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