Counting Points on Genus 2 Curves with Real Multiplication

Details Counting Points on Genus 2 Curves with Real Multiplication Counting Points on Genus 2 Curves with Real Multiplication

2011-06-03

arxiv.org/abs/1106.0661v1

Mathematics

Number Theory

Scientific paper

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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