Counting Points on Genus 2 Curves with Real Multiplication
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 \(\F_{q}\) 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.
Domains
Number Theory [math.NT]
Origin : Files produced by the author(s)
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