Counting Points on Genus 2 Curves with Real Multiplication
نویسندگان
چکیده
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 Fq of large characteristic from Õ(log q) to Õ(log 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.
منابع مشابه
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
Schoof’s classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit isogenies. Moving to Jacobians of genus-2 curves, the current state of the art for point counting is a generalization of Schoof’s algorithm. While we a...
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ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2011 شماره
صفحات -
تاریخ انتشار 2011