Counting Points on Genus 2 Curves with Real Multiplication
Number Theory
2011-06-06 v1
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.
Keywords
Cite
@article{arxiv.1106.0661,
title = {Counting Points on Genus 2 Curves with Real Multiplication},
author = {Pierrick Gaudry and David Kohel and Benjamin Smith},
journal= {arXiv preprint arXiv:1106.0661},
year = {2011}
}