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Modular Polynomials for Genus 2

Published online by Cambridge University Press:  01 February 2010

Reinier Bröker and
Kristin Lauter
Reinier Bröker
Affiliation:
Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA, reinierb@microsoft.com
Kristin Lauter
Affiliation:
Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA, klauter@microsoft.com

Abstract

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Modular polynomials are an important tool in many algorithms involving elliptic curves. In this article we investigate their generalization to the genus 2 case following pioneering work by Gaudry and Dupont. We prove various properties of these genus 2 modular polynomials and give an improved way to explicitly compute them.

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 12 , 2009, pp. 326 - 339
Copyright
Copyright © London Mathematical Society 2009

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