Modular Polynomials for Genus 2

Modular Polynomials for Genus 2

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...

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Veröffentlicht in:LMS journal of computation and mathematics 2009, Vol.12, p.326-339
Hauptverfasser: Bröker, Reinier, Lauter, Kristin
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1461-1570
1461-1570
DOI:10.1112/S1461157000001546