Point Counting On Genus 2 Curves

For cryptographic purposes, counting points on the jacobian variety of a given hyperelliptic curve is of great importance. There has been several approaches to obtain the cardinality of such a group, specially for hyperelliptic curves of genus 2. The best known algorithm for counting points on genus 2 curves over prime fields of large characteristic is a variant of Schoof’s genus 1 algorithm. Following a recent work of Gaudry and Schost, we show how to speed up the current state of the art genus 2 point counting algorithm by proposing various computational improvements to its basic arithmetical ingredients.

Name thesis:degree_name

M Sc

Discipline thesis:degree_discipline

Computer Science

Year dc:date.issued

2011

Author dc:creator

• Doliskani, Javad Nazari

Advisor dc:contributor.advisor

• Schost, Eric

• Point counting
• Hyperelliptic curves
• Schoof’s algorithm
• Elliptic curves

Handle dc:identifier.uri

https://hdl.handle.net/20.500.14721/18464

OAI identifier oai:identifier

oai:uwo.scholaris.ca:20.500.14721/18464