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Paper 2003/253

Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations

Roberto Maria Avanzi

Abstract

This paper presents an implementation of genus 2 and 3 hyperelliptic curves over prime fields, with a comparison with elliptic curves. To allow a fair comparison, we developed an ad-hoc arithmetic library, designed to remove most of the overheads that penalise implementations of curve-based cryptography over prime fields. These overheads get worse for smaller fields, and thus for large genera. We also use techniques such as lazy and incomplete modular reduction, originally developed for performing arithmetic in field extensions, to reduce the number of modular reductions occurring in the formulae for the group operations. The result is that the performance of hyperelliptic curves of genus 2 over prime fields is much closer to the performance of elliptic curves than previously thought. For groups of 192 and 256 bits the difference is about 18% and 15% respectively.

Note: Newer version. Lazy and incomplete reduction applied to EC, too. This improves the average EC performance, but not the best. TIny changes in software library altered some performance data.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Keywords
hyperelliptic curve cryptosystemsfast modular arithmetic
Contact author(s)
mocenigo @ exp-math uni-essen de
History
2003-12-17: last of 7 revisions
2003-12-08: received
See all versions
Short URL
https://ia.cr/2003/253
License
Creative Commons Attribution
CC BY
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