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
-
CC BY
BibTeX
@misc{cryptoeprint:2003/253,
author = {Roberto Maria Avanzi},
title = {Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations},
howpublished = {Cryptology {ePrint} Archive, Paper 2003/253},
year = {2003},
url = {https://eprint.iacr.org/2003/253}
}
