## CryptoDB

### Paper: Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations

Authors: Roberto Maria Avanzi URL: http://eprint.iacr.org/2003/253 Search ePrint Search Google 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.
##### BibTeX
@misc{eprint-2003-11966,
title={Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations},
booktitle={IACR Eprint archive},
keywords={implementation / hyperelliptic curve cryptosystems, fast modular arithmetic},
url={http://eprint.iacr.org/2003/253},
note={ mocenigo@exp-math.uni-essen.de 12403 received 8 Dec 2003, last revised 17 Dec 2003},
author={Roberto Maria Avanzi},
year=2003
}