Welcome to the resource topic for 2003/253
Title:
Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations
Authors: 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.
ePrint: https://eprint.iacr.org/2003/253
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