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2004
Springer

Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations

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Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations
We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3 over prime fields. To achieve a fair comparison between the different types of groups, we developed an ad-hoc arithmetic library, designed to remove most of the overheads that penalize implementations of curve-based cryptography over prime fields. These overheads get worse for smaller fields, and thus for larger genera for a fixed group size. We also use techniques for delaying modular reductions to reduce the amount of modular reductions 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 14% and 15% respectively.
Roberto Maria Avanzi
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where CHES
Authors Roberto Maria Avanzi
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