2004 | OriginalPaper | Buchkapitel
Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations
verfasst von : Roberto Maria Avanzi
Erschienen in: Cryptographic Hardware and Embedded Systems - CHES 2004
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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.