Paper 2003/253

Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations

Roberto Maria Avanzi


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.

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Published elsewhere. Unknown where it was published
hyperelliptic curve cryptosystemsfast modular arithmetic
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mocenigo @ exp-math uni-essen de
2003-12-17: last of 7 revisions
2003-12-08: received
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      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},
      note = {\url{}},
      url = {}
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