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Paper 2003/097

Low Cost Security: Explicit Formulae for Genus 4 Hyperelliptic Curves

Jan Pelzl and Thomas Wollinger and Christof Paar

Abstract

It is widely believed that genus four hyperelliptic curve cryptosystems (HECC) are not attractive for practical applications because of their complexity compared to systems based on lower genera, especially elliptic curves. Our contribution shows that for low cost security applications genus-4 hyperelliptic curves (HEC) can outperform genus-2 HEC and that we can achieve a performance similar to genus-3 HEC. Furthermore our implementation results show that a genus-4 HECC is an alternative cryptosystem to systems based on elliptic curves. In the work at hand we present for the first time explicit formulae for genus-4 HEC, resulting in a 60% speed-up compared to the best published results. In addition we implemented genus-4 HECC on a Pentium4 and an ARM microprocessor. Our implementations on the ARM show that for genus four HECC are only a factor of 1.66 slower than genus-2 curves considering group order ~2^{190}. For the same group order ECC and genus-3 HECC are about a factor of 2 faster than genus-4 curves on the ARM. The two most surprising results are: 1) for low cost security application, namely considering an underlying group of order 2^{128}, HECC with genus 4 outperform genus-2 curves by a factor of 1.46 and has similar performance to genus-3 curves on the ARM and 2) when compared to genus-2 and genus-3, genus-4 HECC are better suited to embedded microprocessors than to general purpose processors.

Metadata
Available format(s)
PDF PS
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
hyperelliptic curvesgenus fourexplicit formulaeefficient implementationlow cost securityembedded applicationcomparison HECC vsECC
Contact author(s)
pelzl @ crypto rub de
History
2003-05-21: received
Short URL
https://ia.cr/2003/097
License
Creative Commons Attribution
CC BY
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