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Paper: Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae

Authors:
Tanja Lange
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URL: http://eprint.iacr.org/2002/121
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Abstract: We extend the explicit formulae for arithmetic on genus two curves of Takahashi and Miyamoto,Doi,Matsuo,Chao,and Tsuji to fields of even characteristic and to arbitrary equation of the curve and slightly improve them. These formulae can be evaluated faster than the more general Cantor algorithm and allow to obtain faster arithmetic on a hyperelliptic genus 2 curve than on elliptic curves. We give timings for implementations using various libraries for the field arithmetic.
BibTeX
@misc{eprint-2002-11644,
  title={Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / elliptic curve cryptosystem, implementation, number theory, hyperellitptic curve cryptosystem, arithmetic, explicit formulae},
  url={http://eprint.iacr.org/2002/121},
  note={ lange@itsc.ruhr-uni-bochum.de 12401 received 16 Aug 2002, last revised 15 Dec 2003},
  author={Tanja Lange},
  year=2002
}