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Paper: The arithmetic of characteristic 2 Kummer surfaces

Authors:
P. Gaudry
D. Lubicz
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URL: http://eprint.iacr.org/2008/133
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Abstract: The purpose of this paper is a description of a model of Kummer surfaces in characteristic 2, together with the associated formulas for the pseudo-group law. Since the classical model has bad reduction, a renormalization of the parameters is required, that can be justified using the theory of algebraic theta functions. The formulas that are obtained are very efficient and may be useful in cryptographic applications. We also show that applying the same strategy to elliptic curves gives Montgomery-like formulas in odd characteristic that are of some interest, and we recover already known formulas by Stam in characteristic 2.
BibTeX
@misc{eprint-2008-17810,
  title={The arithmetic of characteristic 2 Kummer surfaces},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography /},
  url={http://eprint.iacr.org/2008/133},
  note={submitted pierrick.gaudry@gmail.com 13963 received 25 Mar 2008},
  author={P. Gaudry and D. Lubicz},
  year=2008
}