The arithmetic of characteristic 2 Kummer surfaces

P.  Gaudry; D.  Lubicz

Paper 2008/133

The arithmetic of characteristic 2 Kummer surfaces

P. Gaudry and D. Lubicz

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. submitted
Contact author(s): pierrick gaudry @ gmail com
History: 2008-03-25: received
Short URL: https://ia.cr/2008/133
License: CC BY

BibTeX

@misc{cryptoeprint:2008/133,
      author = {P.  Gaudry and D.  Lubicz},
      title = {The arithmetic of characteristic 2 Kummer surfaces},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/133},
      year = {2008},
      url = {https://eprint.iacr.org/2008/133}
}