The arithmetic of characteristic 2 Kummer surfaces
Pierrick Gaudry, David Lubicz · 2008
Abstract. The purpose of this paper is a description of a model of Kum-mer 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 ob-tained 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 inter-est, and we recover already known formulas by Stam in characteristic 2. 1