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The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
- Source :
-
Finite Fields & Their Applications . Apr2009, Vol. 15 Issue 2, p246-260. 15p. - Publication Year :
- 2009
-
Abstract
- 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 faster than the classical ones, and we recover already known formulas by Stam in characteristic 2. [Copyright &y& Elsevier]
- Subjects :
- *DATA encryption
*ALGEBRAIC curves
*ALGEBRAIC varieties
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 15
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 36607508
- Full Text :
- https://doi.org/10.1016/j.ffa.2008.12.006