3532 articles – 5253 references  [version française]

inria-00266565, version 2

The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines

Pierrick Gaudry () 1, David Lubicz 2, 3

Finite Fields and Their Applications 15, 2 (2009) 246-260

  • 1:  CACAO (INRIA Lorraine - LORIA)

  • CNRS : UMR7503 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) France
  • 2:  Centre Electronique de l'Armement (CELAR / DGA)

  • Ministère de la Défense BP 7419 Route Laillé 35174 Bruz France
  • 3:  Institut de Recherche Mathématique de Rennes (IRMAR)
  • http://irmar.univ-rennes1.fr/
    CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne France
  • Available versions :  v1 (2008-03-25) v2 (2009-05-20)

    • Bibliographic reference

    • Type of document: Articles in peer-reviewed journal
    • Domain: Computer Science/Cryptography and Security
    • Title: The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
    • 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.
    • Full text language: English
    • Journal title:
      Finite Fields and Their Applications
      Publisher Elsevier
      ISSN 1071-5797 (eISSN : 1090-2465)
    • Publication date: 2009
    • Audience: international
    • Commercial editor: Elsevier
    • Volume: 15
    • Number: 2
    • Pagination: 246-260
    • DOI: 10.1016/j.ffa.2008.12.006

    Attached file list to this document: 

    PDF
    c2.pdf(259 KB)
     
    • inria-00266565, version 2
    • http://hal.inria.fr/inria-00266565
    • oai:hal.inria.fr:inria-00266565
    • From: Pierrick Gaudry <>
    • Submitted on: Wednesday, 20 May 2009 08:40:20
    • Updated on: Tuesday, 23 March 2010 14:18:44