Random Euclidean Addition Chain Generation and Its Application to Point Multiplication

  • Fabien Herbaut
  • Pierre-Yvan Liardet
  • Nicolas Méloni
  • Yannick Téglia
  • Pascal Véron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6498)

Abstract

Efficiency and security are the two main objectives of every elliptic curve scalar multiplication implementations. Many schemes have been proposed in order to speed up or secure its computation, usually thanks to efficient scalar representation [30,10,24], faster point operation formulae [8,25,13] or new curve shapes [2]. As an alternative to those general methods, authors have suggested to use scalar belonging to some subset with good computational properties [15,14,36,41,42], leading to faster but usually cryptographically weaker systems. In this paper, we use a similar approach. We propose to modify the key generation process using a small Euclidean addition chain c instead of a scalar k. This allows us to use a previous scheme, secure against side channel attacks, but whose efficiency relies on the computation of small chains computing the scalar. We propose two different ways to generate short Euclidean addition chains and give a first theoretical analysis of the size and distribution of the obtained keys. We also propose a new scheme in the context of fixed base point scalar multiplication.

Keywords

point multiplication exponentiation addition chain SPA elliptic curves 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Fabien Herbaut
    • 1
    • 2
  • Pierre-Yvan Liardet
    • 3
  • Nicolas Méloni
    • 1
  • Yannick Téglia
    • 3
  • Pascal Véron
    • 1
  1. 1.IMATHUniversité du Sud Toulon-VarFrance
  2. 2.IUFM de NiceUniversité de NiceFrance
  3. 3.ST Microelectronics, RoussetFrance

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