New Point Addition Formulae for ECC Applications

  • Nicolas Meloni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)


In this paper we propose a new approach to point scalar multiplication on elliptic curves defined over fields of characteristic greater than 3. It is based on new point addition formulae that suit very well to exponentiation algorithms based on Euclidean addition chains. However finding small chains remains a very difficult problem, so we also develop a specific exponentiation algorithm, based on Zeckendorf representation (i.e. representing the scalar k using Fibonacci numbers instead of powers of 2), which takes advantage of our formulae.


elliptic curve scalar multiplication exponentiation Fibonacci addition chains 


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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Nicolas Meloni
    • 1
    • 2
  1. 1.Institut de Mathématiques et de Modélisation de Montpellier, Univ. Montpellier 2France
  2. 2.Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier, CNRS, Univ. Montpellier 2France

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