Novel Precomputation Schemes for Elliptic Curve Cryptosystems

  • Patrick Longa
  • Catherine Gebotys
Conference paper

DOI: 10.1007/978-3-642-01957-9_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5536)
Cite this paper as:
Longa P., Gebotys C. (2009) Novel Precomputation Schemes for Elliptic Curve Cryptosystems. In: Abdalla M., Pointcheval D., Fouque PA., Vergnaud D. (eds) Applied Cryptography and Network Security. ACNS 2009. Lecture Notes in Computer Science, vol 5536. Springer, Berlin, Heidelberg

Abstract

We present an innovative technique to add elliptic curve points with the form P ±Q, and discuss its application to the generation of precomputed tables for the scalar multiplication. Our analysis shows that the proposed schemes offer, to the best of our knowledge, the lowest costs for precomputing points on both single and multiple scalar multiplication and for various elliptic curve forms, including the highly efficient Jacobi quartics and Edwards curves.

Keywords

Elliptic curve cryptosystem scalar multiplication multiple scalar multiplication precomputation scheme conjugate addition 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Patrick Longa
    • 1
  • Catherine Gebotys
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of WaterlooCanada

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