Elliptic Curve Scalar Multiplication Combining Yao’s Algorithm and Double Bases

  • Nicolas Méloni
  • M. Anwar Hasan
Conference paper

DOI: 10.1007/978-3-642-04138-9_22

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5747)
Cite this paper as:
Méloni N., Hasan M.A. (2009) Elliptic Curve Scalar Multiplication Combining Yao’s Algorithm and Double Bases. In: Clavier C., Gaj K. (eds) Cryptographic Hardware and Embedded Systems - CHES 2009. Lecture Notes in Computer Science, vol 5747. Springer, Berlin, Heidelberg


In this paper we propose to take one step back in the use of double base number systems for elliptic curve point scalar multiplication. Using a modified version of Yao’s algorithm, we go back from the popular double base chain representation to a more general double base system. Instead of representing an integer k as \(\sum^n_{i=1}2^{b_i}3^{t_i}\) where (bi) and (ti) are two decreasing sequences, we only set a maximum value for both of them. Then, we analyze the efficiency of our new method using different bases and optimal parameters. In particular, we propose for the first time a binary/Zeckendorf representation for integers, providing interesting results. Finally, we provide a comprehensive comparison to state-of-the-art methods, including a large variety of curve shapes and latest point addition formulae speed-ups.


Double-base number system Zeckendorf representation elliptic curve point scalar multiplication Yao’s algorithm 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nicolas Méloni
    • 1
  • M. Anwar Hasan
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of WaterlooCanada

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