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Communication Dans Un Congrès Année : 2009

Elliptic Curve Point Scalar Multiplication Combining Yao's Algorithm and Double Bases

Résumé

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 $(b_i)$ and $(t_i)$ 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.
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Dates et versions

hal-01279431 , version 1 (26-02-2016)

Identifiants

Citer

Nicolas Méloni, M. A. Hasan. Elliptic Curve Point Scalar Multiplication Combining Yao's Algorithm and Double Bases. Cryptographic Hardware and Embedded Systems - CHES 2009- 11th international workshop, Sep 2009, Lausanne, Switzerland. pp.304--316, ⟨10.1007/978-3-642-04138-9_22⟩. ⟨hal-01279431⟩

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