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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01279431
Contributor : Nicolas Méloni <>
Submitted on : Friday, February 26, 2016 - 11:23:16 AM
Last modification on : Tuesday, June 19, 2018 - 3:50:01 PM
Long-term archiving on: : Friday, May 27, 2016 - 10:46:09 AM

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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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