# Efficient Double Bases for Scalar Multiplication

Abstract : In this paper we present efficient algorithms to take advantage of the double-base number system in the context of elliptic curve scalar multiplication. We propose a generalized version of Yao's exponentiation algorithm allowing the use of general double-base expansions instead of the popular double base chains. We introduce a class of constrained double base expansions and prove that the average density of non-zero terms in such expansions is $O\left(\frac{\log k}{\log \log k}\right)$ for any large integer $k$. We also propose an efficient algorithm for computing constrained expansions and finally provide a comprehensive comparison to double-base chain expansions, including a large variety of curve shapes and various key sizes.
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Journal articles

Cited literature [24 references]

https://hal.archives-ouvertes.fr/hal-01279418
Contributor : Nicolas Méloni <>
Submitted on : Friday, February 26, 2016 - 11:16:49 AM
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### Citation

Nicolas Méloni, M. A. Hasan. Efficient Double Bases for Scalar Multiplication. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2015, 64 (8), pp.2204-2212. ⟨10.1109/TC.2014.2360539⟩. ⟨hal-01279418⟩

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