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.
Domaines
Cryptographie et sécurité [cs.CR]Origine | Fichiers produits par l'(les) auteur(s) |
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