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An average density of τ-adic Naf (τ-NAF) representation: an alternative proof


Citation

Yunos, Faridah and Mohd Atan, Kamel Ariffin (2013) An average density of τ-adic Naf (τ-NAF) representation: an alternative proof. Malaysian Journal of Mathematical Sciences, 7 (1). pp. 111-123. ISSN 1823-8343

Abstract

In order to improve the efficiency of scalar multiplications on elliptic Koblitz curves, expansions of the scalar to a complex base associated with the Frobenius endomorphism are commonly used. One such expansion is the τ-adic Non Adjacent Form (τ-NAF), introduced by Solinas (1997). Some properties of this expansion, such as the average density, are well known. However in the literature there is no description on the same sequences occuring as length- NAF's and length-l τ-NAF's to proof that the average density is approximately 1/3. In this paper we provide an alternative proof of this fact.


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Additional Metadata

Item Type: Article
Divisions: Institute for Mathematical Research
Publisher: Universiti Putra Malaysia Press
Keywords: Anomalous binary curves (Koblitz curves); Scalar multiplication; τ-adic non-adjacent form; Norm
Depositing User: Umikalthom Abdullah
Date Deposited: 17 Jun 2014 07:55
Last Modified: 27 May 2015 01:45
URI: http://psasir.upm.edu.my/id/eprint/30019
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