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

• Main Authors: Yunos, Faridah, Mohd Atan, Kamel Ariffin
• Format: Article
• Language: English
• Published: Universiti Putra Malaysia Press 2013
• Online Access: http://psasir.upm.edu.my/id/eprint/30019/1/30019.pdf; http://psasir.upm.edu.my/id/eprint/30019/; http://einspem.upm.edu.my/journal/volume7.1.php
• Institution: Universiti Putra Malaysia

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.