Sensors 2013, 13, 9483-9512; doi:10.3390/s130709483 OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication Hwajeong Seo 1, Hyunjin Kim 1, Taehwan Park 1, Yeoncheol Lee 1, Zhe Liu 2 and Howon Kim 1;* 1 Computer engineering, Pusan National University, Pusan 609-735, Korea; E-Mails:
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[email protected] (H.K.);
[email protected] (T.P.);
[email protected] (Y.L.) 2 Laboratory of Algorithmics, Cryptology and Security, University of Luxembourg, 6, Rue Richard Coudenhove-Kalergi, Luxembourg L–1359, Luxembourg; E-Mail:
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[email protected]; Tel.: +82-51-510-1010; Fax: +82-51-517-2431. Received: 23 May 2013; in revised form: 12 July 2013 / Accepted: 16 July 2013 / Published: 23 July 2013 Abstract: Elliptic curve cryptography (ECC) is one of the most promising public-key techniques in terms of short key size and various crypto protocols. For this reason, many studies on the implementation of ECC on resource-constrained devices within a practical execution time have been conducted. To this end, we must focus on scalar multiplication, which is the most expensive operation in ECC. A number of studies have proposed pre-computation and advanced scalar multiplication using a non-adjacent form (NAF) representation, and more sophisticated approaches have employed a width-w NAF representation and a modified pre-computation table. In this paper, we propose a new pre-computation method in which zero occurrences are much more frequent than in previous methods.