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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 862508, 7 pages
Research Article

A Novel Elliptic Curve Scalar Multiplication Algorithm against Power Analysis

Shanghai Jiao Tong University, Shanghai 200240, China

Received 13 November 2012; Revised 10 March 2013; Accepted 12 March 2013

Academic Editor: Jun-Juh Yan

Copyright © 2013 Hongming Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nowadays, power analysis attacks are becoming more and more sophisticated. Through power analysis attacks, an attacker can obtain sensitive data stored in smart cards or other embedded devices more efficiently than with any other kind of physical attacks. Among power analysis, simple power analysis (SPA) is probably the most effective against elliptic curve cryptosystem, because an attacker can easily distinguish between point addition and point doubling in a single execution of scalar multiplication. To make elliptic curve scalar multiplication secure against SPA attacks, many methods have been proposed using special point representations. In this paper, a simple but efficient SPA-resistant multiscalar multiplication is proposed. The method is to convert the scalar into a nonadjacent form (NAF) representation at first and then constitute it in a new signed digit representation. This new representation is undertaken at a small precomputation cost, as each representation needs just one doubling and 1/2 additions for each bit. In addition, when combined with randomization techniques, the proposed method can also guard against differential power analysis (DPA) attack.