Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication

Sensors

Hwajeong Seo¹  Hyunjin Kim¹  Taehwan Park¹  Yeoncheol Lee¹  Zhe Liu² 

[1] Computer engineering, Pusan National University, Pusan 609-735, Korea; E-Mails:;Laboratory of Algorithmics, Cryptology and Security, University of Luxembourg, 6, Rue Richard Coudenhove-Kalergi, Luxembourg L–1359, Luxembourg; E-Mail:

关键词: public key cryptography;    elliptic curve cryptography;    scalar multiplication;    fixed-base comb method;    window-NAF method;    efficient implementation;    embedded microprocessor;   

DOI  :  10.3390/s130709483

来源: mdpi

【 摘 要 】

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. This method can be applied to ordinary group scalar multiplication, but it requires large pre-computation table, so we combined the previous method with ours for practical purposes. This novel structure establishes a new feature that adjusts speed performance and table size finely, so we can customize the pre-computation table for our own purposes. Finally, we can establish a customized look-up table for embedded microprocessors.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.