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Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication
Computer engineering, Pusan National University, Pusan 609-735, Korea
Laboratory of Algorithmics, Cryptology and Security, University of Luxembourg, 6, Rue Richard Coudenhove-Kalergi, Luxembourg L–1359, Luxembourg
* Author to whom correspondence should be addressed.
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. 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.
Keywords: public key cryptography; elliptic curve cryptography; scalar multiplication; fixed-base comb method; window-NAF method; efficient implementation; embedded microprocessor
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MDPI and ACS Style
Seo, H.; Kim, H.; Park, T.; Lee, Y.; Liu, Z.; Kim, H. Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication. Sensors 2013, 13, 9483-9512.
Seo H, Kim H, Park T, Lee Y, Liu Z, Kim H. Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication. Sensors. 2013; 13(7):9483-9512.
Seo, Hwajeong; Kim, Hyunjin; Park, Taehwan; Lee, Yeoncheol; Liu, Zhe; Kim, Howon. 2013. "Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication." Sensors 13, no. 7: 9483-9512.