Sensors 2013, 13(7), 9483-9512; doi:10.3390/s130709483

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

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Received: 23 May 2013; in revised form: 12 July 2013 / Accepted: 16 July 2013 / Published: 23 July 2013
(This article belongs to the Section Physical Sensors)
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.
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.

AMA 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(7):9483-9512.

Chicago/Turabian Style

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.

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