Optimization Algorithm for Scalar Multiplication in the Elliptic Curve Cryptography over Prime Field

Authors:
Yuanling Hao;Shiwei Ma;Guanghua Chen;Xiaoli Zhang;Hui Chen;Weimin Zeng
Affiliations:
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, P.R. China 200072;School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, P.R. China 200072;School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, P.R. China 200072;School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, P.R. China 200072;School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, P.R. China 200072;School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, P.R. China 200072
Venue:
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
Year:
2008

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Abstract

Elliptic curve cryptography (ECC) is a major public-key cryptosystem standard in data security systems due to its high strength of security. But its application was limited because of the constraint of its speed. Therefore, it is much necessary to develop efficient method for ECC implementation. In this paper, the efficient algorithm for scalar multiplication in ECC was discussed and the corresponding comparative results were given. An optimization technique based on sliding-window non-adjacent form (NAF-Window) algorithm for the high-speed operation of point doubling and point addition over prime fields in ECC system were proposed. The results of numerical tests and performance comparisons manifested that the proposed algorithm can remarkably improve the computational efficiency of scalar multiplication. Hence, it has practical significance for the implementation of ECC and is expected to be applied to data security.