Research note: A fast modular multiplication method based on the Lempel-Ziv binary tree

Authors:
C. -Y. Chen;T. -C. Liu
Affiliations:
Department of Information Engineering, I-Shou University, Kaohsiung County, Taiwan 84008;Nan-Tai Institute of Technology, Tainan, Taiwan
Venue:
Computer Communications
Year:
1999

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Abstract

In this article, a fast modular multiplication method is presented. The known fastest modular multiplication method by Su and Hwang (F.-F. Su, T. Huang, Comments on iterative modular multiplication without magnitude comparison, Proceedings of the Sixth National Conference on Information Security, Taichung, Taiwan, 1996, pp. 21-22) requires n+11 additions on the average for an n-bit modulus. In Su and Hwang's method, the computed values are not stored for use again. Our method uses the Lempel-Ziv binary tree to store the computed values. According to our analysis, our method is faster than Su and Hwang's for n512. Further, our method only requires 0.6667n additions on the average for sufficiently large n.