Unified parallel systolic multiplier over GF(2m)

Authors:
Chiou-Yng Lee;Yung-Hui Chen;Che-Wun Chiou;Jim-Min Lin
Affiliations:
Department of Computer Information and Network Engineering, Lunghwa University of Science and Technology, Taoyuan County, Taiwan, China;Department of Computer Information and Network Engineering, Lunghwa University of Science and Technology, Taoyuan County, Taiwan, China;Department of Computer Science and Information Engineering, Ching Yun University, Chung-Li, Taiwan, China;Department of Information Engineering and Computer Science, Feng Chia University, Taichung City, Taiwan, China
Venue:
Journal of Computer Science and Technology
Year:
2007

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Abstract

In general, there are three popular basis representations, standard (canonical, polynomial) basis, normal basis, and dual basis, for representing elements in GF(2m). Various basis representations have their distinct advantages and have their different associated multiplication architectures. In this paper, we will present a unified systolic multiplication architecture, by employing Hankel matrix-vector multiplication, for various basis representations. For various element representation in GF(2m), we will show that various basis multiplications can be performed by Hankel matrix-vector multiplications. A comparison with existing and similar structures has shown that the proposed architectures perform well both in space and time complexities.