Abstract
In general, there are three popular basis representations, standard (canonical, polynomial) basis, normal basis, and dual basis, for representing elements in \({\it GF}(2^{m})\). 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 \({\it GF}(2^{m})\), 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.
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Lee, CY., Chen, YH., Chiou, CW. et al. Unified Parallel Systolic Multiplier Over \({\it GF}(2^{m})\) . J Comput Sci Technol 22, 28–38 (2007). https://doi.org/10.1007/s11390-007-9003-0
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DOI: https://doi.org/10.1007/s11390-007-9003-0