Unified Parallel Systolic Multiplier Over ${\it GF}(2^{m})$

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.