Unified Parallel Systolic Multiplier Over GF(2^m)

In general, there are three popular basisrepresentations, standard (canonical, polynomial) basis, normal basis,and dual basis, for representing elements in \it GF(2^m). Variousbasis representations have their distinct advantages and have theirdifferent associated multiplication architectures. In this paper, wewill present a unified systolic multiplication architecture, byemploying Hankel matrix-vector multiplication, for various basisrepresentations. For various element representation in \it GF(2^m),we will show that various basis multiplications can be performed byHankel matrix-vector multiplications. A comparison with existing andsimilar structures has shown that the proposed architectures performwell both in space and time complexities.