A new low complexity parallel multiplier for a class of finite fields

Abstract

In this paper a new low complexity parallel multiplier for characteristic two finite fields GF(2m) is proposed. In particular our multiplier works with field elements represented through both Canonical Basis and Type I Optimal Normal Basis (ONB), provided that the irreducible polynomial generating the field is an All One Polynomial (AOP). The main advantage of the scheme is the resulting space complexity, significantly lower than the one provided by the other fast parallel multipliers currently available in the open literature and belonging to the same class.