Efficient bit serial multiplication using optimal normal bases of type II in GF(2m)

Abstract

Using the self duality of an optimal normal basis of type II in a finite field GF(2m), we present a design of a bit serial multiplier of Berlekamp type. It is shown that our multiplier does not need a basis conversion process and a squaring operation is a simple permutation in our basis. Therefore our multiplier provides a fast and an efficient hardware architecture for a bit serial multiplication of two elements in GF(2m), which is suitable for a cryptographic purpose.