Normal basis of finite fieldGF(2^m)(Corresp.)

Massey and Omura recently developed a new multiplication algorithm for Galois fields based on the normal basis representation. This algorithm shows a much simpler way to perform multiplication in finite field than the conventional method. The necessary and sufficient conditions are presented for an element to generate a normal basis in the field GF(2^{m}), wherem = 2^{k}p^{n}andp^{n}has two as a primitive root. This result provides a way to find a normal basis in the field.