Artin-Schreier extensions of normal bases

In this paper we extend a normal basis of a finite field over its base field to a new basis which permits both computationally inexpensive exponentiation and multiplication. We focus primarily on extensions of the finite field F2. These bases are motivated by Artin-Schreier theory and we conclude that they are particularly useful in Artin-Schreier extensions; that is, extensions F2n of F2 with n a power of two.