Artin–Schreier extensions of normal bases

Abstract

This manuscript deals with extending a normal basis to a new basis which permits both computationally inexpensive exponentiation and multiplication. These new bases are motivated by Artin-Schreier theory, and are particularly useful when creating bases in Artin-Schreier extensions of finite fields.

On finite field arithmetic in characteristic 2

“…This means that we first look for suitable subfields K of F q m containing F q such that there exists an efficient normal basis N of K/F q , and then we extend N to a basis of F q m /F q . In [11] the authors constructed extended bases in characteristic 2 by using Artin-Schreier theory. So they focused on the case when the degree is equal to 2.…”