On finite field arithmetic in characteristic 2

Abstract

We are interested in extending normal bases of F 2 n /F 2 to bases of F 2 nd /F 2 which allow fast arithmetic in F 2 nd. This question has been recently studied by Thomson and Weir in case d is equal to 2. We construct efficient extended bases in case d is equal to 3 and 4. We also give conditions under which Thomson-Weir construction can be combined with ours.