Abstract

In this paper we give some computational results on the multiplicative orders of optimal normal basis generators in F2 n over F2 for n # 1200 whenever the complete factorization of 2 - 1 is known. Our results show that a subclass of optimal normal basis generators always have very high multiplicative orders and are very often primitive. For a given optimal normal basis generator # in F2 n and an arbitrary integer e, we show that # can be computed in O(n v(e)) bit operations, where v(e) is the number of 1's in the binary representation of e.

Citations