On orders of optimal normal basis generators

In this paper we give some computational results on the multiplicative orders of optimal normal basis generators in F2n over F2 for n 1200 whenever the complete factorization of 2n - 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 F2n and an arbitrary integer e, we show that e can be computed in O(n

• Type: Conference
• Year: 1994
• Where: ANTS
• Authors: Shuhong Gao, Scott A. Vanstone
• Keywords: Algorithms, ANTS 1994, Multiplicative Orders, Normal Basis Generator, Optimal Normal Basis