Efficient Inversion Algorithm for Optimal Normal Bases Type II

Abstract

In this paper, we propose an efficient inversion algorithm for optimal normal bases type II. The efficiency of the arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. An inversion algorithm based on reduced multiplication for optimal normal basis is studied. The combination of optimal normal basis and shifted form of the canonical basis is also employed. It is shown that the suggested inversion algorithm reduces the computation time to 45-60 % of the simple algorithm. The algorithm is very effective in composite numbers in which have optimal normal basis type II.