An efficient algorithm for computing inverses in GF(2m) using dual bases

Abstract

This paper propose a new multiplicative inverse algorithm for Galois field GF(2n) whose elements are represented by 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. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. It is shown that the suggested algorithm is suitable for implementation and reduces the computation time to 5-10 % of the normal basis algorithm. © Springer-Verlag Berlin Heidelberg 2003.