Computation of Multiplicative Inverses in GF(2 n ) Using Palindromic Representation

Abstract

This paper proposes an efficient inversion algorithm for Galois field GF(2 n ) whose elements are represented by palindromic polynomials. It is well known that the efficiency of arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. An inversion algorithm based on the palindromic polynomial, which is closely related with the optimal normal basis type II, is studied. A modified Gaussian elimination method is employed to calculate the inverse. 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 prime number in which can not use Itoh and Tsujii method.