Fast Forth Power and Its Application in Inversion Computation for a Special Class of Trinomials

Abstract

This contribution is concerned with an improvement of Itoh and Tsujii’s algorithm for inversion in finite field GF(2^m) using polynomial basis. Unlike the standard version of this algorithm, the proposed algorithm uses forth power and multiplication as main operations. When the field is generated with a special class of irreducible trinomials, an analytical form for fast bit-parallel forth power operation is presented. The proposal can save 1T _X compared with the classic approach, where T _X is the delay of one 2-input XOR gate. Based on this result, the proposed algorithm for inversion achieves even faster performance, roughly improves the delay by $\frac{m}{2}T_X$, at the cost of slight increase in the space complexity compared with the standard version. To the best of our knowledge, this is the first work that proposes the use of forth power in computation of multiplicative inverse using polynomial basis and shows that it can be efficient.