Bit-Parallel Cubing Computation over GF(3^m) for Irreducible Trinomials

Abstract

We propose a parallel pth powering method over an arbitrary finite field GF(p^m). Using the proposed method, we present the explicit formulae for the computation of cubing over a ternary field GF(3^m) which is defined by irreducible trinomials. We show that the field cubing computation for irreducible trinomials, which plays an important role in calculating pairing, can be implemented very efficiently.