Optimal Irreducible Polynomials for GF(2 m ) Arithmetic.
Michael Scott · IACR Cryptology ePrint Archive · 2007
The irreducible polynomials recommended for use by multiple standards documents are in fact far from optimal on many platforms. Specifically they are suboptimal in terms of performance, for the computation of field square roots and in the application of the “almost inverse” field inversion algorithm. In this paper we question the need for the standardisation of irreducible polynomials in the first place, and derive the “best” polynomials to use depending on the underlying processor architecture. Surprisingly it turns out that a trinomial polynomial is in many cases not necessarily the best choice. Finally we make some specific recommendations for some particular types of architecture.