Cryptology ePrint Archive: Report 2007/192
Optimal Irreducible Polynomials for GF(2^m) Arithmetic
Abstract: 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.
Category / Keywords: implementation / Irreducible polynomials, implementation
Date: received 23 May 2007, last revised 30 May 2007
Contact author: mike at computing dcu ie
Available format(s): PDF | BibTeX Citation
Note: More typos fixed, and an appendix added on the calculation of square roots.
Version: 20070530:160024 (All versions of this report)
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