Reverse Engineering of Irreducible Polynomials in GF(2^m) Arithmetic
Abstract
Current techniques for formally verifying circuits implemented in Galois field (GF) arithmetic are limited to those with a known irreducible polynomial P(x). This paper presents a computer algebra based technique that extracts the irreducible polynomial P(x) used in the implementation of a multiplier in GF(2^m). The method is based on first extracting a unique polynomial in Galois field of each output bit independently. P(x) is then obtained by analyzing the algebraic expression in GF(2^m) of each output bit. We demonstrate that this method is able to reverse engineer the irreducible polynomial of an n-bit GF multiplier in n threads. Experiments were performed on Mastrovito and Montgomery multipliers with different P (x), including NIST-recommended polynomials and optimal polynomials for different microprocessor architectures.
Cite
@article{arxiv.1612.04588,
title = {Reverse Engineering of Irreducible Polynomials in GF(2^m) Arithmetic},
author = {Cunxi Yu and Daniel Holcomb and Maciej Ciesielski},
journal= {arXiv preprint arXiv:1612.04588},
year = {2016}
}
Comments
6 pages, 4 figures, DATE 2017, Lausanne, Switzerland, March 27-31, 2017