**Solutions of $x^{q^k}+\cdots+x^{q}+x=a$ in $GF(2^n)$**

*Kwang Ho Kim and Jong Hyok Choe and Dok Nam Lee and Dae Song Go and Sihem Mesnager*

**Abstract: **Though it is well known that the roots of any affine polynomial over
finite field can be computed by a system of linear equations by
using a normal base of the field, such solving approach appears to
be difficult to apply when the field is fairly large. Thus, it may
be of great interest to find explicit representation of the
solutions independently of the field base. This was previously done
only for quadratic equations over binary finite field. This paper
gives explicit representation of solutions for much wider class of
affine polynomials over binary prime field.

**Category / Keywords: **foundations / Linear equation, Binary finite field, Zeros of polynomials, Irreducible polynomials.

**Date: **received 25 May 2019

**Contact author: **smesnager at univ-paris8 fr

**Available format(s): **PDF | BibTeX Citation

**Version: **20190525:180939 (All versions of this report)

**Short URL: **ia.cr/2019/560

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