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

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

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arXiv · 1905.10579

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

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

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Abstract

Though it is well known that the roots of any affine polynomial over a 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 an explicit representation of the solutions independently of the field base. This was previously done only for quadratic equations over a binary finite field. This paper gives an explicit representation of solutions for a much wider class of affine polynomials over a binary prime field.

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Kwang Ho Kim, Jong Hyok Choe, Dok Nam Lee, Dae Song Go, Sihem Mesnager. 2019-05-25. Solutions of $x^{q^k}+\cdots+x^{q}+x=a$ in $GF{2^n}$. https://arxiv.org/abs/1905.10579

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