Cryptology ePrint Archive: Report 2019/560

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.