About one problem from NSUCRYPTO'2017 and the image of cubic function over binary fields

TL;DR

This paper provides a complete solution to a previously unsolved problem regarding the image of a cubic function over binary finite fields, which was posed in the NSUCRYPTO 2017 olympiad.

Contribution

The paper offers the first comprehensive solution to the problem of describing the image of the cubic function over binary fields, filling a gap in the existing literature.

Findings

Complete characterization of the image of the cubic function over binary fields

Resolution of the open problem from NSUCRYPTO 2017

Methodology applicable to similar polynomial image problems

Abstract

The description of the image of cubic function $f(x) = x^3+x$ over finite field $F_{2^n}$ was stated as a problem in the NSUCrypto olympiad in 2017. This problem was marked by organizers as <<unsolved>>. In this work we propose the full solution of this problem.