Bounds on the degree of APN polynomials The Case of $x^{-1}+g(x)$

Leander, Gregor; Rodier, François

Bounds on the degree of APN polynomials The Case of $x^{-1}+g(x)$

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Description

We prove that functions $f:\f{2^m} \to \f{2^m}$ of the form $f(x)=x^{-1}+g(x)$ where $g$ is any non-affine polynomial are APN on at most a finite number of fields $\f{2^m}$. Furthermore we prove that when the degree of $g$ is less then 7 such functions are APN only if $m \le 3$ where these functions are equivalent to $x^3$.