Polynomial functions of degree 20 which are APN infinitely often

We give all the polynomials functions of degree 20 which are APN over an infinity of field extensions and show they are all CCZ-equivalent to the function $x^5$, which is a new step in proving the conjecture of Aubry, McGuire and Rodier.

💡 Research Summary

The paper addresses the long‑standing problem of classifying polynomial functions of even degree that are Almost Perfect Nonlinear (APN) on infinitely many extensions of the binary field 𝔽₂ⁿ. While APN functions are central to the design of cryptographic S‑boxes because they provide optimal resistance against differential attacks, only a handful of degree families have been completely characterized. The authors focus on the next unresolved case: degree 20 polynomials.

The main result is a full classification: any polynomial f ∈ 𝔽₂ⁿ