A few more functions that are not APN infinitely often

Yves Aubry (1) , Gary Mcguire (2) , François Rodier (1)

1 IML - Institut de mathématiques de Luminy
2 Développement de l'enfant

We consider exceptional APN functions on ${\bf F}_{2^m}$, which by definition are functions that are not APN on infinitely many extensions of ${\bf F}_{2^m}$. Our main result is that polynomial functions of odd degree are not exceptional, provided the degree is not a Gold member ($2^k+1$) or a Kasami-Welch number ($4^k-2^k+1$). We also have partial results on functions of even degree, and functions that have degree $2^k+1$.

Mots clés: Boolean functions; APN functions; exceptional polynomials

Domaines: Géométrie algébrique [math.AG]

Yves Aubry, Gary Mcguire, François Rodier. A few more functions that are not APN infinitely often. 2009. ⟨hal-00415755v1⟩