A divisibility criterion for exceptional APN functions

Florian Caullery (1)

1 IML - Institut Mathématiques de Luminy

We are interested in the functions from $\F_{2^m}$ to itself which are Almost Perfectly Nonlinear over infinitely many extensions of $\F_2$, namely, the exceptional APN functions. In particular, we study the case of the polynomial functions of degree $4e$ with $e$ odd and we give a necessary condition on an associated multivariate polynomial for the function to be exceptional APN. We use this condition to confirm the conjecture of Aubry, McGuire and Rodier in some new cases.

Mots clés: vector Boolean functions; almost perfect nonlinear functions; algebraic surface; CCZ-equivalence; Gold function; Kasami function; exceptional number

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Géométrie algébrique [math.AG]

Florian Caullery. A divisibility criterion for exceptional APN functions. 2014. ⟨hal-00985950⟩