A divisibility criterion for exceptional APN functions
Florian Caullery · Contemporary mathematics - American Mathematical Society · 2015
We are interested in the functions from F 2 m \mathbb {F}_{2^m} to itself which are Almost Perfectly Nonlinear over infinitely many extensions of F 2 \mathbb {F}_2 , namely, the exceptional APN functions. In particular, we study the case of the polynomial functions of degree 4 e 4e with e 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.