Characterization of apn functions by means of subfunctions | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).

A vectorial Boolean function F : {0,1} ^ {0,1} is called an APN function if the equation F(x)®F(i®a) = b has at most 2 solutions for any vectors a, b, where a = 0. The complete characterization of APN functions by means of subfunctions is found. It is proved that F is APN function if and only if each of its subfunctions in n - 1 variables is an APN function or has the order of differential uniformity 4 and the admissibility conditions are hold. Some numerical results of this characterization for small number n of variables are presented.