On a secondary construction of quadratic APN functions

Almost perfect nonlinear functions possess the optimal resistance to the differential cryptanalysis and are widely studied. Most known constructions of APN functions are obtained as functions over finite fields $\mathbb{F}_{2^n}$ and very little is known about combinatorial constructions in $\mathbb{F}_2^n$. We consider how to obtain a quadratic APN function in $n+1$ variables from a given quadratic APN function in $n$ variables using special restrictions on new terms.