Abstract
Browning et al. (2010) exhibited almost perfect nonlinear (APN) permutations on F26. This was the first example of an APN permutation on an even degree extension of F2.
In their approach of finding an APN permutation, Browning et al. made use of a necessary and sufficient condition based on the Walsh transform. In this paper, we give an algorithm based on a related necessary condition which checks whether a vectorial Boolean function is CCZ-inequivalent to a permutation.
Using this algorithm, we are able to show that no function belonging to a known family of APN functions is equivalent to a permutation on F22m, where m <= 6 (except for the known case on F26). We also give an EA-invariant based on the condition.
Finally, we give a theoretical proof of the fact that no member of a specific family of APN functions is equivalent to a permutation on doubly-even degree extensions of F2. Access provided by Charles University