  Substitution Boxes (S-boxes) are nonlinear objects often used in the design
of cryptographic algorithms. The design of high quality S-boxes is an
interesting problem that attracts a lot of attention. Many attempts have been
made in recent years to use heuristics to design S-boxes, but the results were
often far from the previously known best obtained ones. Unfortunately, most of
the effort went into exploring different algorithms and fitness functions while
little attention has been given to the understanding why this problem is so
difficult for heuristics. In this paper, we conduct a fitness landscape
analysis to better understand why this problem can be difficult. Among other,
we find that almost each initial starting point has its own local optimum, even
though the networks are highly interconnected.
