Pitfalls and Shortcomings for Decompositions and Alignment

In this paper we, for the first time, study question under which circumstances decomposing a round function of Substitution-Permutation Network is possible uniquely. More precisely, we provide necessary and sufficient criteria non-linear layer on when decomposition unique. Our results in particular imply that, cryptographically strong S-boxes are used, indeed We then apply our findings to notion alignment, pointing out that previous definition allows primitives both aligned unaligned simultaneously. As second result, present experimental data shows alignment might only have limited impact. For this, compare versions cipher PRESENT.