Thinking Outside the Superbox

Designing a block cipher or cryptographic permutation can be approached in many different ways. One such approach, popularized by AES, consists grouping the bits along S-box boundaries, e.g., bytes, and consistently processing them these groups. This aligned approach leads to hierarchical structures like superboxes that make it possible reason about differential linear propagation properties using combinatorial arguments. In contrast, an unaligned avoids any design of transformations. However, without structure, sophisticated computer programs are required investigate primitive. this paper, we formalize notion alignment study four primitives exponents strategies. We propose way analyze interactions between nonlinear layers w.r.t. propagation, use systematically compare non-trivial experiments. show naturally forms clustering, active boxes, two-round trails activity patterns, differentials approximations.