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Paper 2021/293

Thinking Outside the Superbox

Nicolas Bordes, Joan Daemen, Daniël Kuijsters, and Gilles Van Assche


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

Available format(s)
Secret-key cryptography
Publication info
Published by the IACR in CRYPTO 2021
symmetric cryptographypermutationsblock ciphersround functions
Contact author(s)
nicolas bordes @ univ-grenoble-alpes fr
joan daemen @ ru nl
Daniel Kuijsters @ ru nl
gilles-iacr @ noekeon org
2021-06-23: revised
2021-03-07: received
See all versions
Short URL
Creative Commons Attribution


      author = {Nicolas Bordes and Joan Daemen and Daniël Kuijsters and Gilles Van Assche},
      title = {Thinking Outside the Superbox},
      howpublished = {Cryptology ePrint Archive, Paper 2021/293},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/293}},
      url = {https://eprint.iacr.org/2021/293}
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