Naslov
Cellular automata based S-boxes

Autori
Mariot, Luca ; Picek, Stjepan ; Leporati, Alberto ; Jakobović, Domagoj

Izvornik
Cryptography and communications (1936-2447) 11 (2019), 1; 41-62

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Cellular automata ; S-box ; Cryptographic properties ; Heuristics

Sažetak
Cellular Automata (CA) represent an interesting approach to design Substitution Boxes (S-boxes) having good cryptographic properties and low implementation costs. From the cryptographic perspective, up to now there have been only ad- hoc studies about specific kinds of CA, the best known example being the χ nonlinear transformation used in Keccak. In this paper, we undertake a systematic investigation of the cryptographic properties of S-boxes defined by CA, proving some upper bounds on their nonlinearity and differential uniformity. Next, we extend some previous published results about the construction of CA-based S-boxes by means of a heuristic technique, namely Genetic Programming (GP). In particular, we propose a “reverse engineering” method based on De Bruijn graphs to determine whether a specific S-box is expressible through a single CA rule. Then, we use GP to assess if some CA-based S-box with optimal cryptographic properties can be described by a smaller CA. The results show that GP is able to find much smaller CA rules defining the same reference S-boxes up to the size 7×7, suggesting that our method could be used to find more efficient representations of CA-based S-boxes for hardware implementations. Finally, we classify up to affine equivalence all 3×3 and 4×4 CA-based S-boxes.

Izvorni jezik
Engleski

Znanstvena područja
Računarstvo

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