Cellular automata based S-boxes

Created by W.Langdon from gp-bibliography.bib Revision:1.8051

@Article{Mariot:2019:CandC,

• author = "Luca Mariot and Stjepan Picek and Alberto Leporati and Domagoj Jakobovic",
• title = "Cellular automata based {S}-boxes",
• journal = "Cryptography and communications",
• year = "2019",
• volume = "11",
• number = "1",
• pages = "41--62",
• month = jan,
• note = "Special Issue on Boolean Functions and Their Applications",
• keywords = "genetic algorithms, genetic programming, Cellular automata, S-box ,Cryptographic properties, Heuristics",
• ISSN = "1936-2447",
• DOI = "doi:10.1007/s12095-018-0311-8",
• abstract = "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 ki 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 7by7, 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 3by3 and 4by4 CA-based S-boxes.",

}

Genetic Programming entries for Luca Mariot Stjepan Picek Alberto Leporati Domagoj Jakobovic

Citations