Cellular automata based S-boxes View Full Text


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Article Info

DATE

2019-01

AUTHORS

Luca Mariot, Stjepan Picek, Alberto Leporati, Domagoj Jakobovic

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 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. More... »

PAGES

1-22

References to SciGraph publications

  • 2002. The Design of Rijndael, AES — The Advanced Encryption Standard in NONE
  • 2016. Construction of Lightweight S-Boxes Using Feistel and MISTY Structures in SELECTED AREAS IN CRYPTOGRAPHY – SAC 2015
  • 2017-08-08. A cryptographic and coding-theoretic perspective on the global rules of cellular automata in NATURAL COMPUTING
  • 2007. On the Classification of 4 Bit S-Boxes in ARITHMETIC OF FINITE FIELDS
  • 2004. Block Encryption Using Reversible Cellular Automata in CELLULAR AUTOMATA
  • 1998-10-16. Fast Hashing and Stream Encryption with Panama in FAST SOFTWARE ENCRYPTION
  • 1995. S-boxes and round functions with controllable linearity and differential uniformity in FAST SOFTWARE ENCRYPTION
  • 1995. Links between differential and linear cryptanalysis in ADVANCES IN CRYPTOLOGY — EUROCRYPT'94
  • 1994. A new approach to block cipher design in FAST SOFTWARE ENCRYPTION
  • 2005-09. The design of S-boxes by simulated annealing in NEW GENERATION COMPUTING
  • 1993. Cryptography with Dynamical Systems in CELLULAR AUTOMATA AND COOPERATIVE SYSTEMS
  • 2007. PRESENT: An Ultra-Lightweight Block Cipher in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS - CHES 2007
  • 2002-01-18. Efficient Methods for Generating MARS-Like S-Boxes in FAST SOFTWARE ENCRYPTION
  • 2001-05-18. On the construction of highly nonlinear permutations in ADVANCES IN CRYPTOLOGY — EUROCRYPT’ 92
  • 2015. Direct Construction of Recursive MDS Diffusion Layers Using Shortened BCH Codes in FAST SOFTWARE ENCRYPTION
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    http://scigraph.springernature.com/pub.10.1007/s12095-018-0311-8

    DOI

    http://dx.doi.org/10.1007/s12095-018-0311-8

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    34 schema:description 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.
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