Properties of Safe Cellular Automata-Based S-Boxes

  • Miroslaw Szaban
  • Franciszek Seredynski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6068)


In the paper we use recently proposed cellular automata (CA) - based methodology [9] to design 8 ×n (n ≤ 8) S-boxes functionally equivalent to S-boxes used in current cryptographic standards. We provide an exhaustive experimental analysis of the proposed CA-based S-boxes in terms of non-linearity, autocorrelation and scalability, and compare results with other proposals. We show that the proposed CA-based S-boxes have cryptographic properties comparable or better than currently offered classical S-box tables.


Cellular Automata S-boxes Block Cipher Cryptography 


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  1. 1.
    Clark, J.A., Jacob, J.L., Stepney, S.: The Design of S-Boxes by Simulated Annealing. New Generation Computing 23(3), 219–231 (2005)zbMATHCrossRefGoogle Scholar
  2. 2.
    Dowson, E., Millan, W., Simpson, L.: Designing Boolean Functions for Cryptographic Applications. Contributions to General Algebra 12, 1–22 (2000)Google Scholar
  3. 3.
    Federal Information Processing Standards Publication, Fips Pub 46-3, DES (1999),
  4. 4.
    Federal Information Processing Standards Publications, FIPS PUBS 197, AES (2001),
  5. 5.
    Millan, W.: How to Improve the Non-linearity of Bijective S-boxes. LNCS, vol. 143, pp. 181–192. Springer, Heidelberg (1998)Google Scholar
  6. 6.
    Millan, W., Burnett, L., Carter, G., Clark, A., Dawson, E.: Evolutionary Heuristics for Finding Cryptographically Strong S-Boxes. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 263–274. Springer, Heidelberg (1999)Google Scholar
  7. 7.
    Mukhopadhyay, D., Chowdhury, D.R., Rebeiro, C.: Theory of Composing Non-linear Machines with Predictable Cyclic Structures. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 210–219. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Nedjah, N., de Macedo Mourelle, L.: Designing Substitution Boxes for Secure Ciphers. International Journal Innovative Computing and Application 1(1), 86–91 (2007)CrossRefGoogle Scholar
  9. 9.
    Szaban, M., Seredynski, F.: Cryptographically Strong S-Boxes Based on Cellular Automata. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds.) ACRI 2008. LNCS, vol. 5191, pp. 478–485. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Webster, A.F., Tavares, S.: On the Design of S-Boxes. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 523–534. Springer, Heidelberg (1986)Google Scholar
  11. 11.
    Youssef, A., Tavares, S.: Resistance of Balanced S-boxes to Linear and Differential Cryptanalysis. Information Processing Letters 56, 249–252 (1995)zbMATHCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Miroslaw Szaban
    • 1
  • Franciszek Seredynski
    • 2
    • 3
  1. 1.Institute of Computer ScienceUniversity of PodlasieSiedlcePoland
  2. 2.Institute of Computer SciencePolish Academy of SciencesWarsawPoland
  3. 3.Polish-Japanese Institute of Information TechnologyWarsawPoland

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