Achieving Better Security Using Nonlinear Cellular Automata as a Cryptographic Primitive

  • Swapan Maiti
  • Dipanwita Roy Chowdhury
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 834)


Nonlinear functions are essential in different crypto-primitives as they play an important role on the security of a cipher design. Wolfram identified Rule 30 as a powerful nonlinear function for cryptographic applications. However, Meier and Staffelbach mounted an attack (MS attack) against Rule 30 Cellular Automata (CA). MS attack is a real threat on a CA based system. Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide better cryptographic primitives and they are also secure against MS attack.


Cellular Automata Maximum period nonlinear CA Meier and Staffelbach attack Nonlinear functions 


  1. 1.
    NIST SP 800-22: A statistical test suite for random and pseudorandom number generators for cryptographic applications. U.S. Department of Commerce (2010)Google Scholar
  2. 2.
    Bardell, P.: Analysis of cellular automata used as pseudorandom pattern generators. In: Proceedings of the IEEE International Test Conference 1990, Washington, D.C., 10–14 September 1990, pp. 762–768 (1990)Google Scholar
  3. 3.
    Cattell, K., Muzio, J.C.: Synthesis of one-dimensional linear hybrid cellular automata. IEEE Trans. CAD Integr. Circuits Syst. 15(3), 325–335 (1996)CrossRefGoogle Scholar
  4. 4.
    Chaudhuri, P.P., Roy Chowdhury, D., Nandi, S., Chattopadhyay, S.: Additive Cellular Automata: Theory and Applications. IEEE Computer Socity Press, New York (1997)zbMATHGoogle Scholar
  5. 5.
    Formenti, E., Imai, K., Martin, B., Yunès, J.-B.: Advances on random sequence generation by uniform cellular automata. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Computing with New Resources. LNCS, vol. 8808, pp. 56–70. Springer, Cham (2014). Scholar
  6. 6.
    Ghosh, S., Sengupta, A., Saha, D., Roy Chowdhury, D.: A scalable method for constructing non-linear cellular automata with period \(2^n - 1\). In: Cellular Automata: Proceedings of the 11th International Conference on Cellular Automata for Research and Industry, ACRI 2014, Krakow, Poland, 22–25 September 2014, pp. 65–74 (2014)Google Scholar
  7. 7.
    Jose, J., Roy Chowdhury, D.: Four neighbourhood cellular automata as better cryptographic primitives. IACR Cryptology ePrint Archive 2015, 700 (2015)Google Scholar
  8. 8.
    Lacharme, P., Martin, B., Sole, P.: Pseudo-random sequences, Boolean functions and cellular automata. In: Proceedings of Boolean Functions and Cryptographic Applications, pp. 80–95 (2008)Google Scholar
  9. 9.
    Leporati, A., Mariot, L.: 1-resiliency of bipermutive cellular automata rules. In: Kari, J., Kutrib, M., Malcher, A. (eds.) AUTOMATA 2013. LNCS, vol. 8155, pp. 110–123. Springer, Heidelberg (2013). Scholar
  10. 10.
    Maiti, S., Ghosh, S., Roy Chowdhury, D.: On the security of designing a cellular automata based stream cipher. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017, Part II. LNCS, vol. 10343, pp. 406–413. Springer, Cham (2017). Scholar
  11. 11.
    Martin, B.: A Walsh exploration of elementary CA rules. Cell. Autom. 3(2), 145–156 (2008)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Meier, W., Staffelbach, O.: Analysis of pseudo random sequences generated by cellular automata. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 186–199. Springer, Heidelberg (1991). Scholar
  13. 13.
    Neumann, J.V.: The Theory of Self-reproducing Automata. (Edited by A.W. Burks) University of Illinois Press, Urbana (1966)Google Scholar
  14. 14.
    Serra, M., Slater, T., Muzio, J.C., Miller, D.M.: The analysis of one-dimensional linear cellular automata and their aliasing properties. IEEE Trans. CAD Integr. Circuits Syst. 9(7), 767–778 (1990)CrossRefGoogle Scholar
  15. 15.
    Wolfram, S.: Cryptography with cellular automata. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 429–432. Springer, Heidelberg (1986). Scholar
  16. 16.
    Wolfram, S.: Random sequence generation by cellular automata. In: Advances in Applied Mathematics, vol. 7, pp. 123–169 (1986)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Indian Institute of Technology KharagpurKharagpurIndia

Personalised recommendations