Advertisement

Pseudorandom Number Generator Based on Totalistic Cellular Automaton

  • Miroslaw SzabanEmail author
Conference paper
  • 288 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11657)

Abstract

In this paper, is considered a problem of selection rules for one-dimensional (1D) totalistic cellular automaton (TCA), which is used for generation of pseudorandom sequences which could be useful in cryptography. The quality of pseudorandom bit sequences generated by TCA-based pseudorandom number generator (PRNG) depends on appropriately selected totalistic rules assigned to CA cells. There is presented a methodology of selecting TCA rules, starting from initial selection based on application Entropy of bit streams generated by the TCA. Next, the selected rules were examined with the use of the NIST SP 800-22rev1a tests and the Diehard set of Marsaglia tests. In the paper was analyzed, the uniform TCA with totalistic rules with neighborhood radius equal to 1, 2, 3, and 4. During the studies, selected sets of TCA are presented as a new set of CA rules, which can be used as quite cryptographically strong TCA-based PRNG, supplying a new huge space of keys.

Keywords

Cellular automaton Pseudorandom number generator Totalistic rules Cryptography 

References

  1. 1.
    Formenti, E., Imai, K., Martin, B., Yunès, J.-B.: Advances on Random sequence generation by uniform cellular automata. Computing with New Resources - Essays Dedicated to J. Gruska on the Occasion of His 80th Birthday, pp. 56–70 (2014)Google Scholar
  2. 2.
    Guan, P.: Cellular automaton public-key cryptosystem. Complex Syst. 1, 51–56 (1987)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Habutsu, T., Nishio, Y., Sasase, I., Mori, S.: A secret key cryptosystem by iterating a chaotic map. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 127–140. Springer, Heidelberg (1991).  https://doi.org/10.1007/3-540-46416-6_11CrossRefGoogle Scholar
  4. 4.
    Hortensius, R.D., McLeod, R.D., Card, H.C.: Parallel random number generation for VLSI systems using cellular automata. IEEE Trans. Comput. 38, 1466–1473 (1989)CrossRefGoogle Scholar
  5. 5.
    Hosseini, S.M., Karimi, H., Jahan, M.V.: Generating pseudo-random numbers by combining two systems with complex behaviors. J. Inform. Secur. Appl. 19(2), 149–162 (2014)Google Scholar
  6. 6.
    Kari, J.: Cryptosystems based on reversible cellular automata (1992)Google Scholar
  7. 7.
    Leporati, A., Mariot, L.: Cryptographic properties of bipermutive cellular automata rules. J. Cell. Automata 9(5–6), 437–475 (2014)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)zbMATHGoogle Scholar
  9. 9.
    Marsaglia, G.: The Marsaglia Random Number CDROM including the Diehard Battery of Tests of Randomness, Florida State University (1995)Google Scholar
  10. 10.
    Nandi, S., Kar, B.K., Chaudhuri, P.P.: Theory and applications of cellular automata in cryptography. IEEE Trans. Comput. 43, 1346–1357 (1994)MathSciNetCrossRefGoogle Scholar
  11. 11.
    National Institute of Standards and Technology (NIST), Special Publication 800–22 (2010), A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. http://csrc.nist.gov/publications/nistpubs/800-22-rev1a/SP800-22rev1a.pdf
  12. 12.
    Schneier, B.: Applied Cryptography. Wiley, New York (1996)zbMATHGoogle Scholar
  13. 13.
    Seredynski, F., Bouvry, P., Zomaya, A.: Cellular automata computation and secret key cryptography. Parallel Comput. 30, 753–766 (2004)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Sipper, M., Tomassini, M.: Generating parallel random number generators by cellular programming. Int. J. Mod. Phys. C 7(2), 181–190 (1996)CrossRefGoogle Scholar
  15. 15.
    Szaban, M., Seredynski, F.: Designing conflict free cellular automata-based PRNG. J. Cell. Automata 13(3), 229–246 (2018)MathSciNetGoogle Scholar
  16. 16.
    Tomassini, M., Perrenoud, M.: Stream cyphers with one- and two-dimensional cellular automata. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., Schwefel, H.-P. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 722–731. Springer, Heidelberg (2000).  https://doi.org/10.1007/3-540-45356-3_71CrossRefGoogle Scholar
  17. 17.
    Sienkiewicz, M.: Project, implementation and analysis of pseudorandom number generator based on one dimensional totalistic cellular automata. Master thesis (2017). (in Polish)Google Scholar
  18. 18.
    Tomassini, M., Sipper, M.: On the generation of high-quality random numbers by two-dimensional cellular automata. IEEE Trans. Comput. 49(10), 1140–1151 (2000)zbMATHGoogle Scholar
  19. 19.
    Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644 (1983)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Wolfram, S.: Cryptography with cellular automata. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 429–432. Springer, Heidelberg (1986).  https://doi.org/10.1007/3-540-39799-X_32CrossRefGoogle Scholar
  21. 21.
    Wolfram, S.: A New Kind of Science. Wolfram Media (2002)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Computer Science, Siedlce University of Natural Sciences and HumanitiesSiedlcePoland

Personalised recommendations