On the Use of Linear Cellular Automata for the Synthesis of Cryptographic Sequences

  • A. Fúster-Sabater
  • P. Caballero-Gil
  • O. Delgado
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5271)


This work shows that a class of cryptographic sequences, the so-called interleaved sequences, can be generated by means of linear hybrid cellular automata. More precisely, linear multiplicative polynomial cellular automata generate all the components of this family of interleaved sequences. As an illustrative example, the linearization procedure of the self-shrinking generator is described. In this way, popular nonlinear sequence generators with cryptographic application are linearized in terms of simple cellular automata.


interleaved sequence linear cellular automata self-shrinking generator cryptography 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gong, G.: Theory and Applications of q-ary Interleaved Sequences. IEEE Trans. Information Theory 147, 400–411 (1995)CrossRefGoogle Scholar
  2. 2.
    Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, Laguna Hill (1982)Google Scholar
  3. 3.
    Fúster-Sabater, A.: Run Distribution in Nonlinear Binary Generators. Applied Mathematics Letters 17, 1427–1432 (2004)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Jennings, S.M.: Multiplexed Sequences: Some Properties. In: Advances in Cryptology 1981 - 1997. LNCS, vol. 149. Springer, Heidelberg (1983)Google Scholar
  5. 5.
    Beth, T., Piper, F.: The Stop-and-Go Generator. In: Beth, T., Cot, N., Ingemarsson, I. (eds.) EUROCRYPT 1984. LNCS, vol. 209, pp. 124–132. Springer, Heidelberg (1985)Google Scholar
  6. 6.
    Gollmann, D., Chambers, W.G.: Clock-Controlled Shift Register. IEEE J. Selected Areas Commun. 7, 525–533 (1989)CrossRefGoogle Scholar
  7. 7.
    Coppersmith, D., Krawczyk, H., Mansour, A.: The Shrinking Generator. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 22–39. Springer, Heidelberg (1994)Google Scholar
  8. 8.
    Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge (1986)MATHGoogle Scholar
  9. 9.
    Kari, J.: A Survey of Cellular Automata. Theoretical Computer Science 334, 3–39 (2005)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Chaudhuri, P.P., Chowdhury, D.R., Nandi, S., Chatterjee, S.: Additive Cellular Automata-Theory and Applications, vol. 1. IEEE Computer Society Press, Los Alamitos (1997)MATHGoogle Scholar
  11. 11.
    Serra, M., Slater, T., Muzio, J.C., Miller, D.M.: The Analysis of One-dimensional Linear Cellular Automata and Their Aliasing Properties. IEEE Trans. on Computer-Aided Design 9(7), 767–778 (1990)CrossRefGoogle Scholar
  12. 12.
    Fúster-Sabater, A., Caballero-Gil, P., Delgado, O.: Solving Linear Difference Equations by means of Cellular Automata. In: Corchado, E., Corchado, J.M., Abraham, A. (eds.) Innovations in Hybrid Intelligent Systems. Advances in Soft Computing Series, vol. 44, pp. 183–190. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Cattell, K., Muzzio, J.C.: Synthesis of One-Dimensional Linear Cellular Automata. IEEE Trans. Computers-Aided Design 15, 325–335 (1996)CrossRefGoogle Scholar
  14. 14.
    Meier, W., Staffelbach, O.: The Shelf-Shrinking Generator. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 205–214. Springer, Heidelberg (1995)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • A. Fúster-Sabater
    • 1
  • P. Caballero-Gil
    • 2
  • O. Delgado
    • 1
  1. 1.Instituto de Física Aplicada, C.S.I.C.MadridSpain
  2. 2.DEIOCUniversity of La LagunaLa LagunaSpain

Personalised recommendations