Skip to main content
SpringerLink
Log in

On the Use of Cellular Automata in Symmetric Cryptography

  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

Abstract

In this work, pseudorandom sequence generators based on finite fields have been analyzed from the point of view of their cryptographic application. In fact, a class of nonlinear sequence generators has been modelled in terms of linear cellular automata. The algorithm that converts the given generator into a linear model based on automata is very simple and is based on the concatenation of a basic structure. Once the generator has been linearized, a cryptanalytic attack that exploits the weaknesses of such a model has been developed. Linear cellular structures easily model sequence generators with application in stream cipher cryptography.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Assis, F., Pedreira, C.: An architecture for computing Zech's logarithms in GF(2m). IEEE Trans. Comput. 49(5), 519–524 (2000)

    Article  MathSciNet  Google Scholar 

  2. Bao, F.: Crytanalysis of a new cellular automata cryptosystem. 8th Australasian Conference on Information Security and Privacy – ACISP 2003. Lecture Notes in Computer Science, vol. 2727, pp. 416–427. Springer, Berlin Heidelberg New York (2003)

  3. Blackburn, S., Merphy, S., Paterson, K.: Comments on ‘Theory and applications of cellular automata in cryptography’. IEEE Trans. Comput. 46, 637–638 (1997)

    Article  MathSciNet  Google Scholar 

  4. Cattell, K., Muzio, J.: Analysis of one-dimensional linear hybrid cellular automata over GF(q). IEEE Trans. Comput. 45(7), 782–792 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cattell, K., Muzio, J.: Synthesis of one-dimensional linear hybrid cellular automata. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 15(3), 325–335 (1996)

    Article  Google Scholar 

  6. Cattell, K., Shujian, Z.: Minimal cost one-dimensional linear hybrid cellular automata of degree through 500. J. Electron. Test.: Theory Appl. 6, 255–258 (1995)

    Article  Google Scholar 

  7. Cattell, K., Muzio, J.: A linear cellular automata algorithm: Theory. Department of Computer Science. University of Victoria, Canada, Tech. Rep. DCS-161-IR, 1991

  8. Coppersmith, D., Krawczyk H., Mansour, Y.: The shrinking generator. Advances in Cryptology –CRYPTO'93. Lecture Notes in Computer Science, vol. 773, pp. 22–39. Springer, Berlin Heidelberg New York (1994)

  9. Cho, S., Un-Sook, C., Yoon-Hee, H.: Computing phase shifts of maximum-length 90/150 Cellular automata sequences. Proc. of ACRI 2004. Lecture Notes on Computer Science, vol. 3305, pp. 31–39. Springer, Berlin Heidelberg New York (2004)

  10. Das, A.K., Ganguly, A., Dasgupta, A., Bhawmik, S., Chaudhuri, P.P.: Efficient characterisation of cellular automata. IEE Proc., Part E. 1, 81–87 (1990)

    Google Scholar 

  11. Golomb, S.: Shift-Register Sequences (revised edition). Aegean Park, Laguna Hills, California (1982)

  12. Gong, G.: Theory and applications of q-ary interleaved sequences. IEEE Trans. Inform. Theory 41, 400–411 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Golic, J., O'Connors, L.: A cryptanalysis of clock-controlled shift registers with multiple steps. Cryptography: Policy and Algorithms 41, 174–185 (1995)

    Google Scholar 

  14. Johansson, T.: Complexity correlation attacks on two clock-controlled Generators. Proc. of Asiacrypt'98. Lecture Notes in Computer Science, vol. 1426, pp. 342–356. Springer, Berlin Heidelberg New York (1998)

  15. Kanso, A.: Clock-controlled shrinking generator of feedback shift registers. 8th Australasian Conference on Information Security and Privacy – ACISP 2003. Lecture Notes in Computer Science, vol. 2727, pp. 443–451. Springer, Berlin Heidelberg New York (2003)

  16. Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Cambridge University Press, Cambridge, UK (1986)

    MATH  Google Scholar 

  17. Martin, O., Odlyzko, A.M., Wolfram, S.: Algebraic properties of cellular automata. Comm. Math. Phys. 93, 219–258 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  18. Menezes, A.J., van Oorschot, P., Vanstone, S.A.: Handbook of Applied Cryptography. CRC, New York (1997)

    MATH  Google Scholar 

  19. Nandi, S., Kar, B.K., Chaudhuri, P.P.: Theory and applications of cellular automata in cryptography. IEEE Trans. Comput. 43, 1346–1357 (1994)

    Article  MathSciNet  Google Scholar 

  20. Rueppel, R.A.: Stream ciphers. In: Simmons G.J. (ed.) Contemporary Cryptology, The Science of Information, pp. 65–134. IEEE, Piscataway, New Jersey (1992)

  21. Serra, M., Slater, T., Muzio, J., Miller, D.M.: The analysis of one-dimensional linear cellular automata and their aliasing properties. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 9(7), 767–778 (1990)

    Article  Google Scholar 

  22. Simpson, L. et al. Clock-a probabilistic correlation attack on the shrinking generator. Proc. of Australasian Conference on Information Security and Privacy – ACISP 1998. Lecture Notes in Computer Science, vol. 1438, pp. 147–158. Springer, Berlin Heidelberg New York (1998)

  23. Wolfram, S.: Random sequence generation by cellular automata. Adv. Appl. Math. 7(123), (1986)

  24. Wolfram, S.: Cryptography with cellular automata. Advances in Cryptology – CRYPTO'85. Lecture Notes in Computer Science, vol. 218, pp. 22–39. Springer, Berlin Heidelberg New York (1994)

  25. Zhang, S.: Quantitative analysis for linear hybrid CA and LFSR as BIST generators for sequential faults. J. Electron. Test. 7(3), 209–221 (1995)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Física Aplicada, C.S.I.C., 28006, Madrid, Spain

    A. Fúster-Sabater

  2. DEIOC, University of La Laguna, 38271, La Laguna, Tenerife, Spain

    P. Caballero-Gil

Authors
  1. A. Fúster-Sabater
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Caballero-Gil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Fúster-Sabater.

Additional information

Work supported by Ministerio de Educación y Ciencia (Spain), Projects SEG2004-02418 and SEG2004-04352-C04-03.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fúster-Sabater, A., Caballero-Gil, P. On the Use of Cellular Automata in Symmetric Cryptography. Acta Appl Math 93, 215–236 (2006). https://doi.org/10.1007/s10440-006-9041-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-006-9041-6

Mathematics Subject Classifications (2000)

Key words

Search

Navigation