Skip to main content
SpringerLink
Log in
Book cover

Innovations in Hybrid Intelligent Systems pp 183–190Cite as

Solving Linear Difference Equations by Means of Cellular Automata

  • Chapter

Part of the book series: Advances in Soft Computing ((AINSC,volume 44))

Abstract

In this work, it is shown that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are binary sequences with application in cryptography. In this sense, we propose CA-based linear models that realize the solutions of difference equations as well as behave as cryptographic keystream generators. Due to the simple transition rules that govern these CA, the implementation of such models is quite easy. Some illustrative examples complete the work.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beth, T., Piper, F.: The Stop-and-Go Generator. In Proc. EUROCRYPT’84. LNCS, vol. 228, pp. 124–132. Springer, Heidelberg (1985)

    Google Scholar 

  2. Bluetooth, Specifications of the Bluetooth system, http://www.bluetooth.com/

    Google Scholar 

  3. Caballero-Gil, P., Fúster-Sabater, A.: A Wide Family of Nonlinear Filter Functions with a Large Linear Span. Information Sciences. 164, 197–207 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cattell, K., Muzzio, J.C.: Synthesis of One-Dimensional Linear Cellular Automata. IEEE Trans. Computers-Aided Design, 15, 325–335 (1996)

    Article  Google Scholar 

  5. Coppersmith, D., Krawczyk, H., Mansour, A.: The Shrinking Generator. In Proc. ECRYPTO’93. LNCS, vol. 773, pp. 22–39. Springer, Heidelberg (1994)

    Google Scholar 

  6. Fúster-Sabater, A.: Run Distribution in Nonlinear Binary Generators. Applied Mathematics Letters. 17, 1427–1432 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gollmann, D., Chambers, W.G.: Clock-Controlled Shift Register. IEEE J. Selected Areas Commun. 7, 525–533 (1989)

    Article  Google Scholar 

  8. Golomb, S.W.: Shift Register-Sequences. Aegean Park Press, Laguna Hill, (1982)

    Google Scholar 

  9. Gong, G.: Theory and Applications of q-ary Interleaved Sequences. IEEE Trans. Information Theory. 41, 400–411 (1995)

    Article  MATH  Google Scholar 

  10. GSM, Global Systems for Mobile Communications, available at http://cryptome.org/gsm-a512.htm

    Google Scholar 

  11. Jennings, S.M.: Multiplexed Sequences: Some Properties. In Proc. EUROCRYPT’83. LNCS, vol. 149, Springer, Heidelberg (1983)

    Google Scholar 

  12. Kari, J.: A Survey of Cellular Automata. Theoretical Computer Science. 334, 3–39 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  14. Rivest, R.L.: RSA Data Security. Inc., March 12 (1998)

    Google Scholar 

  15. Wolfram, S.: Random Sequence generation by Cellular Automata. Advances in Applied Mathematics. 123(7) (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Física Aplicada, C.S.I.C., Serrano 144, 28006, Madrid, Spain

    A. Fúster-Sabater & O. Delgado

  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

  3. O. Delgado
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Escuela Politécnica Superior Campus Vena, Edifico C, Universidad de Burgos, C/Francisco de Vitoria s/n, 09006, Burgos, Spain

    Emilio Corchado

  2. Departamento de Informática y Automática Facultad de Ciencias, Universidad de Salamanca, Plaza de la Merced S/N, 37008, Salamanca, Spain

    Juan M. Corchado

  3. Centre for Quantifiable Quality of Service in Communication Systems (Q2S) Centre of Excellence, Norwegian University of Science and Technology, O.S. Bragstads plass 2E, 7491, Trondheim, Norway

    Ajith Abraham

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fúster-Sabater, A., Caballero-Gil, P., Delgado, O. (2007). 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, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74972-1_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74972-1_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74971-4

  • Online ISBN: 978-3-540-74972-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation