Skip to main content
SpringerLink
Log in

Binary Synchronization of Complex Dynamics in Cellular Automata and its Applications in Compressed Sensing and Cryptography

  • Conference paper
Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering

Part of the book series: Studies in Computational Intelligence ((SCI,volume 483))

  • 867 Accesses

Abstract

Complex dynamics of the type used in random number generators may emerge in elementary cellular automata with properly designed structures and cells. This chapter reviews recent results in quantifying the complexity of the dynamics in cellular automata with an emphasis on the recently discovered phenomenon called binary synchronization. It allows that two cellular automata systems with the same structure will synchronize (the receiver will duplicate the n-dimensional state vector of the transmitter) receiving only a single bit stream, produced by the output of a single cell of the transmitter cellular automaton. The decoding of this stream is possible only when the structure of the cellular automata (encryption key) is known. It is shown how the key space may be increased using various methods (e.g. using hybrid models or perturbing the cellular network model into a small-worlds model). Applications in cryptography, spread spectrum communications, and compressed sensing are reviewed. Some particularities for the implementation of such cellular automata systems in FPGA technologies are provided.

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

Access this chapter

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
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baraniuk, R., Cevher, V., Duarte, M., Hedge, C.: Model-based compressive sensing. IEEE Trans. Inform. Theory 56(4), 1982–2001 (2010)

    Article  MathSciNet  Google Scholar 

  2. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 821, 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  3. Kolumban, G., Kennedy, M.P., Chua, L.O.: The role of synchronization in digital communication using chaos– Part II: Chaotic modulation and chaotic synchronization. IEEE Trans. Circuits and Syst. I 1140, 1129–1140 (1998)

    Article  MathSciNet  Google Scholar 

  4. López-Mancilla, D., Cruz-Hernández, C.: Output synchronization of chaotic systems: Model-matching approach with application to secure communication. Nonlinear Dynamics and Systems Theory 5(2), 141–156 (2005)

    MathSciNet  MATH  Google Scholar 

  5. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Breaking two secure communication systems based on chaotic masking. IEEE Trans. on Circuits and Systems II: Express Briefs 51, 505–506 (2004)

    Article  Google Scholar 

  6. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, 2129–2151 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kanso, A., Smaoui, N.: Logistic chaotic maps for binary numbers generations. Chaos, Solitons and Fractals 40, 2557–2568 (2009)

    Article  MathSciNet  Google Scholar 

  8. Pareek, N.K., Patidar, V., Sud, K.K.: Cryptography using multiple onedimensional chaotic maps. Commun. Nonlinear Sci. Numer. Simul. 10(7), 715–723 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Yi, X.: Hash function based on chaotic tent maps. IEEE Trans. Circuits Syst. II, Exp. Briefs 52(6), 354–357 (2005)

    Article  Google Scholar 

  10. Vlad, A., Luca, A., Frunzete, M.: Computational Measurements of the Transient Time and of the Sampling Distance That Enables Statistical Independence in the Logistic Map. In: Gervasi, O., Taniar, D., Murgante, B., Laganà, A., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2009, Part II. LNCS, vol. 5593, pp. 703–718. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Takens, F.: Detecting strange attractors in turbulence. In: Rand, D.A., Young, L.-S. (eds.) Dynamical Systems and Turbulence. Lecture Notes in Mathematics, vol. 898, pp. 366–381. Springer (1981)

    Google Scholar 

  12. Djemai, M., Barbot, J.P., Boutat, D.: New type of data transmission using a synchronization of chaotic systems. International Journal of Bifurcation and Chaos 15, 207–223 (2005)

    Article  MATH  Google Scholar 

  13. Dimitriev, A.S., Hasler, M., Kassian, G.A., Khilinsky, A.D.: Chaotic synchronization of 2-D maps via information transmission. In: Proceedings of 2001 International Symposium on Nonlinear Theory and its Applications, vol. 1, pp. 79–82 (2001)

    Google Scholar 

  14. Dogaru, R., Chua, L.O., Murgan, A.T.: Secure communication based on binary synchronization of chaos in cellular neural networks. In: Proceedings SCS 1997, Int’l Symposium on Circuits and Systems, Iasi, Romania, pp. 97–100 (1997)

    Google Scholar 

  15. Dogaru, R., Dogaru, I., Kim, H.: Binary chaos synchronization in elementary cellular automata. Int. J. Bifurcation Chaos 19(9), 2871–2884 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Chua, L.O.: A Nonlinear Dynamics Perspective of Wolfram’s New Kind of Science (Vol I-IV). World Scientific Series on Nonlinear Science, Series A, vol. 57, 68, 76. World Scientic Publishing Company (2006, 2009, 2011)

    Google Scholar 

  17. Cho, S.J., Choi, U.S., Kim, H.D., Hwang, Y.H., Kim, J.G., Heo, S.H.: New synthesis of one-dimensional 90/150 linear hybrid group CA. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 26(9), 1720–1724 (2007)

    Article  Google Scholar 

  18. Seredynski, F., Bouvry, P., Zomaya, A.Y.: Cellular automata computations and secret key cryptography. Parallel Comput. 30(5-6), 753–766 (2004)

    Article  MathSciNet  Google Scholar 

  19. Urias, J., Salazar, G., Ugalde, E.: Synchronization of cellular automaton pairs. Chaos 8, 814–818 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. Dogaru, I., Dogaru, R.: Algebraic Normal Form for Rapid Prototyping of Elementary Hybrid Cellular Automata in FPGA. In: Proceedings ISEEE 2010, Galati, Romania, pp. 273–276 (September 2010)

    Google Scholar 

  21. Dogaru, R.: Hybrid Cellular Automata as Pseudo-Random Number Generators with Binary Synchronization Property. In: Proceedings of the International Symposium on Signals Circuits and Systems (ISSCS 2009), Iasi, Romania, pp. 389–392 (July 2009)

    Google Scholar 

  22. Dogaru, R.: HCA101: A chaotic map based on cellular automata with binary synchronization properties. In: Proceedings of The 8th Int’l Conference on Communications, COMM 2010, Bucharest, Romania, June 10-12, pp. 41–44 (2010)

    Google Scholar 

  23. Marsaglia, G.: Diehard (2012), http://stat.fsu.edu/~geo/diehard.html

  24. Ronjom, S., Abdelraheem, M., Danielsen, L.E.: TT and ANF Representations of Boolean functions. In: Online Database of Boolean Functions (2007), http://www.selmer.uib.no/odbf/help/ttanf.pdf

  25. Fernandez-Berni, J., Carmona-Galan, R., Carranza-Gonzalez, L.: FLIP-Q: A QCIF Resolution Focal-Plane Array for Low-Power Image Processing. IEEE Journal of Solid-State Circuits 46(3), 669–680 (2011)

    Article  Google Scholar 

  26. Dogaru, R., Dogaru, I., Kim, H.: Chaotic Scan: A Low Complexity Video Transmission System for Efficiently Sending Relevant Image Features. IEEE Trans. on Circuits and Systems for Video Technology 20(2), 317–321 (2010)

    Article  Google Scholar 

  27. Tam, W.M., Lau, F.C.M., Tse, C.K.: Digital Communications With Chaos. Elsevier, Oxford (2007)

    Google Scholar 

  28. Dogaru, R., Kim, H., Dogaru, I.: Binary Synchronization in Cellular Automata for Building Compact CDMA Systems. In: Proceedings of the International Symposium on Signals Circuits and Systems (ISSCS 2009), Iasi, Romania, pp. 393–396 (July 2009)

    Google Scholar 

  29. Jovic, B., Unsworth, C.P.: Performance comparison of multi-user chaos-based DS-CDMA synchronisation unit within AWGN and Rayleigh fading channel. Electronics Letters 43(18) (August 31, 2007)

    Google Scholar 

  30. Jovic, B., Unsworth, C.P.: Chaos-based multi-user time division multiplexing communication system. IET Commun. 1(4), 549–555 (2007)

    Article  Google Scholar 

  31. Dubrova, E.: How to speed-up your NLFSR-based stream cipher. In: Proceedings of Design, Automation & Test in Europe Conference & Exhibition (DATE 2009), pp. 878–881 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Applied Electronics and Information Engineering, Natural Computing Laboratory, University ”Politehnica” of Bucharest, Room B232, Bvd. Iuliu Maniu 1-3, Sector 6, Bucharest, Romania

    Radu Dogaru & Ioana Dogaru

Authors
  1. Radu Dogaru
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ioana Dogaru
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Radu Dogaru .

Editor information

Editors and Affiliations

  1. Institut für Intelligente, Systemtechnol0, Alpen Adria Universität Klagenfurt, Universitätsstraße 65-67, Klagenfurt, 9020, Austria

    Kyandoghere Kyamakya

  2. , Lehrgebiet Informationstechnik, FernUniversität in Hagen, Universitätsstraße 27, Hagen, 58097, Germany

    Wolfgang A. Halang

  3. , Institut für Theoretische, Leibniz Universität Hannover, Appelstr. 9A, Hannover, 30167, Germany

    Wolfgang Mathis

  4. , Lakeside Park, Alpen-Adria Universität Klagenfurt, Haus B04, Klagenfurt, 9020, Austria

    Jean Chamberlain Chedjou

  5. Fernuniversität Hagen, Philipp-Reis-Gebäude, Hagen, 58084, Germany

    Zhong Li

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dogaru, R., Dogaru, I. (2013). Binary Synchronization of Complex Dynamics in Cellular Automata and its Applications in Compressed Sensing and Cryptography. In: Kyamakya, K., Halang, W., Mathis, W., Chedjou, J., Li, Z. (eds) Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering. Studies in Computational Intelligence, vol 483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37781-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37781-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37780-8

  • Online ISBN: 978-3-642-37781-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation