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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baraniuk, R., Cevher, V., Duarte, M., Hedge, C.: Model-based compressive sensing. IEEE Trans. Inform. Theory 56(4), 1982–2001 (2010)
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 821, 821–824 (1990)
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)
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)
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)
Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, 2129–2151 (2006)
Kanso, A., Smaoui, N.: Logistic chaotic maps for binary numbers generations. Chaos, Solitons and Fractals 40, 2557–2568 (2009)
Pareek, N.K., Patidar, V., Sud, K.K.: Cryptography using multiple onedimensional chaotic maps. Commun. Nonlinear Sci. Numer. Simul. 10(7), 715–723 (2005)
Yi, X.: Hash function based on chaotic tent maps. IEEE Trans. Circuits Syst. II, Exp. Briefs 52(6), 354–357 (2005)
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)
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)
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)
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)
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)
Dogaru, R., Dogaru, I., Kim, H.: Binary chaos synchronization in elementary cellular automata. Int. J. Bifurcation Chaos 19(9), 2871–2884 (2009)
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)
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)
Seredynski, F., Bouvry, P., Zomaya, A.Y.: Cellular automata computations and secret key cryptography. Parallel Comput. 30(5-6), 753–766 (2004)
Urias, J., Salazar, G., Ugalde, E.: Synchronization of cellular automaton pairs. Chaos 8, 814–818 (1998)
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)
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)
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)
Marsaglia, G.: Diehard (2012), http://stat.fsu.edu/~geo/diehard.html
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
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)
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)
Tam, W.M., Lau, F.C.M., Tse, C.K.: Digital Communications With Chaos. Elsevier, Oxford (2007)
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)
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)
Jovic, B., Unsworth, C.P.: Chaos-based multi-user time division multiplexing communication system. IET Commun. 1(4), 549–555 (2007)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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)