Abstract
In this chapter, secure computer communication based on synchronized hyperchaotic maps is presented. In particular, we appeal to model-matching approach from nonlinear control theory to synchronize the outputs of two coupled hyperchaotic Rössler maps. An application to secure e-mail communication for confidential information is given. By using a hyperchaotic encryption scheme, we show that output synchronization of hyperchaotic Rössler maps is indeed suitable for encryption, transmission, and decryption of information.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aguilar-Bustos A.Y., Cruz-Hernández C.: Synchronization of discrete-time hyperchaotic systems through extended Kalman filtering. Nonlinear Dynamics Systems Theory. 6, 319–336 (2006)
Aguilar-Bustos A.Y., Cruz-Hernández C.: Synchronization of discrete-time hyperchaotic systems: an application in communications. Chaos, Solitons & Fractals. 41, 1301–1310 (2009)
Alvarez G., Montoya F., Romera M., Pastor G.: Breaking parameter modulated chaotic secure communication system. Chaos, Solitons & Fractals. 24, 783–787 (2004)
Charge P., Fournier-Prunaret D., Guglielmi V.: Features analysis of a parametric PWL chaotic map and its utilization for secure transmissions. Chaos, Solitons & Fractals. 38, 1411–1422 (2008)
Chen M., Zhou D., Shang Y.: A sliding mode observer based secure communication scheme. Chaos, Solitons & Fractals. 25, 573–578 (2005)
Chen L.Q.: An open plus closed loop control for discrete chaos and hyperchaos. Phys. Lett. A281, 327–333 (2001)
Cruz-Hernández C., Nijmeijer H.: Synchronization through filtering. Int. J. Bifurct. Chaos. 10, 763–775 (2000)
Cruz-Hernández C., Posadas C., Sira-Ramírez H.: Synchronization of two hyperchaotic Chua circuits: A generalized Hamiltonian systems approach. Proceedings of the 15th IFAC World Congress, Barcelona, Spain, (2002)
Cruz-Hernández C.: Synchronization of time-delay Chua’s oscillator with application to secure communication. Nonlinear Dynamics Systems Theory. 4, 1–13 (2004)
Cruz-Hernández C., Serrano-Guerrero H.: Cryptosystems based on synchronized Chua’s circuits. Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, (2005)
Cruz-Hernández C., López-Mancilla D., García V., Serrano H., Núez R.: Experimental realization of binary signal transmission using chaos. J. Circ. Syst. Comput. 14, 453–468 (2005)
Cruz-Hernández C., Romero-Haros N.: Communicating via synchronized time-delay Chua’s circuits. Commun. Nonlinear Sci. Numer. Simul. 13, 645–659 (2008)
Cruz-Hernández C., Martynyuk A.A.: Advances in chaotic dynamics with applications. Series on Stability, Oscillations, and Optimization of Systems, Cambridge Scientific Publishers. London 4 (2009)
Cuomo K.M., Oppenheim A.V., Strogratz S.H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circ. Syst. II. 40, 626–633 (1993)
Dedieu H., Kennedy M.P., Hasler M.: Chaotic shift keying: Modulation and demodulation of a chaotic carrier using self-synchronizing Chuas circuits. IEEE Trans Circ Syst II. 40, 634–642 (1993)
Gao T., Chen Z., Yuan Z., Yu D.: Adaptive synchronization of a new hyperchaotic system with uncertain parameters. Chaos, Solitons & Fractals. 33, 922–928 (2007)
Grassi G.: Observer-based hyperchaos synchronization in cascaded discrete-time systems. Chaos, Solitons & Fractals. 40, 1029–1039 (2009)
Hyun C.H., Kim J.H., Kim E., Park M.: Adaptive fuzzy observer based synchronization design and secure communications of chaotic systems. Chaos, Solitons & Fractals. 27, 930–940 (2006)
Itoh M., Yang T., Chua L.O.: Conditions for impulsive synchronization of chaotic & hyperchaotic systems. Int. J. Bifurct. Chaos. 11, 551–560 (2001)
Kia F., Reza R., Hossein K.: An application of Chen system for secure chaotic communication based on extended Kalman filter and multi-shift cipher algorithm. Commun. Nonlinear Sci. Numer. Simul. 13, 763–781 (2008)
López-Mancilla D., Cruz-Hernández C.: Output synchronization of chaotic systems: model matching approach with application to secure communication. Nonlinear Dynamics Systems Theory. 5, 141–156 (2005)
López-Mancilla D., Cruz-Hernández C.: A note on chaos-based communication schemes. Revista Mexicana de Fsica. 51, 265–269 (2005)
López-Mancilla D., Cruz-Hernández C.: Output synchronization of chaotic systems under nonvanishing perturbations. Chaos, Solitons & Fractals. 37, 1172–1186 (2008)
Mensour B., Longtin A.: Synchronization of delay-differential equations with application to private communication. Phys Lett. A244, 59–70 (1998)
Monaco S., Normand-Cyrot D.: Minimum phase nonlinear discrete-time systems and feedback stabilization. In Proceedings of the 26th Conference on Decision and Control, Los Angeles, CA, USA, 979-986 (1987)
Nijmeijer H., Mareels I.M.Y.: An observer looks at synchronization. IEEE Trans. Circ. Syst. I. 44, 882–890 (1997)
Pecora L.M., Carroll T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)
Pérez G., Cerdeira H.A.: Extracting messages masked by chaos. Phys. Rev. Lett. 74, 1970–1973 (1995)
Posadas-Castillo C., Cruz-Hernández C., López-Mancilla D.: Synchronization of chaotic neural networks: a generalized Hamiltonian systems approach in Hybrid Intelligent Systems, Studies in Fuzziness and Soft Computing. Springer 208 (2007)
Posadas-Castillo C., Cruz-Hernández C., López-Gutiérrez R.M.: Synchronization in arrays of chaotic neural networks in Foundations of Fuzzy Logic and Soft Computing, LNAI. Springer 4529 (2007)
Posadas-Castillo C., López-Gutiérrez R.M., Cruz-Hernández C.: Synchronization of chaotic solid state Nd:YAG lasers: application to secure communication. Commun. Nonlinear Sci. Numer. Simul. 13, 1655–1667 (2008)
Sira-Ramírez H., Cruz-Hernández C.: Synchronization of chaotic systems: A generalized Hamiltonian systems approach. Int. J. Bifurct. Chaos. 11, 1381–1395 (2001)
Schneier, B.: Applied cryptography: protocols, algorithms, and source code in C. Wiley and Sons, Inc. (1996)
Short M., Parker A.T.: Unmasking a hyperchaotic communication scheme. Phys. Rev. E58, 1159–1162 (1998)
Tamaševičius A., Čenys A., Namajūnas A., Mykolaitis G.: Synchronising hyperchaos in infinitedimensional dynamical systems. Chaos, Solitons & Fractals. 9, 1403–1408 (1998)
Tang F.: An adaptive synchronization strategy based on active control for demodulating message hidden in chaotic signals. Chaos, Solitons & Fractals. 37, 1090–1096 (2008)
Vincent U.E.: Synchronization of identical and non-identical 4-D chaotic systems using active control. Chaos, Solitons & Fractals. 37, 1065–1075 (2008)
Wei-Der C.: Digital secure communication via chaotic systems. Digital Signal Processing (2008)
Yang T., Wu C.W., Chua L.O.: Cryptography based on chaotic systems. IEEE Trans. Circ. Syst. I. 44, 469–472 (1997)
Yang Y., Ma X.K., Zhang H.: Synchronization and parameter identification of high-dimensional discrete chaotic systems via parametric adaptive control. Chaos, Solitons & Fractals, 28, 244–251 (2006)
Yan J.J., Yang Y.S., Chiang T.Y., Chen C.Y.: Robust synchronization of unified chaotic via sliding mode control. Chaos, Solitons & Fractals. 34, 947–954 (2007)
Yan Z., Yu P.: Hyperchaos synchronization and control on a new hyperchaotic attractor. Chaos, Solitons & Fractals. 35, 333–345 (2008)
Zhong-Ping J.A.: A note on chaotic on chaotic secure communication systems. IEEE Trans. Circ. Syst. I. 49, 92–96 (2002)
Acknowledgements
This work was supported by the CONACYT, México under Research Grants No. J49593-Y, 48396-Y and P50051-Y. E. Tlelo-Cuautle was Visiting Researcher at University of California Riverside during 2009–2010 under a sabbatical leave CONACyT grant.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag London Limited
About this chapter
Cite this chapter
Aguilar-Bustos, A.Y., Cruz-Hernández, C., López-Gutiérrez, R.M., Tlelo-Cuautle, E., Posadas-Castillo, C. (2010). Hyperchaotic Encryption for Secure E-Mail Communication. In: Chbeir, R., Badr, Y., Abraham, A., Hassanien, AE. (eds) Emergent Web Intelligence: Advanced Information Retrieval. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/978-1-84996-074-8_18
Download citation
DOI: https://doi.org/10.1007/978-1-84996-074-8_18
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-84996-073-1
Online ISBN: 978-1-84996-074-8
eBook Packages: Computer ScienceComputer Science (R0)