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Synchronization of the unified chaotic system and application in secure communication. (English) Zbl 1221.94047
Summary: We study the synchronization of the unified chaotic system via optimal linear feedback control and the potential use of chaos in cryptography, through the presentation of a chaos-based algorithm for encryption.

94A60 Cryptography
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N99 Applications of dynamical systems
93D15 Stabilization of systems by feedback
Full Text: DOI
[1] Alvarez, G.; Li, S., Breaking network security based on synchronized, Comput commun, 27, 1679-1681, (2004)
[2] Alvarez, G.; Li, S.; Montoya, F.; Pastor, G.; Romera, M., Breaking projective chaos synchronization secure communication using filtering and generalized synchronization, Chaos, solitons fractals, 24, 775-783, (2004) · Zbl 1068.94002
[3] Alvarez, G.; Li, S.; Montoya, F.; Pastor, G.; Romera, M., Breaking a secure communication scheme based on the phase synchronization of chaotic systems, Chaos, 14, 274-278, (2004)
[4] Alvarez, G.; Li, S., Some basic requirements for chaos-based cryptosystems, Int J bifurc chaos appl sci eng, 16, 8, 2129-2152, (2006) · Zbl 1192.94088
[5] Cherrier, E.; Boutayeb, M.; Ragot, J., Observer-based synchronization and input recovery for a class of chaotic models, IEEE trans circ syst – part I, 53, 1977-1988, (2006)
[6] Cuomo, K.M.; Oppenheim, A.V., Circuit implementation of synchronized chaos with applications to communications, Phys rev lett, 71, 65-68, (1993)
[7] Elabbasy, E.M.; Agiza, H.N.; El-Dessoky, M.M., Global chaos synchronization for four scroll attractor by nonlinear control, Sci res essay, 1, 3, 65-71, (2006)
[8] Emadzadeh AA, Haeri M. Global Synchronization of two different chaotic systems via nonlinear control. In: Proceedings of the ICCAS, Gyeonggi-Do, Korea; 2005.
[9] Galias Z. Study of synchronization of linearly coupled hyperchaotic systems. In: Proceedings of the European conference on circuit theory and design, vol. 1; 1997. p. 296-301.
[10] Garfinkel, S.; Spafford, G., Practical unix and Internet security, (1996), O’ Reilly & Associates Inc. Sebastopol (CA), USA
[11] Ghosh, D.; Chowdhury, A.R.; Saha, P., On the various kinds of synchronization in delayed duffing – van der Pol system, Commun nonlinear sci numer simulat, 13, 790-803, (2008) · Zbl 1221.34196
[12] Ghosh, D.; Banerjee, S.; Chowdhury, A.R., Synchronization between variable time-delayed systems and cryptography, Euro phys lett, 80, 30006-30012, (2007)
[13] Grassi G, Mascolo S. Design of nonlinear observers for hyperchaos synchronization using a scalar signal. In: Proceedings of the IEEE, vol. 3; 1998. p. 283-6.
[14] Grassi, G.; Mascolo, S., Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal, IEEE trans circ syst I - fundam theor appl, 44, 10, 1011-1014, (1997)
[15] Ott, E.; Grebogi, C.; Yorke, J.A., Controlling chaos, Phys rev lett, 64, 1196-1199, (1990) · Zbl 0964.37501
[16] Grzybowski JMV, Rafikov M. Sincronização do sistema caótico unificado via controle ótimo linear feedback com aplicação em comunicação. In: Proceedings of the XXX CNMAC, Florianópolis, Brazil; 2007.
[17] Harb AM, Ahmad WM. Chaotic systems synchronization in secure communication systems. In: Proceedings of the 2006 World congress in computer science computer engineering, and applied computing, Las Vegas; 2006.
[18] Hwang, C.C.; Chow, H.Y.; Wang, Y.K., A new feedback control of a modified chua’s circuit system, Physica D, 92, 95-100, (1996) · Zbl 0925.93366
[19] Jiang, G.P.; Chen, G.; Tang, W.K.S., A new criterion for chaos synchronization using linear state feedback control, Int J bifurc chaos, 13, 8, 2343-2351, (2003) · Zbl 1064.37515
[20] Kocarev, L.; Parlitz, U., General approach for chaotic synchronization with applications to communications, Phys rev lett, 74, 25, 5028-5031, (1995)
[21] Li, D.; Lu, J.; Wu, X., Linearly coupled synchronization of the unified chaotic systems and the Lorenz systems, Chaos, solitons fractals, 23, 79-85, (2005) · Zbl 1063.37030
[22] Lu, J.; Wu, X.; Han, X.; Lü, J., Adaptive feedback synchronization of a unified chaotic system, Phys lett A, 329, 327-333, (2004) · Zbl 1209.93119
[23] Lu, J.; Wu, X.; Lü, J., Synchronization of a unified chaotic system and the application in secure communication, Phys lett A, 305, 365-370, (2002) · Zbl 1005.37012
[24] Mancilla, D.; Hernandez, C., A note on chaos-based communication schemes, Rev mex Fís, 51, 3, 265-269, (2005)
[25] Mascolo S. Backstepping design for controlling Lorenz chaos. In: Proceedings of the 36th conference on decision and control, San Diego, CA, USA; 1997.
[26] Min, L.; Jing, J., A new theorem to synchronization of unified chaotic systems via adaptive control, Chaos, solitons fractals, 24, 5, 1363-1371, (2004)
[27] Pecora, L.; Carroll, T., Synchronization in chaotic systems, Phys rev lett, 64, 8, 821-824, (1990) · Zbl 0938.37019
[28] Pogromsky, A.; Nijmeijer, H., Observer-based robust synchronization of dynamical systems, Int J bifurc chaos, 8, 11, 2243-2254, (1998) · Zbl 1140.93468
[29] Rafikov, M.; Balthazar, J.M., On control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Commun nonlinear sci numer simulat, 13, 1246-1255, (2008) · Zbl 1221.93230
[30] Sobhy MI, Shehata AR. Chaotic algorithm for data encryption. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing, vol. 1; 2001. p. i-xcii.
[31] Sobhy MI, Shehata AR. Methods of attacking chaotic encryption and countermeasures. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing, vol. 2; 2001. p. 1001-4.
[32] Tian, L.; Xu, J.; Sun, M., Chaos synchronization of the energy resource chaotic system with active control, Int J nonlinear sci, 3, 228-234, (2001) · Zbl 1394.34132
[33] Wang, C.; Ge, S.S., Adaptive backstepping control of uncertain Lorenz system, Int J bifurc chaos, 11, 4, 1115-1119, (2001) · Zbl 1090.93536
[34] Wong, K.W.; Kwok, B.S.H.; Law, W.S., A fast image encryption scheme based on chaotic standard map, Phys lett A, 298, 238-242, (2002)
[35] Yang, T.; Yang, C.M.; Yang, L.B., A detailed study of adaptive control of chaotic systems with unknown parameters, Dyn contr, 8, 255-267, (1998) · Zbl 0921.93025
[36] Yassen, M.T., Chaos synchronization between two different chaotic systems using active control, Chaos, solitons fractals, 23, 131-140, (2005) · Zbl 1091.93520
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