A New Secure Communication Model Based on Synchronization of Coupled Multidelay Feedback Systems

Recent research result has shown that two multidelay feedback systems can synchronize each other under different schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating synchronization. There, the driving signal is significantly complex due that it is constituted by multiple nonlinear transformations of delayed state variable. In this paper, a secure communication model is proposed based on synchronization of coupled multidelay feedback systems, in which the plain signal is mixed with a complex signal at the transmitter side and it is precisely retrieved at the receiver side. The effectiveness of the proposed model is demonstrated and verified in the specific example, where the message signal is masked directly by the complex signal and security is examined under the breaking method of power spectrum analysis.

Authors:

• Thang Manh Hoang

Keywords:

• chaos synchronization
• time-delayed system
• chaosbasedsecure communications

References:

[1] L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems,"
Phys. Rev. Lett., vol. 64, pp. 821-824, 1990.
[2] M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling
and Synchronization. Singapore: World Scientific, 1996.
[3] S. K. Han, C. Kurrer, and Y. Kuramoto, "Dephasing and bursting in
coupled neural oscillators," Phys. Rev. Lett., vol. 75, pp. 3190-3193,
1995.
[4] B. Blasius, A. Huppert, and L. Stone, "Complex dynamics and phase
synchronization in spatially extended ecological systems," Nature,
vol. 399, pp. 354-359, 1999.
[5] T. Yang, "A survey of chaotic secure communication systems," Int. J.
Comp. Cog., vol. 2, pp. 81-130, 2004.
[6] N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel,
"Generalized synchronization of chaos in directionally coupled chaotic
systems," Phys. Rev. E, vol. 51, pp. 980-994, 1995.
[7] R. Mainieri and J. Rehacek, "Projective synchronization in threedimensional
chaotic systems," Phys. Rev. Lett., vol. 82, pp. 3042-3045,
1999.
[8] M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag
synchronization in coupled chaotic oscillators," Phys. Rev. Lett., vol. 78,
pp. 4193-4196, 1997.
[9] H. U. Voss, "Anticipating chaotic synchronization," Phys. Rev. E, vol. 61,
pp. 5115-5119, 2000.
[10] M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "Phase synchronization
of chaotic oscillators," Phys. Rev. Lett., vol. 76, pp. 1804-1807, 1996.
[11] T. M. Hoang and M. Nakagawa, "Projective-lag synchronization of
coupled multidelay feedback systems," J. Phys. Soc. Jpn., vol. 75,
pp. 094801.1-094801.6, 2006.
[12] T. M. Hoang and M. Nakagawa, "Anticipating and projective-
anticipating synchronization of coupled multidelay feedback systems,"
Phys. Lett. A, vol. 365, pp. 407-411, 2007.
[13] K. M. Cuomo and A. V. Oppenheim, "Circuit implementation of
synchronized chaos with applications to communications," Phys. Rev.
Lett., vol. 71, pp. 65-68, 1993.
[14] U. Parlitz, L. O. Chua, L. Kocarev, K. S. Halle, and A. Shang,
"Transmission of digital signals by chaotic synchronization," Int. J. Bifur.
Chaos, vol. 2, pp. 973-977, 1992.
[15] G. Kolumb'an, M. P. Kennedy, and L. O. Chua, "The role of synchronization
in digital communication using chaos-Part I: Fundamentals of
digital communications," IEEE Trans. Circuits Syst. I, vol. 44, pp. 927-
936, 1997.
[16] H. Dedieu, M. P. Kennedy, and M. Hasler, "Chaos shift keying: Modulation
and demodulation of a chaotic carrier using seft-synchronizing
Chua-s circuits," IEEE Trans. Circuits Syst. II, vol. 40, pp. 634-642,
1993.
[17] T. M. Hoang and M. Nakagawa, "New encoding model for chaosbased
secure communication," J. Phys. Soc. Jpn., vol. 75, pp. 034801.1-
034801.10, 2006.
[18] J. D. Farmer, "Chaotic attractors of an infinite-dimensional dynamical
system," Physica D, vol. 4, pp. 366-393, 1982.
[19] K. M. Short and A. T. Parker, "Unmasking a hyperchaotic communication
scheme," Phys. Rev. E, vol. 58, pp. 1159-1162, 1998.
[20] T. M. Hoang, D. T. Minh, and M. Nakagawa, "Synchronization of multidelay
feedback systems with multi-delay driving signal," J. Phys. Soc.
Jpn., vol. 74, pp. 2374-2378, 2005.
[21] N. N. Krasovskii, Stability of Motion. Standford: Standford University
Press, 1963.
[22] J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential
Equations. New York: Springer, 1993.
[23] G. Perez and H. A. Cerdeira, "Extracting messages masked by chaos,"
Phys. Rev. Lett., vol. 74, pp. 1970-1973, 1995.
[24] T. Yang, L. B. Yang, and C. M. Yang, "Breaking chaotic switching using
generalized synchronization: Examples," IEEE Trans. Circuits Syst. I,
vol. 45, pp. 1062-1067, 1998.
[25] T. Yang, L. B. Yang, and C. M. Yang, "Breaking chaotic secure
communication using a spectrogram," Phys. Lett. A, vol. 247, pp. 105-
111, 1998.
[26] T. Yang, "Recovery of digital signals from chaotic switching," Int. J.
Circuit Theory & Applications, vol. 23, pp. 611-615, 1995.
[27] G. A' lvarez, F. Montoya, M. Romera, and G. Pastor, "Breaking two
secure communication systems based on chaotic masking," IEEE Trans.
Circuits Syst. II, vol. 51, pp. 505-506, 2004.
[28] G. A' lvarez, F. Montoya, M. Romera, and G. Pastor, "Cryptanalyzing an
improved security modulated chaotic encryption scheme using ciphertext
absolute value," Chaos, Solitons and Fractals, vol. 23, pp. 1749-1756,
2005.
[29] G. A' lvarez and S. Li, "Breaking network security based on synchronization
chaos," Computer Communication, vol. 27, pp. 1679-1681, 2004.
[30] S. Li, G. A' lvarez, and G. Chen, "Breaking a chaos-based secure
communication scheme designed by an improved modulation method,"
Chaos, Solitons and Fractals, vol. 25, pp. 109-120, 2005.
[31] S. Li, G. A' lvarez, G. Chen, and X. Mou, "Breaking a chaos-noisebased
secure communication scheme," Chaos, vol. 15, pp. 013703.1-
013703.10, 2005.
[32] T. M. Hoang and M. Nakagawa, "Enhancing security for chaos-based
communication system with change in synchronization manifolds- delay
and in encoder-s parameters," J. Phys. Soc. Jpn., vol. 75, pp. 064801.1-
064801.12, 2006.