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

Authors: Thang Manh Hoang

Abstract:

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.

Keywords: chaos synchronization, time-delayed system, chaosbasedsecure communications

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1329807

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.