A Two-Channel Secure Communication Using Fractional Chaotic Systems

Authors: Long Jye Sheu, Wei Ching Chen, Yen Chu Chen, Wei Tai Weng

Abstract:

In this paper, a two-channel secure communication using fractional chaotic systems is presented. Conditions for chaos synchronization have been investigated theoretically by using Laplace transform. To illustrate the effectiveness of the proposed scheme, a numerical example is presented. The keys, key space, key selection rules and sensitivity to keys are discussed in detail. Results show that the original plaintexts have been well masked in the ciphertexts yet recovered faithfully and efficiently by the present schemes.

Keywords: fractional chaotic systems, synchronization, securecommunication.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079582

References:

[1] E. N. Lorenz, "Deterministic nonperiodic flow," Journal Atmospheric Sciences, Vol. 20, pp. 130-141, 1963.
[2] H. Fujisaka and T. Yamada, "Stability theory of synchronized motion in coupled-oscillator systems," Progress in Theoretic Physics, Vol. 69, pp. 32-47, 1983.
[3] L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Physical Review Letters, Vol. 64, pp. 821-824, 1990.
[4] T. Yang, "A survey of chaotic secure communication systems," International Journal of Computational Cognition, Vol. 2, pp. 81-130, 2004.
[5] Z. P. Jiang, "A note on chaotic secure communication systems," IEEE Trans. Circuits Syst.-I Fund. Theory Appl., Vol. 49, pp. 92-96, 2002.
[6] Z. Li and D. Xu, "A secure communication scheme using projective chaos synchronization," Chaos Solitons Fractals, Vol. 22, pp. 477-481, 2004.
[7] A. B. Orue, V. Fernandex, G. Alvarez, G. Pastor, M. Romera, S. Li and F. Montoya, "Determination of the parameters for a Lorenz system and application to break the security of two-channel chaotic cryptosystems," Physis Letters A, Vol. 372, pp. 5588-5592, 2008.
[8] I. Petras, "A note on the fractional-order Chua-s system," Chaos Solitons Fractals, Vol. 38, pp. 140-147, 2008.
[9] T. T. Hartley, C. F. Lorenzo and H. K. Qammer, "Chaos in a fractional Chua-s system," IEEE Circuit Systems Theory Application, Vol. 42, pp. 485-490, 1995.
[10] L. J. Sheu, H. K. Chen, J. H. Chen and L. M. Tam, "Chaotic dynamics of the fractionally damped Duffing equation," Chaos Solitons Fractals, Vol. 32, pp. 1459-68, 2007.
[11] C. P. Li and G. J. Peng, "Chaos in Chen-s system with a fractional order," Chaos Solitons Fractals, Vol. 20, pp. 442-450, 2004.
[12] W. H. Deng and C. P. Li, "Chaos synchronization of the fractional Lu system," Physica A, Vol. 353, pp. 61-72, 2005.
[13] L. J. Guo, "Chaotic dynamics and synchronization of fractional-order Arneodo-s systems," Chaos Solitons Fractals, Vol. 26, pp. 1125-1133, 2005.
[14] L. J. Sheu, H. K. Chen, J. H. Chen and L. M. Tam, "Chaos in a new system with fractional order," Chaos Solitons Fractals, Vol. 31, pp. 1203-1212, 2007.
[15] W. Zhang, S. Zhou, H. Li and H. Zhu, "Chaos in a fractional-order Rossler system," Chaos Solitons Fractals, Vol. 42, pp. 1684-1691, 2009.
[16] I. Podlubny, "Geometric and physical interpretation of fractional integral and fractional derivatives," Journal of Fractional Calculus, Vol. 5, pp. 367-386, 2002.
[17] A. Kiani-B, K. Fallahi, N. Pariz and H. Leung, "A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter," Commu. Nonlin. Sci. Num. Simul., Vol. 14, pp. 863-879, 2009.
[18] I. Podlubny, Fractional differential equations, Academic Press, New York, 1999.
[19] M. Caputo, "Linear models of dissipation whose Q is almost frequency independent-II," Geophys J R Astron. Soc., Vol. 13, pp. 529-539, 1967.
[20] K. Diethelm, N. J. Ford and A. D. Freed, "A predictor-corrector approach for the numerical solution of fractional differential equations," Nonlinear Dynamics, Vol. 29, pp. 3-22, 2002.