Four-dimensional hyperchaotic system and application research in signal encryption

Transcription

1 ELECTRI C MACHINES AND CONTROL Vol. 16 No. 3 Mar Lyapunov TP 273 A X Four-dimensional hyperchaotic system and application research in signal encryption YU Chun-yu 1 ZHU Jian-liang 2 GUO Jian-ying 1 1. College of Measure-control Technology and Communication Engineering Harbin University of Science and Technology Harbin China 2. College of Electrical and Electronic Engineering Harbin University of Science and Technology Harbin China Abstract In order to obtain complex chaotic signal source a four-dimensional 4 - D hyperchaotic system was constructed and a new signal encryption algorithm based on the 4 - D system was also proposed. A system model was established and the model was investigated via Lyapunov Exponent phase-path of the system realization circuit and phase-path of the circuit. According to chaotic hiding and also to realize signal encryption the 4 - D system was selected as a signal source of chaotic encryption communication then question encrypted signals were added to chaotic source signals finally the password was set by means of combining application of iteration times and arithmetic operation of chaotic signals. The simulation results show that a perfect agreement between phase-paths of the system and phase-paths of realization circuit thus the designed system is a 4 - D hyperchaotic system and the signal encryption technique based on four-dimensional hyperchaotic system is effective and practical which provids a new method for informational encryption. Key words chaotic signal source four-dimensional hyperchaotic system attractor circuit realization information encryption AA04Z

2 V = x 1 + x 2 + x 3 + x 4 = - a - c = x 1 x 2 x 3 x 4 e - 28t Liao 6 Feki 7 Cuomo 8 Dudieu 9 Matlab Matlab Multisim 1 x = - ax + ay y = bx + u - xz 1 z = - cz + xy u = dx a = 25 b = 35 c = 3 d = Lyapunov 1 Lyapunov 1 Lyapunov Fig. 1 Lyapunov Exponents LE k LE1 = k LE2-3 k LE4 = = k LE3 = 1 Lyapunov Fig Hyperchaotic attactors of System 1

3 LF353 AD x y z u Multisim 4 3 Matlab Fig. 3 Circuit for Realizing Hyperchaotic System 1 Fig Hyperchaotic attactors of System a b 5

4 Fig. 5 5 Simulation Model of Square Wave Signal to be Encrypted Fig. 6 6 Simulation of Square Wave Signal to be Encrypted and Decrypted 4 Lyapunov 1 Lyapunov 1 Lü J Yu S M Leung H 2 Matlab Multisim 3 4 J Chen G. Experimental verification of multi-directional multi-scroll chaotic attractors J. IEEE Transactions on Circuits and Systems I Yu S M Lü J Leung H Chen G. Design and implementation of n-scroll chaotic attractors from a general Jerk circuit J. IEEE Transactions on Circuits and Systems Lü J Chen G Yu X H Leung H. Design and analysis of multiscroll chaotic attractors from saturated function series J. IEEE Transactions on Circuits and Systems I J WANG Guangyi QIU Shuisheng XU Zhiyi. A new three-dimensional quadratic chaotic system and its circuitry implementation. Acta Physica Sinica

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