Research On The Chaotic Encryption And Synchronization Applications Based On High Dimensions Nonlinear Systems

Chaotic theory is a new scientifically discipline derived by nonlinear science.The researches of chaotic control and synchronization are proper throughout the world.These research results are excellent and applied in turbulence,chemical system and secure communication system.The merits in high dimensional chaotic maps include multiple positive Lyapunov exponents,anti-degradation in finite precision computation in computers,more power in chaotic behaviours.These merits have positive effects in applications of chaotic control and synchronizations.This paper is devoted in the high dimensional chaotic systems explorations of chaotic control and synchronizations and chaotic image encryptions.The main achievements are summarized as follows:(1)Taking Behnia encryption algorithm based on low dimensional chaotic system as an example,the author analyzed the security of this kind of algorithm.By avoiding the flaws of Behnia,I improved the Behnia algorithm so as to make this kind of algorithm resist the chosen-plaintext attack.I also proposed single image and multi-miages encryptions schemes based on the Logistic map,Sine map.(2)The author analyzed the strengths and weaknesses of the low dimensional chaos based schemes.The low dimensional chaos based schemes can not resist the problem of finite precision computaions.For compensations the weakness of the low dimensional chaos which cannot resist the finite precision computation under modern computers,I studied the high dimensional chaos and the corresponding image encryption schemes such as Lorenz system and DNA sequences based image encryption scheme,CML based encryption scheme and FSNCML based encryption scheme.(3)The author deeply studied hyper-chaotic systems and the corresponding synchronizations,such as unified chaos and hyper-Rossler system.For the unified chaos,three cases including subtle variations,parameter variations and subtle variations under unknown parameters were studied.I designed the controllers which meet the three cases and obtained the corresponding synchronization systems.For the hyper Rossler system,we designed the slaver systems for two cases including the master system with higher and lower dimension than the slaver system respectively;and obtained two synchronization systems.(4)The author deeply studied the anti-synchronization of the hyper chaos.The adaptive control method was employed for anti-synchronization control.Therefore,the author obtained the corresponding controller and implemented anti-synchronization of the hyper chaos.For test simulations,the hyper Chen system and Henon-Heiles system were employed for the verification.In the test results,this anti-synchronization system can identify the unknown parameters and implement anti-synchronization successfully.By researching and analyzing the encryption algorithm and chaotic synchronization based on the high-dimensional chaotic system,we can improve the performance,security and stability of chaotic secure communication system.Provides a good solution for the industry of confidential communication.