The Secret Communication And Its Circuit Implementation Based On The Fractional-order Chaotic System Synchronization

Fractional-order chaotic system has a complex dynamical behavior. Integer-orderdifferential system is a special case of the fractional-order differential system. Integer-orderchaotic system is just the result of the practical chaotic system’s idealized processing. Actually,in order to describe the practical chaotic system’s dynamics precisely, fractional-orderdifferential and integral operator may be used. Because of the fractional-order chaotic system’more complicated dynamic characteristics, it can be used in the secret communication toachieve higher security.In this thesis, the fractional-order chaotic system’s dynamic behavior is studied. Throughthe mathematical derivation, three kind of universal synchronization controller, which can berealized easily in engineering, for the fractional-order chaotic system have been acquired. Thefirst one is the self-adaptive synchronization controller that is based on the sliding modecontrol. The second one is the single-driving-variable self-adaptive synchronization controller.The last one is the single-driving-variable time-delay synchronization controller. Theanalytical expressions for three kinds of synchronization controller are presented. Accordingto the result of numerical simulation, circuit simulation and implementation, it is proved thatall schemes are effective and feasible.On the basis of the self-adaptive synchronization controller, which is based on the slidingmode control, for the fractional-order chaotic system, a secret communication scheme viaparametric modulation is designed. The circuit simulation and implementation of this schemeis provided. The analysis of results show that this scheme is better to realize secretcommunication and is applied easily in engineering. This scheme is universal to some extent.Through discussion, some further improvement of this scheme is presented. In this thesis,there is a brief discussion on other secret communication scheme which is based on thissynchronization controller for the fractional-order chaotic system. All results show that thiscontroller is universal and can be applied to other communication scheme, such as chaoticmasking and parametric modulation.On the basis of the self-adaptive synchronization, which is based on the single drivingparater, for the fractional-order chaotic system, a chaotic maksing secret communicationscheme is designed. It is showed that this scheme can realize secret communicationeffectively by the results of the circuit simulation and implementation. This scheme can alsobe applied to parametric modulation and Spread Spectrum Communication (SSC). Thisscheme is also universal in part. The limitation of this scheme is present by discussion.Allowing for the inevitable delay during practical communication, based on the scheme above,a new scheme of spread spectrum communication for the fractional-order chaotic system issuggested. By examples, circuit simulation and implementation of this scheme is presented.Results show that this scheme is applicable and effective. It also shows that this scheme isvery simple and valid both in theoretical security and in practical implementation. Thisscheme is worth to be generalized.