| In recent years, with wide application in secret communication, many researchers focus on the chaos synchronization in nonlinear science and communication technology. Thus various methods ~[1-5] on chaos control and chaos synchronization have been put forward. These methods mostly adopt variable coupling way, which often brings some problems into the chaos model designing actually, and secret communication with chaos synchronization is under-secret for the appearance of corresponding attack technology. Secret communication system with chaos concealing based on driving-responding synchronization can be crack down by the way of the phase space reconstruction, the noise cutting down or the parameter estimation on chaos synchronization, above which are effective attack methods to the communication system secret on chaos synchronization except the scheme of parameter modulating at present.~[6]Concretely speaking, privacy of chaos communication system comes from the characteristics of chaos transmission signal, which is similar to noise, difficult predicting, and wide band. It can be disguised as the random noise, and difficult to perceive. The sensitive dependence of chaos transmitting signal to initial value makes its evolution law very difficult to obtain, and at the same time, frequency spectrum of signal planned to encrypt can be hided in wide frequency band range of chaos transmitting signal successfully.Researches on the privacy of chaos communicate system have been launched in some document, in which the communication mode of the adding concealing is adopted mainly. Concretely, the communication mode can be written as s(t) =h(x) +m(t). Namely the transmitting signal s(t) is the direct superimposition of low dimension of chaos signal h(x) and message signal m(t), which requiring the amplitude of m (t) to be far smaller than the amplitude of s (t) at the same time. Because the characteristic frequency of m (t) falls at the centre frequency band of h(x), therefore no matter in time domain or frequency domain, the information signals would be all concealed, and m(t) could not be separated from s(t) by utilizing the traditional linear method.~[7]But the privacy of this kind of communication is dissatisfactory ~[8,9] .The reason is that s(t) can be regarded as pure determinacy signal; m(t) is the weak noise hiding among them. According to the theory of phase space reconstruction~[10],after getting enough data from s(t), the chaos dynamical system equationin the driving end can be reconstructed, and then s(t) can be filtered. Information signal can be easily got from the residual signal of filtering wave.As what is mentioned above, from this point that chaos synchronization is just means but secret communication is the true purpose; we study the application of chaos synchronization in secret communication.Since chaos synchronization of the coupling form is not easy to realize technically,and chaos synchronization of the regular parameter is very easy to be broken through by the method of phase space reconstruction. Additionally, chaos system is equally sensitive to the parameter, the mismatch of the parameter of the components and parts, which form the chaotic system, will inevitably influence the performance of synchronization, so we have designed a kind of varying-parameter and uncoupled method to overcome above-mentioned defects. In this article, firstly Logistic map and Lorenz system are taken into account as two typical examples to provide the general meaning of the kind of chaos synchronization method based on driving parameter^11' . "Only when the variable range of the driven parameter includes the range in which the controlled system would have the periodical solution or the steady equalization point solution, the synchronism may just be realized. And while the variable range of the driven parameter totally in the chaos range of the controlled system, the synchronization can not be realized because there is no attraction of the common convergence goal.From the mechanism of realizing chaos synchronization, it can be said that the kind of uncoupled and varying-parameter method of chaos synchronization is obviously different from other methods. The synchronization comes to be realized by the nature of controlled systematic its own convergence, and the chaotic nature of the controlled system under the synchronization state, by the external chaos driving."Then the unified system ^12' with only one parameter is considered as the studying model as well as Logistic system with only one parameter as the driving system. Based on the above methods, we provide the design of secret communication scheme, the most remarkable characteristic of the scheme is to adopt uncoupled chaos synchronization method, because the driven parameter changes with time, the driven system is uncertain in fact, the chaos dynamical system equation in the driving end will not be reconstructed by... |
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