| Some researchers have pointed out that there exists a tight relationship between chaos and cryptography. Many fundamental characteristics of chaos, such as the ergodicity, mixing and exactness property and the sensitivity to initial conditions, can be connected with the confusion and diffusion property in cryptography. So it is a natural idea to use chaos to enrich the design of new ciphers.It has been found that dynamics of chaotic systems can easily collapse in the digital world (such as periodic pseudo orbits, the loss of ergodicity, mixing, invariant measure and positive Lyapunov exponent and etc), and the dynamical degradation may make some negative influences on the performance of digital chaos-based applications.The main contents of this paper include the research on the theory of dynamical degradation and application (chaotic cipher) of digital chaos in information security. The main research contents and originality of this paper can be summarized as follows:1. Dynamical degradation of digital chaos obtained in computer or other digital devices has been studied firstly, and then we point out that the perturbation-based solution (perturbing system variable and/or perturbing control parameter) is the best one. In this paper, a scheme on perturbing the values of variables in the digital 3D-Baker map has been proposed, in which the variants x and y are selectively diffused so as to perturb the whole system. Theoretical analyses indicate that the perturbed dynamical system is still a chaos system (it still has two positive Lyapunov exponents as one of the most important characteristics).The experimental results show that this scheme is effective.2. A MPEG-2 video encryption algorithm based on 1D-piecewise linear chaotic map is given out. In the algorithm, selectively encrypting the data of all the Slice level is used to encrypt the whole video sequence; meanwhile, we also apply digital 3D-Baker map to generate the external key of Group Of Pictures (GOP), so that it can decrease the computational overhead on its random retrievals. Since the encrypted object is a compressed MPEG-2 video, and then there is no need to encode and compress the video, the overhead of encryption and decryption is dramatically decreased. At the same time, sizes of files or the compression ratios of video sequence will not be changed, and the encrypted data can still be recognizable to the MPEG-2 decoder.3. Up till now, Baptista's cryptosystem scheme and its improved versions can not effectively solve some problems, such as long cryptographs, slow encryption speed, non-uniform distribution of cipher text, lower security and so on. A chaos encryption scheme based on carrier is put forward, in which the novel point is that we use carrier instead of looking-up table. Compared with the looking-up table, carrier can be selected flexibly because it could be digital resources or private resources promised by sender and receiver. A chaotic map is exploited to produce the "embedding positions"; during encrypting, cryptosystem behaves as a stream cipher. The style of encryption is determined by the control-function, which can enhance the security of... |
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