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The application of complex chaotic systems to pseudo-random sequence generation is the major method to generate high-performance pseudo-random numbers. This system will have multiple positive Lyapunov values with reasonable parameters, which have complex chaotic characteristics and security. It has complex chaotic dynamic characteristics. It is an artificial neural network based on Hopfield Neural Network and Cellular Automata. The CNNs is a nonlinear dynamic chaotic system.
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It is an effective solution to adopt a hyper-chaotic system with multiple positive Lyapunov value and sequence generation algorithm with the best random performance. In fact, a complex high-dimensional chaotic system can improve the security of the pseudo-random sequence and enhance the anti-decoding ability of the system. Although these methods can increase the key space, the weakness is that their cycle is short. Qi designed a pseudo-random number generator using the discrete hyper-chaotic mapping system. Wang generated a pseudo-random sequence of good random performance by using a three-dimensional Lorenz system. In addition, there are also some other algorithms to generate a pseudo-random number based on high dimensional chaotic. Although they can obtain high-performance pseudo-random sequences, they also have some problems such as computational complexity and low utilization because of multiple chaotic iterations. Both of these two algorithms used multiple chaotic iterations to generate pseudo-random numbers. Han proposed an algorithm to generate the pseudo-random number based on the discrete chaotic synchronization system, and Dong proposed an algorithm to generate the pseudo-random number based on the cellular neural networks (CNNs). Bo proposed a random sequence algorithm based on knight cruising, which can achieve good randomness, but the knight cruising path is complex. Some other methods such as shift registered sequence generator and compound prime number generator also have weak random performance. Because of the generation circle of the pseudo-random number depends on the initial values, the statistical performance of these pseudo-random numbers is not perfect. At present, some common algorithms such as taking the middle number or the congruence method. Studying the algorithm which can generate a random number with high randomness is becoming an important topic of information security. The random number has an important effect on data encryption, network information security, image communication, and satellite navigation.