Chaotic Sequence Cipher Algorithm Based on Discrete Anti-control

Abstract

Aiming at the degeneracy problem of discrete chaotic dynamics system in the digital domain, an algorithm that can configure the Lyapunov exponents of the system to be all positive is proposed.The algorithm is based on the principle of chaos anti-control.First, a feedback matrix is introduced.All the parameters in the set are specified carefully, and it is proved from a theore-tical point of view that the algorithm can configure the Lyapunov exponent to be fully positive.Subsequently, the boundedness of the system orbit and the finiteness of the Lyapunov exponent are proved, and the numerical simulation analysis and performance comparison of the configuration are carried out through several examples, so as to verify that the algorithm can produce a discrete chaotic system without degenerate.There are certain advantages in numerical accuracy and algorithm running time.The configured chaotic system is then used to generate the sequence and then quantized.The quantization scheme is to take out the effective digital combination of the sequence.Some dynamic transformation processing on the sequence can enhance the randomness and complexity of the output sequence.We convert the transformed output sequence into a binary sequence, perform a number of randomness and statistical tests, and compare the performance with the general chaotic sequence.The test results show that the sequence has better random characteristics and can be used in a chaotic sequence cipher system.

Keywords

• anti-control|lyapunov exponent|chaotic system|sequence cipher