Study Of The Complexity Of The Algorithm Of Discrete Chaotic Systems

The application of chaos in field of information security has become ahot topic. The complexity analysis of chaotic systems is a very importantaspect of system security performance. There is a close relationshipbetween the complexity and the system's cryptogram performance. Thecomplexity of time series generated by discret chaotic system is analyzedand studied by using different methods, especially, the new TD-ERCSdiscret chaotic system is discussed in the paper, and its complexity iscompared with the other common discret chaotic systems. First, the spacestructure complexity of each chaotic system is observed by phase spaceobservation method, the magnitude of the complexity is approximatelygained. Then, the complexity is measured through the methods ofbehavior complexity and structure complexity. In the method of behaviorcomplexity, based on Kolmogorov complexity, classic Limpel-Zivalgorithm, ApEn algorithm and PE algorithm are used respectively insingle dimension and multiplied dimensions approach. The complexityvalue of some systems is calculated, including Logistic system, Tentsystem, Henon system, Sected linear reflection system and TD-ERCSsystem. The results show that the behavior complexity of TD-ERCSsystem is greater than other chaotic systems, and the complexity valuechanges a little as the change of its parameters. In the aspect of structurecomplexity, the Fourier Transform and Wavelet Transform are used to getthe Spectral Entropy and Wavelet Entropy, which are used to describe thecomplexity of the discret chaotic systems. The results indicate that thefrequency spectral complexity of TD-ERCS system is about the samewith other discret chaotic system, and the structure complexity is alsovery great. In a conclusion, the hehaviour complexity of TD-ERCSsystem is better than that of other chaotic systems, and it has the samestructure complexity as other discret chaotic systems. It is an applicablechaotic system which can be used for cryptography application and hasbroad application foreground in the field of information secure.