The Complexity Algorithms Research Of Chaotic Sequences Based On Entropy Theory

With rapid development of science and technology,information security problem becomes much more important.The chaos is one of the most famous science foundations of 20^th century,which has been applied to information security and secure communication research for its sensitivity to initial conditions and inherent randomness and so on.The inherent randomness of different chaotic signals are also different,good randomness is an important foundation to realize better information security and secret communication.Randomness,therefore,as an important aspect of chaotic dynamics'characteristic becomes an important research content in information security and secret communication.The complexity of the chaotic system is to measures the level of similarity between the chaotic sequences and the random sequences.The better complexity of the chaotic sequences,the better its ability to anti-interference and resistance to intercept.The complexity analysis of the chaotic sequences can help us to understand the complex characteristics of chaotic systems better.In this thesis,we use the measure algorithm based on entropy theory to assess and analyze the complexity of the chaotic sequences and apply relevant feature extraction algorithm to improve the chaotic sequences for better randomness.We optimize and improve the measure algorithm based on entropy theory and enhance the computational efficiency of the algorithm.The main researches are as follows:?1?Based on the ideas and features of genetic algorithm,the complexity feature extraction algorithm based on GA is proposed.We use the subsequences as chromosomes,and use the approximate entropy as fitness function,optimally select the subsequences through the crossover operation to find the subsequences which have bigger complexity.Then,the dual complexity feature extraction algorithm based on GA is proposed,we added the permutation entropyalgorithm in the fitness function to measure the chromosomes and improved the crossover operation strategy,and find the better subsequences which have the better randomness.?2?The principal component analysis?PCA?which based on discrete K-L transformation is an effective statistical analysis method in statistical data analysis,feature extraction and data compression.The method simplifies multiple related variables into a linear combination of several irrelevant variables,through the less-comprehensive index as much as possible to replace many of the original data,and can reflect the information provided by the original data.We proposed the signal feature extraction algorithm based on PCA,and extracts sequences'feature which generated by Logistic mapping.Then we measured the complexity of the reconstructed chaotic sequences by the permutation entropy algorithm.The testing results show that the complexity of the reconstruction sequences is significantly higher than the original sequences.?3?Based on the characteristics of the digital chaotic sequences,we optimized and improved the approximate entropy and permutation entropy algorithms.We proposed fast calculation method based on the hash process in permutation entropy algorithms.The improved algorithms have a great improvement in the operational efficiency.?4?Based on the principle and the development of the present situation of GPU,the approximate entropy and permutation entropy acceleration algorithms based on GPU are proposed for measuring the complexity of the digital chaotic sequences.The result and accuracy of the accelerate algorithms are consistent with the original algorithms and the running times of algorithmsgot a raise,at the same time,the algorithms also weaken the algorithm running time dependence of parameters.The experimental results provide a experimental basisfor the application of chaotic sequence in information security.