Research On The Excellent Sequence Based On Intelligent Optimization Algorithm

Encryption is an important way to effectively ensure information security. Stream cipher isan important encryption technology. We need some reasonable indicators to analyzecryptosystem as an encryption technology is necessary to identify its strengths and weaknesses.The strength of stream cipher strength totally depends on the randomness and unpredictability ofthe pseudo-random sequences, which is affected by period and linear complexity, etc.. It is foundthat sequences with large period and high linear complexity may not be safe. So k-error linearcomplexity becomes a new indicator which is paid more attention to by the researchers. Thetraditional mathematical methods have limitations in the research of the linear complexitycombined with the k-error linear complexity. In recent years, computer intelligence hasdemonstrated a strong vitality in cryptography study.This paper described the relevant background of the stream cipher and its indicators,analyzed the research difficulties of the traditional methods, and then introduced Cat SwarmOptimization and Genetic Algorithm. And apply Cat Swarm Optimization algorithm to theresearch of the complexity of binary sequence, Genetic Algorithm to the research of binaryFermat Sequence. The main research contents are as follows:1、 Introduced the algorithm of Cat Swarm Optimization Algorithm and Genetic Algorithm,and do some feasibility analysis for using those two algorithms in stream ciphers. And itproves that those two algorithms can be used to the research of stream ciphers.2、 Defined2n-periodic binary sequence with high linear complexity and high k-error linearcomplexity as excellent sequence, and design algorithm to study the features of2n-periodic binary excellent sequence based on Cat Swarm Optimization Algorithm.First select N-periodic binary sequences, N=32,64,128,512,1024and even longer, k=N/4, searching with various parameters, and compute the linear complexity profiles ofresults using Lauder-Paterson algorithm, in order to get excellent sequence. Thenobtained the law of k-error linear complexity of N-periodic binary excellent sequenceby the designed algorithm, which meets the formula N-2k+1. Then obtained theproportion of excellent sequence in all binary sequences of the same period by the designed algorithm is1/4.3、Defined Fermat Sequence and the steps to generate such p2periodic binary Fermat Sequences, then combine Genetic Algorithm and the algorithm to calculate linear complexity to the research of k-error linear complexity of Fermat Sequence from which we can get a lot for1-error linear complexity and the changed positions for it. And finally we get the rule for such sequences as:the changed position for1-error was the n*pth while n=0,1,2,...,p-1, p is a prime, and2is the primitive element module p2.