Research On The Excellent Sequence Of Period P~n Over GF(q) Based On Intelligent Optimization Algorithm

Cryptography is the subject to research encryption and decryption, especially keeping advantage in special or confidential organizations, such as wireless communication and diplomatic communication etc. Stream cipher is also known as sequential cipher, it has the advantages of fast switching and low ratio of error propagation, the hardware circuit is simpler than traditional methods. The intensity of pseudo random sequences is defined by the randomness and unpredictability of stream cipher key which generated by key stream generator. Period and linear complexity are two important criterion to measure its unpredictability. But as research continues,some scholars found that only these are not enough, it can’t guarantee the stability of sequences.Then they defined a new concept called k-error linear complexity. Intelligent optimization algorithm for multi-objective optimization problem provides a solving framework for this kind of problem.Based on the binary excellent sequence, we study the q-ary sequence in depth. Cat swarm intelligent optimization algorithm can solve the issue that cannot be solved by traditional algorithm. The main contents include:1. Analyzed the defects of binary excellent sequence, for specific k, it cannot guarantee the sequence to meet the characteristics of 1)-0,1...n=(rp=kr;2. Studied the application of cat swarm algorithm to sequences with period pn over GF(q).Design a reasonable fitness function to improve the standard of excellent sequence. Results of N=9,27,243,729,2187 where p=3, q=5,7,11...show that they have the same characteristics,On the basis of the experimental results, we find the linear complexity of sequences meet:NLC(S) ￡; k-error linear complexity k-N(S)LCk￡;3. According to the definition of linear complexity and the 2-adic complexity, here speculated and verified that sequences with high linear complexity and high 2-adic complexity are easy to be found, but sequences with high linear complexity and low 2-adic complexity are nonexistence. Two types of complexity are based on orders of register that generates this class of sequences, therefore they in terms of theory should be a positive correlation with each other. We selected binary sequences of period of 32, 64, 128, 256, 512, 1024, and 2048 in experiment. The experimental results by cat swarm optimization algorithm show that, the former is relatively easy to find, but the latter did not occur in the experimental output. We also found out the characteristics of the first type of sequence:NLC ￡,￡1-a LC N.And the time cost is positive linear correlation with cat group number, period N, and the number of iteration number.