The Construction Research Of 2~n-periodic Sequences Base On K-error Linear Complexity

Cryptology as a synthetic discipline is a science of technology which is researching encryption and decryption. Encryption means to encrypt the plaintext and this process is to ensure the information security. On the contrary, decryption is to decipher the ciphertext and get the plaintext. Stream cipher is a important section in cryptology. The security level of stream cipher is related to cipher key sequence, so the research of cipher key sequence is very important in cryptology.The linear complexity and the k-error linear complexity are important indicators to measure strength of stream ciphers. So in the procedure of researching the property of binary sequence, the linear complexity and k error linear complexity is likely to be not only required, but essential. If the linear complexity of stream ciphers is very high, but sometimes it is not stability. This problem had been solved when the concept of K error linear complexity was appear, so the k error linear complexity is more important in researching the stream ciphers. And the cube theory is important, as well. Because cube theory could turn the complexity process to the simpleness and convenience in procedure of research the stream ciphers. In this paper, we use a construction approach and the cube theory to research cipher key sequence which have stationary linear complexity and k-error linear complexity. In this paper, we have the follow conclusion:1. Base on the Games-Chan algorithm and use the cube-theory to analysis the 2n -periodic binary sequence, which have the first descent point in 2-error and the second descent point in 6-error point. And we give the related properties as well. In the end, we give the counting formula, which meet the condition of L6(s(n))>L5(s(n))=…=L2(s(n))>L1(s(n))=L(s(n)).2. By using the cube theory to construct the sequence, which have been give the linear complexity and k error linear complexity. And those sequence must match the conditions of L9(s(n))>L8(s(n))=L7(s(n))>L6(s(n))=…=L2(s(n))>L1(s(n))=L(s(n)) and WH(s(n))= 9.3. According the cube theory and using construction approach to research the 3-error linear complexity distribution of 2n-periodic binary sequences.