Study On The Distribution Of Binary Periodic Sequences With K-error Linear Complexity

In the era of development of information technology, cryptography has become a better comprehensive science and technology, its value and importance has been fully recognized, it is to study encryption and decryption. Stream Cipher cryptography as an important part, and select the key sequence determines the sequence of password security. Therefore, further study of the key stream sequence help enhance the safety performance of stream ciphers.In the process of study stream ciphers,it is important to find the key measure of the strength of the flow indicators. Some scholars found a measure of the strength of the key sequence indicators: linear complexity and k-error linear complexity.In this paper,we use Games-Chan algorithm,the cube theory and a construction approach to research cipher key sequence of linear complexity and k-error linear complexity of the general distribution. We obtained the follow conclusion:1. Study the 2ⁿ-periodic binary sequences with 4-error linear complexity as the first descent point and 8-error linear complexity as the second descent point, and analyze the relationship between the first and second descent point, and deduce the full count formula of satisfied this condition.2. Study the relationship and count formula of the binary sequences with 2-error linear complexity as the first descent point, 4-error linear complexity as the second descent point and 8-error linear complexity as the third descent point, hat satisfies the condition 0=L₈(s^s)<L₄(s^s)<L₂(s^s)<2ⁿ sequence and nature, and the data obtained by programming, for verification.3. By programming and experimental data verified third descent point formula of 2ⁿ-periodic sequences with k-error linear complexity.