关键词: 周期序列, 线性复杂度, k错线性复杂度, 方体理论

Abstract: The linear complexity and the k-error linear complexity are important indicators to measure the strength of stream ciphers, and the higher of those two indicators could resistance the plaintext attack than others, generally. In order to research the sequence of stream cipher, this paper uses a structural approach and cube theory in investigating the 2ⁿ-periodic binary sequences with 6-error linear complexity as the second descent point, and gets all the possible value forms of 6-error linear complexity. This paper analyzes and derives the complete counting functions of 2ⁿ-periodic binary sequences with the given first descent point 2-error linear complexity and second descent point 6-error linear complexity. With the method proposed in this paper, other second or third descent point of the k-error linear complexity for 2n-periodic binary sequences can be obtained.

Key words: periodic sequence, linear complexity, k-error linear complexity, cube theory