Research On Linear Complexity Of Sequences Based On The Cube Theory

Cryptography is an ancient integrated discipline, which is full of mysterious. It is not limited to the mathematics and computer science, but surpasses the traditional academic disciplines.Stream cipher plays an important role in modern cryptography. The security of Stream cipher depends on its key stream sequences. The linear complexity is one of the most important measurement of key stream sequences strength. However, a sequence with high linear complexity is not a necessarily safe key stream sequence.Thus another important measurement was introduced, which called the k-error linear complexity.After study the cube theory, we research the linear complexity of 2n-periodic binary sequences, as well as the k-error linear complexity. The main results are as follows:1.On the basis of the cube theory, which is based on the Games-Chan algorithm,we investigate the decomposition of 2n-periodic binary sequences. Especially, we investigate the standard cube decomposition, which the result is unique.2.Based on the cube theory, we investigate the 2n-periodic binary sequences, in which the first descent point is 2-error linear complexity and the second descent point is 8-error linear complexity. First, we analyze the relationship between the first descent point and the second descent point, and give all the possible values of the2-error linear complexity and the 8-error linear complexity. Next, we derive the complete counting functions of the 2n-periodic binary sequences, with 2-error linear complexity as the first descent point and 8-error linear complexity as the second descent point. Meanwhile, all the results are proved by the computer program.3.Based on the cube theory, we investigate some properties of the 2n-periodic binary sequences, the Hamming weight of which is thirteen, with 1-error linear complexity as the first descent point, 3-error linear complexity as the second descent point and 13-error linear complexity as the third descent point. And we derive the complete counting functions of these 2n-periodic binary sequences. Meanwhile, all the results are proved by the computer program.