Research On Error Linear Complexity Of Periodic Sequences Based On Cube Theory

Cryptography can protect our secret information and provide the key theory and technology for the information security, now it has become an important means for assisting the development of information technology. Sequence cipher (Stream cipher) which belongs to the symmetric cipher of the cryptography system, plays a significant role in the cryptography theoretical system.The linear complexity and stability of sequence cipher are important indicators for measure its strength. When a small number of elements in the sequence are changed, the linear complexity of sequences won’t decline sharply, this means it has a high k-error linear complexity. So the k-error linear complexity is an important indicator to measure the stability of the sequence. Also, because the cube theory can express the change of sequence more clearly, so it plays an important role in the study of the k-error linear complexity of stream cipher. The main work of this thesis is to do some research about the periodic sequences combining with the cube theory, and the main results are as follow:1. Using the standard cube decomposition method, based on the Games-Chan algorithm, combining with the cube-theory and screening method, analyzed the binary periodic sequence which set 4-error as the first descent point and 12-error as the second descent point, and obtained the relevant properties. Finally, we got the formula which matching the condition L12(s(n))<L10 (s(n))=L4 (s(n))<L2 (s(n))=L(s(n)).2. Combining with the cube-theory and the Games-Chan algorithm, the k-error linear complexity of the binary periodic sequence is constructed by using the method of construction. The binary periodic sequences with 2,6 and 8 as the descent point has been constructed, which matching the conditions of 0=L8(s(n))<L6(s(n))<L4(s(n))= L2(s{n))<L(s(n)).3. The related properties of k-error linear complexity of binary sequence with period 2" has been researched by using standard cube decomposition and screening method. Then according to the k-error cube decomposition, discussed the formula of calculating the second decline. Finally, verified the second drop point formula by computer programming, and the result shows that the formula is correct.