Construction And Analysis Of New Interleaved Sequences

Pseudo-random sequences are widely used in the fields of secure communication,spread spectrum communication,pseudo-code ranging,delay measurement,radar navigation,and signal synchronization currently.The binary pseudo-random sequence can be used as the key stream sequence of the stream cipher,and the security strength of the stream cipher algorithm depends entirely on the nature of the key stream sequence.In essence,the pseudo-random sequence has the properties of periodicity,balance,and autocorrelation,linear complexity and2-adic complexity.Therefore,the study of the pseudo-random nature of the key stream sequence is the central topic of stream ciphers.So the theoretical study of pseudo-random sequences is mainly divided into two aspects: one is the construction of sequence,using interleaved techniques,circles and other methods to generate sequences;On the other hand,the analysis of the constructed sequences ensures that the sequence complies with cryptographic requirements and is used.The work of this paper is mainly divided into three parts.Firstly,using the interleaved technique,two kinds of binary interleaved sequences with the optimal autocorrelation values are constructed.Then,we investigate their linear complexities and give the exact values to determine whether these sequences meet the requirements of cryptography.Secondly,we calculated the linear complexity of two classes of interleaved sequences,and the minimal polynomial of the sequence are given.It is proved that the sequence is safe under certain conditions.Finally,we given the general formula of the interleaved sequence to calculate its autocorrelation values.The main research results are:(1)Taking the binary sequence pairs with optimal autocorrelation as the column sequence to interleave,so we obtain two types of binary interleaved sequences with optimal autocorrelation and period of 2N,and give their autocorrelation function value distributions and the linear complexity;(2)We calculate the linear complexity of two classes of interleaved sequences with low autocorrelation。The results show that both sequences have high linear complexity,which can effectively resist the attack of B-M algorithm;(3)We given the general method of the interleaved sequence with period of 4N to calculate its autocorrelation values,and verified by examples;(4)Using Magma software to write the program to verify theoretical results of the above calculation.The results show that theoretical values and experimental values are consistent.