Research On Pseudo-Random Properties Of Interleaved Sequences

Pseudo-random sequences are widely used in secret communication,spread spectrum communication system,pseudo-random code ranging,delay measurement,radar navigation and signal synchronization currently.The binary Pseudo-random sequences can be used as key stream sequences in the stream cipher,the safety strength of stream cipher algorithm totally depend on the randomness and unpredictability.Therefore,the research on pseudo-random property of the key stream sequence is the key issue of stream cipher.The theoretical research of pseudo-random sequence mainly includes the construction of new sequence and the analysis of pseudo-random properties of sequences.There are two goals in the construction of pseudo-random sequence:one is to construct a sequence with two-valued auto-correlation,three-valued auto-correlation or with low auto-correlation;the other is to construct a sequence with high linear complexity.In addition,the pseudo-random properties of a sequence also includes periodicity,balance,run-length distribution and so on.The work of this paper is divided into two parts.Firstly,we construct two types of binary interleaved sequences with low auto-correlation by using the sequence interleaving technique,secondly,we investigate their linear complexities and give the exact values to determine whether these sequences meet the requirements of cryptography.The main research results are:(1)This paper takes the sample sequences and complement sequence of the binary ideal auto-correlation sequence with period of N=3mod4 as the column sequence to interleave,so we obtain two types of binary interleaved sequences with low auto-correlation of period of 4N,and give their auto-correlation function value distributions;(2)This paper takes the Legendre sequence with period of N=3mod8 as the base sequence of interleaved sequence,and we calculate the linear complexity of two sequences when the shift(?)the results show that both sequences have high linear complexity,which can effectively resist the attack of B-M algorithm;(3)This paper uses Magma software to write the program to verify theoretical results that we calculate above.The results show that theoretical values and experimental values are consistent.