Research On 2-adic Complexity Of Several Types Of Pseudo-random Sequences

The security of the stream cipher system depends heavily on the pseudo-random nature of the key stream sequence.The index system to measure the pseudo-random nature of the sequence includes period,autocorrelation,linear complexity and so on.In recent years,2-adic complexity has been proposed as the minimum series of a class of nonlinear shift registers corresponding to the sequence,and it is an important security index to measure the ability of the key stream sequence to resist attacks from the rational approximation algorithm.In this paper,based on the theory of polynomials,index sum theories over finite fields,and the theory of generalized cyclotomy on residual class rings,this paper studies the 2-adic complexity of several types of second-order Ding-Helleseth generalized cyclotomic sequences with periodicity.These sequences have been proved to have good autocorrelation properties and linear complexity.In this paper,the 2-adic complexity of the sequence is calculated by analyzing the properties of the Gaussian period and the determinant of the circulant matrix of the sequence studied,and verified by computer simulation results.The results show that the 2-adic complexity of these types of sequences is at least pq-q-1,and the 2-adic complexity of some of them can even reach the best.This shows that they are sufficient to resist attacks from rational approximation algorithms and achieve the security as a stream cipher key stream.