The Linear Complexity Of Two Class Of Binary Sequences

The linear complexity of pseudorandom sequences has been a significant research topic.In recent decades,many scholars have studied and constructed many pseudorandom sequences with great linear complexity.Research on the application of Fermat Quotient and its extension function in cryptography is a new research direction in 2011,which has attracted the attention to many scholars.The study of linear complexity of sequence has not only important theoretical significance,but also practical application value.The specific results are as follows:(1)In this thesis,we give the definition of generalized euler quotient.discusses some properties of the generalized Euler quotient,A class of pseudorandom binary sequences is constructed by using generalized Euler quotients.especially,in the case of p(odd prime)mod 4 remainder 3,the linear complexity is only 1 less than the period.(2)Highest level sequence of generalized Euler quotient is constructed and the linear complexity is studied.(3)Based on the method of number theory.a class of pseudorandom sequence is constructed.the balance of the sequence is investigated.and the linear complexity is obtained.