Constructions And Properties Analysis Of Several Classes Of Pseudo-random Sequences

Pseudo-random sequences are widely used in digital communications,radar ranging,cryptography,information hiding and other fields.Pseudo-random sequences constructed by algebraic methods have low correlation and high linear complexity,which have been hot research topics of sequence design in recent years.In this thesis,we focus on the construction and properties of pseudo-random sequences.Using the tools in number theory such as cyclotom and Euler quotient,several classes of pseudo-random sequences are constructed and their cryptographic properties are analyzed.The main results are listed as follows:1.By using the Euler quotient modulus pq,a class of r-ary sequence with period pq2 is constructed.The linear complexity and minimal polynomial of the new sequence are determined.The results show that the new defined r-ary sequence has high linear complexity.Therefore,it can resist B-M algorithm attack.2.Two class of balanced quaternary sequence pairs with periods N≡5(mod 8)are constructed by using cyclotom of order 4.And the cross-correlation values of those sequence pairs are calculated.The results show that maximum outof-phase autocorrelation magnitude of those sequences pairs are no more than(?).Therefore,these two class of sequence pairs are almost optimal.3.Based on additive and multiplicative characters over Galois rings,a family of sequences of period pk-1 with low correlation value is constructed.The new constructed sequence family has family size(M-1)(pk-1)rpkr(e-1)and alphabet size Mpe.At the same time,the upper bound of the correlation values of the newly constructed sequence family is calculated.