Study On Construction And Properties Of Pseudo-Random Sequences

Pseudo-random sequences have wide applications in cryptography, coding, spread spectrum communication and many other engineerings. Families of sequences for such applications are desired to have low autocorrelation, low cross-correlation, and large linear complexity. The author obtains main results as follows:(1) The relations between a difference-balanced d-form function and a cyclic difference set, a cyclic relative difference set and a cyclic divisible difference set are discussed. Some former results are deepened.(2) A new way to construct cyclic divisible difference sets is proposed.(3) The relation between a d-form p—ary sequence with ideal autocorrelation and a difference-balanced d-form function is investigated. The results show that, under certain conditions, a d-form p—ary sequence possesses ideal autocorrelation if and only if its corresponding d-form function is difference-balanced .(4) The autocorrelation and linear complexity of the some new generalized cyclotomic sequences with respect to p~2, which are suggested by Ding and Helleseth , are discussed. The results show that all of these sequences possess high linear complexity.(5) For the new generalized cyclotomic sequences of period pq suggested by Ding and Helleseth, autocorrelation function of the ones of order 2 and linear complexity of the ones of order 4 are calculated. The results show that the autocorrelation function is three-valued under certain conditions, and the linear complexity are large enough to prevent from the attacks of BM algorithm.(6) The linear complexity and minimal polynomials of two classes of Whiteman generalized cyclotomic sequences are calculated. The results show that most of these sequences have high linear complexity.(7) Some new binary sequences with large linear complexity and low autocorrelation are presented. These sequences can be obtained by modifying Jacobi sequences.