The Construction Of De Bruijn Sequences Based On Cascade Connection Register And Pure Cycling Register

The sequences have been widely used in cryptography, communication and other se-curity domains. With the development of the related attacks and algebraic attacks, NFSR sequences replacing LFSR sequences is the focus of the research of sequences ciphers. The de Bruijn sequences are special and important NFSR. sequences, and the research of them is a hot topic. In this thesis, we mainly study two methods of constructing de Bruijn sequences. The first one is based on cascade connection. We firstly introduce the mutual transformation between the parallel connection and cascade connection of LFSR, then ac-cording to this relationship, a new cascade connection of an NFSR into an LFSR is given.The cycle structure of cascade connection register and a method to determine the smaller cycles are provided. At last we deduce the method to find the conjugate pairs and generate new de Bruijn sequences. The second construction is beased on pure cycling register. First of all, we study the cycle structure of pure cycling register.We provide the relation between the number of pure cycling register cycles and cyclotomic coset numbers. Then we use the insertion method to construct the de Bruijn sequences. The results of generating de Bruijn sequences in this thesis enrich the research of de Bruijn sequences, and have important application.