Applications Of FCSR And Its Sequence In Stream Cipher

Applications of Feedback-with-Carry-Shift-Register and its sequence in stream ciphei are discussed in this thesis. To begin with, theory of FCSR and its sequence is summarized and investigated. Furthermore, emphasis is placed on the vaule of 2-adic complexity. A conclusion is drawn that the vaule lies in the relation between 2-adic complexity and lineai complexity of a same seqence. Fact that there exists sequence with high linear complexity but low 2-adic complexity is given and analyzed. The value of 2-adic complexity in cryptanalysis can be directly drawn from the very fact. A series of problems are opened based on the value and discussions are done in various depth. Some good results are obtained in these problems such as the 2-adic complexity distribution of periodic sequences and the stability of 2-adic complexity. The value of FCSR in stream cipher design is discussed at the same time. In the last section of this thesis, generations of FCSR and possible applications in other domain are summarized.