The Cryptological Properties Of N-ary Feedback With Carry Shift Register

The cryptological properties of the N-ary Feedback-with-Carry-Shift-Register (N-FCSR) Sequences are diseussed in this thesis, N-ary Feedback-with-Carry-Shift-Register Sequences are researched with respect to memory requirements, initial loading, Period, graph of states, complexity and distributional properties of their output sequences. Many parallels with the theory of 2-ary Feedback-with-Carry-Shift-Register(FCSR) Sequences are presented. This thesis is based on the background of the intrinsic relationship among N-FCSR sequences, N-adic numbers and rational numbers with odd Prime numbers as denominators. Some new cryptological properties of the N-FCSR sequences are Proved. The relation between the connection number of N-FCSR and the graph of the states is depicted, the number of the periodic state is got, the existence of the maximum possible circle is proved and the length of the circle is got; A new sufficient and necessary condition under which a N-FCSR sequence is a periodic sequence is proved; the properties of the summation cipher is also analyzed in the paper and we get some new results.