Word-oriented Linear Feedback Shift Registers: σ−LFSRs

A new family of word-oriented linear feedback shift registers named σ−LFSRs is presented and analyzed in this paper. σ−LFSRs are constructed by few fundamental instructions so that they have high efficiency. Comparing with the theory of classical LFSRs, we research on the basic properties of σ−LFSRs, such as minimal polynomial, state graph, coordinate sequence, and the properties of primitive σ−LFSRs etc. We also give an algorithm to search for primitive σ−LFSRs and obtained many primitive σ−LFSRs with special properties such as HHZ-1 or HHZ-2. At the same time, we apply σ−LFSRs on the construction of RNGs and stream ciphers. Our results show that σ−LFSRs with high efficiency and good pseudorandom properties can be used as building blocks in the design of modern stream ciphers. 2000 Mathematics Subject Classification: 11T71, 11T06, 20G40, 15A33