Review of Feedback with Carry Shift Register

Feedback with carry shift registers (FCSRs) is an arithmetic analogue of linear feedback shift registers (LFSRs). FCSRs has been extensively concerned for three reasons: 2-adic number theory can be used as FCSRs’s theoretical foundation; sequences with good statistical properties can be derived; another important standard to judge whether a sequence is safe or not has been proposed. In this paper the basic properties of FCSRs in the three above-mentioned fields are described. The research direction and future development of the technology are summarized in the end.