Linear complexity of a type of clock-controlled sequence

A new type of cascaded clock-controlled system is proposed. There are r + 1 linear feedback shift registers (LFSRs) of length n in the system if the degree of cascade connection is r. It is proved that for an rth degree cascade the output sequences have linear complexity n σri=0 (2n − 1)i. period (2n −1)r+1 and good statistical properties. Such a model can generate key stream sequences of stream ciphers in computer applications.