On Decomposition of an NFSR into a Cascade Connection of Two Smaller, by Tian Tian and Wen-Feng Qi

Nonlinear feedback shift registers (NFSRs) are an important type of sequence generators used for building stream ciphers. The shift register used in Grain, one of eSTREAM finalists, is a cascade connection of two NFSRs, which is also known as nonlinear product-feedback shift registers proposed in 1970. This paper provides a series of algorithms to decompose a given NFSR into a cascade connection of two smaller NFSRs. By decomposing an NFSR into a cascade connection of two smaller NFSRs, some properties regarding cycle structure of the original NFSR could be known.