On Decomposition of an NFSR into a Cascade Connection of Two Smaller

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.