Further Results on the Decomposition of an NFSR Into the Cascade Connection of an NFSR Into an LFSR

Nonlinear feedback shift registers (NFSRs) are widely used in stream cipher design as building blocks. In this paper, we study the problem of decomposing an NFSR into the cascade connection of an NFSR into a linear feedback shift register (LFSR), which is a kind of concatenation of an NFSR and LFSR. A necessary and sufficient condition for such decomposition is provided and other algebraic properties about such decomposition are also studied. Based on these theoretical results, a binary decision diagram (BDD)-based algorithm for such decomposition is proposed. Compared with the previous algorithm proposed by Ma et al., our algorithm can find more accurate candidate LFSR and the algebraic properties presented in this paper guarantee that the memory requirement during our verification is linear in the size of the BDD of the NFSRs characteristic function.