Stability of (n, k) nonlinear feedback shift registers

Abstract

In this paper, the (n, k) nonlinear feedback shift register (NLFSR) is regarded as a Boolean network (BN). Semi-tensor product (STP) of matrices is used to convert (n, k) NLFSR into an equivalent algebraic equation. Based on STP of matrices, a novel way is proposed to study stability of (n, k) NLFSR and the periodicity of (n, k) NLFSR. First, the stability of the (n, k) NLFSR is investigated, and we propose an algorithm to judge the stability of an (n, k) NLFSR. Second, we reveal relationship between the minimal period of output sequence of a cycle for an (n, k) NLFSR and the length of the cycle. Third, we investigate the period of (n, k) NLFSR. Some existing methods can only be used to investigate the cycle of the (n, k) NLFSR, while in this paper, we can simultaneously investigate stability of an (n, k) NLFSR and the period of (n, k) NLFSR by using the method of STP.