On degeneracy problem of NFSRs via semi-tensor product
Xinyu Zhao, Biao Wang, Shuqian Zhu, Jun‐e Feng · 2020
The degeneracy problem of nonlinear feedback shift registers (NFSRs) is investigated in this paper. A new method for finding sub-families included in a family of NFSR sequences is proposed. First, the algebraic form of Fibonacci NFSR is proposed by viewing the NFSR as a Boolean network. Some properties of the algebraic expression are provided. Then, the observability of NFSRs is defined and the observability matrix is constructed, based on some explicit forms two algorithms for obtaining the observability matrix are obtained. A way to find sub-families of the given NFSR is derived and some sufficient and necessary conditions are obtained. Finally, an example is presented to depict the theoretical results.