@Article{cmc.2020.06702,
AUTHOR = {Bo Gao, Xuan Liu, Xiaobo Wu, Shudong Li, Zhongzhou Lan, Hui Lu, Boyan Liu},
TITLE = {Stability of Nonlinear Feedback Shift Registers with Periodic Input},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {62},
YEAR = {2020},
NUMBER = {2},
PAGES = {833--847},
URL = {http://www.techscience.com/cmc/v62n2/38279},
ISSN = {1546-2226},
ABSTRACT = {The stability of Non-Linear Feedback Shift Registers (NFSRs) plays an 
important role in the cryptographic security. Due to the complexity of nonlinear systems 
and the lack of efficient algebraic tools, the theorems related to the stability of NFSRs are 
still not well-developed. In this paper, we view the NFSR with periodic inputs as a 
Boolean control network. Based on the mathematical tool of semi-tensor product (STP), 
the Boolean network can be mapped into an algebraic form. Through these basic theories, 
we analyze the state space of non-autonomous NFSRs, and discuss the stability of an 
NFSR with periodic inputs of limited length or unlimited length. The simulation results 
are provided to prove the efficiency of the model. Based on these works, we can provide 
a method to analyze the stability of the NFSR with periodic input, including limited 
length and unlimited length. By this, we can efficiently reduce the computational 
complexity, and its efficiency is demonstrated by applying the theorem in simulations 
dealing with the stability of a non-autonomous NFSR.},
DOI = {10.32604/cmc.2020.06702}
}