Open Access
ARTICLE
Stability of Nonlinear Feedback Shift Registers with Periodic Input
Bo Gao1, *, Xuan Liu1, Xiaobo Wu1, *, Shudong Li2, *, Zhongzhou Lan1, Hui Lu2, *, Boyan Liu1
1 School of Computer Information Management, Inner Mongolia University of Finance and Economics, Hohhot, 010051, China.
2 Cyberspace Institute of Advanced Technology, Guangzhou University, Guangzhou, 510006, China.
3 School of Electrical and Electronic Engineering, University of Manchester, Manchester M13 9PL, UK.
* Corresponding Authors: Bo Gao. Email: ;
Shudong Li. Email: .
Computers, Materials & Continua 2020, 62(2), 833-847. https://doi.org/10.32604/cmc.2020.06702
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.
Keywords
Cite This Article
B. Gao, X. Liu, X. Wu, S. Li, Z. Lan
et al., "Stability of nonlinear feedback shift registers with periodic input,"
Computers, Materials & Continua, vol. 62, no.2, pp. 833–847, 2020. https://doi.org/10.32604/cmc.2020.06702