Vol.62, No.2, 2020, pp.833-847, doi:10.32604/cmc.2020.06702
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: gaobonmghhht@163.com;
Shudong Li. Email: lishudong@gzhu.edu.cn.
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
Non-Linear Feedback Shift Register (NFSR), Boolean Network (BN), SemiTensor Product (STP), transition matrix, stability, periodic input.