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A novel method for reconstructing period with single input in NFSR

Author

Listed:
  • Gao, Bo
  • Liu, Xuan
  • Lan, Zhongzhou
  • Fu, Rongrong

Abstract

Non-Linear Feedback Shift Registers (NFSRs) are a generalization of Liner Feedback Shift Registers (LFSRs). The study of NFSR sequence helps to analyze the cryptographical security of NFSR-based stream cipher. Due to lack of efficient algebraic tools, the period of NFSR still remains an open crucial theoretical problem. In this paper, we view the NFSR as a Boolean network (BN), so that the study about the period of NFSR can be viewed as the study about period of BN. Furthermore, based on the mathematical tool of semi-tensor product (STP), a Boolean network can be mapped into an algebraic form. For these, we put forward a method for reconstructing the period of NFSR with single input. Especially, we propose a procedure to choose the controlled states and steer the controlled states from initial state to desirable one. At last, the general derivation is exemplified by numerical simulations for a kind of NFSR.

Suggested Citation

  • Gao, Bo & Liu, Xuan & Lan, Zhongzhou & Fu, Rongrong, 2018. "A novel method for reconstructing period with single input in NFSR," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 36-40.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:36-40
    DOI: 10.1016/j.chaos.2018.01.012
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    References listed on IDEAS

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    1. Gao, Bo & Deng, Zheng-hong & Zhao, Da-wei & Song, Qun, 2017. "State analysis of Boolean control networks with impulsive and uncertain disturbances," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 187-192.
    2. Li, Xianghua & Wang, Zhen & Gao, Chao & Shi, Lei, 2017. "Reasoning human emotional responses from large-scale social and public media," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 182-193.
    3. Chao Gao & Zhen Wang & Xianghua Li & Zili Zhang & Wei Zeng, 2016. "PR-Index: Using the h-Index and PageRank for Determining True Impact," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-13, September.
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    Cited by:

    1. Gao, Bo & Liu, Xuan & Lan, Zhong-Zhou & Hong, Jie & Zhang, Wenguang, 2021. "The evolution of cooperation with preferential selection in voluntary public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    2. Zhe Gao & Jun-e Feng, 2022. "Research Status of Nonlinear Feedback Shift Register Based on Semi-Tensor Product," Mathematics, MDPI, vol. 10(19), pages 1-14, September.
    3. Gao, Bo & liu, Xuan & Hou, Shuxia & Jia, Danyang & Du, Mingjing, 2019. "Resolving public goods dilemma by giving the poor more support," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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