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Linearization of multi-valued nonlinear feedback shift registers

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Abstract

Nonlinear feedback shift registers (NFSRs) have been used in many stream ciphers for cryptographic security. The linearization of NFSRs is to describe their state transitions using some matrices. Such matrices are called their state transition matrices. Compared to extensive work on binary NFSRs, much less work has been done on multi-valued NFSRs. This paper uses a semi-tensor product approach to investigate the linearization of multi-valued NFSRs, by viewing them as logical networks. A new state transition matrix is found for a multi-valued NFSR, which can be simply computed from the truth table of its feedback function. The new state transition matrix is easier to compute and is more explicit than the existing results. Some properties of the state transition matrix are provided as well, which are helpful to theoretically analyze multi-valued NFSRs.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Haiyan Wang, Jianghua Zhong & Dongdai Lin

Authors
  1. Haiyan Wang
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  2. Jianghua Zhong
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  3. Dongdai Lin
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Corresponding author

Correspondence to Haiyan Wang.

Additional information

This research is supported by the National Science Foundation of China under Grant Nos. 61379139 and 11526215 and the “Strategic Priority Research Program” of the Chinese Academy of Sciences, under Grant No. XDA06010701.

This paper was recommended for publication by Editor DENG Yingpu.

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Cite this article

Wang, H., Zhong, J. & Lin, D. Linearization of multi-valued nonlinear feedback shift registers. J Syst Sci Complex 30, 494–509 (2017). https://doi.org/10.1007/s11424-016-5156-7

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  • DOI: https://doi.org/10.1007/s11424-016-5156-7

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