On a class of isomorphic NFSRs

Two nonlinear feedback shift registers (NFSRs) of the same stage number are called isomorphic if their state diagrams are of the same cycle structure. In this paper, we focus on a class of isomorphic NFSRs that are derived from a previous work (Zhao et al. in Des Codes Cryptogr 86(12):2775–2790, 201...

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Published in:Designs, codes, and cryptography codes, and cryptography, 2020-06, Vol.88 (6), p.1205-1226
Main Authors: Zhao, Xiao-Xin, Zheng, Qun-Xiong, Wang, Zhong-Xiao, Qi, Wen-Feng
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Language:English
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Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Nonlinear feedback
Shift registers
State (computer science)
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description Two nonlinear feedback shift registers (NFSRs) of the same stage number are called isomorphic if their state diagrams are of the same cycle structure. In this paper, we focus on a class of isomorphic NFSRs that are derived from a previous work (Zhao et al. in Des Codes Cryptogr 86(12):2775–2790, 2018). First, we give an explicit formula for counting this class of isomorphic NFSRs, which generalizes the previous result given by Rozhkov (Discret Math Appl 20(2):127–155, 2010). Then we study the inherent relation of the affine sub-families among these NFSRs. The obtained result shows that the analysis of the affine sub-families of these NFSRs could be reduced to the analysis of the affine sub-families of a specific NFSR. Finally, we present a Galois representation of some specific isomorphic NFSRs whose periods of the output sequences are controllable.
doi_str_mv 10.1007/s10623-020-00742-x
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subjects Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Nonlinear feedback
Shift registers
State (computer science)
title On a class of isomorphic NFSRs
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