A generic method for investigating nonsingular Galois NFSRs

Let n be a positive integer. An n -stage Galois NFSR has n registers and each register is updated by a feedback function. Then a Galois NFSR is called nonsingular if every register generates (strictly) periodic sequences, i.e., no branch points. In this paper, a generic method for investigating nons...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2022-02, Vol.90 (2), p.387-408
Main Authors: Wang, Xiao-Juan, Tian, Tian, Qi, Wen-Feng
Format: Article
Language:English
Subjects:
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
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Summary:Let n be a positive integer. An n -stage Galois NFSR has n registers and each register is updated by a feedback function. Then a Galois NFSR is called nonsingular if every register generates (strictly) periodic sequences, i.e., no branch points. In this paper, a generic method for investigating nonsingular Galois NFSRs is provided. Two fundamental concepts that are standard Galois NFSRs and the simplified feedback function of a standard Galois NFSR are proposed. Based on the new concepts, a sufficient condition is given for nonsingular Galois NFSRs. In particular, for the class of Galois NFSRs with linear simplified feedback functions, a necessary and sufficient condition is presented.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-021-00982-5