Grain-like structures with minimal and maximal period sequences

Wang, Zhongxiao; Zheng, Qun-Xiong; Zhao, Xiaoxin; Feng, Xun‐Li

doi:10.1007/s10623-020-00839-3

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…Zhong and Lin [19] gave strong results on uniqueness of cascade decomposition FSRð f Þ: * FSRðgÞ: . Additionally, the periods of sequences generated by the grain-like structures are studied [20][21][22][23][24].…”

Section: Iet Information Securitymentioning

confidence: 99%

Deciding Irreducibility/Indecomposability of Feedback Shift Registers Is NP-Hard

Wang

2024

IET Information Security

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Feedback shift registers (FSRs) are used as a fundamental component in electronics and confidential communication. A FSR f is said to be reducible if all the output sequences of another FSR g can also be generated by f and the FSR g costs less memory than f. A FSR is said to be decomposable if it has the same set of output sequences as a cascade connection of two FSRs. Two polynomial-time computable transformations from Boolean circuits to FSRs are proposed such that the output FSR of the first (resp. second) transformation is irreducible (resp. indecomposable) if and only if the input Boolean circuit is satisfiable. Through the two transformations, it is proved that deciding irreducibility (indecomposability) of FSRs is NP-hard. Additionally, FSRs are constructed to show that there exist infinitely many irreducible (resp. indecomposable) FSRs which are decomposable (resp. reducible).

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Section: Iet Information Securitymentioning

confidence: 99%

Deciding Irreducibility/Indecomposability of Feedback Shift Registers Is NP-Hard

Wang

2024

IET Information Security

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“…According to whether there is input, NFSRs can be divided into autonomous NFSRs and non-autonomous NFSRs. According to the research problems, in addition to stream cipher algorithm designs [17][18][19][20][21] and attacks [22,23], the theoretical study can be summarized into three parts: (1) equivalence and decomposition [24][25][26], irreducible NFSRs [27,28] and affine sub-families [14,29]; (2) nonsingularity [10,30,31]; (3) period [32][33][34] and de Bruijn sequences [35][36][37][38] and so on. However, due to the lack of suitable mathematical means, the research on NFSR still has a long way to go.…”

Section: Introductionmentioning

confidence: 99%

Research Status of Nonlinear Feedback Shift Register Based on Semi-Tensor Product

Gao

Feng

2022

Mathematics

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Nonlinear feedback shift registers (NFSRs) are the main components of stream ciphers and convolutional decoders. Recent years have seen an increase in the requirement for information security, which has sparked NFSR research. However, the NFSR study is very imperfect as a result of the lack of appropriate mathematical tools. Many scholars have discovered in recent years that the introduction of semi-tensor products (STP) of matrices can overcome this issue because STP can convert the NFSR into a quasi-linear form. As a result of STP, new NFSR research has emerged from a different angle. In view of this, in order to generalize the latest achievements of NFSRs based on STP and provide some directions for future development, the research results are summarized and sorted out, broadly including the modeling of NFSRs, the analysis of the structure of NFSRs, and the study of the properties of NFSRs.

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Generalized cycle joining method and its application to the construction of long-period Galois NFSRs

Pan,

Zhong,

Lin

2024

Des. Codes Cryptogr.

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Grain-like structures with minimal and maximal period sequences

Cited by 3 publications

References 9 publications

Deciding Irreducibility/Indecomposability of Feedback Shift Registers Is NP-Hard

Deciding Irreducibility/Indecomposability of Feedback Shift Registers Is NP-Hard

Research Status of Nonlinear Feedback Shift Register Based on Semi-Tensor Product

Generalized cycle joining method and its application to the construction of long-period Galois NFSRs

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