Nonsingularity of Trivium-like cascade FSRs over finite fields via semi-tensor product

In stream cipher designing, nonsingularity is a crucial requirement to ensure that the feedback shift registers (FSRs) do not produce keys that are equivalent to one another. This study uses a semi-tensor product to examine the nonsingularity of Trivium-like cascade FSRs over a finite field. The Tri...

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Bibliographic Details
Published in:International journal of control 2024-03, Vol.97 (3), p.589-599
Main Authors: Gao, Zhe, Feng, Jun-e
Format: Article
Language:English
Subjects:
Algorithms
Encryption
Feedback
Fields (mathematics)
Logical networks
Mathematical analysis
nonsingularity
semi-tensor product
Shift registers
Tensors
Trivium-like cascade FSRs
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Summary:In stream cipher designing, nonsingularity is a crucial requirement to ensure that the feedback shift registers (FSRs) do not produce keys that are equivalent to one another. This study uses a semi-tensor product to examine the nonsingularity of Trivium-like cascade FSRs over a finite field. The Trivium-like cascade FSRs are expressed algebraically using the semi-tensor product, allowing them to be viewed as logical networks and introducing a novel state transition matrix. Several necessary and sufficient conditions for the nonsingularity of FSRs and Trivium-like cascade FSRs over a finite field are established by dividing the structural matrices of feedback functions into different parts. These findings are also applicable to binary FSRs and binary Trivium-like cascade FSRs.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2022.2160825