Reducing the Dynamical Degradation of Digital Chaotic Maps with Time-Delay Linear Feedback and Parameter Perturbation

Digital chaotic maps are not secure enough for cryptographic applications due to their dynamical degradation. In order to improve their dynamics, in this paper, a novel method with time-delay linear feedback and parameter perturbation is proposed. The delayed state variable is used to construct the...

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Bibliographic Details
Published in:Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-12
Main Authors: Liu, Bocheng, Liu, Lingfeng, Xiang, Hongyue
Format: Article
Language:English
Subjects:
Chaos theory
Complexity
Correlation analysis
Cryptography
Degradation
Delay
Digital mapping
Feedback
Methods
Parameters
Perturbation
Pseudorandom
State variable
Trajectory analysis
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Summary:Digital chaotic maps are not secure enough for cryptographic applications due to their dynamical degradation. In order to improve their dynamics, in this paper, a novel method with time-delay linear feedback and parameter perturbation is proposed. The delayed state variable is used to construct the linear feedback function and parameter perturbation function. This method is universal for all different digital chaotic maps. Here, two examples are presented: one is 1D logistic map and the other is 2D Baker map. To show the effectiveness of this method, we take some numerical experiments, including trajectory and phase space analysis, correlation analysis, period analysis, and complexity analysis. All the numerical results prove that the method can greatly improve the dynamics of digital chaotic maps and is quite competitive with other proposed methods. Furthermore, a simple pseudorandom bit generator (PRBG) based on digital Baker map is proposed to show its potential application. The proposed PRBG is completely constructed by the digital chaotic map, without any other complex operations. Several numerical results indicate that this PRBG has good randomness and high complexity level.
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/4926937