An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption

Ding, Dawei; Wang, Wei; Yang, Zongli; Hu, Yongbing; Wang, Jin; Wang, Mouyuan; Niu, Yan; Zhu, Haifei

doi:10.1016/j.chaos.2023.113841

Cited by 29 publications

(11 citation statements)

References 54 publications

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“…A bifurcation diagram is a tool to visualize the randomness of chaotic systems, and Lyapunov exponents (LE) are an important index to evaluate the chaotic identity of dynamic systems [ 1 ]. In this paper, the bifurcation diagram and Lyapunov exponent diagram of the above four one-dimensional chaotic maps are given.…”

Section: N -Dimensional Chaotic Modelmentioning

confidence: 99%

“…In recent years, nonlinear theory has received more and more attention. As a typical branch of nonlinear theory, chaos theory has been widely used in mathematics, medicine, physics, computer science, astronomy, ecology, and other scientific and engineering fields since its emergence [ 1 ]. A nonlinear system exhibiting chaotic behavior should possess high sensitivity, ergodicity, unpredictability, and initial value sensitivity, as per Devaney’s definition [ 2 ].…”

Section: Introductionmentioning

confidence: 99%

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An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images

Yang,

Chang,

Feng

et al. 2024

Entropy

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The drawbacks of a one-dimensional chaotic map are its straightforward structure, abrupt intervals, and ease of signal prediction. Richer performance and a more complicated structure are required for multidimensional chaotic mapping. To address the shortcomings of current chaotic systems, an n-dimensional cosine-transform-based chaotic system (nD-CTBCS) with a chaotic coupling model is suggested in this study. To create chaotic maps of any desired dimension, nD-CTBCS can take advantage of already-existing 1D chaotic maps as seed chaotic maps. Three two-dimensional chaotic maps are provided as examples to illustrate the impact. The findings of the evaluation and experiments demonstrate that the newly created chaotic maps function better, have broader chaotic intervals, and display hyperchaotic behavior. To further demonstrate the practicability of nD-CTBCS, a reversible data hiding scheme is proposed for the secure communication of medical images. The experimental results show that the proposed method has higher security than the existing methods.

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Section: N -Dimensional Chaotic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images

Yang,

Chang,

Feng

et al. 2024

Entropy

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“…Equation ( 10) is a polynomial. Equation (11) is the Jacobi matrix of equation (10). Equation (12) yields the Jacobi matrix from observation 1 to observation n. Suppose…”

Section: Proof Of Reasonablenessmentioning

confidence: 99%

“…Although the low-dimensional chaotic model has the advantages of simple structure and easy calculation, with the surge of computer computing power, the complexity of the low-dimensional chaotic model as well as the limited parameter range can no longer meet the security requirements. And the multidimensional chaotic model has a higher complexity, which has attracted extensive attention from scholars [10][11][12][13]. Although the multidimensional chaotic map has better chaotic characteristics, the dynamics degradation problem will still occur inevitably in the limited precision.…”

Section: Introductionmentioning

confidence: 99%

A two-dimensional chaotic model and its application in image encryption

Lei,

Liu

2024

Phys. Scr.

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In this paper, we propose a rule that follows a time-varying delay construction method and construct a time-varying delay scheme based on it. This construction scheme is also combined with a polynomial to obtain a novel two-dimensional chaotic model. Both mathematical analysis and experimental results show that the model satisfies the chaos condition. Good experimental results have been achieved in complexity analysis, information entropy analysis, and Auto-correlation analysis, and have certain competitiveness. The obtained chaotic model is also applied to the image encryption algorithm. The experimental results show that the encryption algorithm has high security and can effectively resist noise attacks, shear attacks, differential attacks.

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“…However, SVD will introduces a faster increase in computational complexity faster as the matrix dimension grows. The remaining two methods share similarities with the approach proposed by Dawei Ding [2]. Both involve configuring the coefficient matrix as an upper triangular matrix and achieving Lyapunov exponent control by setting up diagonal elements.…”

Section: Introductionmentioning

confidence: 99%

Construction Algorithm of Non-degenerate Complex Domain Chaotic System with Application on PRNG

Dai,

Wang,

Han

et al. 2024

Preprint

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Based on the theory of eigenvalue estimation, this paper proposes a construction algorithm for N-dimensional discrete non-degenerate chaotic system defined in complex domain. Through theoretical analysis, it's proved that the system constructed by the algorithm not only exhibits non-degenerate properties in complex domain, but also maintains non-degeneracy for its real and imaginary components. In order to verify the effectiveness and feasibility, the example of a three-dimensional discrete complex domain chaotic system is taken. The dynamic properties of this system is thoroughly analyzed including the chaotic generation mechanism, Lyapunov exponents (LEs), chaotic phase diagram and sequence statistical characteristics. The algorithm reversely manages the positional relationship between the Gerschgorin disk of the coefficient matrix and the unit circle, ensuring all eigenvalues fall within the desired range. Subsequently, a non-degenerate chaotic system is constructed in which all LEs are positive. Finally, the algorithm is applied to a Pseudo-Random Number Generator (PRNG), and various indicators are experimentally analyzed. The results demonstrate that the constructed PRNG exhibits favorable statistical characteristics and is excellent for application in secure communication.

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An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption

Cited by 29 publications

References 54 publications

An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images

An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images

A two-dimensional chaotic model and its application in image encryption

Construction Algorithm of Non-degenerate Complex Domain Chaotic System with Application on PRNG

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