A novel method of constructing high-dimensional digital chaotic systems on finite-state automata*

An image encryption algorithm is proposed in this paper based on a new four-dimensional hyperchaotic system, a neural mechanism, a Galois field and an improved Feistel block structure, which improves the efficiency and enhances the security of the encryption algorithm. Firstly, a four-dimensional hyperchaotic system with a large key space and chaotic dynamics performance is proposed and combined with a cloud model, in which a more complex and random sequence is constructed as the key stream, and the problem of chaotic periodicity is solved. Then, the key stream is combined with the neural mechanism, Galois field and improved Feistel block structure to scramble and diffuse the image encryption. Finally, the experimental results and security analysis show that the encryption algorithm has a good encryption effect and high encryption efficiency, is secure, and can meet the requirements of practical applications.

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“…In addition, the histogram variance can be used to measure the uniformity of a histogram. [58,59] The definition is as follows:…”

Section: Safety Analysis 51 Histogram Analysismentioning

confidence: 99%

Neural-mechanism-driven image block encryption algorithm incorporating a hyperchaotic system and cloud model

Fang

Liu

et al. 2022

Chinese Phys. B

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“…3(c), only small parts of this system are in chaos. When the control parameter is within [5,18], the LE of the Lorenz map is positive, and the system is in chaos. In other regions, the LE jumps and changes randomly, which harms the practical application of chaos.…”

Section: Enhanced Lorenz Mapmentioning

confidence: 99%

“…[17] Secondly, chaos degradation may occur when chaotic behaviors are simulated in finite precision. Some extremely approached states may overlap and appear to be precision truncated, [18] which causes the chaotic behaviors that originally had infinite states to degrade to inevitable periodic behaviors. Thirdly, existing chaotic maps show chaotic behaviors only in limited regions.…”

Section: Introductionmentioning

confidence: 99%

Exponential sine chaotification model for enhancing chaos and its hardware implementation

Wang¹,

Li²,

Luo³

2022

Chinese Phys. B

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Chaotic systems have been intensively studied for their roles in many applications like cryptography, secure communications, nonlinear controls, etc. However, the limited complexity of existing chaotic systems weakens chaos-based practical applications. Designing chaotic maps with high complexity is attractive. This paper proposes the exponential sine chaotification model (ESCM), a method of using exponential sine function as a nonlinear transform model, to enhance the complexity of chaotic maps. To verify the performance of the ESCM, we firstly demonstrated it through theoretical analysis. Then, to exhibit the high efficiency and usability of ESCM, we applied ESCM to one-dimensional (1D) and multi-dimensional (MD) chaotic systems. The effects were examined by the Lyapunov exponent and found enhanced chaotic maps have much more complicated dynamics behaviors compared to their originals. To validate the simplicity of ESCM in hardware implementation, we simulate three enhanced chaotic maps using the digital signal processor (DSP). To explore the ESCM in practical application, we applied ESCM to image encryption. Results verified that the ESCM can make previous chaos maps competitive to usage in image encryption.

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“…Dissipative chaos widely exists in physical systems, such as Chua's circuit, [1] double pendulum, [2] ballistic Dirac fermion systems, [3] the Peyrard-Bishop-Dauxois DNA model, [4] and some artificial nonlinear systems. [5][6][7] In contrast to dissipative chaos, conservative chaos can only be found in some theoretical models in the fields of celestial mechanics, molecular dynamics and hydrodynamics, such as the Hénon-Heiles system describing the motion of a star in a cylindrically symmetric and gravitationally smooth galactic potential, [8] two coupled anharmonic oscillators associated with molecular dynamics, [9] coupled Bloch oscillator equations representing electronic excitations of molecular dimers, [10] and hydrodynamic pilotwave system. [11] So far, the existing results have shown that the conservative chaos can be generated by Hamiltonian systems [12,13] as well as thermostatted systems.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system

Li¹,

Chen²,

Wang³

et al. 2022

Chinese Phys. B

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The thermostatted system is a conservative system different from Hamiltonian systems, and has attracted much attention because of its rich and different nonlinear dynamics. We report and analyze the multiple equilibria and curve axes of the cluster-shaped conservative flows generated from a generalized thermostatted system. It is found that the cluster-shaped structure is reflected in the geometry of the Hamiltonian, such as isosurfaces and local centers, and the shapes of cluster-shaped chaotic flows and invariant tori rely on the isosurfaces determined by initial conditions, while the numbers of clusters are subject to the local centers solved by the Hessian matrix of the Hamiltonian. Moreover, the study shows that the cluster-shaped chaotic flows and invariant tori are chained together by curve axes, which are the segments of equilibrium curves of the generalized thermostatted system. Furthermore, the interesting results are vividly demonstrated by the numerical simulations.

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A novel method of constructing high-dimensional digital chaotic systems on finite-state automata*

Cited by 6 publications

References 31 publications

Neural-mechanism-driven image block encryption algorithm incorporating a hyperchaotic system and cloud model

Neural-mechanism-driven image block encryption algorithm incorporating a hyperchaotic system and cloud model

Exponential sine chaotification model for enhancing chaos and its hardware implementation

Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system

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