Novel discrete chaotic system via fractal transformation and its DSP implementation

Dai, Shengqiu; Sun, Kehui; Ai, Wei; Peng, Yuexi

doi:10.1142/s0217984920504291

Cited by 12 publications

(5 citation statements)

References 31 publications

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“…Fractals exhibits the self-similar behavior. It indicates that an object is totally or approximately similar to a part of itself [47]. If the matrix F meets the following 3 characteristics, we call this matrix F a Fractal Sorting Matrix (FSM) [48]:…”

Section: Fractal Theorymentioning

confidence: 99%

A new 2D-HLSM-CECP hyperchaotic map and its application on image encryption using fractal-based permutation and cross coupled diffusion

Zhang,

Wang

et al. 2024

Preprint

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To enhance the security of the image encryption algorithm (IEA) based on chaotic system, this paper firstly introduced a new hyperchaotic map called two-dimensional hyperchaotic Logistic-Sine map coupled exponential control parameter (2D-HLSM-CECP) coupled with the two-dimensional Logistic map and the Sine map, which displays better hyperchaotic behavior and randomness than some existing chaotic systems. Then, this work further represents a novel IEA based on 2D-HLSM-CECP, fractal sorting matrix and cross coupled diffusion. The new 2D-HLSM-CECP is used to generate two chaotic sequences, which played a significant role in the whole encryption and decryption part. All pixels of the plain-image are confused and diffused based on fractal sorting matrix and global cross coupled operation respectively. Theoretical analysis and simulation results demonstrate that the 2D-HLSM-CECP-IEA has splendid achievement in well-known security indicators. Thus, the 2D-HLSM-CECP-IEA is highly secure as a conclusion.

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Section: Fractal Theorymentioning

confidence: 99%

A new 2D-HLSM-CECP hyperchaotic map and its application on image encryption using fractal-based permutation and cross coupled diffusion

Zhang,

Wang

et al. 2024

Preprint

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show abstract

“…In 1963, Lorenz [2] proposed the concept of chaos theory. Since then, scholars began to study various chaotic models, such as continuous chaotic system [3][4][5], discrete chaotic system [6,7], complex chaotic system [8][9][10], time-delay chaotic system [11,12] and fractional chaotic system [13][14][15]. Due to the unpredictability, ergodicity and extremely sensitivity to initial conditions of chaotic system [16], it is eminently suitable for chaotic cryptography.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a fractional-order hyperchaotic system and its application in image encryption

Shi¹,

An²,

Yang³

et al. 2022

Phys. Scr.

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Compared with integer order chaotic systems, fractional order chaotic systems can reflect natural phenomena more accurately, which are more suitable for chaotic cryptosystems. In order to explore the application of fractional order chaotic system in cryptography, a novel fractional order hyperchaotic system is constructed and implemented on DSP platform. More progressively, based on Adomian decomposition method, the dynamic behavior is studied by phase diagram, bifurcation diagram, Lyapunov exponent spectrum and spectral entropy (SE) complexity. It is found that each parameter and order have a large range of intervals that can keep the system in a hyperchaotic state. Therefore, the hyperchaotic sequences generated by the constructed fractional order hyperchaotic system have sufficient randomness and are well suited for applications in secure communications. In addition, a color image encryption scheme is designed based on the fractional order hyperchaotic system and DNA dynamic coding. Firstly, the improved Arnold algorithm is used to scramble the original image, then the column cyclic shift method is applied for secondary scrambling, and finally the pixel value is diffused by DNA sequence operation. The security analysis results indicate that the designed encryption algorithm can not only encrypt images effectively, but also has high security and can resist various common attacks.

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“…He et al used CADM to analyze the dynamic characteristics of a fractional-order hyperchaotic system [18]. At present, there is little research on using fractional-order chaotic systems for communication security [19][20][21]. Therefore, this paper uses the ADM decomposition method to analyze the fractional-order dynamics of the new Lü chaotic system and applies it to the image encryption scheme.…”

Section: Introductionmentioning

confidence: 99%

Design of Clothing with Encrypted Information of Lost Children Information Based on Chaotic System and DNA Theory

Cui

Liu

2022

AUTEX Research Journal

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The encryption design is partly based on the fractional chaotic system and DNA theory. First, the dynamic characteristics of the newly proposed fractional Lü chaotic system are analyzed, and based on the analysis, a multi-image encryption algorithm is proposed. That is, the Arnold scrambling algorithm is used to scramble the image matrix, and then the DNA encryption theory is used to diffuse the image matrix. Among them, the scrambling step and the diffusion step are based on the chaotic sequence, and the encrypted image is finally obtained. Finally, the new encryption algorithm is evaluated, and the results show that the key space of the new encryption algorithm is further expanded and is very sensitive to key changes. The algorithm can effectively destroy the correlation of the original image, and can resist various cracking attacks. In summary, the multi-image encryption algorithm proposed in this paper has good encryption performance and provides a theoretical basis for practical applications. By reading those labels, children's identity and other relevant information can be acquired. This method may help police to obtain information on lost children and find their family rapidly.

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Novel discrete chaotic system via fractal transformation and its DSP implementation

Cited by 12 publications

References 31 publications

A new 2D-HLSM-CECP hyperchaotic map and its application on image encryption using fractal-based permutation and cross coupled diffusion

A new 2D-HLSM-CECP hyperchaotic map and its application on image encryption using fractal-based permutation and cross coupled diffusion

Dynamic analysis of a fractional-order hyperchaotic system and its application in image encryption

Design of Clothing with Encrypted Information of Lost Children Information Based on Chaotic System and DNA Theory

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