Constructing Discrete Chaotic Systems with Positive Lyapunov Exponents

Wang, Chuanfu; Fan, Chunlei; Ding, Qun

doi:10.1142/s0218127418500840

Cited by 58 publications

(28 citation statements)

References 22 publications

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“…Chaotic time series are widely used in information elds for their initial sensitivity, nonlinearity, aperiodicity, and randomness. ese chaotic behaviors are consistent with the "confusion" and "di usion" in Shannon's information theory [1], which provides a basis for chaotic pseudorandom sequence generator, chaotic secure communication, and other information elds [2][3][4][5][6][7][8]. However, when chaotic systems are realized in digital circuits, chaotic behavior will degenerate [9].…”

Section: Introductionmentioning

confidence: 63%

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Wang

Ding

2019

Complexity

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When chaotic systems are realized in digital circuits, their chaotic behavior will degenerate into short periodic behavior. Short periodic behavior brings hidden dangers to the application of digitized chaotic systems. In this paper, an approach based on the introduction of additional parameters to counteract the short periodic behavior of digitized chaotic time series is discussed. We analyze the ways that perturbation sources are introduced in parameters and variables and prove that the period of digitized chaotic time series generated by a digitized logistic map is improved e ciently. Furthermore, experimental implementation shows that the digitized chaotic time series has great complexity, approximate entropy, and randomness, and the perturbed digitized logistic map can be used as a secure pseudorandom sequence generator for information encryption.

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Section: Introductionmentioning

confidence: 63%

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Wang

Ding

2019

Complexity

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“…Because the low-dimensional chaotic map structure is simple, its trajectory parameters and initial values are easy to predict, and the commonly used chaotic systems have been widely known by the public [19,20]. Therefore, using existing low-dimensional chaotic signals will threaten the security of image encryption [21].…”

Section: New Three-dimensional Chaotic Systemmentioning

confidence: 99%

“…In Formula (19), P(m i ) represents the probability of m i appearing in the image m. In this paper, the 8-bit Lena image is selected, with an ideal information entropy value of H m = 8. In 8-bit digital image analysis, the more random the encrypted image is, the closer the information entropy is to 8.…”

Section: Information Entropy Analysismentioning

confidence: 99%

Image Encryption Scheme with Compressed Sensing Based on New Three-Dimensional Chaotic System

Xie

Guo

et al. 2019

Entropy

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In this paper, a new three-dimensional chaotic system is proposed for image encryption. The core of the encryption algorithm is the combination of chaotic system and compressed sensing, which can complete image encryption and compression at the same time. The Lyapunov exponent, bifurcation diagram and complexity of the new three-dimensional chaotic system are analyzed. The performance analysis shows that the chaotic system has two positive Lyapunov exponents and high complexity. In the encryption scheme, a new chaotic system is used as the measurement matrix for compressed sensing, and Arnold is used to scrambling the image further. The proposed method has better reconfiguration ability in the compressible range of the algorithm compared with other methods. The experimental results show that the proposed encryption scheme has good encryption effect and image compression capability.

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“…At this time, system (1) has no less than two positive Lyapunov exponentials; thus it has hyperchaotic characteristics [10]. The randomness of the system is greatly increased [11] which means it has a better performance in color image encryption.…”

Section: Hyperchaotic Systemmentioning

confidence: 99%

A Hyperchaotic Color Image Encryption Algorithm and Security Analysis

Zhao

Liu

et al. 2019

Security and Communication Networks

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The current common color image encryption algorithms applying “scrambling-diffusion” have some problems, such as the small key space, the cumbersome encryption process, and the security vulnerability. Aiming at these problems, this paper proposes a new color image encryption algorithm based on the hyperchaotic system and applying “transforming-scrambling-diffusion” model. Before scrambling, in accordance with the plaintext itself attributes, the number of iterations was calculated, all the pixel values of color image were transformed into gray code iteratively, and then the chaotic sequence was generated from the four-dimensional hyperchaotic system. Pixel matrix after gray code transformation was converted to one-dimensional matrix. The chaotic sequence was sorted and the one-dimensional matrix was changed positions correspondingly to complete the whole domain scrambling. And then, bit-operation was executed for image diffusion. The ciphertext can be obtained by matrix transformation. The key sensitivity, histogram, information entropy, correlation, and other evaluation indexes were calculated and analyzed through the simulation experiment. Compared with other algorithms, it can be proved that the encryption algorithm has the strong antiattack ability.

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Constructing Discrete Chaotic Systems with Positive Lyapunov Exponents

Cited by 58 publications

References 22 publications

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Image Encryption Scheme with Compressed Sensing Based on New Three-Dimensional Chaotic System

A Hyperchaotic Color Image Encryption Algorithm and Security Analysis

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