A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng

doi:10.1142/s0218127417501036

Cited by 40 publications

(20 citation statements)

References 33 publications

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“…(9) does not require too much additional resource consumption. Compared with other methods, such as using a higher-dimensional chaotic map [18,19], multiple cascading chaotic systems [20,21], transforming into di erent nite elds [28,29], or perturbing the chaotic systems [9,[22][23][24][25], the proposed method has a simpler structure. e Lorenz chaotic system is used in [9] to perturb the logistic map, whereas in this paper, the m-sequence is used to perturb the logistic map.…”

Section: Balance Analysismentioning

confidence: 99%

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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: Balance Analysismentioning

confidence: 99%

“…If two digitized logistic maps are both in short periodic orbits, then the nal output digitized chaotic time series will show short periodic behavior. (4) Perturbing the chaotic system [9,[22][23][24][25]. Perturbation sources can be introduced in variables and parameters.…”

Section: Introductionmentioning

confidence: 99%

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Wang

Ding

2019

Complexity

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“…The fourth is the perturbation mechanism [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. Liu and Lin [ 23 ] created perturbation chaotic systems to perturb state variables and system parameters with a logistic map. Liu and Luo [ 24 ] proposed a continuous Chen system to perturb both the parameters and the inputs of the Chebyshev system.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Shi

Deng

2021

Entropy

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Dynamical degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based cryptosystems. The existing solutions mainly focus on the compensation of dynamical properties rather than on the elimination of the inherent biases of chaotic systems. In this paper, a unidirectional hybrid control method is proposed to improve the dynamical properties and to eliminate the biases of digital chaotic maps. A continuous chaotic system is introduced to provide external feedback control of the given digital chaotic map. Three different control modes are investigated, and the influence of control parameter on the properties of the controlled system is discussed. The experimental results show that the proposed method can not only improve the dynamical degradation of the digital chaotic map but also make the controlled digital system produce outputs with desirable performances. Finally, a pseudorandom number generator (PRNG) is proposed. Statistical analysis shows that the PRNG has good randomness and almost ideal entropy values.

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“…Beside that, the period of orbits produced by a chaotic map can be lengthened by several methods as suggested in Reference [ 19 ]. Two of such methods are perturbation on chaotic states by another chaotic map [ 20 , 21 ] and by using linear feedback shift register (LFSR) [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

Novel Models of Image Permutation and Diffusion Based on Perturbed Digital Chaos

Hoang

Assad

2020

Entropy

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Most of chaos-based cryptosystems utilize stationary dynamics of chaos for the permutation and diffusion, and many of those are successfully attacked. In this paper, novel models of the image permutation and diffusion are proposed, in which chaotic map is perturbed at bit level on state variables, on control parameters or on both. Amounts of perturbation are initially the coordinate of pixels in the permutation, the value of ciphered word in the diffusion, and then a value extracted from state variables in every iteration. Under the persistent perturbation, dynamics of chaotic map is nonstationary and dependent on the image content. The simulation results and analyses demonstrate the effectiveness of the proposed models by means of the good statistical properties of transformed image obtained after just only a single round.

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A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

Cited by 40 publications

References 33 publications

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Constructing Digitized Chaotic Time Series with a Guaranteed Enhanced Period

Hybrid Control of Digital Baker Map with Application to Pseudo-Random Number Generator

Novel Models of Image Permutation and Diffusion Based on Perturbed Digital Chaos

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