A cascading method for constructing new discrete chaotic systems with better randomness

Yuan, Fang; Deng, Yue; Li, Yuxia; Chen, Guanrong

doi:10.1063/1.5094936

Cited by 29 publications

(11 citation statements)

References 29 publications

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“…[22][23][24][25] In addition, a cascade method of forming a series of new systems by cascading two chaotic subsystems was proposed in our previous papers. [26,27] Theoretical verification and experimental results manifested that the Lyapunov exponents and chaotic space of the new cascade chaotic system are much larger than those of subsystems.…”

Section: Introductionmentioning

confidence: 99%

Cascade discrete memristive maps for enhancing chaos*

Yuan¹,

Bai²,

Li³

2021

Chinese Phys. B

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Continuous-time memristor (CM) has been widely used to generate chaotic oscillations. However, discrete memristor (DM) has not been received adequate attention. Motivated by the cascade structure in electronic circuits, this paper introduces a method to cascade discrete memristive maps for generating chaos and hyperchaos. For a discrete-memristor seed map, it can be self-cascaded many times to get more parameters and complex structures, but with larger chaotic areas and Lyapunov exponents. Comparisons of dynamic characteristics between the seed map and cascading maps are explored. Meanwhile, numerical simulation results are verified by the hardware implementation.

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Section: Introductionmentioning

confidence: 99%

Cascade discrete memristive maps for enhancing chaos*

Yuan¹,

Bai²,

Li³

2021

Chinese Phys. B

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“…In [10,11], the authors employ a skipping technique to enhance the randomness of the chaotic outputs (called self-cascading in [11]). Instead of iterating with the original map f , it uses its d-times iterated one f d [12].…”

Section: Introductionmentioning

confidence: 99%

“…If the iterations are alternated between different maps, the method is called switching; this is also proposed in [11] (called hybrid-cascading there), in [13,14]. The limitation is that the maps must have common convergence domains, or at least common areas, which are not easy to find (lacks in generality).…”

Section: Introductionmentioning

confidence: 99%

From Continuous-Time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology

Micco

Antonelli

Rosso

2021

Entropy

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The use of chaotic systems in electronics, such as Pseudo-Random Number Generators (PRNGs), is very appealing. Among them, continuous-time ones are used less because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems’ statistical and chaotic behavior. We employ an approach based on interpreting the time step as a parameter of the new “maps”. From our analysis, it follows that to use them as PRNGs, two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, which can be applied to any continuous-time chaotic system. We analyze the generated sequences by means of quantifiers based on information theory (permutation entropy, permutation complexity, and causal entropy × complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.

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“…High-dimensional chaotic systems such as three-dimensional Lorenz chaotic systems [36,37], and Chen System [38] and Yu System [39,40] et al have more dimensional and higher complexity. Especially hyper-chaotic systems [41,42] have two or more Lyapunov exponents greater than 0 and larger key space and higher complexity. Hyperchaotic systems have been wildly used in chaotic image encryption scheme [28,[43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Protecting Compressive Ghost Imaging with Hyperchaotic System and DNA Encoding

et al. 2020

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As computational ghost imaging is widely used in the military, radar, and other fields, its security and efficiency became more and more important. In this paper, we propose a compressive ghost imaging encryption scheme based on the hyper-chaotic system, DNA encoding, and KSVD algorithm for the first time. First, a 4-dimensional hyper-chaotic system is used to generate four long pseudorandom sequences and diffuse the sequences with DNA operation to get the phase mask sequence, and then N phase mask matrixes are generated from the sequences. Second, in order to improve the reconstruction efficiency, KSVD algorithm is used to generate dictionary D to sparse the image. The transmission key of the proposed scheme includes the initial values of hyper-chaotic and dictionary D, which has plaintext correlation and big key space. Compared with the existing compressive ghost imaging encryption scheme, the proposed scheme is more sensitive to initial values and more complexity and has smaller transmission key, which makes the encryption scheme more secure, and the reconstruction efficiency is higher too. Simulation results and security analysis demonstrate the good performance of the proposed scheme.

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A cascading method for constructing new discrete chaotic systems with better randomness

Cited by 29 publications

References 29 publications

Cascade discrete memristive maps for enhancing chaos*

Cascade discrete memristive maps for enhancing chaos*

From Continuous-Time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology

Protecting Compressive Ghost Imaging with Hyperchaotic System and DNA Encoding

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