Digitally generating true orbits of binary shift chaotic maps and their conjugates

Öztürk, İsmail; Kılıç, Recai

doi:10.1016/j.cnsns.2018.02.039

Cited by 11 publications

(3 citation statements)

References 29 publications

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“…Our main contribution is demonstrated by reducing logical resource consumption per bit while preserving the chaotic properties of the map and countering the dynamical degradation. Compared to other state-of-the-art articles in the literature [3,[21][22][23], our proposed tent map demonstrates a reduction in resource consumption per bit of at least 60%.…”

Section: Introductionmentioning

confidence: 83%

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A Hardware-Efficient Perturbation Method to the Digital Tent Map

et al. 2023

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Digital chaotic systems used in various applications such as signal processing, artificial intelligence, and communications often suffer from the issue of dynamical degradation. This paper proposes a solution to address this problem in the digital tent map. Our proposed method includes a simple and optimized hardware architecture, along with a hardware-efficient perturbation method, to create a high-performance computing system that retains its chaotic properties. We implemented our proposed architecture using an FPGA (Field-Programmable Gate Array) and the 1’s complement fixed-point format. Our results demonstrate that the implemented digital circuit reduces logical resource consumption compared to state-of-the-art references and exhibits pseudo-random nature, as confirmed by various statistical tests. We validated our proposed pseudo-random number generator in a hardware architecture for particle swarm optimization, demonstrating its effectiveness.

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Section: Introductionmentioning

confidence: 83%

“…However, the tent map displays dynamical degradation when µ = 2, resulting in a periodic function. Indeed, orbits of binary shift chaotic maps eventually converge to zero [23]. In this way, we apply an XOR gate between the least two significant bits.…”

Section: Methodsmentioning

confidence: 99%

A Hardware-Efficient Perturbation Method to the Digital Tent Map

et al. 2023

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“…With the initial value

, the Chebyshev chaotic sequence is produced by applying Equation (3) recursively. On its excellent randomness, sensitivity to initial values, spatial ergodicity, and easy implementation in physical electric circuits [ 21 ], Chebyshev chaos is widely valued.…”

Section: Chebyshev Chaotic Sequence and Sample Distancementioning

confidence: 99%

A Method of Constructing Measurement Matrix for Compressed Sensing by Chebyshev Chaotic Sequence

Miao

Wu³

2020

Entropy

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In this paper, the problem of constructing the measurement matrix in compressed sensing is addressed. In compressed sensing, constructing a measurement matrix of good performance and easy hardware implementation is of interest. It has been recently shown that the measurement matrices constructed by Logistic or Tent chaotic sequences satisfy the restricted isometric property (RIP) with a certain probability and are easy to be implemented in the physical electric circuit. However, a large sample distance that means large resources consumption is required to obtain uncorrelated samples from these sequences in the construction. To solve this problem, we propose a method of constructing the measurement matrix by the Chebyshev chaotic sequence. The method effectively reduces the sample distance and the proposed measurement matrix is proved to satisfy the RIP with high probability on the assumption that the sampled elements are statistically independent. Simulation results show that the proposed measurement matrix has comparable reconstruction performance to that of the existing chaotic matrices for compressed sensing.

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Utilizing true periodic orbits in chaos-based cryptography

Öztürk

Kılıç

2021

Nonlinear Dyn

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Digitally generating true orbits of binary shift chaotic maps and their conjugates

Cited by 11 publications

References 29 publications

A Hardware-Efficient Perturbation Method to the Digital Tent Map

A Hardware-Efficient Perturbation Method to the Digital Tent Map

A Method of Constructing Measurement Matrix for Compressed Sensing by Chebyshev Chaotic Sequence

Utilizing true periodic orbits in chaos-based cryptography

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