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Keywords = Arnold cat map

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29 pages, 4563 KB  
Article
Performance Enhancement of Secure Image Transmission over ACO-OFDM VLC Systems Through Chaos Encryption and PAPR Reduction
by Elhadi Mehallel, Abdelhalim Rabehi, Ghadjati Mohamed, Abdelaziz Rabehi, Imad Eddine Tibermacine and Mustapha Habib
Electronics 2026, 15(1), 43; https://doi.org/10.3390/electronics15010043 - 22 Dec 2025
Viewed by 313
Abstract
Visible Light Communication (VLC) systems commonly employ optical orthogonal frequency division multiplexing (O-OFDM) to achieve high data rates, benefiting from its robustness against multipath effects and intersymbol interference (ISI). However, a key limitation of asymmetrically clipped direct current biased optical–OFDM (ACO-OFDM) systems lies [...] Read more.
Visible Light Communication (VLC) systems commonly employ optical orthogonal frequency division multiplexing (O-OFDM) to achieve high data rates, benefiting from its robustness against multipath effects and intersymbol interference (ISI). However, a key limitation of asymmetrically clipped direct current biased optical–OFDM (ACO-OFDM) systems lies in their inherently high peak-to-average power ratio (PAPR), which significantly affects signal quality and system performance. This paper proposes a joint chaotic encryption and modified μ-non-linear logarithmic companding (μ-MLCT) scheme for ACO-OFDM–based VLC systems to simultaneously enhance security and reduce PAPR. First, image data is encrypted at the upper layer using a hybrid chaotic system (HCS) combined with Arnold’s cat map (ACM), mapped to quadrature amplitude modulation (QAM) symbols and further encrypted through chaos-based symbol scrambling to strengthen security. A μ-MLCT transformation is then applied to mitigate PAPR and enhance both peak signal-to-noise ratio (PSNR) and bit-error-ratio (BER) performance. A mathematical model of the proposed secured ACO-OFDM system is developed, and the corresponding BER expression is derived and validated through simulation. Simulation results and security analyses confirm the effectiveness of the proposed solution, showing gains of approximately 13 dB improvement in PSNR, 2 dB in BER performance, and a PAPR reduction of about 9.2 dB. The secured μ-MLCT-ACO-OFDM not only enhances transmission security but also effectively reduces PAPR without degrading PSNR and BER. As a result, it offers a robust and efficient solution for secure image transmission with low PAPR, making it well-suitable for emerging wireless networks such as cognitive and 5G/6G systems. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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16 pages, 4215 KB  
Article
An Enhanced Reptile Search Algorithm for Inverse Modeling of Unsaturated Seepage Parameters in Clay Core Rockfill Dam Using Monitoring Data during Operation
by Zhangxin Huang, Zhenzhong Shen, Liqun Xu and Yiqing Sun
Mathematics 2024, 12(15), 2412; https://doi.org/10.3390/math12152412 - 2 Aug 2024
Cited by 1 | Viewed by 1545
Abstract
The seepage characteristics of clay core walls are crucial for the seepage safety of core rockfill dams, with the permeability coefficient in the unsaturated zone being nonlinear. To accurately determine the unsaturated seepage parameters in clay core rockfill dams, this paper first proposes [...] Read more.
The seepage characteristics of clay core walls are crucial for the seepage safety of core rockfill dams, with the permeability coefficient in the unsaturated zone being nonlinear. To accurately determine the unsaturated seepage parameters in clay core rockfill dams, this paper first proposes an enhanced reptile search algorithm (ERSA) by applying three improvement strategies: Arnold’s cat chaotic map, nonlinear evolutionary factor, and adaptive Cauchy–Gaussian mutation with variable weight. Then, by integrating the ERSA with the unsaturated seepage finite element method, an inverse modeling approach is developed. This approach is applied to an actual rockfill dam with operational monitoring data to determine the unsaturated seepage parameters of the clay core. Results indicate that the ERSA outperforms the original RSA in test functions, and the calculation results of the seepage parameters determined through inversion are consistent with the monitoring data, showing an overall mean absolute error of 1.086 m. The inverse modeling approach provides a valuable reference for determining unsaturated seepage parameters in similar clay core rockfill dams. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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20 pages, 522 KB  
Article
Behavior of Correlation Functions in the Dynamics of the Multiparticle Quantum Arnol’d Cat
by Giorgio Mantica
Entropy 2024, 26(7), 572; https://doi.org/10.3390/e26070572 - 30 Jun 2024
Viewed by 1556
Abstract
The multi-particle Arnol’d cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renowned map that bears its name. It is obtained following the Joos–Zeh prescription for decoherence by adding a number of scattering particles [...] Read more.
The multi-particle Arnol’d cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renowned map that bears its name. It is obtained following the Joos–Zeh prescription for decoherence by adding a number of scattering particles in the configuration space of the cat. Quantization follows swiftly if the Hamiltonian approach, rather than the semiclassical approach, is adopted. The author has studied this system in a series of previous works, focusing on the problem of quantum–classical correspondence. In this paper, the dynamics of this system are tested by two related yet different indicators: the time autocorrelation function of the canonical position and the out-of-time correlator of position and momentum. Full article
(This article belongs to the Section Statistical Physics)
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22 pages, 10921 KB  
Article
Secure NIfTI Image Authentication Scheme for Modern Healthcare System
by Kamred Udham Singh, Turki Aljrees, Ankit Kumar and Teekam Singh
Appl. Sci. 2023, 13(9), 5308; https://doi.org/10.3390/app13095308 - 24 Apr 2023
Cited by 7 | Viewed by 2413
Abstract
Advances in digital neuroimaging technologies, i.e., MRI and CT scan technology, have radically changed illness diagnosis in the global healthcare system. Digital imaging technologies produce NIfTI images after scanning the patient’s body. COVID-19 spared on a worldwide effort to detect the lung infection. [...] Read more.
Advances in digital neuroimaging technologies, i.e., MRI and CT scan technology, have radically changed illness diagnosis in the global healthcare system. Digital imaging technologies produce NIfTI images after scanning the patient’s body. COVID-19 spared on a worldwide effort to detect the lung infection. CT scans have been performed on billions of COVID-19 patients in recent years, resulting in a massive amount of NIfTI images being produced and communicated over the internet for diagnosis. The dissemination of these medical photographs over the internet has resulted in a significant problem for the healthcare system to maintain its integrity, protect its intellectual property rights, and address other ethical considerations. Another significant issue is how radiologists recognize tempered medical images, sometimes leading to the wrong diagnosis. Thus, the healthcare system requires a robust and reliable watermarking method for these images. Several image watermarking approaches for .jpg, .dcm, .png, .bmp, and other image formats have been developed, but no substantial contribution to NIfTI images (.nii format) has been made. This research suggests a hybrid watermarking method for NIfTI images that employs Slantlet Transform (SLT), Lifting Wavelet Transform (LWT), and Arnold Cat Map. The suggested technique performed well against various attacks. Compared to earlier approaches, the results show that this method is more robust and invisible. Full article
(This article belongs to the Special Issue Digital Image Security and Privacy Protection)
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18 pages, 18243 KB  
Article
Physical-Layer Security in Power-Domain NOMA Based on Different Chaotic Maps
by Mariam Abu Al-Atta, Karim A. Said, Mohamed A. Mohamed and Walid Raslan
Entropy 2023, 25(1), 140; https://doi.org/10.3390/e25010140 - 10 Jan 2023
Cited by 6 | Viewed by 2746
Abstract
Nonorthogonal multiple access (NOMA) is a relevant technology for realizing the primary goals of next-generation wireless networks, such as high connectivity and stability. Because a rising number of users are becoming connected, user data security has become a critical issue. Many chaotic communication [...] Read more.
Nonorthogonal multiple access (NOMA) is a relevant technology for realizing the primary goals of next-generation wireless networks, such as high connectivity and stability. Because a rising number of users are becoming connected, user data security has become a critical issue. Many chaotic communication systems have been established to address this important issue via exhibition of affordable physical-layer-security solutions. In this study, we propose a chaotic downlink NOMA (C-DL-NOMA) system over the additive white Gaussian noise and Rayleigh-fading channels to enhance the security of the DL-NOMA system. The proposed algorithm is based on a coherent analog modulation technique that combines various chaotic maps for chaotic masking of encrypted data. On the transmitter, chaotic encryption was used for transmitted data with fixed power-allocation-level control, whereas on the receiver, successive interference-cancellation demodulation was utilized to detect multiple users, after which chaotic decryption was performed. Simulation results were evaluated based on security analyses, such as statistical analysis (histogram and correlation analyses and information entropy), bit-error-rate performance, and achievable-data-rate performance. According to these security analyses and numerical results, the proposed C-DL-NOMA system outperformed traditional unencrypted NOMA systems. Full article
(This article belongs to the Section Complexity)
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13 pages, 745 KB  
Article
Secure Image Encryption Using Chaotic, Hybrid Chaotic and Block Cipher Approach
by Nirmal Chaudhary, Tej Bahadur Shahi and Arjun Neupane
J. Imaging 2022, 8(6), 167; https://doi.org/10.3390/jimaging8060167 - 10 Jun 2022
Cited by 45 | Viewed by 6031
Abstract
Secure image transmission is one of the most challenging problems in the age of communication technology. Millions of people use and transfer images for either personal or commercial purposes over the internet. One way of achieving secure image transmission over the network is [...] Read more.
Secure image transmission is one of the most challenging problems in the age of communication technology. Millions of people use and transfer images for either personal or commercial purposes over the internet. One way of achieving secure image transmission over the network is encryption techniques that convert the original image into a non-understandable or scrambled form, called a cipher image, so that even if the attacker gets access to the cipher they would not be able to retrieve the original image. In this study, chaos-based image encryption and block cipher techniques are implemented and analyzed for image encryption. Arnold cat map in combination with a logistic map are used as native chaotic and hybrid chaotic approaches respectively whereas advanced encryption standard (AES) is used as a block cipher approach. The chaotic and AES methods are applied to encrypt images and are subjected to measures of different performance parameters such as peak signal to noise ratio (PSNR), number of pixels change rate (NPCR), unified average changing intensity (UACI), and histogram and computation time analysis to measure the strength of each algorithm. The results show that the hybrid chaotic map has better NPCR and UACI values which makes it more robust to differential attacks or chosen plain text attacks. The Arnold cat map is computationally efficient in comparison to the other two approaches. However, AES has a lower PSNR value (7.53 to 11.93) and has more variation between histograms of original and cipher images, thereby indicating that it is more resistant to statistical attacks than the other two approaches. Full article
(This article belongs to the Special Issue Visualisation and Cybersecurity)
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18 pages, 7589 KB  
Article
A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography
by La Zakaria, Endah Yuliani and Asmiati Asmiati
Algorithms 2021, 14(4), 124; https://doi.org/10.3390/a14040124 - 16 Apr 2021
Cited by 2 | Viewed by 2786
Abstract
Cryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms. In particular, the Arnold’s cat and the sine-Gordon linear maps can be [...] Read more.
Cryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms. In particular, the Arnold’s cat and the sine-Gordon linear maps can be used in cryptographic algorithms for encoding digital images. In this article, a two-dimensional linear mKdV map derived from an ordinary difference mKdV equation will be used in a cryptographic encoding algorithm. The proposed encoding algorithm will be compared with those generated using sine-Gordon and Arnold’s cat maps via the correlations between adjacent pixels in the encrypted image and the uniformity of the pixel distribution. Note that the mKdV map is derived from the partial discrete mKdV equation with Consistency Around the Cube (CAC) properties, whereas the sine-Gordon map is derived from the partial discrete sine-Gordon equation, which does not have CAC properties. Full article
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17 pages, 4782 KB  
Article
Novel Bioinspired Approach Based on Chaotic Dynamics for Robot Patrolling Missions with Adversaries
by Daniel-Ioan Curiac, Ovidiu Banias, Constantin Volosencu and Christian-Daniel Curiac
Entropy 2018, 20(5), 378; https://doi.org/10.3390/e20050378 - 18 May 2018
Cited by 24 | Viewed by 5250
Abstract
Living organisms have developed and optimized ingenious defense strategies based on positional entropy. One of the most significant examples in this respect is known as protean behavior, where a prey animal under threat performs unpredictable zig-zag movements in order to confuse, delay or [...] Read more.
Living organisms have developed and optimized ingenious defense strategies based on positional entropy. One of the most significant examples in this respect is known as protean behavior, where a prey animal under threat performs unpredictable zig-zag movements in order to confuse, delay or escape the predator. This kind of defensive behavior can inspire efficient strategies for patrolling robots evolving in the presence of adversaries. The main goal of our proposed bioinspired method is to implement the protean behavior by altering the reference path of the robot with sudden and erratic direction changes without endangering the robot’s overall mission. By this, a foe intending to target and destroy the mobile robot from a distance has less time for acquiring and retaining the proper sight alignment. The method uses the chaotic dynamics of the 2D Arnold’s cat map as a primary source of positional entropy and transfers this feature to every reference path segment using the kinematic relative motion concept. The effectiveness of this novel biologically inspired method is validated through extensive and realistic simulation case studies. Full article
(This article belongs to the Section Complexity)
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10 pages, 5288 KB  
Article
A New Two-Dimensional Map with Hidden Attractors
by Chuanfu Wang and Qun Ding
Entropy 2018, 20(5), 322; https://doi.org/10.3390/e20050322 - 27 Apr 2018
Cited by 47 | Viewed by 5895
Abstract
The investigations of hidden attractors are mainly in continuous-time dynamic systems, and there are a few investigations of hidden attractors in discrete-time dynamic systems. The classical chaotic attractors of the Logistic map, Tent map, Henon map, Arnold’s cat map, and other widely-known chaotic [...] Read more.
The investigations of hidden attractors are mainly in continuous-time dynamic systems, and there are a few investigations of hidden attractors in discrete-time dynamic systems. The classical chaotic attractors of the Logistic map, Tent map, Henon map, Arnold’s cat map, and other widely-known chaotic attractors are those excited from unstable fixed points. In this paper, the hidden dynamics of a new two-dimensional map inspired by Arnold’s cat map is investigated, and the existence of fixed points and their stabilities are studied in detail. Full article
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16 pages, 1932 KB  
Article
A Maximum Entropy-Based Chaotic Time-Variant Fragile Watermarking Scheme for Image Tampering Detection
by Young-Long Chen, Her-Terng Yau and Guo-Jheng Yang
Entropy 2013, 15(8), 3170-3185; https://doi.org/10.3390/e15083260 - 5 Aug 2013
Cited by 22 | Viewed by 5147
Abstract
The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on [...] Read more.
The fragile watermarking technique is used to protect intellectual property rights while also providing security and rigorous protection. In order to protect the copyright of the creators, it can be implanted in some representative text or totem. Because all of the media on the Internet are digital, protection has become a critical issue, and determining how to use digital watermarks to protect digital media is thus the topic of our research. This paper uses the Logistic map with parameter u = 4 to generate chaotic dynamic behavior with the maximum entropy 1. This approach increases the security and rigor of the protection. The main research target of information hiding is determining how to hide confidential data so that the naked eye cannot see the difference. Next, we introduce one method of information hiding. Generally speaking, if the image only goes through Arnold’s cat map and the Logistic map, it seems to lack sufficient security. Therefore, our emphasis is on controlling Arnold’s cat map and the initial value of the chaos system to undergo small changes and generate different chaos sequences. Thus, the current time is used to not only make encryption more stringent but also to enhance the security of the digital media. Full article
(This article belongs to the Special Issue Dynamical Systems)
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