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Keywords = chaotic baker map

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20 pages, 3886 KB  
Article
High-Security Image Encryption Using Baker Map Confusion and Extended PWAM Chaotic Diffusion
by Ayman H. Abd El-Aziem, Marwa Hussien Mohamed and Ahmed Abdelhafeez
Computers 2026, 15(2), 106; https://doi.org/10.3390/computers15020106 - 3 Feb 2026
Cited by 1 | Viewed by 502
Abstract
The heavy use of digital images across network systems has become a major concern regarding data confidentiality and unauthorized access. Conventional image encryption techniques hardly achieve high security levels efficiently, especially in real-time and resource-constrained environments. These challenges motivate the development of more [...] Read more.
The heavy use of digital images across network systems has become a major concern regarding data confidentiality and unauthorized access. Conventional image encryption techniques hardly achieve high security levels efficiently, especially in real-time and resource-constrained environments. These challenges motivate the development of more robust and efficient encryption mechanisms. In this paper, a dual-chaotic image encryption framework is developed where two complementary chaotic systems are combined to effectively realize confusion and diffusion. The proposed method uses a chaotic permutation mechanism to find the pixel positions and enhanced chaotic diffusion to change the pixel values for eliminating the statistical correlations. An extended family of piecewise affine chaotic maps is designed to enhance the dynamic range and complexity of the diffusion process for strengthening the resistance capability against cryptographic attacks. Intensive experimental validations confirm that the proposed scheme well obscures the visual information and strongly reduces the pixel correlations in the encrypted images. High entropy values, uniform histogram distributions, high resistance to differential attacks, and improved robustness are further evidenced by statistical and security analyses compared to some conventional image encryption techniques. The results also show extremely low computational overheads, hence allowing for efficient implementation. The proposed encryption framework provides more security for digital image transmission and storage, and the performances are still practical. Given its robustness, efficiency, and scalability, it is equally adequate for real-time multi-media applications and secure communication systems, hence promising to offer a reliable solution for modern image protection requirements. Full article
(This article belongs to the Special Issue Multimedia Data and Network Security)
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23 pages, 12620 KB  
Article
The Color Image Watermarking Algorithm Based on Quantum Discrete Wavelet Transform and Chaotic Mapping
by Yikang Yuan, Wenbo Zhao, Zhongyan Li and Wanquan Liu
Symmetry 2026, 18(1), 33; https://doi.org/10.3390/sym18010033 - 24 Dec 2025
Viewed by 661
Abstract
Quantum watermarking is a technique that embeds specific information into a quantum carrier for the purpose of digital copyright protection. In this paper, we propose a novel color image watermarking algorithm that integrates quantum discrete wavelet transform with Sinusoidal–Tent mapping and baker mapping. [...] Read more.
Quantum watermarking is a technique that embeds specific information into a quantum carrier for the purpose of digital copyright protection. In this paper, we propose a novel color image watermarking algorithm that integrates quantum discrete wavelet transform with Sinusoidal–Tent mapping and baker mapping. Initially, chaotic sequences are generated using Sinusoidal–Tent mapping to determine the channels suitable for watermark embedding. Subsequently, a one-level quantum Haar wavelet transform is applied to the selected channel to decompose the image. The watermarked image is then scrambled via discrete baker mapping, and the scrambled image is embedded into the High-High subbands. The invisibility of the watermark is evaluated by calculating the peak signal-to-noise ratio, Structural similarity index measure, and Learned Perceptual Image Patch Similarity, with comparisons made against the color histogram. The robustness of the proposed algorithm is assessed through the calculation of Normalized Cross-Correlation. In the simulation results, PSNR is close to 63, SSIM is close to 1, LPIPS is close to 0.001, and NCC is close to 0.97. This indicates that the proposed watermarking algorithm exhibits excellent visual quality and a robust capability to withstand various attacks. Additionally, through ablation study, the contribution of each technique to overall performance was systematically evaluated. Full article
(This article belongs to the Section Computer)
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16 pages, 3825 KB  
Article
Statistical Image Analysis on Liquid-Liquid Mixing Uniformity of Micro-Scale Pipeline with Chaotic Structure
by Haotian Wang, Kai Yang, Hua Wang, Jingyuan Wu and Qingtai Xiao
Energies 2023, 16(4), 2045; https://doi.org/10.3390/en16042045 - 19 Feb 2023
Cited by 5 | Viewed by 2881
Abstract
The aim of this work is to introduce a novel statistical technique for quantifying the concentration field uniformity of the liquid-liquid mixing process within a micro-scale chaotic pipeline. For illustration, the microscale liquid-liquid mixer in which the inlet direction is parallel to the [...] Read more.
The aim of this work is to introduce a novel statistical technique for quantifying the concentration field uniformity of the liquid-liquid mixing process within a micro-scale chaotic pipeline. For illustration, the microscale liquid-liquid mixer in which the inlet direction is parallel to the mixing unit is designed by using the chaotic pipeline with Baker map. Meanwhile, the non-uniformity coefficient method is adopted quantificationally instead of qualitatively estimating the concentration field uniformity of the chaotic micromixer based on uniform design theory and image analysis. Results show that the concentration distribution of the chaotic mixing process of liquid-liquid under various working conditions is obtained by solving the steady-state Navier–Stokes and diffusion convection equations. The average contribution ratio of the three basic mixing units of the chaotic Baker pipeline to the concentration field uniformity is approximately 6:3:1, which is calculated aligned with the fluid flow direction successively. The optimal mixing uniformity can be obtained as the initial velocity is 0.05 m/s and the diffusion coefficient is 5 × 10−9 m2/s, respectively. The reliability of the new method for estimating the concentration field uniformity parameters is explained from three dimensions. The statistical image analysis technique is illustrated to be reliable and effective in yielding accurate concentration field information of the simulated chaotic mixer. Furthermore, it can be adapted to examine a variety of concentration distribution issues in which concentrations are evaluated under distinct scales. Full article
(This article belongs to the Special Issue Advanced Analysis of Heat Transfer and Energy Conversion)
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26 pages, 9664 KB  
Article
Efficient Multi-Biometric Secure-Storage Scheme Based on Deep Learning and Crypto-Mapping Techniques
by Ahmed Sedik, Ahmed A. Abd El-Latif, Mudasir Ahmad Wani, Fathi E. Abd El-Samie, Nariman Abdel-Salam Bauomy and Fatma G. Hashad
Mathematics 2023, 11(3), 703; https://doi.org/10.3390/math11030703 - 30 Jan 2023
Cited by 16 | Viewed by 3446
Abstract
Cybersecurity has been one of the interesting research fields that attract researchers to investigate new approaches. One of the recent research trends in this field is cancelable biometric template generation, which depends on the storage of a cipher (cancelable) template instead of the [...] Read more.
Cybersecurity has been one of the interesting research fields that attract researchers to investigate new approaches. One of the recent research trends in this field is cancelable biometric template generation, which depends on the storage of a cipher (cancelable) template instead of the original biometric template. This trend ensures the confidential and secure storage of the biometrics of a certain individual. This paper presents a cancelable multi-biometric system based on deep fusion and wavelet transformations. The deep fusion part is based on convolution (Conv.), convolution transpose (Conv.Trans.), and additional layers. In addition, the deployed wavelet transformations are based on both integer wavelet transforms (IWT) and discrete wavelet transforms (DWT). Moreover, a random kernel generation subsystem is proposed in this work. The proposed kernel generation method is based on chaotic map modalities, including the Baker map and modified logistic map. The proposed system is implemented on four biometric images, namely fingerprint, iris, face, and palm images. Furthermore, it is validated by comparison with other works in the literature. The comparison reveals that the proposed system shows superior performance regarding the quality of encryption and confidentiality of generated cancelable templates from the original input biometrics. Full article
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52 pages, 9913 KB  
Review
Quantum Chaos in the Dynamics of Molecules
by Kazuo Takatsuka
Entropy 2023, 25(1), 63; https://doi.org/10.3390/e25010063 - 29 Dec 2022
Cited by 12 | Viewed by 6934
Abstract
Quantum chaos is reviewed from the viewpoint of “what is molecule?”, particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum [...] Read more.
Quantum chaos is reviewed from the viewpoint of “what is molecule?”, particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is “bifurcation and merging” of quantum wavepackets, rather than “stretching and folding” of the baker’s transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule. Full article
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18 pages, 26150 KB  
Article
A Multilayered Audio Signal Encryption Approach for Secure Voice Communication
by Hanaa A. Abdallah and Souham Meshoul
Electronics 2023, 12(1), 2; https://doi.org/10.3390/electronics12010002 - 20 Dec 2022
Cited by 27 | Viewed by 6416
Abstract
In this paper, multilayer cryptosystems for encrypting audio communications are proposed. These cryptosystems combine audio signals with other active concealing signals, such as speech signals, by continuously fusing the audio signal with a speech signal without silent periods. The goal of these cryptosystems [...] Read more.
In this paper, multilayer cryptosystems for encrypting audio communications are proposed. These cryptosystems combine audio signals with other active concealing signals, such as speech signals, by continuously fusing the audio signal with a speech signal without silent periods. The goal of these cryptosystems is to prevent unauthorized parties from listening to encrypted audio communications. Preprocessing is performed on both the speech signal and the audio signal before they are combined, as this is necessary to get the signals ready for fusion. Instead of encoding and decoding methods, the cryptosystems rely on the values of audio samples, which allows for saving time while increasing their resistance to hackers and environments with a noisy background. The main feature of the proposed approach is to consider three levels of encryption namely fusion, substitution, and permutation where various combinations are considered. The resulting cryptosystems are compared to the one-dimensional logistic map-based encryption techniques and other state-of-the-art methods. The performance of the suggested cryptosystems is evaluated by the use of the histogram, structural similarity index, signal-to-noise ratio (SNR), log-likelihood ratio, spectrum distortion, and correlation coefficient in simulated testing. A comparative analysis in relation to the encryption of logistic maps is given. This research demonstrates that increasing the level of encryption results in increased security. It is obvious that the proposed salting-based encryption method and the multilayer DCT/DST cryptosystem offer better levels of security as they attain the lowest SNR values, −25 dB and −2.5 dB, respectively. In terms of the used evaluation metrics, the proposed multilayer cryptosystem achieved the best results in discrete cosine transform and discrete sine transform, demonstrating a very promising performance. Full article
(This article belongs to the Special Issue Advances in Intelligent Systems and Networks)
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25 pages, 80707 KB  
Article
A Novel Plain-Text Related Image Encryption Algorithm Based on LB Compound Chaotic Map
by Shijie Zhang, Lingfeng Liu and Hongyue Xiang
Mathematics 2021, 9(21), 2778; https://doi.org/10.3390/math9212778 - 2 Nov 2021
Cited by 13 | Viewed by 2541
Abstract
Chaos systems have been widely used in image encryption algorithms. In this article, we introduce an LB (Logistic-Baker) compound chaotic map that can greatly improve the complexity of original Logistic map and Baker map, as well as the generated sequences have pseudo-randomness. Furthermore, [...] Read more.
Chaos systems have been widely used in image encryption algorithms. In this article, we introduce an LB (Logistic-Baker) compound chaotic map that can greatly improve the complexity of original Logistic map and Baker map, as well as the generated sequences have pseudo-randomness. Furthermore, based on the LB compound chaotic map, an image encryption algorithm is proposed. To resist the differential attack, and enhance the sensitivity of plain-text, the parameters of this algorithm are plain-text related. In this algorithm, the compound chaotic function is influenced by the plain-text image; thus, the specific form of this chaotic map, and its dynamics will be different when encrypting different images. Numerical experiment results indicate that the effect of this novel plain-text related image encryption scheme is excellent, as well as can be competitive with other corresponding algorithms. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Chaos Theory)
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18 pages, 1449 KB  
Article
Exact Analysis of the Finite Precision Error Generated in Important Chaotic Maps and Complete Numerical Remedy of These Schemes
by Constantinos Chalatsis, Constantin Papaodysseus, Dimitris Arabadjis, Athanasios Rafail Mamatsis and Nikolaos V. Karadimas
Informatics 2021, 8(3), 54; https://doi.org/10.3390/informatics8030054 - 15 Aug 2021
Viewed by 3056
Abstract
A first aim of the present work is the determination of the actual sources of the “finite precision error” generation and accumulation in two important algorithms: Bernoulli’s map and the folded Baker’s map. These two computational schemes attract the attention of a growing [...] Read more.
A first aim of the present work is the determination of the actual sources of the “finite precision error” generation and accumulation in two important algorithms: Bernoulli’s map and the folded Baker’s map. These two computational schemes attract the attention of a growing number of researchers, in connection with a wide range of applications. However, both Bernoulli’s and Baker’s maps, when implemented in a contemporary computing machine, suffer from a very serious numerical error due to the finite word length. This error, causally, causes a failure of these two algorithms after a relatively very small number of iterations. In the present manuscript, novel methods for eliminating this numerical error are presented. In fact, the introduced approach succeeds in executing the Bernoulli’s map and the folded Baker’s map in a computing machine for many hundreds of thousands of iterations, offering results practically free of finite precision error. These successful techniques are based on the determination and understanding of the substantial sources of finite precision (round-off) error, which is generated and accumulated in these two important chaotic maps. Full article
(This article belongs to the Special Issue Computer Arithmetic Adapting to a Changing World)
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34 pages, 996 KB  
Review
The Liang-Kleeman Information Flow: Theory and Applications
by X. San Liang
Entropy 2013, 15(1), 327-360; https://doi.org/10.3390/e15010327 - 18 Jan 2013
Cited by 88 | Viewed by 19022
Abstract
Information flow, or information transfer as it may be referred to, is a fundamental notion in general physics which has wide applications in scientific disciplines. Recently, a rigorous formalism has been established with respect to both deterministic and stochastic systems, with flow measures [...] Read more.
Information flow, or information transfer as it may be referred to, is a fundamental notion in general physics which has wide applications in scientific disciplines. Recently, a rigorous formalism has been established with respect to both deterministic and stochastic systems, with flow measures explicitly obtained. These measures possess some important properties, among which is flow or transfer asymmetry. The formalism has been validated and put to application with a variety of benchmark systems, such as the baker transformation, Hénon map, truncated Burgers-Hopf system, Langevin equation, etc. In the chaotic Burgers-Hopf system, all the transfers, save for one, are essentially zero, indicating that the processes underlying a dynamical phenomenon, albeit complex, could be simple. (Truth is simple.) In the Langevin equation case, it is found that there could be no information flowing from one certain time series to another series, though the two are highly correlated. Information flow/transfer provides a potential measure of the cause–effect relation between dynamical events, a relation usually hidden behind the correlation in a traditional sense. Full article
(This article belongs to the Special Issue Transfer Entropy)
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