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With the rapid growth of the Internet of Things (IoT), the Internet of Medical Things (IoMT) has emerged as a critical sector that enhances convenience and plays a vital role in saving lives. IoMT devices facilitate remote access and control of various medical tools, significantly improving accessibility in the healthcare field. However, the connectivity of these devices to the internet makes them vulnerable to adversarial attacks. Safeguarding medical data becomes a paramount concern, particularly when precise biometric readings are required without compromising patient safety. This paper proposes a fast encryption mechanism to protect the color information in medical videos utilized within the IoMT environment. Our approach involves scrambling medical video frames using a rapid block-splitting method combined with simple operations. Subsequently, the scrambled frames are encrypted using different keys generated from the logistic map. To ensure the practicality of our proposed method in the IoMT setting, we implement the encryption mechanism on a cost-effective Raspberry Pi platform. To evaluate the effectiveness of our proposed mechanism, we conduct comprehensive simulations and security analyses. Notably, we investigate medical test videos during the evaluation process, further validating the applicability of our method. The results confirm our proposed mechanism's robustness by hiding patterns in original videos, achieving high entropy to increase randomness in encrypted videos, reducing the correlation between adjacent pixels in encrypted videos, and resisting various attacks. [ABSTRACT FROM AUTHOR]

Secure transfer of digital images is an important issue in modern image communications. The complexity of encryption algorithms and their key space is a guarantee for security and robustness issues, and the algorithms are competing in this regard while considering time complexity constraints. In this paper, it is tried to increase the encryption complexity and unpredictability of the encryption scheme using different phases of chaos game representation (GCR), logistic map diffusion, and convolutional auto-encoder-based image representation. In the proposed scheme, the original image's pixels are first turned into a binary sequence, after which the CGR algorithm is applied to create a sequence of coordinates in the CGR space. These coordinates are used as the first key, and the pixels of the original image are aligned with this key. Additionally, the second key is generated using the chaotic logistic map to increase the complexity of the key. After that, a randomly weighted convolutional auto-encoder is applied, and the encrypted image resulting from the first two stages is fed to the network for simultaneous diffusion and compression for further complexity increment. The applied convolutional auto-encoder does not require training, and it offers a significant amount of key space, which helps robustness against various attacks. Resulting from the experiments, the average entropy of the encrypted images is relatively high, while the considerable value of the NPCR and UACI criteria denotes the robustness of the approach against differential attacks. This algorithm has demonstrated superiority on both grayscale and color images. [ABSTRACT FROM AUTHOR]

Definition: This entry examines Lorenz's error growth models with quadratic and cubic hypotheses, highlighting their mathematical connections to the non-dissipative Lorenz 1963 model. The quadratic error growth model is the logistic ordinary differential equation (ODE) with a quadratic nonlinear term, while the cubic model is derived by replacing the quadratic term with a cubic one. A variable transformation shows that the cubic model can be converted to the same form as the logistic ODE. The relationship between the continuous logistic ODE and its discrete version, the logistic map, illustrates chaotic behaviors, demonstrating computational chaos with large time steps. A variant of the logistic ODE is proposed to show how finite predictability horizons can be determined, emphasizing the continuous dependence on initial conditions (CDIC) related to stable and unstable asymptotic values. This review also presents the mathematical relationship between the logistic ODE and the non-dissipative Lorenz 1963 model. [ABSTRACT FROM AUTHOR]

This paper examines the intricate dynamics of the logistic map involving impulsive forces that depend on the state. The conditions of stability and border-collision bifurcation (BCB) of periodic orbits are presented. The two-parameter dynamical regions and the two-parameter bifurcation diagram of the system with respect to the system parameter and the strength of impulsive force are constructed. The periodic tongues are given to show that the BCB is critical for the dynamics of the logistic map with state-dependent impulsive forces. Finally, the bifurcation curves are provided to disclose the mechanisms of several bifurcation scenarios closely related to the BCB, including the period increment scenario and the period-adding scenario. [ABSTRACT FROM AUTHOR]

In this research, we have proposed a color image encryption model based on a three-dimensional chaotic logistic map and the JAYA algorithm. The 3-D chaotic logistic map generates three random keys for the color image. Further, the JAYA algorithm is utilized to find the parameter values of a 3-D chaotic logistic map based on the objective function. The JAYA algorithm is chosen because no parameter tuning is required and it has a better convergence rate to find the best solution over others. After generating the random key, exclusive-OR, and pixel-level bits are shuffled to get the final encrypted image. With the typical collection of color images, the simulation assessment was performed. The outcome indicates that the distorted image is entirely noisy. In comparison to best-practice approaches described in the literature, the suggested model outperforms them in terms of entropy while demonstrating poor PSNR and CC. [ABSTRACT FROM AUTHOR]

Atherosclerosis, a leading cause of cardiovascular disease, necessitates advanced and innovative modeling techniques to better understand and predict plaque dynamics. The present work presents two distinct hypothetical models inspired by different research fields: the logistic map from chaos theory and Markov models from stochastic processes. The logistic map effectively models the nonlinear progression and sudden changes in plaque stability, reflecting the chaotic nature of atherosclerotic events. In contrast, Markov models, including traditional Markov chains, spatial Markov models, and Markov random fields, provide a probabilistic framework to assess plaque stability and transitions. Spatial Markov models, visualized through heatmaps, highlight the spatial distribution of transition probabilities, emphasizing local interactions and dependencies. Markov random fields incorporate complex spatial interactions, inspired by advances in physics and computational biology, but present challenges in parameter estimation and computational complexity. While these hypothetical models offer promising insights, they require rigorous validation with real-world data to confirm their accuracy and applicability. This study underscores the importance of interdisciplinary approaches in developing theoretical models for atherosclerotic plaques. [ABSTRACT FROM AUTHOR]

Unarguably performance is a critical factor to the success of any cipher. Al-Beit Serpent is more secure than advanced encryption standard (AES), it faces limitations such as speed and memory requirement. Hence, this paper proffers a text encryption method that ameliorates the performance by running Serpent in parallel using the counter (CTR) encryption mode and further enhances the security by generating sub-keys for each block using logistic map. The intricate logistic map generated keys adds robustness to the proposed algorithm. Comprehensive experiments using Python 3.9 on commonly used metrics verify the efficacy of the proposed method in terms of execution time, central processing unit (CPU) usage, security analysis including key space, strict avalanche effect and its randomness. The encryption/decryption reduction rate reached up to 80.81%. It is worthy of note that it is effectually resistant to brute force attacks having a large key space in addition to its dependency on the number of blocks besides the randomly generated keys. The enhanced Serpent was examined using the statistical test suite (STS) recommended by the National Institute of Standards and Technology (NIST) and verified its randomness by passing all tests. Furthermore, it efficaciously resisted statistical analysis, particularly histogram and correlation coefficient analysis. Moreover, it prevails over current methods when juxtaposed with them in terms of performance, key space, key sensitivity, avalanche effect, histogram analysis and correlation coefficient, ergo affirming its efficiency. [ABSTRACT FROM AUTHOR]

The goal of cryptography is to provide algorithms that safeguard sensitive information sent via unprotected networks. These methods encrypt the information, making it unintelligible even if adversaries manage to get it. The substitution box (S-box) structure is the most significant and nonlinear component of the Advanced Encryption Standard (AES) algorithm. In the algorithm, the S-box supplies the confusion or mixing process. A highly non-linearity-valued S-box significantly boosts defenses against a range of threats. Unfortunately, the achievable encryption throughput is constrained by the computationally costly nature of creating S-boxes. This emphasizes the necessity of creating new S-box generators with the best strength and minimum computing requirements to provide optimal security. We presented an efficient approach that uses the composition of Frobenius automorphism and Mobius transformation of G F (2 8) . In this way, we got two highly nonlinear permutations that can produce millions of S-boxes with very strong cryptographic strength. The dynamic behavior of the proposed generator is analyzed by clarifying the requirements for generating distinct S-boxes and ensuring that the produced S-boxes have a uniform probability distribution. Our generator can produce S-boxes with robust cryptographic features, according to a thorough security study. Our novel generation method for building S-boxes efficiently combines the benefits of both algebraic modeling and chaotic mapping, providing a solid basis for building robust S-boxes. Our approach can guarantee that the produced S-boxes have strong variety and outstanding comprehensive performance by using the ergodicity of the chaotic system. Additionally, the experimental findings presented in this study validate that the dynamic S-boxes generated by our technique not only satisfy the criteria for creating encryption methods but also provide enhanced security for picture encryption. Furthermore, our approach generates S-boxes with good efficiency. Our technique has a wide range of possible applications in cryptography, including the creation of dynamic S-boxes for encryption algorithms and high-performance S-boxes for image security. In light of current security risks and computing demands, our theoretical and computational evaluations indicate that our S-box generator is a good contender for real-world applications. [ABSTRACT FROM AUTHOR]

This entry examines Lorenz’s error growth models with quadratic and cubic hypotheses, highlighting their mathematical connections to the non-dissipative Lorenz 1963 model. The quadratic error growth model is the logistic ordinary differential equation (ODE) with a quadratic nonlinear term, while the cubic model is derived by replacing the quadratic term with a cubic one. A variable transformation shows that the cubic model can be converted to the same form as the logistic ODE. The relationship between the continuous logistic ODE and its discrete version, the logistic map, illustrates chaotic behaviors, demonstrating computational chaos with large time steps. A variant of the logistic ODE is proposed to show how finite predictability horizons can be determined, emphasizing the continuous dependence on initial conditions (CDIC) related to stable and unstable asymptotic values. This review also presents the mathematical relationship between the logistic ODE and the non-dissipative Lorenz 1963 model.

Face recognition uses biometric technologies to identify humans based on their facial characteristics. This method is commonly used to restrict information access control. The benefits of face recognition systems encompass their ease of use and security. The human face recognition process consists of face detection, face tracking, and face recognition. The process uses some algorithms: the Viola-Jones for face detection, the Kanade-Lucas-Tomasi (KLT) for face tracking, and the principal component analysis (PCA) for face recognition. Furthermore, this research proposed face recognition with an encryption process to protect the data stored in a database. The encryption process consists of two main processes: confusion and diffusion. The confusion process is randomizing the position of the original image pixels. This research utilized the Arnold’s cat map (ACM) for the confusion process, and the diffusion process was performed using the XOR operation with the key generated from the 1D chaos system. Three different 1D chaos systems, namely logistic map, Bernoulli map, and tent map, were compared to see which chaos system had the best encryption results. Tests were conducted by comparing various parameters on the three proposed 1D chaos systems, including correlation coefficient, histogram analysis, entropy value, number of pixel rate changes (NPCR), and unified average change intensity (UACI). Based on testing the image encryption results, the diffusion process utilizing the tent map produced the best image encryption compared to other chaotic systems.

Despite the easy construction and low hardware cost of the lower-order chaotic maps, they tend to endure a restricted set of controlling parameters and convergence periodicity, making them inappropriate for many real-time implementations of ciphering devices. To provide solution to above stated difficulty, a high dimensional image cryptosystem is proposed in this work. This study offers a novel Five Dimensional Gauss-Logistic DNA System (GLDS). The 5D GLDS is a complex five dimensional combination with DNA encoding of two popular 2D chaotic systems. Due to extensive pixel scrambling, the cryptographic complexity of the 5D Gauss Logistic Map is significantly increased. Further it is used with another hybrid chaotic maps combination, to realize the enhanced security in this work. The latter hybrid system incorporates a triad map, namely, the Standard map, Sine map, and Logistic map, which makes the system more resilient to attacks. The results show that the encoded image's histograms are equally distributed, with entropy values that are significantly closer to their bit depth. The system allows for a very large key space that can withstand crypto attacks. The statistical findings and security analysis indicate that the proposed 5D GLDS provides quality security when compared to some established cryptographic threats. [ABSTRACT FROM AUTHOR]

One technique, especially in chaos-based cryptographic applications, is to include the message in the evolution of the dynamical system. This paper aims to find out if and to what extent the statistical behavior of the chaotic system is affected by the message inclusion in its dynamic evolution. The study is illustrated by the dynamical system described by the logistic map in cryptographic applications based on images. The evaluation of the statistical behavior was performed on an original scheme proposed. The Monte Carlo analysis of the applied Kolmogorov–Smirnov statistical test revealed that the dynamical system in the processing scheme with message inclusion does not modify its proper statistical behavior (revealed by definition relation). This was possible due to the proposed scheme designed. Namely, this scheme contains a decision switch which, supported by an appropriate choice of the magnitude of the scaling factor, ensures that the values of the dynamical system are maintained in the definition domain. The proposed framework for analyzing the statistical properties and for preserving the dynamical system behavior is one main contribution of this research. The message inclusion scheme also provides an enhancement with cryptographic mixing functions applied internally; the statistical behavior of the dynamical system is also analyzed in this case. Thus, the paper contributes to the theoretical complex characterization of the dynamical system considering also the message inclusion case. [ABSTRACT FROM AUTHOR]

The parallel computing power of quantum computing and the special properties of qubits provide an effective solution for image processing tasks. This paper presents a quantum image encryption algorithm based on Fisher–Yates algorithm and Logistic mapping. Firstly, the Fisher–Yates algorithm is used to generate three key sequences, one of which is used to encode the coordinate qubits of the image. Using the other two keys and the preset rules, the quantum coordinate scrambling operation is designed based on the encoded coordinate qubit, which effectively scrambles the spatial information of the plaintext image. Next, another set of key sequences is generated, one of which is used to encode the color qubits of the image. Using two other key sequences and different rules, a qubit plane scrambling operation based on coded color qubits is designed, and the color information of image is scrambled successfully. Finally, the quantum key image is generated based on Logistic mapping, and the key image is scrambled based on Fisher–Yates algorithm to improve the key complexity. The final ciphertext image is obtained by performing XOR operation between the original image and the scrambled key image. The complete quantum circuit diagram of the scheme is given in this paper. The experimental results and security analysis prove the effectiveness of the scheme, which provides a large key space and the computational complexity is only O(n). [ABSTRACT FROM AUTHOR]

Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks. [ABSTRACT FROM AUTHOR]

This paper details with a color image encryption algorithm based on bit-plane permutation and dynamic Deoxyribonucleic acid (DNA) technology (CIEA-BPD) is proposed by using Logistic map. The proposed scheme is using Logistic map for generating permutation sequence to shuffle the color bit planes of three components and masking matrices combined with DNA technology to diffuse the pixel value of the color image. Through classical security analysis, CIEA-BPD can withstand different attacks. Experimental results verify that CIEA-BPD can efficiently encrypt a random-like cipher-image with a high degree of security. [ABSTRACT FROM AUTHOR]

A proposed algorithm for digital image encryption is presented in this paper. It combines permutation and substitution techniques. Logistic map which is a chaos function is used in both techniques. Before encrypting, the keystream is generated first from the logistics map. Then, the plain image's pixel positions are shuffled with perfect shuffle permutation based on ascending keystream order, thereby executing the permutation process. Next, the pixel values are substituted using the XOR operation with a keystream which is also generated from the logistic map. Pixels are operated in cipher block chain mode. This research aim is to develop an image encryption algorithm, especially in the permutation process, that has high resistance to attacks by crackers. The attack types observed in this research include statistical attacks, permutation matrix attacks, differential attacks, as well as brute force attacks. From the experimental results and analysis of the proposed algorithm indicate that it has high resistance from all those attacks. [ABSTRACT FROM AUTHOR]

Images are considered crucial for conveying information due to their visualisation properties and capacity to hold a large amount of data. To safeguard image data from potential risks of information leakage, numerous image encryption algorithms have been developed. These algorithms often make use of chaotic maps, known for their high unpredictability, ergodicity, and sensitivity to parameters and initial values. This paper introduces a new chaos-based digital image encryption algorithm to protect digital images from unauthorised access or attacks. The algorithm heavily relies on permutation and diffusion processes. Specifically, it employs two rounds of pixel permutation using a Tinkerbell chaotic map sequence on the source image and two rounds of pixel diffusion using the Linear Feedback Shift Register and Logistic Map sequences on the permuted image. The encryption algorithm's effectiveness is thoroughly examined through various cryptanalysis techniques, including key space analysis, information entropy, correlation coefficient, differential attack, key sensitivity, histogram analysis, occlusion attack, noise attack, and encryption execution time. The experimental results are then compared with the most recent literature to demonstrate the algorithm's reliability and its ability to withstand diverse attacks. Notably, the proposed algorithm stands out as a secure and viable encryption solution, requiring less computational time than previous studies, thus making it a more practical option for real-world applications. [ABSTRACT FROM AUTHOR]

Abstract In the last few years, multimedia technology has made tremendous strides. These days, the Web is frequently used to transfer multimedia content, including audio, video, and photos. However, the Internet is a very vulnerable medium with many security holes. To ensure that multimedia content carried across unprotected channels, like the Internet, is secure and private, several encryption techniques have been proposed. New encryption strategies must be developed because multimedia data streams cannot be encrypted using traditional methods. Therefore, the main goal of the recommended system is to present an analytical research approach for introducing a sophisticated framework wherein the suggested encryption technologies' efficacy is increased through the use of deep neural networks (DNNs). The robustness of the DNN principle is coupled with a discrete memristor-based logistic chaotic map notion for enhanced security performance. In this paper, three distinct encryption algorithms—Arnie cat with an artificial neural network (ANN), Henon map with an ANN, and logistic map with a DNN—are compared for security and performance with the suggested algorithm. Correlation coefficients, information entropy, number of pixels changing rate (NPCR), encryption quality, and encryption duration are the cryptographic analysis parameters examined here. The results show that the recommended implementation enhances security performance without degrading image quality. The proposed algorithm achieves 35.9% of UACI, 99.95% of NPCR, and 7.997231 of entropy.

This paper presents a new method of generating chaotic maps that do not have fixed points. The method uses an appropriate transformation of functions defined on the unit square in such a way that the newly created projection has no fixed points. In this way, countless new chaotic mappings can be created, both piecewise linear and nonlinear, that belong to the family of systems with hidden attractors. The new family of maps is presented in three examples showing phase diagrams, bifurcation diagrams, and space parameters of the Lyapunov exponent. The discussed examples of mappings were created by appropriate logistic and tent mapping transformations, and their combination. In addition, this paper analyzes the applications of the new families of chaotic mappings in chaotic cryptography. Furthermore, an algorithm for generating pseudorandom bit values (PRBG) is also presented based on the examples of proposed mappings. [ABSTRACT FROM AUTHOR]

Chaotic systems have good characteristics, such as sensitivity to initial value and parameter, ergodicity, certainty and so on. Using chaos to generate pseudo-random sequences for encryption has good efficiency and security. However, due to the limitation of computing precision, the chaotic sequence running on the computer will enter a cycle after several times of iterations. In this paper, a control method is proposed to reduce this phenomenon. In this method, one chaotic map is used to adjust the parameters of another chaotic map, which makes the sequence generated by this model has good dynamic characteristics under a low computing precision. To prove the effectiveness of this model, two examples are provided. Furthermore, the dynamical performances of these two chaotic systems have been demonstrated by a series of analyses. [ABSTRACT FROM AUTHOR]

To prevent sensitive images shared on social media from being stolen, researchers are seeking to find and innovate image encryption algorithms. Since attackers attempt to exploit it to access encrypted images, the problem of generating keys as the first stage of any encryption algorithm is regarded as a critical problem. This issue was dealt with in this paper through the use of the logistic map. This map must be calculated using specific conditions and special parameters to maintain its chaos. The Diffie-Hellman key exchange algorithm was modified to address this problem since the shared keys now consist of a 16-element vector. The first two elements will be used for a logistic map. The entire vector was used to create a self-invertible matrix. The encryption level entails two operations: the first is matrix multiplication with a vector, and the second is a bitwise XOR operation between two matrices. A proposed encryption algorithm is capable of producing encrypted images that are challenging to decrypt through the use of stringent security tests. The outcomes of each test show how well the proposed encryption algorithm performs compared with other algorithms and how to resist the attacks. [ABSTRACT FROM AUTHOR]

To further enhance the security of image encryption, a new chaos-based image encryption algorithm (IEA) based on discrete Fourier transform and Joseph traversal is proposed to encrypt the plain image in both the frequency domain and space domain simultaneously. In the proposed IEA, the logistic map is used to generate the appropriate chaotic sequence, and the improved Joseph traversal is used to scramble the image in different starting positions and variable step sizes. Then, block diffusion is performed at the end. The main finding concerning the proposed IEA is that the combination of discrete Fourier transform and Joseph traversal can enhance the security of the image information, which has been validated by measuring the performance in resisting the common types of attacks. [ABSTRACT FROM AUTHOR]

In this paper, we study the q-deformed logistic map in Mann orbit (superior orbit) which is a two-step fixed point iterative algorithm. The main aim of this paper is to investigate the whole dynamical behavior of the proposed map through various techniques such as fixed point and stability approach, time-series analysis, bifurcation plot, Lyapunov exponent and cobweb diagram. We notice that the chaotic behavior of q-deformed logistic map can be controlled by choosing control parameters carefully. The convergence and stability range of the map can be increased substantially. Moreover, with the help of bifurcation diagrams, we prove that the stability performance of this map is larger than that of existing other one dimensional chaotic maps. This map may have better applications than that of classical logistic map in various situations as its stability performance is larger. [ABSTRACT FROM AUTHOR]

Three one-dimensional maps are presented. The maps are analysed with a combination of Feigenbaum diagrams, the calculation of global Lyapunov exponents, and the evaluation of fixed points. It is shown that in certain cases period two orbits can be evaluated by careful observation of the form of the related pairs of equations. A range of classroom exercises are provided to enable students to investigate the maps further. [ABSTRACT FROM AUTHOR]

In the last few years, multimedia technology has made tremendous strides. These days, the Web is frequently used to transfer multimedia content, including audio, video, and photos. However, the Internet is a very vulnerable medium with many security holes. To ensure that multimedia content carried across unprotected channels, like the Internet, is secure and private, several encryption techniques have been proposed. New encryption strategies must be developed because multimedia data streams cannot be encrypted using traditional methods. Therefore, the main goal of the recommended system is to present an analytical research approach for introducing a sophisticated framework wherein the suggested encryption technologies' efficacy is increased through the use of deep neural networks (DNNs). The robustness of the DNN principle is coupled with a discrete memristor-based logistic chaotic map notion for enhanced security performance. In this paper, three distinct encryption algorithms—Arnie cat with an artificial neural network (ANN), Henon map with an ANN, and logistic map with a DNN—are compared for security and performance with the suggested algorithm. Correlation coefficients, information entropy, number of pixels changing rate (NPCR), encryption quality, and encryption duration are the cryptographic analysis parameters examined here. The results show that the recommended implementation enhances security performance without degrading image quality. The proposed algorithm achieves 35.9% of UACI, 99.95% of NPCR, and 7.997231 of entropy. [ABSTRACT FROM AUTHOR]

We study reservoir computing, a machine learning method, from the viewpoint of learning dynamics. We present numerical results of learning the dynamics of the logistic map, one of the typical examples of chaotic dynamical systems, using a 30-node reservoir and a three-node reservoir. When the learning is successful, an attractor that is smoothly conjugate to the logistic map to be learned is observed in the phase space of the reservoir. Inspired by this numerical result, we introduce a degenerate reservoir system and use it to mathematically confirm this observation. We also show that reservoir computing can learn information about dynamics not included in the training data, which we believe is a remarkable feature of reservoir computing compared to other machine learning methods. We discuss this feature in connection with the above observation that there is a smooth conjugacy between the attractor in the reservoir and the dynamics to be learned. [ABSTRACT FROM AUTHOR]

The secrecy of various forms of multimedia data constitutes a significant aspect of the cybersecurity field. In this case, chaos-based image ciphers can be adapted. Chaotic image encryption has been investigated in the literature using different transformation domains, such as spatial, discrete Fourier transform, wavelet transform, etc. Although some frequency-based cryptosystems exhibit favorable confusion properties, they may suffer in terms of diffusion properties and fail in terms of some statistical characteristics, which make them vulnerable to various statistical, analytical, and differential attacks. In this regard, we adopt a dual-domain (wavelet and spatial domains) image cryptosystem and propose a novel diffusion process in the wavelet domain to address the problem of weak resilience against the aforementioned attacks. The proposed diffusion process in the wavelet domain is applied only on 1/16 of the pixels of the plain image, which makes it computationally more efficient compared to the existing wavelet domain-based works. In addition, the proposed cryptosystem solves the bell shape histogram problem associated with some frequency-based cryptosystems, which has been verified using different performance metrics in our simulation results. We also introduce a novel key-dependent chaotic variable generator to generate the required initial conditions and control parameters for the adopted enhanced chaotic map. The superiority of the proposed algorithm compared to some of the existing state-of-the-art has been verified through various performance metrics. These include different types of correlation coefficients, histogram visualization, histogram deviation, irregular deviation, mean square error, chi-square test, entropy test, and differential analysis.

Substitution boxes (S-Boxes) are essential elements of modern block ciphers, serving as non-linear characteristics that enhance the resistance of these ciphers against cryptanalysis. This research presents a new approach for constructing lightweight S-Boxes that possess strong cryptographic characteristics by combining an enhanced logistic map and an enhanced sine map. The proposed novel algorithm has optimized multiple parameters according to the security threshold set. This study has conducted the most comprehensive evaluation of criteria for S-Boxes to date. The analysis results of the generated $4\times 4$ and $5\times 5$ S-Boxes have achieved optimal criteria in terms of the Strict Avalanche Criterion (SAC) and the Bit Independence Criterion (BIC) that no previous S-Boxes have achieved. Furthermore, parameters related to side-channel attack resistance have been optimized in the design stage of S-Boxes. The constructed S-Boxes with high security can be applied to replace S-Boxes of the same size in existing algorithms or to develop lightweight block cipher algorithms. This research has made a significant contribution to the construction of S-Boxes.

Medical image encryption is essential to protect the privacy and confidentiality of patients’ medical records. Deep learning-based encryption, which leverages the nonlinear characteristics of neural networks, has emerged as a promising new method for protecting medical images. In this paper, we present insights into deep learning-based medical image encryption and propose a novel end-to-end medical image encryption scheme based on these insights that leverages feature encoding and decoding for encrypting and decrypting images. Firstly, we explore a method that combines keys generated by the Logistic Map with encoded plaintext image features to improve network diffusion performance. Secondly, we employ a reversible neural network to enhance plaintext image reconstruction while maintaining encryption effectiveness. Finally, we propose a series of novel loss functions to measure the cost with the ideal cryptographic algorithm and continuously optimize our network. Experimental results demonstrate that our scheme improves the performance of image encryption and decryption and resists brute force attacks, statistical attacks, noise and cropping attacks.

Researchers concentrate on data security using cryptography, using different approaches to protect confidential data, such as digital images holding private information. They use cryptography techniques, frequently using elliptic curves and chaotic structures for secure transmission. This paper introduces a novel technique for constructing S- boxes and their application in color image encryption. The utilization of discrete chaotic maps and elliptic curves results in low computational complexity, which is crucial for high-speed communication systems. The generation of S- boxes is based on elliptic curves over prime fields and discrete chaotic maps. The color image encryption scheme involves permutation, substitution, and bit-wise XOR operations of key with the color image’s corresponding substituted channels. The resistance of the newly constructed s-boxes against common attacks, such as linear, differential, and algebraic attacks, is analyzed by evaluating their non-linearity, linear approximation probability, differential approximation probability, bit avalanche criterion, and bit independence criterion. The encrypted images have strong resistance against statistical and differential attacks. Experimental results demonstrate that the newly constructed scheme can efficiently generate numerous distinct, uncorrelated, and secure S- boxes, outperforming some well-known existing techniques. The non-linearity of the proposed s-box is 107.5 and the entropy of the ciphered image of Baboon is 7.9989. The security analysis indicates that the color-encrypted image offers fast and higher protection against attacks, making it suitable for real-time applications with high security requirements.

In cryptography, a mode of operation is the way of processing plaintext and encrypted text blocks within a block cipher algorithm, or it is the presentation of a method of chaining blocks in a block cipher. Several models exist with their strengths, some are more vulnerable than others, and some combine authentication and security concepts. In this paper, a new mode of operation is proposed, inspired by the braid of long hair which we call mode CBLCH (Cipher Braided Long Hair Chaining). The HILL cipher will be used to validate it and to compare it with ECB (Electronic Code-Book: code dictionary) and CBC mode (Cipher Block Chaining: sequence of blocks) by the influence of a pixel change on the plaint-image and the encrypted image.

This study focuses on the application of the logistic map algorithm in the Python programming language for digital image encryption and decryption. It investigates the impact of image type, image size, and logistic map parameter values on computational speed, memory usage, encryption, and decryption results. Three image sizes (300px 300px, 500px x 500px, and 1024px x 1024px) are considered in TIFF, JPG, and PNG formats. The digital image encryption and Decryption process utilizes the logistic map algorithm implemented in Python. Various parameter values are tested for each image type and size to analyze encryption and decryption outcomes. The findings indicate that the type of image does not affect memory usage, which remains consistent regardless of image type. However, image type significantly influences the decryption results and computation time. In particular, the TIFF image type exhibits the fastest computation time, with durations of 0.17188 seconds, 0.28125 seconds, and 1.10938 seconds for 300px x 300px, 500px x 500px, and 1024px x 1024px images, respectively. In addition, the encryption results vary depending on the type of image. The logistic map algorithm is unable to restore encryption results accurately for JPG images. Furthermore, research highlights that higher values of x, Mu and Chaos lead to narrower histogram values, resulting in improved encryption outcomes. This study contributes to the field by exploring the application of the logistic map algorithm in Python and analyzing the effects of image type, image size, and Logistic Map parameter values on computation time, memory usage, and digital image encryption and Decryption results. Prior research has not extensively addressed these aspects in relation to the Logistic Map algorithm in Python.

Atherosclerosis, a leading cause of cardiovascular disease, necessitates advanced and innovative modeling techniques to better understand and predict plaque dynamics. The present work presents two distinct hypothetical models inspired by different research fields: the logistic map from chaos theory and Markov models from stochastic processes. The logistic map effectively models the nonlinear progression and sudden changes in plaque stability, reflecting the chaotic nature of atherosclerotic events. In contrast, Markov models, including traditional Markov chains, spatial Markov models, and Markov random fields, provide a probabilistic framework to assess plaque stability and transitions. Spatial Markov models, visualized through heatmaps, highlight the spatial distribution of transition probabilities, emphasizing local interactions and dependencies. Markov random fields incorporate complex spatial interactions, inspired by advances in physics and computational biology, but present challenges in parameter estimation and computational complexity. While these hypothetical models offer promising insights, they require rigorous validation with real-world data to confirm their accuracy and applicability. This study underscores the importance of interdisciplinary approaches in developing theoretical models for atherosclerotic plaques.

In an era characterized by unparalleled levels of data exchange and communication, ensuring the security of network transmissions emerges as a paramount concern. This paper undertakes a comprehensive exploration aimed at bolstering network security through the integration of Chaotic Maps with the robust ChaCha20 encryption algorithm. This pioneering approach seeks to introduce an additional stratum of intricacy and unpredictability to data encryption processes, thereby augmenting the confidentiality and integrity of information in transit. The investigation delves deeply into the theoretical underpinnings, practical implementation intricacies, thorough security analysis, and diverse real-world applications of this enhanced encryption framework. By offering a multifaceted examination, this study provides invaluable insights and guidance not only for network professionals but also for researchers operating within this dynamic field. Through its rigorous examination and innovative proposals, this paper contributes significantly to the ongoing discourse surrounding network security enhancement strategies. [ABSTRACT FROM AUTHOR]

Economic dispatch, emission dispatch, or their combination (EcD, EmD, EED) are essential issues in power systems optimization that focus on optimizing the efficient and sustainable use of energy resources to meet power demand. A new algorithm is proposed in this article to solve the dispatch problems with/without considering wind units. It is based on the Social Group Optimization (SGO) algorithm, but some features related to the selection and update of heuristics used to generate new solutions are changed. By applying the highly disruptive polynomial operator (HDP) and by generating sequences of random and chaotic numbers, the perturbation of the vectors composing the heuristics is achieved in our Modified Social Group Optimization (MSGO). Its effectiveness was investigated in 10-unit and 40-unit power systems, considering valve-point effects, transmission line losses, and inclusion of wind-based sources, implemented in four case studies. The results obtained for the 10-unit system indicate a very good MSGO performance, in terms of cost and emissions. The average cost reduction of MSGO compared to SGO is 368.1 $/h, 416.7 $/h, and 525.0 $/h for the 40-unit systems. The inclusion of wind units leads to 10% reduction in cost and 45% in emissions. Our modifications to MSGO lead to better convergence and higher-quality solutions than SGO or other competing algorithms. [ABSTRACT FROM AUTHOR]

The work presented here is a high dimensional color image encryption architecture (HDIEA) founded on the Lorenz-Gauss-Logistic (LGL) encryption algorithm. The primary objective is to demonstrate that both the proposed novel five-dimensional (5D) Gauss-Logistic and four-dimensional (4D) Lorenz system are operating in a hyper-chaotic condition. The visual study of their most important characteristics, such as the sensitivity of the starting value of both maps and the Lyapunov exponent of the 5D Gauss Logistic map, is carried out. The Runge–Kutta technique is used to discretise the Lorenz system in order to construct a pseudo-random sequence generation for the control parameter that has a greater degree of randomness. The 5D Gauss-Logistic system is then selected to serve as the principal hyper-chaotic mapping scheme. The simulation results demonstrate that the suggested image encryption method is successful according to the NIST test and has powerful anti-attack, a larger key space as large as 2847, which is prone to multiple attacks, and key sensitivity capabilities. Also, the pixel correlation reached −0.0019, −0.0016, and −0.0069, while the information entropy was at 7.9996. This demonstrates the excellent scrambling effect of the proposed approach, which is capable of greatly improving the color image security performance. [ABSTRACT FROM AUTHOR]

Image encryption plays a crucial role in ensuring the security and confidentiality of digital image data. This study explores an image encryption approach that employs the RC4 algorithm with the chaotic Logistic Map and with varying key lengths. The encryption quality assesses using metrics such as Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), The Normalized Cross Correlation Coefficient (NCC), Structural Similarity Index Measure (SSIM), and Histogram. Results demonstrated that the Logistic Map-based encryption method successfully balanced image quality and security. The study's contributions lie in offering valuable insights into image encryption techniques, providing a practical method for secure image communication and storage. [ABSTRACT FROM AUTHOR]

The media content shared on the internet has increased tremendously nowadays. The streaming service has major role in contributing to internet traffic all over the world. As the major content shared are in the form of images and rapid increase in computing power a better and complex encryption standard is needed to protect this data from being leaked to unauthorized person. Our proposed system makes use of chaotic maps, deoxyribonucleic acid (DNA) coding and ribonucleic acid (RNA) coding technique to encrypt the image. As videos are nothing but collection of images played at the rate of minimum 30 frames/images per second, this methodology can also be used to encrypt videos. The complexity and dynamic nature of chaotic systems makes decryption of content by unauthorized personal difficult. The hybrid usage of chaotic systems along with DNA and RNA sequencing improves the encryption efficiency of the algorithm and also makes it possible to decrypt the images at the same time without consuming too much of computation power. [ABSTRACT FROM AUTHOR]

Several cancelable biometric procedures have been developed to preserve personal data security. This research presents a cancelable biometric authentication mechanism to ensure personal data security, while maintaining the biometric templates secure from hackers. Therefore, our major approach is to provide a new authentication system based on 3D chaotic maps, Piecewise Linear Chaotic Map (PWLCM), logistic map, and Deoxyribonucleic Acid (DNA) sequencing theory. The approach is based on confusion as well as a diffusion. Firstly, a 3D chaotic map is made up to allow 3D chaos creation, chaos histogram equalization, row rotation, column rotation, and XOR operation. Secondly, the PWLCM and the Logistic Map are used for generating the main values required to make use of the DNA theory to generate the key image. Thirdly, DNA theory is applied as a second encryption algorithm on the output of the 3D chaotic algorithm. Fourthly, the intermediate image is decoded, rotated 90 degrees anticlockwise, and used in the following step in the DNA encoding process. Finally, step 3 is repeated on columns to acquire the final encrypted image. The proposed framework hides all discriminative properties of biometric templates, resulting in a fully unspecified biometric pattern. Various face, as well as palmprint biometric datasets, have been examined and evaluated. Various evaluation factors are employed to examine the efficiency of the recommended cryptography algorithm including Area under the Receiver Operating Characteristic (AROC), False Acceptance Rate (FAR), histogram analysis, Histogram Deviation ( D H ), correlation coefficient, Structural Similarity Index Metric (SSIM), and Peak Signal-to-Noise Ratio (PSNR). The computational results prove that the proposed cryptosystem is trustworthy. A comparative study of the recommended approach with various strategies is also provided. Simulation studies illustrate that the suggested approach produces an average AROC of approximately 1, an average FAR of 6.2 × 10 - 3 , an average D H of 0.8755, and finally, an average PSNR of 8.2061. [ABSTRACT FROM AUTHOR]

Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks.