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Currently, despite advances in the analysis of dynamical systems, there are still doubts about the transition between both stable and chaotic behaviors. In this research, we will explain the transition of a system that develops between two dynamic systems that have already been studied: the classical logistic model and a new chaotic system. This research addresses the study of the transition of both the system and its behaviors using computational techniques, where cobweb diagrams, time series, bifurcation diagrams, and even a graphical visualization for the maximum Lyapunov exponent will be visualized. Using a graphical and numerical methodology, bifurcation points were identified that revealed the transition of behaviors at different points. This resulted in a deep understanding of the dynamics of the system, thus highlighting the importance of incorporating computational analysis in dynamic systems, which greatly contributes to the efficient modeling of natural phenomena. [ABSTRACT FROM AUTHOR]

This study presents a novel encryption method for RGB (Red–Green–Blue) color images that combines scrambling techniques with the logistic map equation. In this method, image scrambling serves as a reversible transformation, rendering the image unintelligible to unauthorized users and thus enhancing security against potential attacks. The proposed encryption scheme, called Bit-Plane Representation of Quantum Images (BRQI), utilizes quantum operations in conjunction with a one-dimensional chaotic system to increase encryption efficiency. The encryption algorithm operates in two phases: first, the quantum image undergoes scrambling through bit-plane manipulation, and second, the scrambled image is mixed with a key image generated using the logistic map. To assess the performance of the algorithm, simulations and analyses were conducted, evaluating parameters such as entropy (a measure of disorder) and correlation coefficients to confirm the effectiveness and robustness of this algorithm in safeguarding and encoding color images. The results show that the proposed quantum color image encryption algorithm surpasses classical methods in terms of security, robustness, and computational complexity. [ABSTRACT FROM AUTHOR]

Coupled map lattices are a popular and computationally simpler model of pattern formation in nonlinear systems. In this work, we investigate three-site interactions with linear multiplicative coupling in one-dimensional coupled logistic maps that cannot be decomposed into pairwise interactions. We observe the transition to synchronization and the transition to long-range order in space. We coarse-grain the phase space in regions and denote them by spin values. We use two quantifiers the flip rate F(t) that quantify departure from expected band-periodicity as an order parameter. We also study a non-Markovian quantity, known as persistence P(t) to study dynamic phase transitions. Following transitions are observed. (a) Transition to two band attractor state: At this transition F(t) as well as P(t) shows a power-law decay in the range of coupling parameters. Here all sites reach one of the bands. The F(t) as well as P(t) decays as power-law with the decay exponent δ1=0.46 and η1=0.28, respectively. (b) The transition from a fluctuating chaotic state to a homogeneous synchronized fixed point: Here both the quantifiers F(t) and P(t) show power-law decay with decay exponent δ2=1 and η2=0.11, respectively. We compare the transitions with the case, where pairwise interactions are also present. The spatiotemporal evolution is analyzed as the coupling parameter is varied. [ABSTRACT FROM AUTHOR]

The rise of IoT has also brought technological developments and threats. Edge computing has become a vital solution for most networks and demands resource-constrained operations. This work presents a lightweight data encryption scheme based on the Sierpinski Triangle Fractal, Chaotic Logistic map and their FPGA implementation on Intel Cyclone IV E. The size of the fractal geometry emerges from the number of bits in the input. Hence, this algorithm is an input-aware cryptosystem that simultaneously handles all input bits using rotation, random data fitting and diffusion. Further, round keys are supplied through the logistic map, and three incarnations of their FPGA implementations were investigated against randomness. Worst-case inputs have been taken to evaluate the design, and the results are validated through standard metrics. Round keys and cipher data have passed the NIST SP 800–22 test suites, thus evidence of the randomness. The proposed cryptosystem consumes only 944 logic elements (0.8%) and cipher 27/128/256 bits of data concurrently on Cyclone IV E FPGA. Encryption time has been calculated as 400 ns for 50 MHz of operating clock. [ABSTRACT FROM AUTHOR]

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This paper proposes a new entropy-sensitive based data coding algorithm for the secure communication of image information between transceiver systems. The proposed algorithm utilizes chaos theory and the image information content of the reference image to create sensitivity on the decoding side for a high level of secrecy. It successfully recovers secret images at the receiver’s side using secret code series derived from both the secret and reference images, instead of direct transmission of secret image. The image information can be retrieved only through the same reference image, the same system parameters and identical code series using the proper decoding technique at the receiver. Quantitative results indicate that the average coding time for 128x128 images is approximately 0.27 seconds, while the extraction time averages 0.19 seconds, yielding impressive rates of 0.487 Mbps and 0.677 Mbps, respectively. Moreover, according to qualitative results, even a single-bit change in the reference image leads to a complete inability to decode the secret image, highlighting the robustness and security of the algorithm. Experimental results on various images show that the proposed algorithm is reliable, fast and effective in securing confidential image information.

Encryption is crucial because of how integral to daily life things like smartphones, computers, and the internet have become. It's almost inconceivable to think about getting by without it. Everything from paying bills and buying goods to email and social networking is done online nowadays. Participating in measures that can prevent illegal access to our accounts, data, and devices is more crucial than ever. In this study, we combined a 256-by-256-pixel cover picture with a 128-by-128-pixel inner image using the logistic map (the chaotic function), where both images were in the PNG format. where the encrypted image is converted to a grayscale image and then encrypted through the logistic function. the output of this process is chaotic data that has been converted into binary data to be encrypted again through the colors of the cover image (red, green and blue) each separately and measuring the standard factors to know the strength of the system. The bit error rate was calculated after measuring the signal-to-noise ratio (SNR), system similarity(SSIM), and Peak Signal to Noise Ratio(PSNR) for these three hues. Using the logistic map, all three colors were found to be equally secure during encryption in the chaotic signal and due to unpredictability.

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]

Thedivergence from the unstable fixed point of the fractional difference logistic map is investigated in this paper. In contrary to the classical logistic map, the memory horizon of the fractional difference logistic map reaches the initial condition. And though higher order orbits do not exist in the fractional difference logistic map, a trajectory started at the unstable fixed point may continuously remain at the fixed point as the number of iterations tends to infinity. Such an effect is well known for the classical logistic map, but less so in the fractional difference logistic map. It appears that this effect depends on the accuracy of the floating point arithmetic. It is demonstrated that the divergence from the unstable fixed point of the fractional difference logistic map is a completely computational artifact. Using double precision, approximately 32% values of a from the interval 2.7 < a ≤ 3.7 diverge from the unstable fixed point. [ABSTRACT FROM AUTHOR]

Relay node deployment in wireless sensor network (WSN) is significantly explored in specialized literature. There is a wide spectrum of performance issues like connectivity, coverage, energy efficiency, latency of packet delivery that have been considered as the target criteria to be optimized with the deployment strategies of relay nodes. The dynamic variation of different attributes of the sensor nodes leverages a heterogeneous topology. None of the literature has considered a heterogeneity-aware relay node placement strategy to pacify the effect of structural diversity on network performance. In this work, we propose chaos genetic algorithm-based relay node placement (CGARP) which takes care of the structural heterogeneity of WSN. CGARP is based on chaos genetic algorithm (CGA), which overcomes the problem of premature convergence of genetic algorithm. Tent Map-based generation of the initial population and Logistic Map-based chaotic crossover enable CGARP to work well in WSN. The proposed technique has been compared with other relay node placement solutions available in the literature. CGARP achieves 68% improvement in average network lifetime in a 2D grid. It also results in 27% better connectivity and 23% improvement in the usage of relay nodes compared to EERP. The results are obtained through properly designed experiments with simulated realistic environments. These results substantiate the improvements achieved by the proposed approach. [ABSTRACT FROM AUTHOR]

Tampering an image became more manageable due to the advent of photo editing software. So, it is essential to detect and correct the tampered locations. This article presents an image watermarking scheme that applies a modified version of 8 data bits and 4 redundant bits of Hamming code. It operates over a block of 3 pixels at a time. The 24 bits of the 3 pixels are rearranged and divided into 2 processing units, each comprising 12 bits. Out of 12 bits in a unit, 4 bits are used as redundant bits, and 8 bits are used as data bits. Watermark bits (WBs) are generated from data bits using a logistic map (LM) and stored in redundant bit positions. Experimental results reveal that this proposed technique maintains a fair balance for both capacity and distortion. The measured capacity is 2.67 bits per pixel (bpp) with a 39.21 decibels (dB) distortion. The estimated structural similarity (SSIM) is 0.9844, and the accuracy is 0.9999. Furthermore, it was also found that the proposed technique performs fairly well compared to existing techniques in capacity and distortion. [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]

In recent years, conventional logistic maps have been applied across various fields including modeling and security, owing to their versatility and utility. However, their reliance on a single modifiable parameter limits their adaptability. This paper aims to explore generalized logistic maps with arbitrary powers, which offer greater flexibility compared to the standard logistic map. By introducing additional parameters in the form of arbitrary powers, these maps exhibit increased degrees of freedom, thus expanding their applicability across a wider spectrum of scenarios. Consequently, the conventional logistic map emerges as a specific instance within the proposed framework. The inclusion of arbitrary powers enriches system dynamics, enabling a more nuanced exploration of system behavior in diverse contexts. Through a series of illustrations, this study investigates the influence of arbitrary powers and equation parameters on equilibrium points, their positions, stability conditions, basin of attraction, and bifurcation diagrams, including the emergence of chaotic behavior. [ABSTRACT FROM AUTHOR]

This paper proposes a new entropy-sensitive based data coding algorithm for the secure communication of image information between transceiver systems. The proposed algorithm utilizes chaos theory and the image information content of the reference image to create sensitivity on the decoding side for a high level of secrecy. It successfully recovers secret images at the receiver's side using secret code series derived from both the secret and reference images, instead of direct transmission of secret image. The image information can be retrieved only through the same reference image, the same system parameters and identical code series using the proper decoding technique at the receiver. Quantitative results indicate that the average coding time for 128x128 images is approximately 0.27 seconds, while the extraction time averages 0.19 seconds, yielding impressive rates of 0.487 Mbps and 0.677 Mbps, respectively. Moreover, according to qualitative results, even a single-bit change in the reference image leads to a complete inability to decode the secret image, highlighting the robustness and security of the algorithm. Experimental results on various images show that the proposed algorithm is reliable, fast and effective in securing confidential image information. [ABSTRACT FROM AUTHOR]

The security of digital images is increasingly important as the Internet is a growing concern due to the ease with which images can be shared via the Internet. These images need to be protected, and cryptography is the way to achieve this--chaos-based encryption, to be more specific. This work describes a technique of image encryption for colour images using a logistic map with a two-dimensional S-Box and the Hénon 2D map for encryption. The given method S-Box is cleared by several important parameters of evaluation of S-Box and is estimated by such indicators as resistance to the differential attacks, histograms, correlations, and entropy. The results show good efficiency, which can be seen in figures of UACI being equal to 34. 5847%, NPCR at 98. 87%, and entropy at 7. 9994 of the Lena images, 9985 of the Lena images. [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]

Consider a class of quasi-periodically forced logistic maps T × [ 0 , 1 ] ↺: (θ , x) ↦ (θ + ω , c (θ) x (1 − x)) (T = R / Z) , where ω is an irrational frequency and α(θ) is a specific bimodal function. We prove that under weak Liouvillean condition on frequency, the strange non-chaotic attractor occurs with negative Lyapunov exponent. This extends the result in [Bjerklov, CMP, 2009]. [ABSTRACT FROM AUTHOR]

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]

Encryption is crucial because of how integral to daily life things like smartphones, computers, and the internet have become. It's almost inconceivable to think about getting by without it. Everything from paying bills and buying goods to email and social networking is done online nowadays. Participating in measures that can prevent illegal access to our accounts, data, and devices is more crucial than ever. In this study, we combined a 256-by-256-pixel cover picture with a 128-by-128-pixel inner image using the logistic map (the chaotic function), where both images were in the PNG format. where the encrypted image is converted to a grayscale image and then encrypted through the logistic function. the output of this process is chaotic data that has been converted into binary data to be encrypted again through the colors of the cover image (red, green and blue) each separately and measuring the standard factors to know the strength of the system. The bit error rate was calculated after measuring the signal-to-noise ratio (SNR), system similarity(SSIM), and Peak Signal to Noise Ratio(PSNR) for these three hues. Using the logistic map, all three colors were found to be equally secure during encryption in the chaotic signal and due to unpredictability. [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.

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]

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]

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]

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]

Chaotic map-based techniques for image encryption have been widely reported in recent years as a very active area of research. Most of these methods suffer either from slow encryption speeds, efficiency at the cost of security, or violate any one of these two criteria. This work introduces a new algorithm designed with a logistic map, the lightweight PRESENT algorithm, and the AES S-box that can reconcile both efficiency and security requirements. It starts generating some initial parameters for the logistic map using BLAKE2b, which is calculated based on an input image, a shared key and an initialization vector IV. We take the initially computed parameters from the first BLAKE2b hash, set up the logistic map, and use it to generate a sequence of pseudorandom numbers. These random numbers are critically important because they determine how we should rearrange and mix the blocks during encryption. After PRESENT encryption is applied, we apply the AES S-box to replace values in the block. The introduced substitutions are biased by the chaotic values generated by the logistic map to introduce further confusion. In order to evaluate the performance of the algorithm, a set of metrics such as correlation coefficient, entropy, "mean square error (MSE)", "peak signal-tonoise ratio (PSNR)", histogram, "number of pixel change rate (NPCR)", "unified average changing intensity (UACI)", and key space will be utilized. Experimental evaluations reveal that the algorithm holds great promise, with security features at a higher level and with excellent resistance to differential attacks. [ABSTRACT FROM AUTHOR]

This paper deals with the integration of the as logistic map with the different fuzzy number generators, resulting in a hybrid approach of encryption that can leverage the strengths and randomness of both chaotic dynamics and fuzzy logic. The chaotic maps are influenced by the Gaussian fuzzification, which produces bifurcation diagrams that have the fundamental structure of the system's dynamics. By analyzing the chaotic behavior of the various maps and their impact on generating the pseudo-random sequences which can be suitable for the encryption, the fuzzy numbers are added to modify the chaotic systems. The proposed hybrid encryption approach is expected to address the limitations of single chaotic map usage and thus to represent a more effective and efficient encryption approach. The proper security analysis and cryptanalysis of the chaotic encryption algorithms are very important to recognize probable vulnerabilities at the very beginning. Optimization methods for a particular device i.e., GPUs (Graphics Processing Units) or FPGAs, as well as parallel processing exploration, will be the key to improving these algorithms in real-world applications. [ABSTRACT FROM AUTHOR]

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]

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.

This study presents a novel encryption method for RGB (Red–Green–Blue) color images that combines scrambling techniques with the logistic map equation. In this method, image scrambling serves as a reversible transformation, rendering the image unintelligible to unauthorized users and thus enhancing security against potential attacks. The proposed encryption scheme, called Bit-Plane Representation of Quantum Images (BRQI), utilizes quantum operations in conjunction with a one-dimensional chaotic system to increase encryption efficiency. The encryption algorithm operates in two phases: first, the quantum image undergoes scrambling through bit-plane manipulation, and second, the scrambled image is mixed with a key image generated using the logistic map. To assess the performance of the algorithm, simulations and analyses were conducted, evaluating parameters such as entropy (a measure of disorder) and correlation coefficients to confirm the effectiveness and robustness of this algorithm in safeguarding and encoding color images. The results show that the proposed quantum color image encryption algorithm surpasses classical methods in terms of security, robustness, and computational complexity.

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]

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]

There are big challenges to handle the content authentication and tamper detection in speech watermarking techniques. These challenges can be addressed using the detection of epoch locations, logistic mapping, verification of the tamper locations, and the Min algorithm. Epoch events provide the variable length epoch intervals, and it has been used to find the variable lengths of frame segments in this work. The logistic mapping provides strong security for original signals. They can provide a robust and secure method that addresses copyright issues, illegal intentional, or unintentional modifications, and tampered locations. In this paper, we have implemented an epoch event based speech watermarking technique for tamper detection using the logistic map method. It has been observed that the simulation results demonstrated that the PRE value is approximately more than 82% and the PESQ value lies between excellent and good. It means that there are no significant differences between original and watermarked signals and we have obtained a highly imperceptible, robust, and secure system. Moreover, the overall simulation results of the proposed method provide the better solution as well as more security than existing methods. [ABSTRACT FROM AUTHOR]