Three-dimensional Chaotic Map Research Articles

Unmanned ship image encryption method based on a new four-wing three-dimensional chaotic system and compressed sensing

This paper presents a three-dimensional chaotic map with five equilibrium points, which, unlike the classic Lorenz system, possesses a symmetric four-wing structure. Through detailed dynamical analysis and verification, the excellent chaotic properties of this map have been proven. Based on this system, an improved lightweight unmanned surface vehicle (USV) image information encryption system is designed. Given the constraints of USV equipment, the system first compresses images to enhance their storage capacity and transmission efficiency. Subsequently, an enhanced lightweight Feistel network encryption method is developed, utilizing a diagonal interpolation permutation model to ensure the security of the encryption process and reduce its complexity through a block structure. Simulation experiments and data analysis demonstrate that this algorithm effectively ensures the security of image information within the USV system. The use of compressed sensing and a block encryption structure reduces the complexity of the encryption process, thereby enhancing both the encryption efficiency and the transmission efficiency.

SIELNet: 3-D Chaotic-Map-Based Secure Image Encryption Using Customized Residual Dense Spatial Network

The continuous development of Industry 5.0 technology has brought great convenience to people’s work and life. However, during digital data transmission and storage, the data may be accessed by unauthorized persons, resulting in privacy disclosure. Therefore, efficient data protection is always a high demand to solve this realistic problem. This work proposes a secure encryption algorithm, SIELNet, for colour images. First, we introduce a new three-dimensional chaotic map to encrypt colour images, obtaining the cipher images with a relationship to the plain images. We provide its excellent chaotic behaviour through standard randomness test. Secondly, we use a customized residual dense spatial network to perform the task of lossy image reconstruction from an encrypted, compressed image, which solves the constrained super-resolution task. Extensive experimental results on four public datasets demonstrate the superior performance of SIELNet against state-of-the-art techniques with excellent reconstruction quality. We believe the secure design of SIELNet can contribute to the favourable data integrity application of Industry 5.0.

YOLO-based ROI selection for joint encryption and compression of medical images with reconstruction through super-resolution network

Medical images contain significant patient information, and this confidential data should not be accessed without proper authorisation. Concurrently, due to the high redundancy of image data, compression is necessary to minimise image size and efficiently utilise network resources. This paper presents an effective joint encryption and compression method for medical images that prevent critical data leakage while reducing redundancy. Initially, a powerful real-time object detection method, You Only Look Once v7, is employed to accurately and swiftly detect the region of interest (ROI) within the medical images. Subsequently, a joint three-dimensional chaotic map and Huffman encoding are applied to secure medical images without compromising the compression ratio or increasing the time cost. Lastly, a super-resolution network is established at the receiver end to better reconstruct the ROI image for precise diagnostic purposes. The comprehensive experimental analysis demonstrates that our method delivers high levels of security, compression, and visual quality performance on standard datasets used in smart healthcare applications, at a minimum. Furthermore, our approach outperforms other competitive state-of-the-art schemes when compared. We hope this study will inspire further research within the healthcare community.

An Image Encryption Transmission Scheme Based on a Polynomial Chaotic Map.

Most existing chaotic systems have many drawbacks in engineering applications, such as the discontinuous range of chaotic parameters, weak chaotic properties, uneven chaotic sequence outputs, and dynamic degradation. Therefore, based on the above, this paper proposes a new method for the design of a three-dimensional chaotic map. One can obtain the desired number of positive Lyapunov exponents, and can also obtain the desired value of positive Lyapunov exponents. Simulation results show that the proposed system has complex chaotic behavior and high complexity. Finally, the method is implemented into an image encryption transmission scheme and experimental results show that the proposed image encryption scheme can resist brute force attacks, correlation attacks, and differential attacks, so it has a higher security.

Simulink modeling and dynamic characteristics of discrete memristor chaotic system

<sec>In the last two years, the discrete memristor has been proposed, and it is in the early stages of research. Now, it is particularly important to use various simulation softwares to expand the applications of the discrete memristor model. Based on the difference operator, in this paper, a discrete memristor model with quadratic nonlinearity is constructed. The addition, subtraction, multiplication and division of the discrete memristor mathematical model are clarified, and the charge <i>q</i> is obtained by combining the discrete-time summation module, thereby realizing the Simulink simulation of the discrete memristor. The simulation results show that the designed memristor meets the three fingerprints of memristor, indicating that the designed discrete memristor belongs to generalized memristor.</sec><sec>Using memristors to construct chaotic systems is one of the current research hotspots, but most of the literature is about the introduction of continuous memristors into continuous chaotic systems. In this paper, the obtained discrete memristor is introduced into a three-dimensional chaotic map which is mentioned in a Sprott’s book titled as <i>Chaos and Time-Series Analysis</i>, and a new four-dimensional memristor chaotic map is designed. Meanwhile, the Simulink model of the chaotic map is established. It is found that attractors with different sizes and shapes can be observed by changing the parameters in the Simulink model, indicating that the changes of system parameters and memristor parameters can change the dynamic behavior of the system. The analyses of equilibria and equilibrium stability show that the four-dimensional chaotic map has infinite equilibrium points. The Lyapunov exponent spectra and bifurcation diagrams of the circuit imply that the map can transform between weak chaotic state, chaotic state, and hyperchaotic state. Meanwhile, the multistability and coexisting attractors are analyzed under different initial conditions. Moreover, by comparing the results of measuring the complexity, it is found that the chaotic map with discrete memristor has richer dynamical behaviors and higher complexity than the original map.</sec><sec>From the perspective of system modeling, in this paper the discrete memristor modeling and discrete memristor map designing are discussed based on the Matlab/Simulink. It further verifies the realizability and lays a foundation for the future applications of discrete memristor.</sec>

A three-dimensional chaotic map and their applications to digital audio security

In nonlinear dynamical systems, chaotic behavior is an attractive characteristic that has been broadly examined and researched over the most recent few decades. The chaotic systems are widely used in artificial intelligence and cryptology. Especially, these are considered efficient for multimedia data security. This manuscript has introduced a novel three dimensional (3-D) chaotic systems. The proposed maps are investigated through bifurcation diagrams and phase plots. The resulting diagrams demonstrates the chaotic attractor characteristic and the dynamic behavior of the suggested maps. Furthermore, a lossless audio encryption scheme is introduced utilizing the proposed chaotic maps. In the suggested scheme, the suggested 3-D chaotic sequences are utilized to shuffle the audio data points to achieve the diffusion property. In the confusion module, initially, the sequence of the audio data is divided into 8-bit and 7-bit sequences. Subsequently, the separated sequences are then substituted with different good quality substitution boxes, which are generated through a Mobius transformation over Galois fields. The suggested encryption algorithm is applied to the different audio files of various sizes and characters. The experimental results have revealed that the proposed scheme is capable to secure all kinds of audio files. The security analysis shows that the suggested scheme is capable to withstand differential and statistical attacks.

A Novel Color Image Encryption Algorithm Based on Three-Dimensional Chaotic Maps and Reconstruction Techniques

In the paper, a novel color image encryption scheme is proposed by use of the three-dimensional chaotic maps and some data reconstruction techniques. In the diffusion process of the encryption algorithm, the three-dimensional chaotic Logistic map is introduced to changes the pixel value of the plain image. Meanwhile, in the confusion process, the three-dimensional chaotic Cat map is applied to deal with the position of the image pixels. Moreover, some data reconstruction techniques are employed for the better encryption result. Furthermore, the corresponding decryption algorithm is also given. The significant advantages of our method are the effectiveness and simplicity, and our proposed method breaks the correlation between image pixel layers, offers a large key space and against differential and statistical attacks effectively. Finally, the superiority of the proposed algorithm will be shown by the experimental results, security analysis, and the corresponding comparisons with literature.

A Dual Layer Secure Data Encryption and Hiding Scheme for Color Images Using the Three-Dimensional Chaotic Map and Lah Transformation

The rapid increase in the usage of multimedia content and transmission over the internet demands data securing techniques. In this work, a data encryption technique using a three-dimensional chaotic map and highly nonlinear substitution boxes for the encryption of secret images, followed by a data hiding scheme based on Lah transformation i-e the secret image is first encrypted and then hide in the cover image. For data hiding, integer’s polynomial sequence is generated using addition and multiplication in coefficient form by evaluating pixels of images, secret bits of Lah transformed encrypted image are embedded in the LhTs coefficient of cover image partitioned into the cluster of four bits. To ensure minimum distortion coefficient adjustment is done before the embedding process. To obtain the stego image inverse Lah transformation is applied after the embedding process. The security analysis of the proposed dual layer data security scheme is performed, the result shows that the proposed system bearing strong immunity against various cryptographic attacks.

Signal separation in an aggregation of chaotic signals

Abstract Signal separation has many applications in different fields, such as biology. In real-world applications, sometimes, the combined signals are not independent, and their separation is not easy with common methods and needs proper approaches. In this paper, it is assumed that the summation of chaotic signals from one chaotic system is available, and the system's equations are known. The aim is to separate the signals from that summation. The proposed method relies on generating some equations, solving them, and then checking the solutions to be in the attractor region. We examine our method on a two-dimensional and a three-dimensional chaotic map and then generalize it to a continuous-time chaotic flow.

Parallel Encryption of Noisy Images Based on Sequence Generator and Chaotic Measurement Matrix

With the rapid development of information technology in today’s society, the security of transmission and the storage capacity of hardware are increasingly required in the process of image transmission. Compressed sensing technology can achieve data sampling and compression at the rate far lower than that of the Nyquist sampling theorem and can effectively improve the efficiency of information transmission. Aiming at the problem of weak security of compressed sensing, this study combines the cryptographic characteristics of chaotic systems with compressed sensing technology. In the actual research process, the existing image encryption technology needs to be applied to the hardware. This paper focuses on the combination of image encryption based on compressed sensing and digital logic circuits. We propose a novel technology of parallel image encryption based on a sequence generator. It uses a three-dimensional chaotic map with multiple stability to generate a measurement matrix. This study also analyzes the effectiveness, reliability, and security of the parallel encryption algorithm for source noise pollution with different distribution characteristics. Simulation results show that parallel encryption technology can effectively improve the efficiency of information transmission and greatly enhance its security through key space expansion.

A novel method for digital image steganography based on a new three-dimensional chaotic map

This paper, presents a novel chaos-based image steganography algorithm. Because of efficient property of chaos based security systems besides steganography applicability in providing secure communication, chaos based steganography algorithms served as a hot topic in recent researches. The proposed scheme possess novelties and advantageous such as: 1) Introducing a novel 3-dimensional chaotic map (LCA map) with strong chaotic characteristics and maximum Lyapunov exponent 20.58, which is used for generating three chaotic sequences, each of them represents the number of row, column, and colour component, respectively. 2) Utilizing random selection procedure for selecting subsequences with length of 2L, which L is the length of secret message 3) Specifying L pairs of triples host positions for embedding LSBs and MSBs of secret message by using three high level chaotic maps. 4) Entering some parameters dependent on elementary initial values, host image, and secret message features as a key point for adding additional layer of security alongside providing high sensitivity. 5) Providing high capacity for embedding secret message, which is equal to 50 % of whole image capacity (Mź×źNź×ź12). The proposed method could be applied in different criterion such as, confidential communication and data storing, protection of data alteration, and etc. Our experimental results guarantees that our scheme is not only robust against differential attacks, but also has promising results such as highly sensitive keys, Quality index, PSNR, MSE, and hiding capacity as shown in statistical security analysis.

Optical image encryption scheme using 3-D chaotic map based joint image scrambling and random encoding in gyrator domains

We demonstrate an optical image encryption scheme using 3-D chaotic map based joint image scrambling and random encoding in gyrator domains. A novel image confusion approach that can well address the drawbacks of typical image permutation ciphers is developed to firstly shuffle the plaintext. Then the scrambled image is random phase encoded in the spatial domain and gyrator transform domain. A three-dimensional chaotic map is introduced to generate key stream elements. Simulations demonstrate that the cryptosystem has satisfactory cryptographic features and owns high robustness against noise perturbation as well as occlusion attack.

Generalized Synchronization of Time-Delayed Discrete Systems

This paper establishes two theorems for two time-delayed (chaotic) discrete systems to achieve time-delayed generalized synchronization (TDGS). These two theorems uncover the general forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems.

An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps

Abstract Tang et al. proposed a novel method for obtaining S-boxes based on the well-known two-dimensional chaotic Baker map. Unfortunately, some mistakes exist in their paper. The faults are corrected first in this paper and then an extended method is put forward for acquiring cryptographically strong S-boxes. The new scheme employs a three-dimensional chaotic Baker map, which has more intensive chaotic characters than the two-dimensional one. In addition, the cryptographic properties such as the bijective property, the nonlinearity, the strict avalanche criterion, the output bits independence criterion and the equiprobable input/output XOR distribution are analyzed in detail for our S-box and revised Tang et al.’s one, respectively. The results of numerical analysis show that both of the two boxes can resist several attacks effectively and the three-dimensional chaotic map, a stronger sense in chaotic characters, can perform more smartly and more efficiently in designing S-boxes.