Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

Double graph correlation encryption based on hyperchaos

Preventing unauthorized access to sensitive data has always been one of the main concerns in the field of information security. Accordingly, various solutions have been proposed to meet this requirement, among which encryption can be considered as one of the first and most effective solutions. The continuous increase in the computational power of computers and the rapid development of artificial intelligence techniques have made many previous encryption solutions not secure enough to protect data. Therefore, there is always a need to provide new and more efficient strategies for encrypting information. In this article, a two-way approach for information encryption based on chaos theory is presented. To this end, a new chaos model is first proposed. This model, in addition to having a larger key space and high sensitivity to slight key changes, can demonstrate a higher level of chaotic behavior compared to previous models. In the proposed method, first, the input is converted to a vector of bytes and first diffusion is applied on it. Then, the permutation order of chaotic sequence is used for diffusing bytes of data. In the next step, the chaotic sequence is used for applying second diffusion on confused data. Finally, to further reduce the data correlation, an iterative reversible rule-based model is used to apply final diffusion on data. The performance of the proposed method in encrypting image, text, and audio data was evaluated. The analysis of the test results showed that the proposed encryption strategy can demonstrate a pattern close to a random state by reducing data correlation at least 28.57% compared to previous works. Also, the data encrypted by proposed method, show at least 14.15% and 1.79% increment in terms of MSE and BER, respectively. In addition, key sensitivity of 10-28 and average entropy of 7.9993 in the proposed model, indicate its high resistance to brute-force, statistical, plaintext and differential attacks.

An Image Encryption Algorithm Using Cascade Chaotic Map and S-Box

This paper proposed an image algorithm based on a cascaded chaotic system to improve the performance of the encryption algorithm. Firstly, this paper proposed an improved cascaded two-dimensional map 2D-Cosine-Logistic-Sine map (2D-CLSM). Cascade chaotic system offers good advantages in terms of key space, complexity and sensitivity to initial conditions. By using the control parameters and initial values associated with the plaintext, the system generates two chaotic sequences associated with the plaintext image. Then, an S-box construction method is proposed, and an encryption method is designed based on the S-box. Encryption is divided into bit-level encryption and pixel-level encryption, and a diffusion method was devised to improve security and efficiency in bit-level encryption. Performance analysis shows that the encryption algorithm has good security and is easily resistant to various attacks.

Discrete Dynamic Model of a Disease-Causing Organism Caused by 2D-Quantum Tsallis Entropy

Many aspects of the asymmetric organ system are controlled by the symmetry model (R&L) of the disease-causing organism pathway, but sensitive matters like somites and limb buds need to be shielded from its influence. Because symmetric and asymmetric structures develop from similar or nearby matters and utilize many of the same signaling pathways, attaining symmetry is made more difficult. On this note, we aim to generalize some important measurements in view of the 2D-quantum calculus (q-calculus, q-analogues or q-disease), including the dimensional of fractals and Tsallis entropy (2D-quantum Tsallis entropy (2D-QTE)). The process is based on producing a generalization of the maximum value of the Tsallis entropy in view of the quantum calculus. Then by considering the maximum 2D-QTE, we design a discrete system. As an application, by using the 2D-QTE, we depict a discrete dynamic system that is afflicted with a disease-causing organism (DCO). We look at the system’s positive and maximum solutions. Studies are done on equilibrium and stability. We will also develop a novel design for the fundamental reproductive ratio based on the 2D-QTE.

A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis

Data security represents an essential task in the present day, in which chaotic models have an excellent role in designing modern cryptosystems. Here, a novel oscillator with chaotic dynamics is presented and its dynamical properties are investigated. Various properties of the oscillator, like equilibria, bifurcations, and Lyapunov exponents (LEs), are discussed. The designed system has a center point equilibrium and an interesting chaotic attractor. The existence of chaotic dynamics is proved by calculating Lyapunov exponents. The region of attraction for the chaotic attractor is investigated by plotting the basin of attraction. The oscillator has a chaotic attractor in which its basin is entangled with the center point. The complexity of the chaotic dynamic and its entangled basin of attraction make it a proper choice for image encryption. Using the effective properties of the chaotic oscillator, a method to construct pseudo-random numbers (PRNGs) is proposed, then utilizing the generated PRNG sequence for designing secure substitution boxes (S-boxes). Finally, a new image cryptosystem is presented using the proposed PRNG mechanism and the suggested S-box approach. The effectiveness of the suggested mechanisms is evaluated using several assessments, in which the outcomes show the characteristics of the presented mechanisms for reliable cryptographic applications.

Investigation of the Simplest Megastable Chaotic Oscillator with Spatially Triangular Wave Damping

The simplest megastable chaotic system is built by employing a piecewise-linear damping function which is periodic over the spatial domain. The unforced oscillator generates an infinite number of nested limit cycles with constant distances whose strength of attraction decreases gradually as moving to outer ones. The attractors and the basins of attraction of the proposed system are almost compatible with those of the system with sinusoidal damping. However, the nonzero Lyapunov Exponent of the latter is consistently below that of the former. A comparative bifurcation analysis is carried out for periodically forced systems, showing the chaotic behavior of coexisting attractors in specific values of parameters. Changing the bifurcation parameter results in expansion, contraction, merging, and separation of the coexisting attractors, make it challenging to find the corresponding basins. Three symmetric pairs of attractors are observed; each one consists of two symmetric attractors (with respect to the origin) with almost the same values of the corresponding Lyapunov Exponent.

Chaos coordinated neural key synchronization for enhancing security of IoT

The key exchange mechanism in this paper is built utilizing neural network coordination and a hyperchaotic (or chaotic) nonlinear dynamic complex system. This approach is used to send and receive sensitive data between Internet-of-Things (IoT) nodes across a public network. Using phishing, Man-In-The-Middle (MITM), or spoofing attacks, an attacker can easily target sensitive information during the exchange process. Furthermore, minimal research has been made on the exchange of input seed values for creating identical input at both ends of neural networks. The proposed method uses a 5D hyperchaotic or chaotic nonlinear complex structure to ensure the sharing of input seed value across two neural networks, resulting in the identical input on both ends. This study discusses two ways for sharing seed values for neural coordination. The first is a chaotic system with all real variables, whereas the second is a hyperchaotic system with at least one complex variable. Each neural network has its own random weight vector, and the outputs are exchanged. It achieves full coordination in some stages by altering the neuronal weights according to the mutual learning law. The coordinated weights are utilized as a key after the neural coordination technique. The network’s core structure is made up of triple concealed layers. So, determining the inner configuration will be tough for the intruder. The efficiency of the suggested model is validated by simulations, and the findings reveal that the suggested strategy outperforms current equivalent techniques.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors II

According to the pioneering work of Leonov and Kuznetsov [...].

A New Hyperchaotic Map for a Secure Communication Scheme with an Experimental Realization

Using different chaotic systems in secure communication, nonlinear control, and many other applications has revealed that these systems have several drawbacks in different aspects. This can cause unfavorable effects to chaos-based applications. Therefore, presenting a chaotic map with complex behaviors is considered important. In this paper, we introduce a new 2D chaotic map, namely, the 2D infinite-collapse-Sine model (2D-ICSM). Various metrics including Lyapunov exponents and bifurcation diagrams are used to demonstrate the complex dynamics and robust hyperchaotic behavior of the 2D-ICSM. Furthermore, the cross-correlation coefficient, phase space diagram, and Sample Entropy algorithm prove that the 2D-ICSM has a high sensitivity to initial values and parameters, extreme complexity performance, and a much larger hyperchaotic range than existing maps. To empirically verify the efficiency and simplicity of the 2D-ICSM in practical applications, we propose a symmetric secure communication system using the 2D-ICSM. Experimental results are presented to demonstrate the validity of the proposed system.

Fuzzy Evaluation of Crowd Safety Based on Pedestrians' Number and Distribution Entropy

Crowd video monitoring and analysis is a hot topic in computer vision and public management. The pre-evaluation of crowd safety is beneficial to the prediction of crowd status to avoid the occurrence of catastrophic events. This paper proposes a method to evaluate crowd safety based on fuzzy inference. Pedestrian's number and distribution uniformity are considered in a fuzzy inference system as two kinds of attributes of a crowd. Firstly, the pedestrian's number is estimated by the number of foreground pixels. Then, the distribution uniformity of a crowd is calculated using distribution entropy by dividing the monitoring scene into several small areas. Furthermore, through the fuzzy operation, the fuzzy system is constructed by using two input variables (pedestrian's number and distribution entropy) and one output variable (crowd safety status). Finally, inference rules between the crowd safety state and the pedestrian's number and distribution uniformity are constructed to obtain the pre-evaluation of the safety state of the crowd. Three video sequences extracted from different scenes are used in the experiment. Experimental results show that the proposed method can be used to evaluate the safety status of the crowd in a monitoring scene.

A Nonlinear Five-Term System: Symmetry, Chaos, and Prediction

Chaotic systems have attracted considerable attention and been applied in various applications. Investigating simple systems and counterexamples with chaotic behaviors is still an important topic. The purpose of this work was to study a simple symmetrical system including only five nonlinear terms. We discovered the system’s rich behavior such as chaos through phase portraits, bifurcation diagrams, Lyapunov exponents, and entropy. Interestingly, multi-stability was observed when changing system’s initial conditions. Chaos of such a system was predicted by applying a machine learning approach based on a neural network.

Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.