Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.

Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application

Color image encryption using non-dominated sorting genetic algorithm with local chaotic search based 5D chaotic map

Nowadays, the images are transferred through open channels that are subject to potential attacks, so the exchange of image data requires additional security in many fields, such as medical, military, banking, etc. The security factors are essential in preventing the system from brute force and differential attacks. We propose an Enhanced Logistic Map (ELM) while using chaotic maps and simple encryption techniques, such as block scrambling, modified zigzag transformation for encryption phases, including permutation, diffusion, and key stream generation to withstand the attacks. The results of encryption are evaluated while using the histogram, correlation analysis, Number of Pixel Change Rate (NPCR), Unified Average Change Intensity (UACI), Peak-Signal-to-Noise Ratio (PSNR), and entropy. Our results demonstrate the security, reliability, efficiency, and flexibility of the proposed method.

https://www.mdpi.com/1099-4300/21/7/656/pdf

An Image Encryption Scheme Based on Block Scrambling, Modified Zigzag Transformation and Key Generation Using Enhanced Logistic-Tent Map.

In this paper, a new four-dimensional dissipative chaotic system which can produce multiple asymmetric attractors is designed and its dynamical behaviors are analyzed. The basin of attraction reveals the asymmetric multistability of the system. In addition, it is very interesting to observe different types of asymmetric coexisting attractors as the bifurcation parameters change. The spectral entropy complexity chaotic diagrams are used to observe the changes in the sequence complexity when the two bifurcation parameters change simultaneously. Moreover, the difference of the system complexity between the two different initial values is analyzed. In order to facilitate engineering applications, the offset boosting control is introduced to the state variable, and the numerical simulation shows that the offset boosting control scheme can flexibly change the polarity of the chaotic signal. Finally, an analog circuit and a digital circuit were designed to verify the new chaotic system. The new research results will enrich the theoretical basis of multistability, offset boosting control and circuit implementation of chaos.

Dynamical analysis of a new chaotic system: asymmetric multistability, offset boosting control and circuit realization

Image encryption using complex hyper chaotic system by injecting impulse into parameters

Cryptanalysis and constructing S-Box based on chaotic map and backtracking

A new 2D Chebyshev-Sine map with natural evaluation is proposed and its dynamical behavior is analyzed. To investigate its application in information security, a color image encryption algorithm is designed. One-time initial condition expressed as ordered quaternion is extracted from colored non Gaussian noise before each encryption process. The algorithm can achieve desired effect after two rounds by exclusive or (XOR) operation with avalanche effect. Simulation results demonstrated that the speed is fast, so the algorithm is suitable for image encryption over the Cloud.

Construction of a new 2D Chebyshev-Sine map and its application to color image encryption

Color pathological image encryption algorithm using arithmetic over Galois field and coupled hyper chaotic system

Based on the classic quadratic map (CQM) with abundant bifurcations and periodic windows, a new 3D improved coupling quadratic map (3D-ICQM) is constructed, and its phase diagram, Lyapunov exponent...

Hongjun Liu

Papers

Image encryption using complex hyper chaotic system by injecting impulse into parameters

Cryptanalysis and constructing S-Box based on chaotic map and backtracking

Construction of a new 2D Chebyshev-Sine map and its application to color image encryption

Color pathological image encryption algorithm using arithmetic over Galois field and coupled hyper chaotic system

Color Image Encryption with Cipher Feedback and Coupling Chaotic Map