Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors. To investigate how much a chaotic system with multistability behavior is suitable for cryptographic applications, we generate a pseudo-random number generator (PRNG) based on the complexity results of the laser system. The randomness test results show that the generated PRNG from the multistability regions fail to pass most of the statistical tests.

This paper investigates the dynamics of a 3D plasma system that has a single symmetric double-wing attractor moving around symmetric equilibria. Therefore, it is reasonable to assume that changing the space between these wings can degenerate them. Motivated by this concept, we introduce a new controller on the plasma system that can shift its equilibria away from each other, and subsequently break the symmetric double-wing that resembles a butterfly into several independent chaotic attractors. To show the advantage of generating coexisting attractors, we compare between the complexity performance of the multi-stable controlled plasma system and the original plasma system that has single chaotic attractor. Simulation results show that the complexity performance of the multi-stable controlled plasma system is higher than the original system. As a result, and from cryptographic point of view, chaotic ciphers with applying more than one set of initial conditions provide a higher level of security than applying only one set of initial conditions. As an example, we present a new approach for generating S-box based on the multistability behavior of the controlled plasma system. Performance analysis shows that the proposed S-box algorithm can achieve a higher security level and has a better performance than some of the latest algorithms.

NTRU public key cryptosystem relies on computations that are efficiently performed with insignificant storage and time complexity. Many researchers were motivated to improve NTRU performance by replacing the original polynomial ring and mathematical structure with new modified algebraic structures, such as QTRU, OTRU, BITRU, and many others. In this work, a new NTRU-analog cryptosystem called QOBTRU is proposed based on a newly designed algebraic structure called Carternion algebra. QOBTRU is at least quadratic higher than the original NTRU in terms of computational and space complexity. It is intended to have an alternative security and performance attribute upon three chosen highly performed multidimensional NTRU-like cryptosystems, which are QTRU, OTRU, and BITRU. Their comparison with QOBTRU highlighted its strength over them. Some statistical and security analysis is performed to demonstrate its efficiency.