Chaotic system constructed by product trigonometric function and polynomial and applied to color image encryption

Abstract

In the applied research of nonlinear system, the low degree of chaos in the dynamical system leads to the limitation of using the chaos method to solve some practical problems. In this paper, we use the product trigonometric function and ternary polynomial to build a dynamical system, which has strong chaotic characteristics. The dynamical system is constructed by two product trigonometric functions and a ternary linear equation, and its chaotic properties are verified by bifurcation diagrams, Lyapunov exponents, fractal dimensions, etc. The system has many parameters and large parameter intervals and is not prone to cycles. The conditions for the non-divergence of this system are given by mathematical derivation, and it is found that the linear part of the system can be replaced by an arbitrary ternary polynomial system and still not diverge, and the bifurcation diagram is drawn to verify it. Finally, the chaotic sequence is distributed more uniformly in the value domain space by adding the modulo operation. Then, the bit matrix of multiple images is directly permuted by the above system, and the experiment confirms that the histogram, information entropy, and pixel correlation of its encrypted images are satisfactory, as well as a very large key space.

Design of a New Chaotic System with Sine Function: Dynamic Analysis and Offset Boosting Control

“…The complex dynamic behaviour of chaotic system is required for various engineering applications such as image encryption, voice encryption, DCSK, particle motion and secure communication etc. Therefore, the construction of chaotic system using trigonometry function is hot research topic and many researchers proposed chaotic systems based on product trigonometric function (Yu and Yu 2020;Yu and Gong 2022;Sriram et al 2023), hyperbolic sine (Liu et al 2018;Mobayen et al 2020;Hu et al 2022b;Joshi and Ranjan 2020), hyperbolic cosine (Signing et al 2019;Signing and Kengne 2018), cosine function (Yan et al 2022) and tangent and cotangent (Guo and Liang 2021).…”