A new hyperchaotic system with dynamical analysis and its application in image encryption based on STM32

Abstract This paper proposes a new 4D hyperchaotic system based on a modified 3D Lorenz chaotic system. The stability of equilibrium points in this hyperchaotic system is analyzed, with a notable feature being the presence of only one equilibrium point. Subsequently, dynamic characteristics of the new system, such as Lyapunov exponents' spectrum, bifurcation diagram, and chaotic attractors, are analyzed using MATLAB numerical simulation software. The numerical analysis indicates that the hyperchaotic system exhibits hyperchaotic characteristics over a wide range of parameter d values, and its chaotic attractor manifests four states: hyperchaotic, chaotic, periodic, and quasi-periodic. This illustrates the complex dynamic behavior of the hyperchaotic system. Experimental validation is then conducted using embedded hardware STM32, reproducing the four types of chaotic attractors observed in numerical analysis and confirming the accuracy of theoretical analysis. The proposed new hyperchaotic system is deemed effective and reliable. Finally, the system is applied to image encryption, presenting a novel encryption method based on the hyperchaotic system. The designed hyperchaotic encryption sequence satisfies 15 tests of the NIST SP800-22 standard, and experimental verification using STM32 demonstrates the effectiveness, simplicity, non-linearity, and high security of the proposed image encryption algorithm. This method can be extended to applications such as audio encryption, image encryption, video encryption, and other fields.