A new method for constructing discrete hyperchaotic systems with a controllable range of Lyapunov exponents and its application in information security

Since people use chaos extensively for a wide range of applications in data encryption and secure communications, a new method for designing practical high-dimensional discrete hyperchaotic systems is proposed for the first time in this paper. This method controls the range of the Lyapunov exponents in reverse by adding control variables so that the range of the values of the Lyapunov exponents is controlled within a specified interval, which is more suitable for engineering applications. Then, it is mathematically proved that the method ensures that the orbits of chaotic systems are globally finite and their Lyapunov exponents are bounded. In addition, as a practical demonstration of the selective image encryption scheme based on target template matching introduced in this paper, a 6D discrete hyperchaotic system was created, and the analysis of the simulation results verifies the applicability of the 6D hyperchaotic system designed by the method presented in this paper in the field of image encryption.

Automated summary

A new method for designing practical high-dimensional discrete hyperchaotic systems is proposed in this paper. By adding control variables, the method controls the range of the Lyapunov exponents, making it more suitable for engineering applications. Mathematical proof shows that the method ensures finite orbits and bounded Lyapunov exponents of chaotic systems. A 6D discrete hyperchaotic system is created as a practical demonstration of the selective image encryption scheme, confirming the applicability of the method in the field of image encryption.