Application of two-dimensional linear piecewise full mapping function in chaotic image encryption

In recent years, information security has become more and more important. Image encryption technology based on chaos theory has become one of the hot issues in this field. Chaotic system has the characteristics of initial value sensitivity and sequence ergodicity, which is very suitable for image encryption. In this paper, the folded surface is generated by connecting the randomly generated points on the bottom surface and the top surface in the unit space, and the surjective binary function is further constructed. Use this type of function and functions such as planes to construct discrete dynamical system. It is experimentally analyzed that the function has good chaotic characteristics by drawing bifurcation diagram and Lyapunov exponent diagram. The chaotic sequence of the discrete dynamic system is used for image encryption, and its information entropy and correlation coefficient before and after encryption are calculated. It is proved that this kind of system has good chaotic characteristics. This is a new type of chaotic system, which needs further research, analysis and expansion.