Using the judgment theorem of Li-York chaos

this paper generates a class of piecewise linear chaotic maps.Based on the chaotic maps

a constructing theorem of piecewise nonlinear robust chaotic map is proposed.As an application

this theorem is used to construct a piecewise nonlinear robust chaotic map with a polynomial function and a trigonometric function.This study computes the bifurcation diagram of the map.The computed results demonstrate the chaotic robustness features of the map.Three pseudo-random number generators are generated based on the piecewise nonlinear robust chaotic map.On this basis

the generation algorithm of S-boxes is proposed with the property of sensitivity to the initial parameters of the chaotic map.The cryptography performance is tested and the tested results show that generated S-boxes have good cryptographic properties

and can not only better resist the linear and differential attacks

but also provide the foundation and conditions for the research and development of cryptography.