Novel <i>n</i>-Dimensional Nondegenerate Discrete Hyperchaotic Map With Any Desired Lyapunov Exponents

The chaotic system as a source of randomness is very important for chaos-based secure communication. Different from other chaotic maps, this work explores an n-dimensional (n-D) nondegenerate discrete hyperchaotic map with any desired Lyapunov exponents (LEs). First, theoretical analysis proves that the proposed map is chaotic. Based on this proof, it is designed for any desired LEs. To illustrate the effectiveness of the n-dimensional (n-D) new map, we use some chaotic and nonchaotic maps as examples. The simulation results demonstrated that the proposed maps exhibit stronger chaotic properties and more complex dynamic behaviors compared to some previous results. Moreover, the chaotic signals generated by our maps passed NIST and TestU01 tests, which show that our map has better randomness. Furthermore, a chaotic system with higher LEs do not necessarily have higher complexity degree. Next, the proposed map is implemented by hardware digital signal processing platform, indicating the feasibility for industrial applications. More importantly, compared with other maps, the proposed map has simple structure with more complex behaviors and fewer parameters, and it is easy to set the desired LEs. Finally, we design a novel image encryption algorithm based on the proposed chaotic system and dynamic S-boxes. The experimental results show that the proposed chaotic system can be effectively applied in the field of data encryption.