n-Dimensional Hyperchaotic Discrete Maps With Desired Positive Lyapunov Exponents and Its Application in Secure Communication

The significance of high-dimensional chaotic systems with continuous hyperchaotic intervals is more pronounced in engineering applications. Many existing chaotic systems suffer from discontinuities in their chaotic intervals. To address this issue, an $\boldsymbol{n}$-dimensional hyperchaotic discrete map ($\boldsymbol{n}$D-HCDM) based on modulo operations is proposed in this article. Theoretical analysis demonstrates that the Lyapunov exponents (LEs) of the $\boldsymbol{n}$D-HCDM are configurable. To validate the effectiveness of the $\boldsymbol{n}$D-HCDM, two hyperchaotic discrete maps are generated, and numerical simulation experiments confirm the continuous hyperchaotic intervals and outstanding random properties of the $\boldsymbol{n}$D-HCDM proposed in this study. Implementation of these chaotic maps on an ARM-based hardware platform is performed. Finally, the application of the $\boldsymbol{n}$D-HCDM in secure communication is explored, and simulation results indicate that the performance of the $\boldsymbol{n}$D-HCDM surpasses that of some existing chaotic maps.