<i>n</i>-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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>-dimensional hyperchaotic discrete map (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>D-HCDM) based on modulo operations is proposed in this article. Theoretical analysis demonstrates that the Lyapunov exponents (LEs) of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>D-HCDM are configurable. To validate the effectiveness of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>D-HCDM, two hyperchaotic discrete maps are generated, and numerical simulation experiments confirm the continuous hyperchaotic intervals and outstanding random properties of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>D-HCDM proposed in this study. Implementation of these chaotic maps on an ARM-based hardware platform is performed. Finally, the application of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>D-HCDM in secure communication is explored, and simulation results indicate that the performance of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>D-HCDM surpasses that of some existing chaotic maps.