A Nondegenerate n-Dimensional Hyperchaotic Map Model with Application in a Keyed Parallel Hash Function

The construction of multidimensional discrete hyperchaotic maps with ergodicity and larger Lyapunov exponents is desired in cryptography. Here, we have designed a general nD (n = 2) discrete hyperchaotic map (nD-DHCM) model that can generate any nondegenerate nD chaotic map with Lyapunov exponents of desired size through setting the control matrix. To verify the effectiveness of the nD-DHCM, we have provided two illustrative examples and analyzed their dynamic behavior, and the results demonstrated that their state points have ergodicity within a sufficiently large interval. Furthermore, to address the finite precision effect of the simulation platform, we analyzed the relationship between the size of Lyapunov exponent and the randomness of the corresponding state time sequence of the nD-DHCM. Finally, we designed a keyed parallel hash function based on a 6D-DHCM to evaluate the practicability of the nD-DHCM. Experimental results have demonstrated that nD discrete chaotic maps constructed using nD-DHCM have desirable Lyapunov exponents, and can be applied to practical applications.

Automated summary

In this study, a general n-dimensional (n = 2) discrete hyperchaotic map (nD-DHCM) model is designed to generate any nondegenerate nD chaotic map with desired Lyapunov exponents by setting the control matrix. The effectiveness of the nD-DHCM is verified through two illustrative examples, which demonstrate the ergodicity of state points within a sufficiently large interval. Furthermore, the relationship between the size of Lyapunov exponent and the randomness of the corresponding state time sequence of the nD-DHCM is analyzed to address the finite precision effect. Moreover, a keyed parallel hash function based on a 6D-DHCM is designed to evaluate the practicability of the nD-DHCM, which shows that nD discrete chaotic maps constructed using nD-DHCM have desirable Lyapunov exponents and can be applied to practical applications.