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.