A non-degenerate n-dimensional integer domain chaotic map model with application to PRNG

Abstract

To address the limitations of existing chaotic maps, we proposed a non-degenerate n-dimensional (n≥2) integer domain chaotic map (nD-IDCM) model that can construct any non-degenerate n-dimensional integer domain chaotic maps. Moreover, we analyzed its chaotic behavior through Lyapunov exponent, and found that the nD-IDCM generates chaotic sequences in the integer domain, which effectively resolves the issue of finite precision effect when implementing existing chaotic maps on computers or digital devices. To verify the effectiveness of nD-IDCM, we presented two instances to demonstrate how the positive Lyapunov exponents can be regulated by manipulating the parameter matrix. Subsequently, we have scrutinized their dynamical behavior using Kolmogorov entropy, sample entropy, correlation dimension and randomness testing via TestU01. Finally, to assess the feasibility of nD-IDCM, we devised a keyed pseudo random number generator (PRNG) based on a 3D-IDCM that can ensure superior randomness and unpredictability. Experimental results indicated that integer domain chaotic maps constructed using nD-IDCM have desirable Lyapunov exponents and exhibit ergodicity within a sufficient larger chaotic range.