Constructing a non-degenerate 2D chaotic map with application in irreversible PRNG

To solve the weakness of reversibility that exited in some pseudo-random number generators (PRNGs), we designed an enhanced chaos-based irreversible PRNG, in which the irreversibility is implemented through embedding the modular exponentiation into chaotic map, whose inverse function can generate discrete logarithm problem (DLP). First, a non-degenerate 2D exponential hyper chaotic map (2D-EHCM) was constructed, and its dynamic behaviors, such as phase diagram, Lyapunov exponent, Kolmogorov entropy, correlation dimension and randomness, were analyzed and tested. The results demonstrated that the state point trajectories of the 2D-EHCM have ergodicity and strong connection in phase space and a larger range of control parameter. Statistics and security analysis results demonstrated its effectiveness and robustness of the proposed enhanced PRNG with irreversibility.