Hybrid Chaos via Entropy-Greedy Map Switching: A Statistical and Predictability Analysis

We propose and analyse a hybrid chaotic pseudorandom generator that combines the logistic, tent, and Hénon maps under a deterministic entropy-greedy selector. At each step every map proposes a candidate; the selector keeps the one that maximises the plug-in Shannon entropy of a sliding output window, emits it, and advances only the winning map’s state. We benchmark all four generators plus a Mersenne Twister (MT19937) reference on uniformity (Kolmogorov–Smirnov statistic, KS), lag-correlation, entropy, Lyapunov exponent, and sensitivity. The hybrid reduces the logistic KS deviation by 26.9% and the maximum short-lag Pearson correlation by 6.5%. An explicit predictability analysis shows that the logistic and tent states are exposed, giving an adversary 92% one-step accuracy; only the hidden Hénon coordinate blocks free-running cloning, which diverges within about eight steps. Rank-uniformisation drops KS to 2.5×10−5 and passes a NIST SP 800-22 subset, while the lag-1 rank dependence is unchanged. Structural modifications—state masking for all component maps and continuous-time replacements with hidden coordinates—are discussed as routes to reducing predictability.