A Model-Based Empirical Advantage Estimation Framework for Chaos-Based Random Bit Generators

Chaos-based random bit generators are commonly evaluated using statistical randomness tests and entropy, which do not directly quantify an adversarial distinguishing advantage. For the chaos-based RBGs evaluated in this study, no reduction-style cryptographic security proof is claimed. This paper proposes a model-based empirical advantage estimation framework. The proposed empirical threshold combines Lyapunov-based residual distinguishability with extractor-dependent residual distinguishability; its additive form is motivated by a total variation distance (TVD) decomposition, while both terms are empirically defined rather than direct TVD estimates. The framework is evaluated using a logistic map-based RBG under non-chaotic, weak-chaotic, and strong-chaotic regimes. Validation uses a separate dataset and operating-system reference streams; however, eight of sixteen validation functions evaluate statistical properties also used in estimating ϵH, so separation is through separate datasets, reference sets, and thresholds rather than complete feature independence. For the logistic map-based RBG, the empirical criterion is satisfied. Additional chaos-based RBGs yield varying validation outcomes. The framework complements standard randomness testing with a proposed empirical threshold for comparison with the maximum observed empirical advantage under selected finite-sample distinguishers and the stated experimental setup; it does not provide a proven upper bound on arbitrary adversarial advantage.