Efficient and Accurate Min-entropy Estimation Based on Decision Tree for Random Number Generators

High-quality random numbers are essential to communication security, as one of the most important components of cryptographic modules in secure communication protocols. Compared with statistical tests, entropy estimation is considered to be a more essential method for evaluating the quality of random numbers. Prediction-based min-entropy estimators have been proposed and developed as an important branch of randomness testing tools, represented by the predictors included in NIST SP 800-90B (90B) and the estimators based on neural network (NN) in literature. The 90B methods are efficient but suffer inaccuracy in handling complex entropy sources. By contrast, NN-based methods have relatively high prediction accuracy, but the execution cost is too heavy to be implemented as an online test. This paper proposes a decision tree (DT) based entropy estimator, as well as two enhancement techniques: tailored pruning and correlation determination, to tackle the problems in existing approaches. We conduct experiments on various types of entropy sources for evaluation and comparison. The results show that the proposed DT-based estimator achieves prediction accuracy comparable to the state of the art NN-based estimator while reducing the execution time by 99.3%, making it as efficient as 90B predictors. In terms of estimation accuracy, DT-based estimator shows more powerful predictive capability than 90B predictors for complex entropy sources. Particularly, for second-order Markov entropy sources, the prediction accuracy outperforms 90B by 34.6% and TPA-LSTM by 48.7%. We believe that our proposed DT-based estimator can be an important supplement to existing standard entropy estimation methods.