  The min-entropy is a widely used metric to quantify the randomness of
generated random numbers, which measures the difficulty of guessing the most
likely output. It is difficult to accurately estimate the min-entropy of a
non-independent and identically distributed (non-IID) source. Hence, NIST
Special Publication (SP) 800-90B adopts ten different min-entropy estimators
and then conservatively selects the minimum value among ten min-entropy
estimates. Among these estimators, the longest repeated substring (LRS)
estimator estimates the collision entropy instead of the min-entropy by
counting the number of repeated substrings. Since the collision entropy is an
upper bound on the min-entropy, the LRS estimator inherently provides
\emph{overestimated} outputs. In this paper, we propose two techniques to
estimate the min-entropy of a non-IID source accurately. The first technique
resolves the overestimation problem by translating the collision entropy into
the min-entropy. Next, we generalize the LRS estimator by adopting the general
R{\'{e}}nyi entropy instead of the collision entropy (i.e., R{\'{e}}nyi entropy
of order two). We show that adopting a higher order can reduce the variance of
min-entropy estimates. By integrating these techniques, we propose a
generalized LRS estimator that effectively resolves the overestimation problem
and provides stable min-entropy estimates. Theoretical analysis and empirical
results support that the proposed generalized LRS estimator improves the
estimation accuracy significantly, which makes it an appealing alternative to
the LRS estimator.
