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 these 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 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 Rényi entropy instead of the collision entropy (i.e., Rényi 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.

中文翻译：

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用于最小熵估计的广义 LRS 估计器


最小熵是一种广泛使用的指标，用于量化生成的随机数的随机性，它衡量猜测最可能的输出的难度。准确估计非独立同分布（非 IID）源的最小熵是很困难的。因此，NIST Special Publication (SP) 800-90B 采用十种不同的最小熵估计器，然后保守地选择这十种最小熵估计中的最小值。在这些估计器中，最长重复子串（LRS）估计器通过计算重复子串的数量来估计碰撞熵而不是最小熵。由于碰撞熵是最小熵的上限，因此 LRS 估计器本质上会提供高估的输出。在本文中，我们提出了两种技术来准确估计非独立同分布源的最小熵。第一种技术通过将碰撞熵转换为最小熵来解决高估问题。接下来，我们通过采用一般的 Rényi 熵而不是碰撞熵（即二阶 Rényi 熵）来推广 LRS 估计器。我们表明，采用更高的阶数可以减少最小熵估计的方差。通过整合这些技术，我们提出了一种广义的 LRS 估计器，可以有效解决高估问题并提供稳定的最小熵估计。理论分析和实证结果表明，所提出的广义 LRS 估计器显着提高了估计精度，这使其成为 LRS 估计器的有吸引力的替代方案。