Generalized LRS Estimator for Min-Entropy Estimation

Jiheon Woo, Chanhee Yoo, Young Sik Kim, Yuval Cassuto, Yongjune Kim

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3305-3317
Number of pages13
JournalIEEE Transactions on Information Forensics and Security
StatePublished - 2023


  • Cryptography
  • Entropy
  • Estimation
  • Frequency estimation
  • Government
  • Measurement
  • NIST

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Computer Networks and Communications


Dive into the research topics of 'Generalized LRS Estimator for Min-Entropy Estimation'. Together they form a unique fingerprint.

Cite this