Probabilistic Analysis for the Relationship Between Min-Entropy and Guessing Attack

Recently NIST has published the second draft document of recommendation for the entropy sources used for random bit generation. In this document NIST has provided a practical and detailed description about the fact that the min-entropy is closely related to the optimum guessing attack cost. However the argument lacks the mathematical rigour. In this paper we provide an elaborate probabilistic analysis for the relationship between the min-entropy and cost of optimum guessing attack. Moreover we also provide some simulation results in order to investigate the practicality of optimum guessing attack.