Min-entropy

{
  "id": "MLC-T-CYB-002683",
  "term": "Min-entropy",
  "field": "Cybersecurity",
  "definition": "1. A lower bound on the entropy of a random variable. The precise formulation for min-entropy is (-log_2 max p_i) for a discrete distribution having probabilities p_1,...,p_k. Min-entropy is often used as a measure of the unpredictability of a random variable.\n\n2. The min-entropy (in bits) of a random variable X is the largest value m having the property that each observation of X provides at least m bits of information (i.e., the min-entropy of X is the greatest lower bound for the information content of potential observations of X). The min-entropy of a random variable is a lower bound on its entropy. The precise formulation for min-entropy is -(log2 max pi) for a discrete distribution having n possible outputs with probabilities p1,…, pn. Min-entropy is often used as a worst-case measure of the unpredictability of a random variable. Also see [NIST SP 800-90B].\n\n3. The min-entropy (in bits) of a random variable X is the largest value m having the property that each observation of X provides at least m bits of information (i.e., the min-entropy of X is the greatest lower bound for the information content of potential observations of X). The min-entropy of a random variable is a lower bound on its entropy. The precise formulation for min-entropy is (log2 max pi) for a discrete distribution having probabilities p1, ...,pk. Min-entropy is often used as a worst-case measure of the unpredictability of a random variable.\n\n4. The min-entropy (in bits) of a random variable X is the largest value m having the property that each observation of X provides at least m bits of information (i.e., the min-entropy of X is the greatest lower bound for the information content of potential observations of X). The min-entropy of a random variable is a lower bound on its entropy. The precise formulation for min-entropy is - log2 (max pi) for a discrete distribution having event probabilities p1, ..., pk. Min-entropy is often used as a worst-case measure of the unpredictability of a random variable.\n\n5. A measure of the difficulty that an Attacker has to guess the most commonly chosen password used in a system. In this document, entropy is stated in bits. When a password has n-bits of min-entropy then an Attacker requires as many trials to find a user with that password as is needed to guess an n-bit random quantity. The Attacker is assumed to know the most commonly used password(s). See Appendix A.",
  "see_also": [
    "DRBG Mechanism Boundary",
    "Entropy Input"
  ],
  "references": [
    "NIST IR 8427",
    "NIST SP 800-90A Rev. 1",
    "NIST SP 800-90B",
    "NIST SP 800-133 Rev. 2",
    "NIST SP 800-63-2 [Superseded]",
    "NIST CSRC Glossary"
  ],
  "url": "https://mlchart.com/terminology/cybersecurity/min-entropy/"
}