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### min-entropy

Abbreviation(s) and Synonym(s):

None

Definition(s):

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].
Source(s):
NIST SP 800-90A Rev. 1 under Min-entropy

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.
Source(s):
NIST SP 800-90B under Min-entropy

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.
Source(s):
NIST SP 800-63-2 under Min-entropy [Superseded]