Discussion on the Full Entropy Assumption of the SP 800-90 Series

The NIST Special Publication (SP) 800-90 series supports the generation of high-quality random bits for cryptographic and non-cryptographic use. The security strength of a random number generator depends on the unpredictability of its outputs. This unpredictability can be measured in terms of entropy, which the NIST SP 800-90 series measures using min-entropy. A full-entropy bitstring has an amount of entropy equal to its length. Full-entropy bitstrings are important for cryptographic applications, as these bitstrings have ideal randomness properties and may be used for any cryptographic purpose. Due to the difficulty of generating and testing full-entropy bitstrings, the SP 800-90 series assumes that a bitstring has full entropy if the amount of entropy per bit is at least \(1-ε\), where ε is at most \(2^{-32}\). This report provides a justification for the selection of this value of \(ε\).