Editing Random password generator (section)

==Password type and strength==
{{duplication|section=yes|dupe=Password strength|date=August 2018}}

Random password generators normally output a string of symbols of specified length. These can be individual characters from some character set, syllables designed to form pronounceable passwords, or words from some word list to form a [[passphrase]]. The program can be customized to ensure the resulting password complies with the local password policy, say by always producing a mix of letters, numbers and special characters. Such policies typically reduce strength slightly below the formula that follows, because symbols are no longer independently produced.{{Citation needed|date=April 2024}}

The [[Password strength]] of a random password against a particular attack ([[brute-force search]]), can be calculated by computing the [[information entropy]] of the random process that produced it. If each symbol in the password is produced independently and with uniform probability, the entropy in bits is given by the formula <math display="inline">H = L\,\log_2 N</math>, where ''N'' is the number of possible symbols and ''L'' is the number of symbols in the password. The function log<sub>2</sub> is the [[binary logarithm|base-2 logarithm]]. ''H'' is typically measured in [[bit]]s.<ref>Schneier, B: ''Applied Cryptography'', Second edition, page 233 ff.  John Wiley and Sons.</ref><ref name="NIST">{{cite journal | url = http://csrc.nist.gov/publications/nistpubs/800-63/SP800-63V1_0_2.pdf | title = Electronic Authentication Guideline | year = 2006 | publisher = NIST | doi = 10.6028/NIST.SP.800-63v1.0.2 | last1 = Burr | first1 = W. E. | last2 = Dodson | first2 = D. F. | last3 = Polk | first3 = W. T. }}</ref>

Any password generator is limited by the state space of the pseudo-random number generator used if it is based on one. Thus a password generated using a 32-bit generator is limited to 32 bits entropy, regardless of the number of characters the password contains.{{Citation needed|date=April 2024}}