Editing Pseudorandom number generator (section)

{{Short description|Algorithm that generates an approximation of a random number sequence}}
{{Hatnote|This page is about commonly encountered characteristics of pseudorandom number generator algorithms. For the formal concept in theoretical computer science, see [[Pseudorandom generator]].}}
A '''pseudorandom number generator''' ('''PRNG'''), also known as a '''deterministic random bit generator''' ('''DRBG'''),<ref>{{cite journal|last=Barker|first=Elaine|title=Recommendation for Key Management|url=http://csrc.nist.gov/publications/nistpubs/800-57/sp800-57_part1_rev3_general.pdf|journal=NIST Special Publication 800-57|publisher=[[NIST]]|access-date=19 August 2013|author2=Barker, William |author3=Burr, William |author4=Polk, William |author5= Smid, Miles |date=July 2012|doi=10.6028/NIST.SP.800-57p1r3 }}</ref> is  an [[algorithm]] for generating a sequence of numbers whose properties approximate the properties of sequences of [[random number generation|random numbers]]. The PRNG-generated sequence is not truly [[random]], because it is completely determined by an initial value, called the PRNG's ''[[random seed|seed]]'' (which may include truly random values). Although sequences that are closer to truly random can be generated using [[hardware random number generator]]s, '''''pseudorandom number generators''''' are important in practice for their speed in number generation and their reproducibility.<ref>{{Cite web|title = Pseudorandom number generators|url = https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/random-vs-pseudorandom-number-generators|website = Khan Academy|access-date = 2016-01-11}}</ref>

PRNGs are central in applications such as [[simulation]]s (e.g. for the [[Monte Carlo method]]), [[electronic game]]s (e.g. for [[procedural generation]]), and [[cryptography]]. Cryptographic applications require the output not to be predictable from earlier outputs, and more [[cryptographically-secure pseudorandom number generator|elaborate algorithms]], which do not inherit the linearity of simpler PRNGs, are needed.

Good statistical properties are a central requirement for the output of a PRNG. In general, careful mathematical analysis is required to have any confidence that a PRNG generates numbers that are sufficiently close to random to suit the intended use. [[John von Neumann]] cautioned about the misinterpretation of a PRNG as a truly random generator, joking that "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin."<ref>{{cite journal|last=Von Neumann|first=John|title=Various techniques used in connection with random digits|journal=National Bureau of Standards Applied Mathematics Series|year=1951|volume=12|pages=36–38|url=https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf|archive-url=http://web.archive.org/web/20221128083015/https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf |archive-date=28 November 2022 }}</ref>