https://handwiki.org/wiki/index.php?title=Pseudorandomness&feed=atom&action=historyPseudorandomness - Revision history2022-12-03T12:59:07ZRevision history for this page on the wikiMediaWiki 1.38.4https://handwiki.org/wiki/index.php?title=Pseudorandomness&diff=2240252&oldid=prevOhm: update2022-10-24T20:25:05Z<p>update</p>
<p><b>New page</b></p><div>{{Short description|Appearing random but actually being generated by a deterministic, causal process}}<br />
A '''pseudorandom''' sequence of numbers is one that appears to be [[Statistical randomness|statistically random]], despite having been produced by a completely [[Deterministic system|deterministic]] and repeatable process.<ref name=RandomArticle_Phys.NYT2001>{{cite news |newspaper={{wipe|The New York Times}} |url=https://www.nytimes.com/2001/06/12/science/connoisseurs-of-chaos-offer-a-valuable-product-randomness.html |title=Connoisseurs of Chaos Offer A Valuable Product: Randomness |author=George Johnson |date=June 12, 2001}}</ref> <br />
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==Background==<br />
The generation of random numbers has many uses, such as for [[Sampling (statistics)|random sampling]], Monte Carlo methods, [[Engineering:Board game|board game]]s, or gambling. In [[Physics:Physics|physics]], however, most processes, such as gravitational acceleration, are deterministic, meaning that they always produce the same outcome from the same starting point. Some notable exceptions are [[Physics:Radioactive decay|radioactive decay]] and [[Physics:Quantum measurement|quantum measurement]], which are both modeled as being truly random processes in the underlying physics. Since these processes are not practical sources of random numbers, people use pseudorandom numbers, which ideally have the unpredictability of a truly random sequence, despite being generated by a deterministic process.<ref>{{cite book |title=Pseudorandomness|quote=pseudorandomness, the theory of efficiently generating objects that “look random” despite being constructed using little or no randomness|author=S. P. Vadhan |year=2012}}</ref><br />
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In many applications, the deterministic process is a [[Algorithm|computer algorithm]] called a [[Pseudorandom number generator|pseudorandom number generator]], which must first be provided with a number called a [[Random seed|random seed]]. Since the same seed will yield the same sequence every time, it is important that the seed be well chosen and kept hidden, especially in [[Computer security|security]] applications, where the pattern's unpredictability is a critical feature.<ref>{{cite news |newspaper=BBC |title=Web's random numbers are too weak, researchers warn |url=https://www.bbc.com/news/technology-33839925|author=Mark Ward |date=August 9, 2015}}</ref><br />
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In some cases where it is important for the sequence to be demonstrably unpredictable, people have used physical sources of random numbers, such as radioactive decay, atmospheric electromagnetic noise harvested from a radio tuned between stations, or intermixed timings of people's [[Keystroke dynamics|keystrokes]].<ref name=RandomArticle_Phys.NYT2001/><ref name=RandomArticle.SS1998>{{cite magazine |magazine=Sun Server |title=Javatalk: Horseshoes, hand grenades and random numbers |author=Jonathan Knudson |date=January 1998 |pages=16–17}}</ref> The time investment needed to obtain these numbers leads to a compromise: using some of these physics readings as a seed for a pseudorandom number generator.<br />
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==History==<br />
Before modern computing, researchers requiring random numbers would either generate them through various means (dice, cards, roulette wheels,<ref name=":0" /> etc.) or use existing random number tables.<br />
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The first attempt to provide researchers with a ready supply of random digits was in 1927, when the Cambridge University Press published a table of 41,600 digits developed by L.H.C. Tippett. In 1947, the [[Organization:RAND Corporation|RAND Corporation]] generated numbers by the electronic simulation of a roulette wheel;<ref name=":0">{{Cite web|url=http://www.rand.org/pubs/monograph_reports/MR1418/index2.html|title=A Million Random Digits|publisher=RAND Corporation|access-date=2017-03-30}}</ref> the results were eventually published in 1955 as ''A Million Random Digits with 100,000 Normal Deviates''.<br />
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==In computational complexity==<br />
In [[Theoretical computer science|theoretical computer science]], a [[Probability distribution|distribution]] is '''pseudorandom''' against a class of adversaries if no adversary from the class can distinguish it from the uniform distribution with significant advantage.<ref>Oded Goldreich. Computational Complexity: A Conceptual Perspective. Cambridge University Press. 2008.</ref><br />
This notion of pseudorandomness is studied in [[Computational complexity theory|computational complexity theory]] and has applications to [[Cryptography|cryptography]].<br />
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Formally, let ''S'' and ''T'' be finite sets and let '''F''' = {''f'': ''S'' → ''T''} be a class of functions. A [[Probability distribution|distribution]] '''D''' over ''S'' is ε-'''pseudorandom''' against '''F''' if for every ''f'' in '''F''', the statistical distance between the distributions and <math>f(X)</math>, where and <math>X</math> is sampled from '''D''', and <math>f(Y)</math>, where and <math>Y</math> is sampled from the uniform distribution on ''S'', is at most ε.<br />
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In typical applications, the class '''F''' describes a model of computation with bounded resources and one is interested in designing distributions '''D''' with certain properties that are pseudorandom against '''F'''. The distribution '''D''' is often specified as the output of a [[Pseudorandom generator|pseudorandom generator]].<ref>{{cite web|url=https://people.seas.harvard.edu/~salil/pseudorandomness/pseudorandomness-Aug12.pdf|title=Pseudorandomness}}</ref><br />
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==See also==<br />
* [[Cryptographically secure pseudorandom number generator]]<br />
* [[List of random number generators]]<br />
* [[Pseudorandom binary sequence]]<br />
* [[Pseudorandom ensemble]]<br />
* [[Pseudorandom number generator]]<br />
* Quasi-random sequence<br />
* [[Random number generation]]<br />
* [[Pseudorandom noise]]<br />
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==Further reading==<br />
* Donald E. Knuth (1997) ''[[The Art of Computer Programming]], Volume 2: Seminumerical Algorithms (3rd edition)''. Addison-Wesley Professional, {{isbn|0-201-89684-2}}<br />
* Oded Goldreich. (2008) ''[https://books.google.com/books?id=EuguvA-w5OEC Computational Complexity: a conceptual perspective]''. Cambridge University Press. {{isbn|978-0-521-88473-0}}. {{page needed|date=July 2012}} {{Font color|gray|'''(Limited preview at Google Books)'''}}<br />
* {{Cite journal | last1 = Vadhan | first1 = S. P. | doi = 10.1561/0400000010 | title = Pseudorandomness | journal = Foundations and Trends in Theoretical Computer Science | volume = 7 | pages = 1–336 | year = 2012 | issue = 1–3 }}<br />
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== External links ==<br />
* [http://www.fourmilab.ch/hotbits HotBits: Genuine random numbers, generated by radioactive decay]<br />
* [https://web.archive.org/web/20051023025710/http://www.merrymeet.com/jon/usingrandom.html Using and Creating Cryptographic-Quality Random Numbers]<br />
* In RFC 4086, the use of pseudorandom number sequences in cryptography is discussed at length.{{Ref RFC|4086}}<br />
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==References==<br />
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[[Category:Pseudorandomness| ]]<br />
[[Category:Theoretical computer science]]<br />
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{{Sourceattribution|Pseudorandomness}}</div>Ohm