Editing Pseudorandomness (section)

==In computational complexity==
In [[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>
This notion of pseudorandomness is studied in [[computational complexity theory]] and has applications to [[cryptography]].

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 [[total variation distance|statistical distance]] between the distributions <math>f(X)</math> and <math>f(Y)</math>, where <math>X</math> is sampled from '''D''' and <math>Y</math> is sampled from the [[uniform distribution (discrete)|uniform distribution]] on ''S'', is at most ε.

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]].<ref>{{cite web|url=https://people.seas.harvard.edu/~salil/pseudorandomness/pseudorandomness-Aug12.pdf|title=Pseudorandomness}}</ref>