Editing Zero-knowledge proof (section)

== Variants of zero-knowledge ==
Different variants of zero-knowledge can be defined by formalizing the intuitive concept of what is meant by the output of the simulator "looking like" the execution of the real proof protocol in the following ways:

* We speak of ''perfect zero-knowledge'' if the distributions produced by the simulator and the proof protocol are distributed exactly the same. This is for instance the case in the first example above.
* ''Statistical zero-knowledge''<ref>{{cite journal|last1=Sahai|first1=Amit|last2=Vadhan|first2=Salil|title=A complete problem for statistical zero knowledge|journal=Journal of the ACM|date=1 March 2003|volume=50|issue=2|pages=196–249|doi=10.1145/636865.636868|url=http://dash.harvard.edu/bitstream/handle/1/4728406/Vadhan_StatZeroKnow.pdf?sequence=2 |archive-url=https://web.archive.org/web/20150625193124/http://dash.harvard.edu/bitstream/handle/1/4728406/Vadhan_StatZeroKnow.pdf?sequence=2 |archive-date=2015-06-25 |url-status=live|citeseerx=10.1.1.4.3957|s2cid=218593855}}</ref> means that the distributions are not necessarily exactly the same, but they are [[statistically close]], meaning that their statistical difference is a [[negligible function]].
* We speak of ''computational zero-knowledge'' if no efficient algorithm can distinguish the two distributions.