Extractors and pseudo-random generators with optimal seed length

Russell Impagliazzo, Ronen Shaltiel, Avi Wigderson

Research output: Contribution to journalConference articlepeer-review


We give the first construction of a pseudo-random generator with optimal seed length that uses (essentially) arbitrary hardness. It builds on the novel recursive use of the NW-generator in [8], which produced many optimal generators one of which was pseudo-random. This is achieved in two stages - first significantly reducing the number of candidate generators, and then efficiently combining them into one. We also give the first construction of an extractor with optimal seed length, that can handle sub-polynomial entropy levels. It builds on the fundamental connection between extractors and pseudo-random generators discovered by Trevisan, combined with construction above. Moreover, using Kolmogorov Complexity rather than circuit size in the analysis gives super-polynomial savings for our construction, and renders our extractors better than known for all entropy levels.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalUnknown Journal
StatePublished - 2000
Externally publishedYes
Event32nd Annual ACM Symposium on Theory of Computing - Portland, OR, USA
Duration: 21 May 200023 May 2000

ASJC Scopus subject areas

  • Software


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