An efficient reduction from two-source to non-malleable extractors: Achieving near-logarithmic min-entropy

Avraham Ben-Aroya, Dean Doron, Amnon Ta-Shma

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The breakthrough result of Chattopadhyay and Zuckerman (2016) gives a reduction from the construction of explicit two-source extractors to the construction of explicit non-malleable extractors. However, even assuming the existence of optimal explicit non-malleable extractors only gives a two-source extractor (or a Ramsey graph) for poly(log n) entropy, rather than the optimal O(log n). In this paper we modify the construction to solve the above barrier. Using the currently best explicit non-malleable extractors we get an explicit bipartite Ramsey graphs for sets of size 2k, for k = O(log n log log n). Any further improvement in the construction of non-malleable extractors would immediately yield a corresponding two-source extractor. Intuitively, Chattopadhyay and Zuckerman use an extractor as a sampler, and we observe that one could use a weaker object - a somewhere-random condenser with a small entropy gap and a very short seed. We also show how to explicitly construct this weaker object using the error reduction technique of Raz, Reingold and Vadhan (1999), and the constant-degree dispersers of Zuckerman (2006) that also work against extremely small tests.

Original languageEnglish
Title of host publicationSTOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing
EditorsPierre McKenzie, Valerie King, Hamed Hatami
PublisherAssociation for Computing Machinery
Pages1185-1194
Number of pages10
ISBN (Electronic)9781450345286
DOIs
StatePublished - 19 Jun 2017
Event49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada
Duration: 19 Jun 201723 Jun 2017

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F128415
ISSN (Print)0737-8017

Conference

Conference49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017
Country/TerritoryCanada
CityMontreal
Period19/06/1723/06/17

Keywords

  • Condensers
  • Non-malleable extractors
  • Ramsey graphs
  • Two-source extractors

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