A new approach for constructing low-error, two-source extractors

Avraham Ben-Aroya, Eshan Chattopadhyay, Dean Doron, Xin Li, Amnon Ta-Shma

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

7 Scopus citations

Abstract

Our main contribution in this paper is a new reduction from explicit two-source extractors for polynomially-small entropy rate and negligible error to explicit t-non-malleable extractors with seed-length that has a good dependence on t. Our reduction is based on the Chattopadhyay and Zuckerman framework (STOC 2016), and surprisingly we dispense with the use of resilient functions which appeared to be a major ingredient there and in follow-up works. The use of resilient functions posed a fundamental barrier towards achieving negligible error, and our new reduction circumvents this bottleneck. The parameters we require from t-non-malleable extractors for our reduction to work hold in a non-explicit construction, but currently it is not known how to explicitly construct such extractors. As a result we do not give an unconditional construction of an explicit low-error two-source extractor. Nonetheless, we believe our work gives a viable approach for solving the important problem of low-error two-source extractors. Furthermore, our work highlights an existing barrier in constructing low-error two-source extractors, and draws attention to the dependence of the parameter t in the seed-length of the non-malleable extractor. We hope this work would lead to further developments in explicit constructions of both non-malleable and two-source extractors.

Original languageEnglish
Title of host publication33rd Computational Complexity Conference, CCC 2018
EditorsRocco A. Servedio
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages31-319
Number of pages289
ISBN (Electronic)9783959770699
DOIs
StatePublished - 1 Jun 2018
Externally publishedYes
Event33rd Computational Complexity Conference, CCC 2018 - San Diego, United States
Duration: 22 Jun 201824 Jun 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume102
ISSN (Print)1868-8969

Conference

Conference33rd Computational Complexity Conference, CCC 2018
Country/TerritoryUnited States
CitySan Diego
Period22/06/1824/06/18

Keywords

  • Explicit constructions
  • Non-malleable extractors
  • Pseudorandomness
  • Two-source extractors

ASJC Scopus subject areas

  • Software

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