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A New Approach for Constructing Low-Error, Two-Source Extractors

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

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Subject Classification

ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • Two-Source Extractors
  • Non-Malleable Extractors
  • Pseudorandomness
  • Explicit Constructions

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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.

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Avraham Ben-Aroya, Eshan Chattopadhyay, Dean Doron, Xin Li, and Amnon Ta-Shma. A New Approach for Constructing Low-Error, Two-Source Extractors. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CCC.2018.3

Author Details

Avraham Ben-Aroya
  • The Blavatnik School of Computer Science, Tel-Aviv University, Tel Aviv 69978, Israel
Eshan Chattopadhyay
  • Department of Computer Science, Cornell University and School of Mathematics, IAS, Ithaca, NY 14850, USA
  • Princeton, NJ 08540, USA
Dean Doron
  • The Blavatnik School of Computer Science, Tel-Aviv University, Tel Aviv 69978, Israel
Xin Li
  • Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218, USA
Amnon Ta-Shma
  • The Blavatnik School of Computer Science, Tel-Aviv University, Tel Aviv 69978, Israel

Funding

  • Ben-Aroya, Avraham: Supported by the Israel Science Foundation grant no. 994/14.
  • Chattopadhyay, Eshan: Supported by NSF grants CCF-1526952, CCF-1412958 and the Simons Foundation. Part of this work was done when the author was a graduate student in UT Austin and while visiting the Simons Institute for the Theory of Computing at UC Berkeley.
  • Doron, Dean: Supported by the Israel Science Foundation grant no. 994/14. This work was done in part while visiting the Simons Institute for the Theory of Computing at UC Berkeley.
  • Li, Xin: Supported by NSF Grant CCF-1617713.
  • Ta-Shma, Amnon: Supported by the Israel Science Foundation grant no. 994/14. This work was done in part while visiting the Simons Institute for the Theory of Computing at UC Berkeley.

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