NDLI: Three-Source Extractors for Polylogarithmic Min-Entropy

Content Provider	IEEE Xplore Digital Library
Author	Xin Li
Copyright Year	2015
Description	Author affiliation: Dept. of Comput. Sci., Johns Hopkins Univ. Baltimore, Baltimore, MD, USA (Xin Li)
Abstract	We continue the study of constructing explicit extractors for independent general weak random sources. The ultimate goal is to give a construction that matches what is given by the probabilistic method - an extractor for two independent n-bit weak random sources with min-entropy as small as log n + O(1). Previously, the best known result in the two-source case is an extractor by Bourgain [1], which works for min-entropy 0.49n; and the best known result in the general case is an earlier work of the author [2], which gives an extractor for a constant number of independent sources with min-entropy polylog(n). However, the constant in the construction of [2] depends on the hidden constant in the best known seeded extractor, and can be large; moreover the error in that construction is only 1/poly(n). In this paper, we make two important improvements over the result in [2]. First, we construct an explicit extractor for three independent sources on n bits with min-entropy k ≥ polylog(n). In fact, our extractor works for one source with poly-logarithmic min-entropy and another independent block source with two blocks each having poly-logarithmic min-entropy. This significantly improves previous constructions, and the next step would be to break the 0.49n barrier in two-source extractors. Second, we improve the error of the extractor from 1/poly(n) to $2^{-k}^{Ω(1)},$ which is almost optimal and crucial for cryptographic applications. Some of our techniques may be of independent interests.
Starting Page	863
Ending Page	882
File Size	365201
Page Count	20
File Format	PDF
ISBN	9781467381918
ISSN	02725428
DOI	10.1109/FOCS.2015.58
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-10-17
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Yttrium Entropy Cryptography Computer science Probabilistic logic Distributed computing Bipartite graph independent source extractor randomness
Content Type	Text
Resource Type	Article

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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