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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.33

Bit-Fixing Extractors for Almost-Logarithmic Entropy

Authors: Dean Doron and Ori Fridman

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract

An oblivious bit-fixing source is a distribution over {0,1}ⁿ, where k bits are uniform and independent and the rest n-k are fixed a priori to some constant value. Extracting (close to) true randomness from an oblivious bit-fixing source has been studied since the 1980s, with applications in cryptography and complexity theory. We construct explicit extractors for oblivious bit-fixing source that support k = Õ(log n), outputting almost all the entropy with low error. The previous state-of-the-art construction that outputs many bits is due to Rao [Rao, CCC '09], and requires entropy k ≥ log^{c} n for some large constant c. The two key components in our constructions are new low-error affine condensers for poly-logarithmic entropies (that we achieve using techniques from the nonmalleable extractors literature), and a dual use of linear condensers for OBF sources.

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Dean Doron and Ori Fridman. Bit-Fixing Extractors for Almost-Logarithmic Entropy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.33,
  author =	{Doron, Dean and Fridman, Ori},
  title =	{{Bit-Fixing Extractors for Almost-Logarithmic Entropy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{33:1--33:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.33},
  URN =		{urn:nbn:de:0030-drops-243994},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.33},
  annote =	{Keywords: Seedless extractors, oblivious bit-fixing sources}
}

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Bit-Fixing Extractors for Almost-Logarithmic Entropy

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