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Bit-Fixing Extractors for Almost-Logarithmic Entropy

Authors Dean Doron , Ori Fridman

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Subject Classification

ACM Subject Classification
  • Theory of computation → Expander graphs and randomness extractors
Keywords
  • Seedless extractors
  • oblivious bit-fixing sources

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.33

Author Details

Dean Doron
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel
Ori Fridman
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel

Funding

The work is supported in part by NSF-BSF grant #2022644.

Acknowledgements

We thank Jesse Goodman for many helpful and interesting conversations, and Mahdi Cheraghchi for helpful discussion on the cryptographic applications of OBF extractors.

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