2026-07-22T11:19:26Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24399 2025-12-12T15:01:29Z ddc:004 open_access

Bit-Fixing Extractors for Almost-Logarithmic Entropy Doron, Dean Fridman, Ori Seedless extractors oblivious bit-fixing sources 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Dean Doron and Ori Fridman 2025 Is Part Of LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2025.33 urn:nbn:de:0030-drops-243994 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.33 eng https://creativecommons.org/licenses/by/4.0/legalcode