TY - GEN
T1 - Bit-Fixing Extractors for Almost-Logarithmic Entropy
AU - Doron, Dean
AU - Fridman, Ori
N1 - Publisher Copyright:
© Dean Doron and Ori Fridman; licensed under Creative Commons License CC-BY 4.0.
PY - 2025/9/15
Y1 - 2025/9/15
N2 - 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 = Oe(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 ≥ logc 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.
AB - 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 = Oe(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 ≥ logc 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.
KW - Seedless extractors
KW - oblivious bit-fixing sources
UR - https://www.scopus.com/pages/publications/105019527355
U2 - 10.4230/LIPIcs.APPROX/RANDOM.2025.33
DO - 10.4230/LIPIcs.APPROX/RANDOM.2025.33
M3 - Conference contribution
AN - SCOPUS:105019527355
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2025
A2 - Ene, Alina
A2 - Chattopadhyay, Eshan
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 28th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2025 and the 29th International Conference on Randomization and Computation, RANDOM 2025
Y2 - 11 August 2025 through 13 August 2025
ER -