Explicit two-source extractors for near-logarithmic min-entropy
Speaker
Dean Doron
Tel-Aviv University
Host
Pritish Kamath and Akshay Degwekar
CSAIL MIT
Abstract:In this talk, we show an explicit construction of extractors for two independent sources of near-logarithmic min-entropy.
Previous constructions required either polylog(n) min-entropy or more than two sources.
The result extends the breakthrough result of Chattopadhyay and Zuckerman and also uses non-malleable extractors.
The main new ingredient is a somewhere-random condenser with a small entropy gap, used as a sampler.
Our construction can be seen as an efficient reduction to constructing non-malleable extractors, so using very recent constructions of non-malleable extractors (by Cohen and Li) - we will see how to obtain explicit two-source extractor for O(log n loglog n) min-entropy and constant error.
Previous constructions required either polylog(n) min-entropy or more than two sources.
The result extends the breakthrough result of Chattopadhyay and Zuckerman and also uses non-malleable extractors.
The main new ingredient is a somewhere-random condenser with a small entropy gap, used as a sampler.
Our construction can be seen as an efficient reduction to constructing non-malleable extractors, so using very recent constructions of non-malleable extractors (by Cohen and Li) - we will see how to obtain explicit two-source extractor for O(log n loglog n) min-entropy and constant error.