Explicit two-source extractors for near-logarithmic min-entropy

We explicitly construct extractors for two independent n-bit sources of (log n) minentropy. Previous constructions required either polylog(n) min-entropy [CZ15, Mek15] or five sources [Coh16]. Our result extends the breakthrough result of Chattopadhyay and Zuckerman [CZ15] and uses the non-malleable extractor of Cohen [Coh16]. The main new ingredient in our construction is a somewhere-random condenser with a small entropy gap, used as a sampler. We construct such somewhere-random condensers using the error reduction mechanism of Raz et al. [RRV99] together with the high-error, constant degree dispersers of Zuckerman [Zuc06]. ∗The Blavatnik School of Computer Science, Tel-Aviv University, Tel Aviv 69978, Israel. Supported by the Israel science Foundation grant no. 994/14 and by the United States – Israel Binational Science Foundation grant no. 2010120. †The Blavatnik School of Computer Science, Tel-Aviv University, Tel Aviv 69978, Israel. Email: [email protected]. Supported by the Israel science Foundation grant no. 994/14 and by the United States – Israel Binational Science Foundation grant no. 2010120. ‡The Blavatnik School of Computer Science, Tel-Aviv University, Tel Aviv 69978, Israel. Email: [email protected]. Supported by the Israel science Foundation grant no. 994/14 and by the United States – Israel Binational Science Foundation grant no. 2010120. ISSN 1433-8092 Electronic Colloquium on Computational Complexity, Report No. 88 (2016)