Improved Constructions of Two-Source Extractors

TL;DR

This paper improves two-source extractors by increasing their output length from one bit to a polynomial in the min-entropy, while maintaining low error, based on enhanced constructions for non-oblivious bit-fixing sources.

Contribution

It introduces a new extractor for non-oblivious bit-fixing sources that outputs multiple bits, leading to improved two-source extractors with larger output.

Findings

Enhanced extractor outputs polynomially many bits.

Maintained low error rate of $n^{- ext{Omega}(1)}$.

Built on previous work by Chattopadhyay and Zuckerman.

Abstract

In a recent breakthrough \cite{CZ15}, Chattopadhyay and Zuckerman gave an explicit two-source extractor for min-entropy $k \geq \log^C n$ for some large enough constant $C$. However, their extractor only outputs one bit. In this paper, we improve the output of the two-source extractor to $k^{\Omega(1)}$, while the error remains $n^{-\Omega(1)}$. Our improvement is obtained by giving a better extractor for $(q, t, \gamma)$ non-oblivious bit-fixing sources, which can output $t^{\Omega(1)}$ bits instead of one bit as in \cite{CZ15}.