Abstract

Given two independent weak random sources X, Y , with the same length \ell and min-entropies bX,bY whose sum is greater than \ell \Omega(polylog(\ell/\epsilon)), we construct a deterministic two-source extractor (aka "blender") that extracts max(bX,bY) (bX bY-\ell-4log(1/\epsilon)) bits which are \epsilon-close to uniform. In contrast, best previously published construction [4] extracted at most 2(bX bY--\ell-2log(1/\epsilon)) bits. Our main technical tool is a construction of a strong two-source extractor that extracts (bX bY-\ell-2log(1/\epsilon)) bits which are \epsilon-close to being uniform and independent of one of the sources(aka "strong blender"), so that they can later be reused as a seed to a seeded extractor. Our strong two-source extractor construction improves the best previously published construction of such strong blenders [7] by a factor of 2, applies to more sources X and Y , and is considerably simpler than the latter. Our methodology also unifies several of the previous two-source extractor constructions from the literature.

Citations