Extracting all the Randomness from a Weakly Random Source

Abstract

In this paper, we give two explicit constructions of extractors, both of which work for a source of any min-entropy on strings of length n. The first extracts any constant fraction of the min-entropy using O(log^2 n) additional random bits. The second extracts all the min-entropy using O(log 3 n) additional random bits. Both constructions use fewer truly random bits than any previous. construction which works for all min-entropies ans extracts a constant fraction of the min-entropy.