How to Get More Mileage from Randomness Extractors

Let C be a class of distributions over {0, 1}n . A deterministic randomness extractor for C is a function E : {0, 1}n {0, 1}m such that for any X in C the distribution E(X) is statistically close to the uniform distribution. A long line of research deals with explicit constructions of such extractors for various classes C while trying to maximize m. In this paper we give a general transformation that transforms a deterministic extractor E that extracts "few" bits into an extractor E that extracts "almost all the bits present in the source distribution". More precisely, we prove a general theorem saying that if E and C satisfy certain properties, then we can transform E into an extractor E . Our methods build on (and generalize) a technique of Gabizon, Raz and Shaltiel (FOCS 2004) that present such a transformation for the very restricted class C of "oblivious bit-fixing sources". The high level idea is to find properties of E and C which allow "recyc...

• Type: Conference
• Year: 2006
• Where: COCO
• Authors: Ronen Shaltiel
• Keywords: Algorithms, COCO 2006, Deterministic Randomness Extractor, Explicit Constructions, Source Distribution