Extracting Randomness via Repeated Condensing

Extractors (defined by Nisan and Zuckerman) are procedures that use a small number of truly random bits (called the seed) to extract many (almost) truly random bits from arbitrary distributions as long as they have sufficient (min)-entropy. A natural weakening of an extractor is a condenser, whose output distribution has a higher entropy rate than the input distribution (without losing much of the initial entropy). An extractor can be viewed as an ultimate condenser as it outputs a distribution with the maximal entropy rate. In this paper we construct explicit condensers with short seed length. The condenser constructions combine (variants or more efficient versions of) ideas from several works, including the block extraction scheme of [NZ96], the observation made in [SZ98, NTS99] that a failure of the block extraction scheme is also useful, the recursive “win-win” case analysis of [ISW99, ISW00], and the error correction of random sources used in [Tre01]. As a byproduct, (via re...

• Type: Conference
• Year: 2000
• Where: FOCS
• Authors: Omer Reingold, Ronen Shaltiel, Avi Wigderson
• Keywords: Block Extraction Scheme, Entropy Rate, FOCS 2000, Random Bits, Theoretical Computer Science