Construction of extractors using pseudo-random generators

Abstract

We introduce a new approach to construct extractors. Extractors are algorithms that transform a `weakly random' distribution into an almost uniform distribution. Explicit constructions of extractors have a variety of important applications, and tend to be very difficult to achieve. We demonstrate an unsuspected connection between extractors and pseudorandom generators. In fact, we show that every pseudorandom generator of a certain kind is an extractor. A pseudo-random generator construction due to Impagliazzo and Wigderson, once reinterpreted via our connection, is already an extractor that beats most known constructions and solves an important open question. We also show that, using the simpler Nisan-Wigderson generator and standard error-correcting codes, one can build even better extractors with the additional advantage that both the construction and the analysis are extremely simple and admit a short self-contained treatment.