Extractors and Pseudorandom Generators
Luca Trevisan
SpringerReference
We introduce a new approach to constructing 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 obtain.
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 pseudorandom 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 simple and admit a short self-contained description