Simple extractors via constructions of cryptographic pseudo-random generators

Abstract

Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-correcting codes and that are very simple and efficient. For example, one extractor produces each output bit separately in $O(\log^2 n)$ time. These extractors work for weak sources with min entropy $\lambda n$, for arbitrary constant $\lambda > 0$, have seed length $O(\log^2 n)$, and their output length is $\approx n^{\lambda/3}$.