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 λn, for arbitrary constant λ > 0, have seed length O(log 2 n), and their output length is ≈ nλ/3. © Springer-Verlag Berlin Heidelberg 2005.