Simple extractors via constructions of cryptographic pseudo-random generators

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 or 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 approximate to n(lambda/3). (C) 2009 Elsevier B.V. All rights reserved.