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 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 λ n , for arbitrary constant λ > 0 , have seed length O ( log 2 n ) , and their output length is ≈ n λ / 3 .