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    Simple extractors via constructions of cryptographic pseudo-random generators

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    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(log2n)O(\log^2 n) time. These extractors work for weak sources with min entropy λn\lambda n, for arbitrary constant λ>0\lambda > 0, have seed length O(log2n)O(\log^2 n), and their output length is nλ/3\approx n^{\lambda/3}.Comment: 21 pages, an extended abstract will appear in Proc. ICALP 2005; small corrections, some comments and references adde
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