English

Simple extractors via constructions of cryptographic pseudo-random generators

Computational Complexity 2007-05-23 v3 Cryptography and Security

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(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}.

Keywords

Cite

@article{arxiv.cs/0501075,
  title  = {Simple extractors via constructions of cryptographic pseudo-random generators},
  author = {Marius Zimand},
  journal= {arXiv preprint arXiv:cs/0501075},
  year   = {2007}
}

Comments

21 pages, an extended abstract will appear in Proc. ICALP 2005; small corrections, some comments and references added