On extractors, error-correction and hiding all partial information

Randomness extractors (Nisan and Zuckerman, 1996) allow one to obtain nearly perfect randomness from highly imperfect sources randomness, which are only known to contain "scattered" entropy. Not surprisingly, such extractors have found numerous applications in many areas of computer science including cryptography. Aside from extracting randomness, a less known usage of extractors comes from the fact that they hide all deterministic functions of their (high-entropy) input (Dodis and Smith, 2005): in other words, extractors provide certain level of privacy for the imperfect source that they use. In the latter kind of applications, one typically needs extra properties of extractors, such as invertibility, collision-resistance or error-correction. In this abstract we survey some of such usages of extractors, concentrating on several recent results by the author (Dodis et al., 2004 and Dodis and Smith, 2005). The primitives we survey include several flavors of randomness extractors, entropically secure encryption and perfect one-way hash functions. The main technical tools include several variants of the leftover hash lemma, error correcting codes, and the connection between randomness extraction and hiding all partial information. Due to space constraints, many important references and results are not mentioned here; interested reader can find those in the works of Dodis et al. (2004) and Dodis and Smith (2005)