Extracting Correlations

Abstract— Motivated by applications in cryptography, we consider a generalization of randomness extraction and the related notion of privacy amplification to the case of two correlated sources. We introduce the notion of correlation extractors, which extract nearly perfect independent instances of a given joint distribution from imperfect, or “leaky,” instances of the same distribution. More concretely, suppose that Alice holds a and Bob holds b, where (a, b) are obtained by taking n independent samples from a joint distribution (X, Y ) and letting a include all X instances and b include all Y instances. An adversary Eve obtains partial information about (a, b) by choosing a function L with output length t and learning L(a, b). The goal is to design a protocol between Alice and Bob which may use additional fresh randomness, such that for every L as above the following holds. In the end of the interaction, Alice outputs a and Bob outputs b such that (a , b ) are statistically ind...

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky, Amit Sahai
• Keywords: Correlation Extractors, FOCS 2009, Independent Instances, Joint Distribution, Theoretical Computer Science