Distributed correlation generators

Abstract

We study the problem of distributed correlation generators wherein n parties wish to simulate unbounded samples from a joint distribution D = Di x D2 X ... x D[subscript n], once they are initialized using randomness sampled from a (possibly different) correlated distribution. We wish to ensure that these samples are computationally indistinguishable from i.i.d. samples from D. Furthermore, we wish to ensure security even against an adversary who corrupts a subset of the parties and obtains their internal (initialization) state. Our contributions are three-fold. First, we define the notion of distributed (noninteractive) correlation generators and show its connection to other cryptographic primitives. Secondly, assuming the existence of indistinguishability obfuscators, we show a construction of distributed correlation generators for a large and natural class of joint distributions that we call conditionally sampleable distributions. Finally, we show a construction for the subclass of additive-spooky distributions assuming private constrained pseudorandom functions (private CPRFs).