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Membership queries are basic predicate operations that apply to datasets. Quantifications of such queries express global properties between datasets, including subset inclusion and disjointness. These operations are basic tools in set-theoretic data-mining procedures such as frequent-itemset-mining. In this work we formalize a family of such queries syntactically and we consider how they can be evaluated in a privacy-preserving fashion. We present a syntax-driven compiler that produces a protocol for each query and we show that semantically such queries correspond to basic set operation predicates between datasets. Using our compiler and based on the fact that it is syntax-driven, two parties can generate various privacy-preserving protocols with different complexity behavior that allow them to efficiently and securely evaluate the predicate of interest without sharing information about the datasets they possess. Our compiler sheds new light on the complexity of privacy-preserving evaluation of predicates such as disjointness and subset-inclusion and achieves substantial complexity improvements compared to previous works in terms of round as well as communication complexity. In particular, among others, we present protocols for both predicates that require one-round of interaction and have communication less than the size of the universe, while previously the only one round protocols known had communication proportional to the size of the universe. [ABSTRACT FROM AUTHOR]

Two parties, say Alice and Bob, possess two sets of elements that belong to a universe of possible values and wish to test whether these sets are disjoint or not. In this paper we consider the above problem in the setting where Alice and Bob wish to disclose no information to each other about their sets beyond the single bit: "whether the intersection is empty or not." This problem has many applications in commercial settings where two mutually distrustful parties wish to decide with minimum possible disclosure whether there is any overlap between their private datasets. We present three protocols that solve the above problem that meet different efficiency and security objectives and data representation scenarios. Our protocols are based on Homomorphic encryption and in our security analysis, we consider the semi-honest setting as well as the malicious setting. Our most efficient construction for a large universe in terms of overall communication complexity uses a new encryption primitive that we introduce called "superposed encryption." We formalize this notion and provide a construction that may be of independent interest. For dealing with the malicious adversarial setting we take advantage of recent efficient constructions of Universally-Composable commitments based on verifiable encryption as well as zero-knowledge proofs of language membership. [ABSTRACT FROM AUTHOR]