Private and oblivious set and multiset operations

Privacy-preserving set operations and set intersection in particular are a popular research topic. Despite a large body of literature, the great majority of the available solutions are two-party protocols and are not composable. In this work we design a comprehensive suite of secure multi-party protocols for set and multiset operations that are composable, do not assume any knowledge of the sets by the parties carrying out the secure computation, and can be used for secure outsourcing. All of our protocols have communication and computation complexity of O(mlog m) for sets or multisets of size m, which compares favorably with prior work. Furthermore, we are not aware of any results that realize composable operations. Our protocols are secure in the information theoretic sense and are designed to minimize the round complexity.