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 $O(m \log m)$ 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. Practicality of our solutions is shown through experimental
results.
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