Efficient Secure Multiparty Subset Computation

Secure subset problem is important in secure multiparty computation, which is a vital field in cryptography. Most of the existing protocols for this problemcan only keep the elements of one set private, while leaking the elements of the other set. In other words, they cannot solve the secure subset problem perfectly. While a few studies have addressed actual secure subsets, these protocols were mainly based on the oblivious polynomial evaluations with inefficient computation. In this study, we first design an efficient secure subset protocol for sets whose elements are drawn from a known set based on a new encoding method and homomorphic encryption scheme. If the elements of the sets are taken from a large domain, the existing protocol is inefficient. Using the Bloom filter and homomorphic encryption scheme, we further present an efficient protocol with linear computational complexity in the cardinality of the large set, and this is considered to be practical for inputs consisting of a large number of data. However, the second protocol that we design may yield a false positive. This probability can be rapidly decreased by reexecuting the protocol with different hash functions. Furthermore, we present the experimental performance analyses of these protocols.