How to Meet Big Data When Private Set Intersection Realizes Constant Communication Complexity

Electronic information is increasingly often shared among unreliable entities. In this context, one interesting problem involves two parties that secretly want to determine intersection of their respective private data sets while none of them wish to disclose the whole set to other. One can adopt Private Set Intersection (PSI) protocol to address this problem preserving the associated security and privacy issues. This paper presents the first PSI protocol that achieves constant (p(κ)) communication complexity with linear computation overhead and is fast even for the case of large input sets, where p(κ) is a polynomial in security parameter κ. The scheme is proven to be provably secure in the standard model against semi-honest parties. We combine somewhere statistically binding (SSB) hash function with indistinguishability obfuscation (iO) and Bloom filter to construct our PSI protocol.