Provably Secure Private Set Intersection With Constant Communication Complexity

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