Scalable multi-party private set-intersection

In this work we study the problem of private set-intersection in the multi-party setting and design two protocols with the following improvements compared to prior work. First, our protocols are designed in the so-called star network topology, where a designated party communicates with everyone else, and take a new approach of leveraging the 2PC protocol of [FNP04]. This approach minimizes the usage of a broadcast channel, where our semi-honest protocol does not make any use of such a channel and all communication is via point-to-point channels. In addition, the communication complexity of our protocols scales with the number of parties. More concretely, (1) our first semi-honest secure protocol implies communication complexity that is linear in the input sizes, namely O((∑ⁿ _i=1 m_i)·κ) bits of communication where κ is the security parameter and m_i is the size of P_i‘s input set, whereas overall computational overhead is quadratic in the input sizes only for a designated party, and linear for the rest. We further reduce this overhead by employing two types of hashing schemes. (2) Our second protocol is proven secure in the malicious setting. This protocol induces communication complexity O((n²+nm_MAX+nm_MIN log m_MAX)κ) bits of communication where m_MIN (resp. m_MAX) is the minimum (resp. maximum) over all input sets sizes and n is the number of parties.