Paper 2021/484

Efficient Scalable Multi-Party Private Set Intersection Using Oblivious PRF

Alireza Kavousi, Javad Mohajeri, and Mahmoud Salmasizadeh

Abstract

In this paper, we present a concretely efficient protocol for private set intersection (PSI) in the multi-party setting using oblivious pseudorandom function (OPRF). In fact, we generalize the approach used in the work of Chase and Miao [CRYPTO 2020] towards deploying a lightweight multi-point OPRF construction for two-party PSI. Our protocol only includes oblivious transfer (OT) extension and garbled Bloom filter as its main ingredients and avoids computationally expensive operations. From a communication pattern perspective, the protocol consists of two types of interactions. The first type is performed over a star-like communication graph in which one designated party interacts with all other parties via performing OTs as the sender. Besides, parties communicate through a path-like communication graph that involves sending a garbled Bloom filter from the first party to its neighboring party following the last one. This design makes our protocol to be highly scalable due to the independence of each party's complexity from the number of participating parties and thus causes a communication and computation complexities of $O(n\lambda k)$, where $n$ is the set size, $k$ is the number of hash functions, and $\lambda$ is the security parameter. Moreover, the asymptotic complexity of the designated party is $O(tn\lambda)$ which linearly scales with the number of parties $t$. We prove security of the proposed protocol against semi-honest adversaries.