Unbalanced private set intersection with linear communication complexity

The private set intersection (PSI) protocol allows two parties holding a set of integers to compute the intersection of their sets without revealing any additional information to each other. The unbalanced PSI schemes consider a specific setting where a client holds a small set of the size n and a server holds a much larger set of the size m ( n ≪ m ). The communication overhead of state-of-the-art balanced PSI schemes is O ( m + n ) and the unbalanced PSI schemes are O ( n log m ). In this paper, we propose a novel secure unbalanced PSI protocol based on a hash proof system. The communication complexity of our protocol grows only linearly with the size of the small set. In other words, our protocol achieves communication overhead of O ( n ). We test the performance on a personal computer (PC) machine with a local area network (LAN) setting for the network. The experimental results demonstrate that the client only takes 2.01 s of online computation, 4.27 MB of round trip communication to intersect 1600 pieces of 32-bit integers with 2 20 pieces of 32-bit integers with the security parameter λ = 512. Our protocol is efficient and can be applied to resource-constrained devices, such as cell phones.