Efficient Circuit-Based PSI via Cuckoo Hashing

While there has been a lot of progress in designing efficient custom protocols for computing Private Set Intersection (PSI), there has been less research on using generic Multi-Party Computation (MPC) protocols for this task. However, there are many variants of the set intersection functionality that are not addressed by the existing custom PSI solutions and are easy to compute with generic MPC protocols (e.g., comparing the cardinality of the intersection with a threshold or measuring ad conversion rates).\ Generic PSI protocols work over circuits that compute the intersection. For sets of size $n$, the best known circuit constructions conduct $O(n log n)$ or $O(n log n / loglog n)$ comparisons (Huang et al., NDSS'12 and Pinkas et al., {USENIX} Security'15). In this work, we propose new circuit-based protocols for computing emph{variants of the intersection} with an almost linear number of comparisons. Our constructions are based on new variants of Cuckoo hashing in two dimensions.\ We present an asymptotically efficient protocol as well as a protocol with better concrete efficiency. For the latter protocol, we determine the required sizes of tables and circuits experimentally, and show that the run-time is concretely better than that of existing constructions.\ The protocol can be extended to a larger number of parties. The proof technique presented in the full version for analyzing Cuckoo hashing in two dimensions is new and can be generalized to analyzing standard Cuckoo hashing as well as other new variants of it.