Recurrent Private Set Intersection for Unbalanced Databases with Cuckoo Hashing and Leveled FHE

—A Private Set Intersection (PSI) protocol is a cryptographic method allowing two parties, each with a private set, to determine the intersection of their sets without revealing any information about their entries except for the intersection itself. While extensive research has focused on PSI protocols, most studies have centered on scenarios where two parties possess sets of similar sizes, assuming a semi-honest threat model. However, when the sizes of the parties’ sets differ significantly, a generalized solution tends to underperform compared to a specialized one, as recent research has demonstrated. Additionally, conventional PSI protocols are typically designed for a single execution, requiring the entire protocol to be re-executed for each set intersection. This approach is suboptimal for applications such as URL denylisting and email filtering, which may involve multiple set intersections of small sets against a large set (e.g., one for each email received). In this study, we propose a novel PSI protocol optimized for the recurrent setting where parties have unbalanced set sizes. We implement our protocol using Levelled Fully Homomorphic Encryption and Cuckoo hashing, and introduce several optimizations to ensure real-time performance. By utilizing the Microsoft SEAL library, we demonstrate that our protocol can perform private set intersections in 20 ms and 240 ms on 10 Gbps and 100 Mbps networks, respectively. Compared to existing solutions, our protocol offers significant improvements, reducing set intersection times by one order of magnitude on slower networks and by two orders of magnitude on faster networks.