Efficient two-party Private Set Union and circuit-based version for large-scale data set based on novel oblivious filter

Abstract

Private Set Union (PSU) protocol enables secure computation of set unions across multiple parties while preserving input privacy — a critical capability for large-scale data aggregation. To date, two-party PSU schemes predominantly adopt the “split-then-execute” paradigm, which as demonstrated by Jia et al. (2024), inherently suffers from during-execution leakage. While their proposed symmetric-key approach addresses this vulnerability, the dependency on private equality test (PET) protocol additionally introduces non-negligible computational and communication overheads. Meanwhile, research on circuit-PSU protocol capable of securely computing a function (merge, sort or federated learning) over the union set remains blank.

In this paper, we focus on two main objectives: (1) We present an optimized two-party PSU protocol that eliminates during-execution leakage while achieving enhanced efficiency; (2) We propose the first circuit-PSU. Unlike conventional PSU where participant obtains plaintext result, circuit-PSU provides secret-shared outputs that inherently prevent both during-execution leakage and intersection cardinality exposure. Furthermore, circuit-PSU removes the requirement for predefined result recipient and thus can offer superior flexibility. Meanwhile, our technical innovations include an optimized Share Translation (ShareTrans) protocol and a novel Oblivious Filter (OF) primitive that synergistically enhance both PSU and circuit-PSU efficiency. The experimental results indicate that under constrained computational resources (8-core CPU, 16GB RAM), the proposed circuit-PSU achieves a comparatively better improvement in communication complexity compared to existing state-of-the-art schemes, and our two-party PSU also exhibits comparable performance, for example, achieving approximately $4\times$ efficiency improvement over Jia et al. (2024).