Efficient Multi-party Private Set Union Resistant to Maximum Collusion Attacks

Qiang Liu, Joon-Woo Lee

Abstract: Multi-party Private Set Union (MPSU) enables multiple participants to jointly compute the union of their private sets without leaking any additional information beyond the resulting union. Liu et al. (ASIACRYPT 2023) proposed the first scalable MPSU protocol fully based on symmetric key encryption (SKE), which designates one participant as the "leader" responsible for obtaining the final union. However, the protocol assumes that the leader does not collude with other participants, which weakens its practicality. In this work, we design a scalable MPSU protocol, $\Pi_\text{MPSU}^\text{one-leader}$, which tolerates maximum collusion. The protocol relies primarily on SKE supplemented with additive homomorphic encryption (AHE), with the designated leader obtaining the union result. Furthermore, to address the issue of fairness in scenarios where obtaining the result early provides an advantage, we extend $\Pi_\text{MPSU}^\text{one-leader}$ and propose a protocol that allows all participants to receive the union result simultaneously, called $\Pi_\text{MPSU}^\text{leaderless}$. We implement our proposed schemes and conduct a comprehensive comparison against state-of-the-art solutions. The result shows that, for input sizes of $2^{12}$ at a comparable security level, $\Pi_\text{MPSU}^{\text{one-leader}}$ achieves a $663$ times speedup in online runtime compared to the state-of-the-art. Furthermore, it also remains $22$ times faster than half-collusion-tolerant protocol.