Paper 2026/507 Original: eprint.iacr.org/2026/507 ↗

Practically Efficient Linear-Time Server-Aided Private Set Union and Third Party Private Set Operations

Abstract

We present protocols for server-aided private set union (PSU), third-party private set difference (TP-PSD) and third-party private symmetric difference (TP-PSymD), offering both information-theoretically secure and cryptographically secure versions. In addition, we introduce variants of our TP-PSD and TP-PSymD protocols that are designed for practical deployment in settings when certain parties are resource-constrained. In a third-party setting, the receiver who obtains the output is an external inputless party with two other participating input parties. Our protocols for third-party private set operations significantly outperform those of Yeo and Ying (USENIX ’25), improving both asymptotic computational complexity and practical performance. Experimental results demonstrate substantial efficiency gains, including greatly reduced running times and scalability to much larger set sizes. Moreover, our server-aided private set union protocol is several times faster than existing state-of-the-art two-party private set union protocols.