Private Set Operations from Circuit-Based PSI

Private set operations (PSOs) have been extensively studied due to their wide range of applications. In this work, we present a novel framework for constructing advanced PSO protocols by treating circuit-based private set intersection (circuit-PSI) as a block-box building block, complemented by a minimal OT-based postprocessing layer customized for each target functionality. Our framework supports a variety of extensions, including PSI-Sum, which computes the sum of associated values; PSI-Card, which reveals the intersection cardinality; PSI-InnerProd, which computes the inner product over intersecting elements; and a private set union (PSU) protocol-all without leaking intermediate information, a vulnerability known as during-execution leakage. We implement and benchmark our protocols against closely related PSO protocols. The results show that our constructions outperform state-of-the-art protocols in total runtime. An important additional advantage of our approach is the ability to offload expensive OT operations to the setup phase, significantly improving online efficiency. For instance, in terms of online execution time under LAN settings, PSI-Card and PSI-Sum achieve 9.92 - 13× speedups, PSU achieves 10.8 - 11.7×, and PSI-InnerProd demonstrates up to a remarkable 47 - 56× improvement over prior work with comparable communication overhead.