Asymmetric Multi-Party Private Set Union for Large-Repository Updates Without Non-Collusion Assumptions

Multi-party private set union (MPSU) allows multiple parties to compute a union without disclosing private inputs, but most existing protocols focus on balanced settings with comparable input sizes. In large-repository update scenarios, a leader maintains a massive base set while contributors submit small update sets; directly using balanced MPSU makes the online cost scale with the leader’s repository size. We propose AegisUnion, an asymmetric MPSU protocol tailored to large-repository updates. AegisUnion separates repository-dependent computation from online update processing through an offline oblivious key-value store (OKVS) encoding phase. In the online phase, contributors perform private membership determination, cross-contributor private deduplication, conditional payload sharing, and secret-shared shuffling, without revealing raw inputs, repository-overlap relations, inter-contributor duplicates, or the source of each output element. Under the semi-honest model, AegisUnion tolerates any coalition of corrupted parties as long as at least one party remains honest, without non-collusion assumptions. Experiments show that, as the repository grows from $2^{14}$ to $2^{18}$, the online time remains stable at 663–715 ms. At repository size $2^{18}$ and contributor update bound $2^{10}$, AegisUnion achieves about $455\times$ and $454\times$ lower online time than symmetric-key-based MPSU and public-key-based MPSU baselines, respectively, and about $271\times$ and $575\times$ lower online communication.