Privacy-Preserving Authorized Set Matching via Dishonest Majority Multiparty Computation

Private Set Intersection (PSI) enables each party with a private set to compute the intersection without disclosing other information. However, even in maliciously secure PSI, it does not guarantee input authenticity and output integrity, which becomes problematic in certain scenarios. For instance, in Web 3.0, one of the essential requirements is to find common certifiers among the parties. However, if certifier identities are meant to be protected, some parties may attempt to forge certifier identities or intentionally exclude a particular certifier during protocol execution. Recently, the Private Certifier Intersection (PCI), a variant of PSI, has been proposed to address this problem. Nevertheless, it incurs significantly high computational and communication overhead. This work proposes the Private Identity Intersection (PII), which takes private identifiers and corresponding anonymous signatures from mutually distrusting parties as input, verifies them, and delivers the intersection of the successfully verified identifiers to all parties while ensuring the integrity of the output. Furthermore, PII can naturally extend from two to multiple-party settings while resisting the collusion attack. To achieve the ideal functionality of PII, we implement a user-friendly MPC framework called $\mathsf {Oryx}$ without third-party libraries. Based on $\mathsf {Oryx}$, we instantiate PII with two digital signature schemes, one proposed in this paper. Compared to existing work, our PII protocols reduce the computation overhead by up to $163\times$ and the communication overhead by up to $190\times$, representing an improvement of two orders of magnitude. To demonstrate the practicality of our work, we evaluate its performance in WAN environments with bandwidths of 100 Mbps and 500 Mbps, under a fixed latency of 20 ms.