Post-Quantum Private Set Intersection with Ultra-Efficient Online Performance

While tremendous progress has been made towards achieving highly efficient and practical Private Set Intersection (PSI) protocols during the last decade, the development of post-quantum PSI is still far from satisfactory. Existing post-quantum PSI protocols encounter a dilemma: while those based on fully homomorphic encryption (FHE) achieve low online communication, they suffer from significant online computation; conversely, protocols based on post-quantum Oblivious Pseudorandom Functions (OPRFs) exhibit excellent online computational performance but incur substantially high online communication. To overcome this dilemma, we present a lattice-based PSI protocol that achieves optimal online performance in both communication and computation. Our solution introduces two core innovations: a robust signal comparison algorithm based on RLWE key exchange, which determines the intersection through signal consistency rather than direct shared key comparison, and an optimized Oblivious Key–Value Stores (OKVS) implementation featuring a composite key–value mapping for efficient handling of high-dimensional RLWE polynomials. We implement the protocol and conduct extensive benchmarks in both symmetric and asymmetric set-size settings. The results show that our construction achieves the lowest online overhead in both computation and communication among all tests. For example, with asymmetric set sizes $(2^{12},11041)$, the online phase requires only $0.132$ s, yielding $19\times$ and $282\times$ improvements over FHE-based (CCS’21) and OPRF-based (EUROCRYPT’25) protocols, respectively. Even at $(2^{24},11041)$, our online communication time is only 0.201 s, which is $226\times$ and $184\times$ that of FHE-based and OPRF-based PSI, respectively. Additionally, our online communication overhead is the lowest in all tests; however, this comes at the cost of heavy offline communication overhead for very large set sizes, revealing a clear trade-off between pre-computation and online efficiency. This work addresses a critical gap in post-quantum PSI by delivering a protocol that achieves balanced online communication and computational overhead, thereby enabling broader practical deployment.