Cloud-aided multi-party private set intersection using Chinese national cryptographic algorithms

Multi-party private set intersection (MPSI) is a fundamental primitive for privacy-preserving data collaboration, enabling multiple parties to compute the common elements of their private sets without revealing non-intersection elements. Existing MPSI protocols are mainly constructed from international cryptographic primitives, and their adaptation to Chinese commercial cryptographic algorithms remains insufficient for deployment scenarios that require domestic cryptographic compliance. This paper proposes OPRF-MPSI, a cloud-aided MPSI protocol based on SM2 elliptic-curve operations, SM3 hashing, and SM4 encapsulation. The protocol first uses a blinded SM2-based oblivious pseudorandom function (OPRF) to derive deterministic tags for equal inputs while hiding plaintext elements from the cloud server. It then introduces a re-randomized tag-hardening mechanism to decouple blinded OPRF evaluation, hardened tag derivation, and final index matching, reducing cross-stage linkability under a semi-honest cloud model. A Bloom-filter-assisted candidate filtering strategy is further used to reduce the number of indexes involved in exact cloud-side matching. Security analysis shows that, under the elliptic-curve discrete logarithm assumption and the random oracle model, the cloud server cannot recover plaintext elements from protocol messages and learns only bounded leakage, including equality patterns, candidate bucket positions, and the final intersection size. Experiments under multiple party numbers and set sizes indicate that OPRF-MPSI reduces online running time compared with selected MPSI baselines, while incurring higher communication overhead than the most bandwidth-efficient baseline. These results suggest that the protocol is suitable for latency-sensitive cloud-assisted data collaboration scenarios where compatibility with Chinese commercial cryptographic algorithms is required.