Efficient Privacy-Preserving Threshold Private Set Intersection in Cross-Domain Federated Learning Data Alignment

Cross-domain Federated Learning (FL), as an emerging paradigm of distributed machine learning, enables collaborative training across multiple parties while preserving data privacy. However, cross-domain data alignment, as a critical step in FL, often faces the challenge of private data leakage. Applying the Threshold Private Set Intersection (TPSI) protocol to data alignment in cross-domain FL proves to be a secure and efficient solution. Nevertheless, existing two-party or multi-party TPSI protocols commonly rely on high-overhead public-key cryptographic algorithms such as Homomorphic Encryption (HE), resulting in low operational efficiency. In response to these limitations, this work introduces a computationally efficient two-party and multi-party TPSI protocols based on Oblivious Key-Value Store (OKVS) and Threshold Secret Sharing (TSS). To determine whether the intersection cardinality meets the threshold, OKVS is employed to associate elements with secret sub-shares, effectively preventing leakage of intersection cardinality. Additionally, to avoid the exponential combination of secret shares, this paper adopts a Reed-Solomon decoding algorithm based on Fast Fourier Transform (FFT) for secret reconstruction. Furthermore, building upon the two-party TPSI protocol, we design an efficient multi-party TPSI protocol by incorporating unconditional zero-sharing. Finally, a detailed correctness proof and performance analysis of the two protocols demonstrate that the proposed solution is secure, feasible, and applicable to cross-domain FL data alignment scenarios involving varying numbers of participants.