Threshold-Based Private Set Intersection Protocol for Secure Deconfliction in Multi-Jurisdictional Blockchain Investigations

Cross-border blockchain investigations frequently face data isolation challenges where multiple jurisdictions may conduct parallel inquiries into the same suspicious entities, leading to operational conflicts and redundant efforts. This paper presents a purpose-built t-out-of-n watchlist-anchored private set intersection (PSI) protocol, adapting established threshold secret-sharing techniques for secure jurisdictional discovery, enabling agencies to identify overlapping investigative targets without prematurely disclosing sensitive case details. The methodology is built upon Shamir’s Secret Sharing (SSS) and polynomial interpolation over the 2127−1 Mersenne prime field. A deterministic dual-hash field mapping ensures statistical uniformity over the prime field. Experimental validation using the Elliptic++ dataset confirmed the system’s high efficiency. The protocol maintains linear communication complexity of O(n·|S0|), where complexity scales with the watchlist size rather than the full participant dataset and remains stable under varying consensus requirements, where increasing the threshold t results in a marginal increase in total latency. Under the semi-honest adversarial model, the false-positive rate is cryptographically negligible at 2−127. The protocol achieves a hybrid security model wherein share privacy is information-theoretic under SSS, while field mapping and share authentication rely on standard computational assumptions. By integrating native source traceability, this framework provides a practical technological foundation for initiating formal Mutual Legal Assistance Treaty (MLAT) requests based on confidential matches identified across independent investigative workflows.