New Traceable Over-Threshold MP-PSI Protocols Offer Significant Speed Gains

Global: New Traceable Over-Threshold MP-PSI Protocols Offer Significant Speed Gains

Researchers have unveiled two novel protocols for multi‑party private set intersection with threshold (MP‑PSI) that enhance both traceability and efficiency, according to a paper posted on arXiv in December 2025. The work targets scenarios such as digital forensics where participants must identify not only common elements but also the parties holding them, while tolerating semi‑honest behavior among collaborators.

Background on MP‑PSI with Threshold

Traditional MP‑PSI requires an element to appear in every participant’s dataset before it is disclosed. Threshold variants relax this condition, revealing elements present in at least t of n sets. However, existing traceable implementations have been limited to tolerating at most t‑2 semi‑honest participants and have incurred high computational costs.

Efficient Traceable OT‑MP‑PSI (ET‑OT‑MP‑PSI)

The first protocol, named Efficient Traceable OT‑MP‑PSI (ET‑OT‑MP‑PSI), integrates Shamir’s secret sharing with an oblivious programmable pseudorandom function. This combination reduces computational overhead while still resisting up to t‑2 semi‑honest participants.

Security‑Enhanced Traceable OT‑MP‑PSI (ST‑OT‑MP‑PSI)

The second protocol, Security‑Enhanced Traceable OT‑MP‑PSI (ST‑OT‑MP‑PSI), builds on the first by incorporating an oblivious linear evaluation protocol. This addition expands the security guarantee to tolerate up to n‑1 semi‑honest participants.

Performance Compared to Prior Work

Both protocols eliminate the need for special‑party assumptions that were required in the earlier approach by Mahdavi et al. Experimental evaluation for a configuration of n = 5 participants, t = 3, and dataset sizes of 2^14 elements shows that ET‑OT‑MP‑PSI achieves a speedup of 15056 times, while ST‑OT‑MP‑PSI delivers a speedup of 505 times over the Mahdavi et al. method.

Implications for Applied Cryptography

The reported efficiency gains could make traceable over‑threshold MP‑PSI practical for real‑world applications that demand both privacy and accountability, such as collaborative forensic investigations and regulated data sharing among organizations.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.