Practical Traceable Over-Threshold Multi-Party Private Set Intersection

Multi-Party Private Set Intersection (MP-PSI) with threshold enhances the flexibility of MP-PSI by disclosing elements present in at least $t$ participants' sets, rather than requiring elements to appear in all $n$ sets. In scenarios where each participant is responsible for its dataset, e.g., digital forensics, MP-PSI with threshold should disclose both intersection elements and corresponding holders such that elements are traceable and the reliability of intersection is guaranteed. We refer to MP-PSI with threshold supporting traceability as Traceable Over-Threshold MP-PSI (T-OT-MP-PSI). However, research on such protocols remains limited, and existing work tolerates at most $t-2$ semi-honest participants at considerable computational cost. We propose two novel Traceable OT-MP-PSI protocols. The first, Efficient Traceable OT-MP-PSI (ET-OT-MP-PSI), combines Shamir's secret sharing with an oblivious programmable pseudorandom function, achieving significantly improved efficiency with resistance to at most $t-2$ semi-honest participants. The second, Security-enhanced Traceable OT-MP-PSI (ST-OT-MP-PSI), achieves security against up to $n-1$ semi-honest participants by further leveraging the oblivious linear evaluation protocol. Compared to Mahdavi et al.'s protocol, ours eliminate the assumption that certain special parties do not collude. Experimental results demonstrate significant improvements: for $n=5$, $t=3$, and sets of size $2^{14}$, ET-OT-MP-PSI achieves $15056\times$ speedup and ST-OT-MP-PSI achieves $505\times$ speedup over Mahdavi et al.'s protocol.