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Practical Traceable Over-Threshold Multi-Party Private Set Intersection

Le Yang, Weijing You, Huiyang He, Kailiang Ji, Jingqiang Lin

TL;DR

This work addresses the need for traceable over-threshold MP-PSI by introducing two protocols, ET-OT-MP-PSI and ST-OT-MP-PSI, that reveal only intersection elements with at least $t$ holders and the corresponding holders. ET-OT-MP-PSI uses Shamir's secret sharing and OPPRF to achieve efficiency with resilience to up to $t-2$ semi-honest colluders, while ST-OT-MP-PSI adds Oblivious Linear Evaluation (OLE) to attain security against up to $n-1$ semi-honest participants. The authors provide theoretical correctness and security analyses, complexity discussions, and extensive performance evaluations showing substantial speedups over prior work, e.g., up to $15056\times$ for ET-OT-MP-PSI and $505\times$ for ST-OT-MP-PSI in representative settings. These protocols enable accountable, threshold-based private set intersections suitable for privacy-preserving investigations and cross-institutional analyses where traceability is essential, without relying on restrictive non-collusion assumptions of earlier schemes.

Abstract

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.

Practical Traceable Over-Threshold Multi-Party Private Set Intersection

TL;DR

This work addresses the need for traceable over-threshold MP-PSI by introducing two protocols, ET-OT-MP-PSI and ST-OT-MP-PSI, that reveal only intersection elements with at least holders and the corresponding holders. ET-OT-MP-PSI uses Shamir's secret sharing and OPPRF to achieve efficiency with resilience to up to semi-honest colluders, while ST-OT-MP-PSI adds Oblivious Linear Evaluation (OLE) to attain security against up to semi-honest participants. The authors provide theoretical correctness and security analyses, complexity discussions, and extensive performance evaluations showing substantial speedups over prior work, e.g., up to for ET-OT-MP-PSI and for ST-OT-MP-PSI in representative settings. These protocols enable accountable, threshold-based private set intersections suitable for privacy-preserving investigations and cross-institutional analyses where traceability is essential, without relying on restrictive non-collusion assumptions of earlier schemes.

Abstract

Multi-Party Private Set Intersection (MP-PSI) with threshold enhances the flexibility of MP-PSI by disclosing elements present in at least participants' sets, rather than requiring elements to appear in all 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 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 semi-honest participants. The second, Security-enhanced Traceable OT-MP-PSI (ST-OT-MP-PSI), achieves security against up to 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 , , and sets of size , ET-OT-MP-PSI achieves speedup and ST-OT-MP-PSI achieves speedup over Mahdavi et al.'s protocol.
Paper Structure (38 sections, 2 theorems, 11 equations, 8 figures, 4 tables)

This paper contains 38 sections, 2 theorems, 11 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The high-level idea of our protocols
  3. Our Contributions
  4. Preliminaries
  5. Notations
  6. Security Model
  7. Shamir's Secret Sharing
  8. Secret sharing and Reconstruction
  9. Secret shares update
  10. Hashing Schemes
  11. Simple Hashing
  12. Cuckoo Hashing
  13. Oblivious Programmable Pseudorandom Function
  14. Oblivious Linear Evaluation
  15. Traceable Over-Threshold Multi-Party Private Set Intersection
  16. ...and 23 more sections

Key Result

theorem 1

The ET-OT-MP-PSI realizes the functionality $\mathcal{F}_{\text{T-OT-MP-PSI}}^{n,m,t}$ and is secure against collusion among up to $t - 2$ parties in the semi-honest model, given the statistical security parameter $\lambda$ and the computational security parameter $\kappa$.

Figures (8)

  • Figure 1: The OPPRF functionality.
  • Figure 2: Traceable OT-MP-PSI functionality $\mathcal{F}_{\text{T-OT-MP-PSI}}^{n,m,t}$.
  • Figure 3: The overall process of ET-OT-MP-PSI.
  • Figure 4: ET-OT-MP-PSI protocol.
  • Figure 5: The core idea of the shares update phase in ST-OT-MP-PSI.
  • ...and 3 more figures

Theorems & Definitions (8)

  • theorem 1
  • proof
  • theorem 2
  • proof
  • proof
  • proof
  • proof
  • proof