Efficient Fuzzy Private Set Intersection from Secret-shared OPRF

2026-04-16

AI Summary

Existing fuzzy private set intersection (FPSI) protocols under the L_p distance rely either on homomorphic encryption or operations with exponential complexity, resulting in poor efficiency. This work proposes an efficient FPSI protocol that eliminates the need for homomorphic encryption and instead builds solely upon symmetric-key primitives—namely, oblivious programmable pseudorandom functions, secret sharing, and prefix encoding. The protocol achieves linear communication and computational complexity in both set size and dimensionality, and introduces an innovative prefix technique that reduces the dependency on the distance threshold from linear to logarithmic. Experimental results demonstrate that the proposed protocol outperforms recent schemes by Gao et al. (ASIACRYPT’24) and Dang et al. (CCS’25), achieving 12–145× faster runtime and reducing communication overhead by 3–19×.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Privacy

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

Private set intersection (PSI) enables a sender holding a set $Q$ of size $m$ and a receiver holding a set $W$ of size $n$ to securely compute the intersection $Q \cap W$. Fuzzy PSI (FPSI) is a PSI variant where the receiver learns the items $q \in Q$ for which there exists some $w \in W$ satisfying $\mathsf{dist}(q, w) \le δ$ under a given distance metric. Although several FPSI works are proposed for $L_{p}$ distance metrics with $p \in [1, \infty]$, they either heavily rely on expensive homomorphic encryptions, or incur undesirable complexity, e.g., exponential to the element dimension, both of which lead to poor practical efficiency. In this work, we propose efficient FPSI protocols for $L_{p \in [1, \infty]}$ distance metrics, primarily leveraging significantly cheaper symmetric-key operations. Our protocols achieve linear communication and computation complexity in the set sizes $m,n$, the dimension $d$, and the distance threshold $δ$. Our core building block is an oblivious programmable PRF with secret-shared outputs, which may be of independent interest. Furthermore, we incorporate a prefix technique that reduces the dependence on the distance threshold $δ$ to logarithmic, which is particularly suitable for large $δ$. We implement our FPSI protocols and compare them with state-of-the-art constructions. Experimental results demonstrate that our protocols consistently and significantly outperform existing works across all settings. Specifically, our protocols achieve a speedup of $12{\sim}145\times$ in running time and a reduction of $3{\sim}8\times$ in communication cost compared to Gao et al.~(ASIACRYPT'24) and a speedup of $9{\sim}80\times$ in running time and a reduction of $5{\sim}19\times$ in communication cost compared to Dang et al.~(CCS'25).

Problem

• Fuzzy Private Set Intersection
• L_p distance
• practical efficiency
• homomorphic encryption
• computational complexity

Innovation

• Fuzzy Private Set Intersection
• Secret-shared OPRF
• Symmetric-key Cryptography
• Linear Complexity
• Prefix Technique