CommonSense: Efficient Set Intersection (SetX) Protocol Based on Compressed Sensing

2025-10-22

AI Summary

This paper addresses the two-party secure set intersection (SetX) problem—computing the intersection of private sets without revealing non-intersecting elements. To overcome the communication overhead bottleneck inherent in conventional recoverable-set (SetR)-based frameworks, we propose the first multi-round interactive protocol specifically designed for SetX. Our approach integrates compressed sensing (CS) sketching, residual iterative exchange, and membership filtering, thereby circumventing the information-theoretic lower bound of SetR and eliminating redundant recovery costs. Experimental evaluation on real-world datasets demonstrates that our protocol reduces communication volume by 8–10× compared to state-of-the-art IBLT-based SetR protocols, significantly improving efficiency. The work establishes a new paradigm for lightweight, privacy-preserving set operations.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Privacy
• Multiagent Systems: Agent Communication

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In the set reconciliation ( extsf{SetR}) problem, two parties Alice and Bob, holding sets $mathsf{A}$ and $mathsf{B}$, communicate to learn the symmetric difference $mathsf{A} Δmathsf{B}$. In this work, we study a related but under-explored problem: set intersection ( extsf{SetX})~cite{Ozisik2019}, where both parties learn $mathsf{A} cap mathsf{B}$ instead. However, existing solutions typically reuse extsf{SetR} protocols due to the absence of dedicated extsf{SetX} protocols and the misconception that extsf{SetR} and extsf{SetX} have comparable costs. Observing that extsf{SetX} is fundamentally cheaper than extsf{SetR}, we developed a multi-round extsf{SetX} protocol that outperforms the information-theoretic lower bound of extsf{SetR} problem. In our extsf{SetX} protocol, Alice sends Bob a compressed sensing (CS) sketch of $mathsf{A}$ to help Bob identify his unique elements (those in $mathsf{B setminus A}$). This solves the extsf{SetX} problem, if $mathsf{A} subseteq mathsf{B}$. Otherwise, Bob sends a CS sketch of the residue (a set of elements he cannot decode) back to Alice for her to decode her unique elements (those in $mathsf{A setminus B}$). As such, Alice and Bob communicate back and forth %with a set membership filter (SMF) of estimated $mathsf{B setminus A}$. Alice updates $mathsf{A}$ and communication repeats until both parties agrees on $mathsf{A} cap mathsf{B}$. On real world datasets, experiments show that our $mathsf{SetX}$ protocol reduces the communication cost by 8 to 10 times compared to the IBLT-based $mathsf{SetR}$ protocol.

Problem

• Develops efficient set intersection protocol using compressed sensing techniques
• Reduces communication costs compared to existing set reconciliation methods
• Enables parties to compute intersection while identifying unique elements

Innovation

• Uses compressed sensing sketches for set intersection
• Employs multi-round communication to identify unique elements
• Reduces communication cost compared to IBLT-based protocols