CommonSense: Efficient Set Intersection (SetX) Protocol Based on Compressed Sensing
Jingfan Meng, Tianji Yang, Jun Xu

TL;DR
This paper introduces a novel, efficient set intersection protocol based on compressed sensing that significantly reduces communication costs compared to traditional set reconciliation methods.
Contribution
The authors develop a dedicated SetX protocol using compressed sensing, outperforming SetR protocols and the information-theoretic lower bounds for set intersection.
Findings
Reduces communication by 8-10 times on real datasets.
Outperforms IBLT-based SetR protocols in efficiency.
Provides a multi-round protocol for accurate set intersection.
Abstract
In the set reconciliation (\textsf{SetR}) problem, two parties Alice and Bob, holding sets and , communicate to learn the symmetric difference . In this work, we study a related but under-explored problem: set intersection (\textsf{SetX})~\cite{Ozisik2019}, where both parties learn instead. However, existing solutions typically reuse \textsf{SetR} protocols due to the absence of dedicated \textsf{SetX} protocols and the misconception that \textsf{SetR} and \textsf{SetX} have comparable costs. Observing that \textsf{SetX} is fundamentally cheaper than \textsf{SetR}, we developed a multi-round \textsf{SetX} protocol that outperforms the information-theoretic lower bound of \textsf{SetR} problem. In our \textsf{SetX} protocol, Alice sends Bob a compressed sensing (CS) sketch of to help Bob…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Cryptography and Data Security · Complexity and Algorithms in Graphs
