Researchers Introduce Efficient Fuzzy Private Set Union Protocols

Global: Researchers Introduce Efficient Fuzzy Private Set Union Protocols

Researchers have unveiled new fuzzy private set union (FPSU) protocols that broaden private set computation to handle approximate matches, according to a paper posted to arXiv on January 31, 2026. The work proposes a suite of protocols that keep individual input sets private while allowing multiple parties to compute the union of sets that may overlap within a defined tolerance.

Background on Private Set Computations

Private set multi‑party computations (PSMPC) enable participants to jointly evaluate functions without revealing their underlying data, except for what can be inferred from the final output. Traditional private set union (PSU) and private set intersection (PSI) require exact element equality, limiting their use in scenarios where data may be noisy or imprecise.

Introducing Fuzzy Private Set Union

The authors define a structured PSI where elements are considered a match if they lie within a specified distance, termed fuzzy PSI. Extending this idea, fuzzy PSU replaces a receiver’s set X with a collection of d‑dimensional balls ℬ_δ(X), each centered on an element x_i and having radius δ. The resulting union operation combines X with any sender elements Y that fall outside all balls, effectively computing X ∪ {y ∈ Y | y ∉ ℬ_δ(X)}.

Oblivious Key Homomorphic Encryption Retrieval (OKHER)

To support the fuzzy context, the paper introduces a new sub‑protocol called Oblivious Key Homomorphic Encryption Retrieval (OKHER). OKHER builds on prior Oblivious Key‑Value Retrieval (OKVR) techniques but leverages homomorphic encryption to enable secure retrieval of encrypted keys without revealing the underlying data.

Communication Efficiency

Using OKHER and homomorphic encryption, the authors derive asymptotic communication bounds that vary with the structure of the receiver’s dataset. For certain ball configurations, the communication volume scales as O(d m log(δ n)), while more complex arrangements lead to a bound of O(d² m log(δ² n)). These results suggest that the protocols can be tuned to achieve practical efficiency for high‑dimensional data.

Implications and Future Directions

The proposed FPSU protocols could benefit applications such as privacy‑preserving data sharing, collaborative machine‑learning model training, and secure biometric matching, where exact matches are rare. The authors note that further work will explore concrete instantiations, performance benchmarking, and extensions to other distance metrics.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.