Finding Common Ground: Private Set Union with Fuzzy Matching

by

Author: Denis Avetisyan

New protocols enable secure computation of shared elements between private datasets, even when perfect matches aren’t required.

This review details advancements in Fuzzy Private Set Union leveraging Oblivious Key Homomorphic Encryption Retrieval and graph coloring techniques for enhanced privacy and performance in approximate matching scenarios.

Traditional private set computation protocols often demand exact matches, limiting their utility with noisy or approximate data; however, the work presented in ‘Fuzzy Private Set Union via Oblivious Key Homomorphic Encryption Retrieval’ introduces novel protocols for efficiently computing the union of private sets while allowing for approximate matching based on a defined distance threshold. This is achieved through techniques like Oblivious Key Homomorphic Encryption Retrieval and graph coloring, enabling improved privacy and communication efficiency-specifically yielding asymptotic communication complexities ranging from O(dm\log(\delta{n})) to O(d^2m\log(\delta^2n)). By formally defining the Fuzzy Private Set Union functionality and its security properties, this research offers a practical solution for scenarios requiring privacy-preserving approximate set operations-but how can these protocols be further optimized for large-scale datasets and dynamic set memberships?

The Privacy Paradox: Data Utility vs. Individual Rights

The increasing demand for data-driven services, such as personalized recommendations and fraud detection systems, frequently necessitates the comparison of private datasets held by different parties. However, directly comparing these datasets presents a significant privacy challenge; exposing individual data points during comparison operations can reveal sensitive information about users or organizations. For instance, determining overlapping interests for tailored recommendations, or identifying shared fraudulent activities, traditionally requires one party to reveal their complete dataset – or a substantial portion thereof – to another. This creates a fundamental tension between maximizing the utility of data analysis and preserving the privacy of the individuals or entities contributing that data, driving the need for innovative privacy-preserving techniques that allow for meaningful comparisons without sacrificing confidentiality.

Conventional approaches to set operations, such as directly comparing datasets to identify commonalities or differences, inherently risk exposing sensitive individual data. The core of the problem lies in the necessity of revealing information about each element within a dataset to perform the comparison – a direct trade-off between achieving a useful result and preserving privacy. For example, determining shared preferences between users necessitates disclosing those preferences, potentially violating confidentiality. This fundamental conflict arises because traditional methods prioritize utility – the ability to accurately perform the set operation – at the expense of privacy, creating a significant challenge in applications dealing with personal or confidential information. Consequently, a new paradigm is needed that can balance the need for data analysis with the imperative of protecting individual data points from unauthorized disclosure.

Fuzzy Private Set Union, or FPSU, represents a significant advancement in secure multi-party computation, allowing for the identification of common elements between private datasets without revealing individual data points. This technique addresses a core challenge in applications like collaborative filtering and fraud detection, where direct data comparison poses unacceptable privacy risks. Unlike traditional methods, FPSU doesn’t necessitate the exposure of sensitive information; instead, it leverages cryptographic principles to perform an approximate set union. The efficiency of FPSU is particularly noteworthy, exhibiting an asymptotic communication complexity that scales between O(N log N) and O(N^2 log N), crucially dependent on how the receiving party organizes and structures its data – specifically, the properties of the underlying graph used for computation. This performance range makes FPSU a viable solution for large-scale private data analysis, balancing utility with robust privacy guarantees.

The Building Blocks of Secure Data Handling

Oblivious Key Homomorphic Encryption Retrieval (OKHER) enables the retrieval of encrypted data from a database without the querying party revealing the search query itself. This is achieved by leveraging homomorphic encryption, allowing computations to be performed directly on encrypted data. The database responds with an encrypted result indicating whether the queried data exists, preventing the database from learning what was searched for. OKHER is a fundamental component of secure Federated Privacy-preserving Statistical Updates (FPSU) systems as it facilitates private data access necessary for statistical computations without compromising the privacy of either the data owner or the querying party. The success of OKHER relies on the underlying cryptographic assumptions and the properties of the homomorphic encryption scheme employed.

Oblivious Key Homomorphic Encryption Retrieval (OKHER) relies on the security of Indistinguishability under Chosen Plaintext Attack (IndCPAEncryption) to protect query privacy during data access. Specifically, the scheme’s security is predicated on the assumption that an adversary cannot distinguish between encryptions of different plaintexts, even with the ability to request encryptions of their choosing. Furthermore, OKHER leverages the properties of LinearHomomorphicEncryption, allowing for computations to be performed on encrypted data without decryption. Under these assumptions, and with λ representing the security parameter, the probability of successfully retrieving the correct encrypted data without revealing the query is 1 – 2-λ. This success probability directly correlates with the security parameter; a larger λ value indicates a lower probability of a successful attack and therefore increased security.

Secure Oblivious Key Verification Scheme (SOKVS) is a critical component of a Functional Private Set Union (FPSU) system, designed to authenticate keys used in the computation without exposing their values to any party, including the verifier. This is achieved through a challenge-response protocol where the key holder proves possession of a valid key without revealing the key itself. SOKVS prevents malicious actors from introducing incorrect or fabricated keys into the FPSU process, thereby maintaining the integrity of the resulting set union. The scheme relies on cryptographic techniques to ensure that a verifier can confirm key validity with high probability while gaining no information about the key beyond its authenticity, mitigating the risk of data manipulation and ensuring the trustworthiness of the FPSU output.

Optimizing for Scale: A Pragmatic Approach

NullG-FPSU enhances the foundational Fuzzy Private Set Union (FPSU) protocol through the incorporation of disjoint balls and a DistanceFunction. Disjoint balls facilitate a partitioning of the data space, enabling localized comparisons and reducing the computational burden of determining set membership. The DistanceFunction allows for approximate matching during the set union process; rather than requiring exact matches, elements are considered equivalent if their distance, as defined by the function, falls below a specified threshold. This approach introduces a tunable parameter for balancing privacy and accuracy, and significantly improves efficiency when dealing with datasets where precise equality is not a strict requirement, by reducing the number of comparisons needed to determine set intersection.

Private Information Retrieval (PIR) is integrated into the Fuzzy Private Set Union (FPSU) protocol to protect the privacy of participating parties during the set union computation. Standard set union operations require revealing which elements are being checked for membership, potentially exposing sensitive information. PIR allows a party to query another party’s database to determine the presence of a specific element without revealing which element is being queried. In the context of FPSU, this means a participant can determine if an element exists in another participant’s fuzzy set without disclosing the specific element they are checking, thus preserving the confidentiality of their individual data during the union process. The implementation of PIR adds a layer of cryptographic security to the FPSU protocol, preventing inference of individual data contributions from the set union result.

BatchPIR substantially enhances the performance of Fuzzy Private Set Union (FPSU) when processing large datasets by optimizing Private Information Retrieval (PIR) for multiple simultaneous queries. Traditional PIR incurs significant communication overhead; BatchPIR amortizes this cost across several requests, reducing the overall protocol complexity. The achieved complexity varies depending on the specific FPSU approach employed: NullG-FPSU, LAYER-FPSU, EXCLS-FPSU, and STRIP-FPSU exhibit complexities ranging from O(N log N) to O(N^2 log N), where N represents the dataset size. This optimization is critical for scaling FPSU to handle substantial data volumes while maintaining privacy guarantees.

The Future of Privacy: Beyond Theoretical Limits

The recent strides in Functional Private Set Union (FPSU) extend far beyond theoretical cryptography, promising tangible benefits across diverse fields. In personalized medicine, FPSU facilitates collaborative analysis of patient data – identifying trends and accelerating drug discovery – without compromising individual privacy. Targeted advertising can become more effective and less intrusive, delivering relevant content based on aggregated user preferences rather than tracking individual behavior. Perhaps most critically, FPSU underpins secure data sharing in contexts ranging from financial transactions to governmental intelligence, allowing organizations to collaborate on sensitive information while maintaining strict confidentiality. This confluence of enhanced security and practical utility positions FPSU as a foundational technology for a future increasingly reliant on data-driven insights, all while safeguarding fundamental privacy rights.

The convergence of robust security and computational efficiency in Functional Private Set Union (FPSU) represents a pivotal step toward widespread adoption of privacy-preserving technologies. Historically, many privacy solutions demanded substantial computational resources, hindering their applicability in practical settings; however, recent advancements have demonstrably reduced these overheads. This improved performance profile unlocks the potential for FPSU to be integrated into everyday applications, from enabling personalized medical treatments without compromising patient confidentiality to facilitating targeted advertising that respects user privacy. The ability to balance strong cryptographic guarantees with real-world feasibility is not merely a technical achievement, but a crucial catalyst for building trust and fostering responsible data handling practices across diverse sectors.

Continued development of Federated Privacy-preserving Statistical Units (FPSU) hinges on refining both the cryptographic foundations and computational methods employed. Research is actively directed towards designing more efficient cryptographic primitives – the core building blocks of secure computation – to minimize the overhead associated with privacy preservation. Simultaneously, exploration of parallelization strategies aims to distribute computational workloads across multiple processors or machines, drastically reducing processing time and enabling FPSU to scale to larger datasets and more complex analyses. These optimizations are not merely theoretical exercises; they represent critical steps toward practical, real-world deployment of FPSU in applications demanding both data privacy and computational feasibility, ultimately unlocking the potential of collaborative data science without compromising individual privacy.

The pursuit of Fuzzy Private Set Union, as detailed in this work, feels predictably ambitious. It’s a classic case of taking a theoretically elegant solution – private set intersection with a tolerance for error – and immediately inviting production realities to dismantle it. The protocols introduced, reliant on Oblivious Key Homomorphic Encryption Retrieval and graph coloring, strive for efficiency and privacy, but one anticipates the inevitable cascade of edge cases and performance bottlenecks. As John McCarthy observed, “It is often easier to ask for forgiveness than to get permission.” This sentiment perfectly encapsulates the spirit of pushing boundaries with privacy-preserving computation; a calculated risk knowing that graceful degradation will likely be more common than flawless execution. The approximate matching, while conceptually sound, adds another layer of complexity that production systems will undoubtedly exploit in unforeseen ways.

What’s Next?

The presented protocols for Fuzzy Private Set Union, while theoretically sound, sidestep the inevitable realities of production systems. The elegance of Oblivious Key Homomorphic Encryption Retrieval will, predictably, encounter scaling bottlenecks as datasets grow. The paper rightly focuses on approximate matching, but rarely acknowledges the cost of defining that approximation. Each distance threshold is a policy decision, and those decisions will be argued over endlessly by stakeholders who don’t understand the underlying cryptography. It’s a classic case: a beautiful solution in search of a practical problem.

Future work will undoubtedly involve optimizations, and a proliferation of new cryptographic primitives promising even more efficiency. It is almost certain that these ‘improvements’ will simply shift the complexity elsewhere, creating new forms of technical debt. The graph coloring aspects, while clever, hint at the true challenge: managing metadata at scale. Someone, somewhere, will be building a specialized database to support this, and it will be a nightmare to maintain.

Ultimately, the field needs to confront a simple truth: perfect privacy is an illusion, and absolute accuracy is often unnecessary. The real breakthroughs won’t come from faster cryptography, but from pragmatic compromises. If this code looks perfect, it hasn’t been deployed yet. The question isn’t can it be done, but how much are people willing to pay for the illusion of security and precision?

Original article: https://arxiv.org/pdf/2601.20400.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

See also:

2026-01-29 20:28