On the privacy of federated Clustering: A Cryptographic View
The privacy concern in federated clustering has attracted considerable attention in past decades. Many privacy-preserving clustering algorithms leverage cryptographic techniques like homomorphic encryption or secure multiparty computation, to guarantee full privacy, i.e., no additional information i...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
13.12.2023
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Subjects | |
Online Access | Get full text |
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Summary: | The privacy concern in federated clustering has attracted considerable
attention in past decades. Many privacy-preserving clustering algorithms
leverage cryptographic techniques like homomorphic encryption or secure
multiparty computation, to guarantee full privacy, i.e., no additional
information is leaked other than the final output. However, given the iterative
nature of clustering algorithms, consistently encrypting intermediate outputs,
such as centroids, hampers efficiency. This paper delves into this intricate
trade-off, questioning the necessity of continuous encryption in iterative
algorithms. Using the federated K-means clustering as an example, we
mathematically formulate the problem of reconstructing input private data from
the intermediate centroids as a classical cryptographic problem called hidden
subset sum problem (HSSP)-extended from an NP-complete problem called subset
sum problem (SSP). Through an in-depth analysis, we show that existing
lattice-based HSSP attacks fail in reconstructing the private data given the
knowledge of intermediate centroids, thus it is secure to reveal them for the
sake of efficiency. To the best of our knowledge, our work is the first to cast
federated clustering's privacy concerns as a cryptographic problem HSSP such
that a concrete and rigorous analysis can be conducted. |
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DOI: | 10.48550/arxiv.2312.07992 |