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Structure-Aware Private Set Intersection, with Applications to Fuzzy Matching

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

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Abstract

In two-party private set intersection (PSI), Alice holds a set X, Bob holds a set Y, and they learn (only) the contents of \(X \cap Y\). We introduce structure-aware PSI protocols, which take advantage of situations where Alice’s set X is publicly known to have a certain structure. The goal of structure-aware PSI is to have communication that scales with the description size of Alice’s set, rather its cardinality.

We introduce a new generic paradigm for structure-aware PSI based on function secret-sharing (FSS). In short, if there exists compact FSS for a class of structured sets, then there exists a semi-honest PSI protocol that supports this class of input sets, with communication cost proportional only to the FSS share size. Several prior protocols for efficient (plain) PSI can be viewed as special cases of our new paradigm, with an implicit FSS for unstructured sets.

Our PSI protocol can be instantiated from a significantly weaker flavor of FSS, which has not been previously studied. We develop several improved FSS techniques that take advantage of these relaxed requirements, and which are in some cases exponentially better than existing FSS.

Finally, we explore in depth a natural application of structure-aware PSI. If Alice’s set X is the union of many radius-\(\delta \) balls in some metric space, then an intersection between X and Y corresponds to fuzzy PSI, in which the parties learn which of their points are within distance \(\delta \). In structure-aware PSI, the communication cost scales with the number of balls in Alice’s set, rather than their total volume. Our techniques lead to efficient fuzzy PSI for \(\ell _\infty \) and \(\ell _1\) metrics (and approximations of \(\ell _2\) metric) in high dimensions. We implemented this fuzzy PSI protocol for 2-dimensional \(\ell _\infty \) metrics. For reasonable input sizes, our protocol requires 45–60% less time and 85% less communication than competing approaches that simply reduce the problem to plain PSI.

Authors partially supported by NSF award 2150726.

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Notes

  1. 1.

    The original formulation of FSS by Boyle et al. [9] is in terms of functions instead of sets, however in this work we are only interested in boolean set membership functions - hence we reframed the FSS definition.

  2. 2.

    The presence of a \(|B| \log |B|\) term here is deceptive. The protocol would be equally secure if the output of H were \(\kappa \) bits, in which case the length of Bob’s message would be \(|B| \kappa \) bits. What we have written here is an optimization, observing that shorter output of H is possible, namely \(\lambda + \log |A| + \log |B|\) bits. Every PSI protocol that is based on the OPRF paradigm has communication cost of this kind—in order to achieve correctness error bounded by \(2^{-\lambda }\), the OPRF outputs that Bob sends to Alice must have length at least \(\lambda + \log |A| + \log |B|\).

  3. 3.

    Our prototype implementation currently supports only 2 dimensions.

  4. 4.

    Our actual implementation sends twice this amount of data because we do not optimize the base OTs for the case where one of the OT messages is random, as with bFSS shares.

  5. 5.

    The implementation of KKRT that we used has a large expansion factor, which accounts for the difference between this estimate and the actual communication that we measured.

  6. 6.

    https://github.com/asu-crypto/mPSI.

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  1. Oregon State University, Corvallis, USA

    Gayathri Garimella, Mike Rosulek & Jaspal Singh

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  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Garimella, G., Rosulek, M., Singh, J. (2022). Structure-Aware Private Set Intersection, with Applications to Fuzzy Matching. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13507. Springer, Cham. https://doi.org/10.1007/978-3-031-15802-5_12

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