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A Plug-n-Play Framework for Scaling Private Set Intersection to Billion-Sized Sets

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Cryptology and Network Security (CANS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14342))

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Abstract

Motivated by the recent advances in practical secure computation, we design and implement a framework for scaling solutions for the problem of private set intersection (PSI) into the realm of big data. A protocol for PSI enables two parties each holding a set of elements to jointly compute the intersection of these sets without revealing the elements that are not in the intersection. Following a long line of research, recent protocols for PSI only have \({\approx }5\times \) computation and communication overhead over an insecure set intersection. However, this performance is typically demonstrated for set sizes in the order of ten million. In this work, we aim to scale these protocols to efficiently handle set sizes of one billion elements or more.

We achieve this via a careful application of a binning approach that enables parallelizing any arbitrary PSI protocol. Building on this idea, we designed and implemented a framework which takes a pair of PSI executables (i.e., for each of the two parties) that typically works for million-sized sets, and then scales it to billion-sized sets (and beyond). For example, our framework can perform a join of billion-sized sets in 83 min compared to 2000 min of Pinkas et al. (ACM TPS 2018), an improvement of \(25\times \). Furthermore, we present an end-to-end Spark application where two enterprises, each possessing private databases, can perform a restricted class of database join operations (specifically, join operations with only an on clause which is a conjunction of equality checks involving attributes from both parties, followed by a where clause which can be split into conjunctive clauses where each conjunction is a function of a single table) without revealing any data that is not part of the output.

This work was done while all authors were at Visa Research.

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Notes

  1. 1.

    This does not necessarily apply to the setting of unbalanced PSI where the set sizes can be orders of magnitude apart [3, 7, 11, 27, 48]. For instance, [14] do unbalanced PSI with \(2^{28}\) elements on one side and say 1024 elements on the other side.

  2. 2.

    For a further breakdown of this number, [51] note that 30.0 h (88%) are for simple hashing (cuckoo hashing runs in parallel and requires 16.3 h), 3 h (9%) are for computing the OTs, and 1.2 h (4%) are for computing the plaintext intersection.

  3. 3.

    Using \(m \approx n\) in our self-reduction would incur an unacceptable overhead due to padding. Please see Sect. 3.1 on how to choose the optimum value of m.

  4. 4.

    In that Section, they also analyze the choice of m for PSI with unbalanced sets.

  5. 5.

    This is a standard technique to capture protocols in cryptography, for example while designing zero-knowledge compilers that transform a semi-honest secure protocol into a maliciously secure protocol.

  6. 6.

    Most PSI protocols have very few rounds (exceptions include circuit PSI protocols that rely on the GMW compiler).

  7. 7.

    We support any PSI protocol irrespective of the underlying cryptographic assumptions or algorithmic techniques.

  8. 8.

    If we have k worker nodes on each side, then we can run k instances of \(\varPi \) in parallel, and repeat this \(m/k\) times to complete the PSI portion of the execution.

  9. 9.

    Restricting clauses this way enables us to reduce the above problem to the PSI problem. We note that the restriction above can be lifted if we use more sophisticated PSI protocols that can keep the PSI output in secret shared form without revealing it. We leave this for future work.

  10. 10.

    This corresponds to \(\delta _0 = 0.019\) for a bin size of \(\approx \)500K (cf. Sect. 3.1).

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Authors and Affiliations

  1. LinkedIn, Sunnyvale, USA

    Saikrishna Badrinarayanan

  2. Visa Research, Foster City, USA

    Ranjit Kumaresan, Vinjith Nagaraja, Karan Patel, Srinivasan Raghuraman, Peter Rindal & Minghua Xu

  3. Google, Mountain View, USA

    Mihai Christodorescu

  4. MIT, Cambridge, USA

    Srinivasan Raghuraman

  5. The University of Texas at Austin, Austin, USA

    Wei Sun

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  1. University of North Carolina, Greensboro, NC, USA

    Jing Deng

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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    Alexander A. Schwarzmann

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Badrinarayanan, S. et al. (2023). A Plug-n-Play Framework for Scaling Private Set Intersection to Billion-Sized Sets. In: Deng, J., Kolesnikov, V., Schwarzmann, A.A. (eds) Cryptology and Network Security. CANS 2023. Lecture Notes in Computer Science, vol 14342. Springer, Singapore. https://doi.org/10.1007/978-981-99-7563-1_20

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