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Updatable Private Set Intersection Revisited: Extended Functionalities, Deletion, and Worst-Case Complexity

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Advances in Cryptology – ASIACRYPT 2024 (ASIACRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15489))

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Abstract

Private set intersection (PSI) allows two mutually distrusting parties each holding a private set of elements, to learn the intersection of their sets without revealing anything beyond the intersection. Recent work (Badrinarayanan et al., PoPETS’22) initiates the study of updatable PSI (UPSI), which allows the two parties to compute PSI on a regular basis with sets that constantly get updated, where both the computation and communication complexity only grow with the size of the small updates and not the large entire sets. However, there are several limitations of their presented protocols. First, they can only be used to compute the plain PSI functionality and do not support extended functionalities such as PSI-Cardinality and PSI-Sum. Second, they only allow parties to add new elements to their existing set and do not support arbitrary deletion of elements. Finally, their addition-only protocols either require both parties to learn the output or only achieve low complexity in an amortized sense and incur linear worst-case complexity.

In this work, we address all the above limitations. In particular, we study UPSI with semi-honest security in both the addition-only and addition-deletion settings. We present new protocols for both settings that support plain PSI as well as extended functionalities including PSI-Cardinality and PSI-Sum, achieving one-sided output (which implies two-sided output). In the addition-only setting, we also present a protocol for a more general functionality Circuit-PSI that outputs secret shares of the intersection. All of our protocols have worst-case computation and communication complexity that only grow with the set updates instead of the entire sets (except for a polylogarithmic factor). We implement our new UPSI protocols and compare with the state-of-the-art protocols for PSI and extended functionalities. Our protocols compare favorably when the total set sizes are sufficiently large, the new updates are sufficiently small, or in networks with low bandwidth.

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Notes

  1. 1.

    Our constructions work for two sets with different sizes as well, which we elaborate in Sect. 3 and Sect. 4.

  2. 2.

    Note that this holds because the plaintext space for the encryption scheme is \(\mathbb {Z}_q\) for a prime q.

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Acknowledgments

This project is supported in part by the NSF CNS Award 2247352, Brown Data Science Seed Grant, Meta Research Award, Google Research Scholar Award, and Amazon Research Award.

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Authors and Affiliations

  1. LinkedIn, Seattle, USA

    Saikrishna Badrinarayanan

  2. Brown University, Providence, USA

    Peihan Miao, Xinyi Shi, Max Tromanhauser & Ruida Zeng

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  1. Saikrishna Badrinarayanan
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Correspondence to Saikrishna Badrinarayanan .

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  1. Academia Sinica, Taipei, Taiwan

    Kai-Min Chung

  2. NTT Social Informatics Laboratories, Tokyo, Japan

    Yu Sasaki

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Badrinarayanan, S., Miao, P., Shi, X., Tromanhauser, M., Zeng, R. (2025). Updatable Private Set Intersection Revisited: Extended Functionalities, Deletion, and Worst-Case Complexity. In: Chung, KM., Sasaki, Y. (eds) Advances in Cryptology – ASIACRYPT 2024. ASIACRYPT 2024. Lecture Notes in Computer Science, vol 15489. Springer, Singapore. https://doi.org/10.1007/978-981-96-0938-3_7

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