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Private Set Operations from Oblivious Switching

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Public-Key Cryptography – PKC 2021 (PKC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12711))

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Abstract

Private set intersection reveals the intersection of two private sets, but many real-world applications require the parties to learn only partial information about the intersection. In this paper we introduce a new approach for computing arbitrary functions of the intersection, provided that it is safe to also reveal the cardinality of the intersection. In the most general case, our new protocol provides the participants with secret shares of the intersection, which can be fed into any generic 2PC protocol. Certain computations on the intersection can also be done even more directly and efficiently, avoiding this secret-sharing step. These cases include computing only the cardinality of intersection, or the “cardinality-sum” application proposed in Ion et al. (ePrint 2017). Compared to the state-of-the-art protocol for computing on intersection (Pinkas et al., Eurocrypt 2019), our protocol has about \(2.5-3\times \) less communication, and has faster running time on slower (50 Mbps) networks.

Our new techniques can also be used to privately compute the union of two sets as easily as computing the intersection. Our protocol concretely improves the leading private set union protocol (Kolesnikov et al., Asiacrypt 2020) by a factor of \(2-2.5\times \), depending on the network speed. We then show how private set union can be used in a simple way to realize the “Private-ID” functionality suggested by Buddhavarapu et al. (ePrint 2020). Our protocol is significantly faster than the prior Private-ID protocol, especially on fast networks.

All of our protocols are in the two-party setting and are secure against semi-honest adversaries.

Authors from Oregon State University - Partially supported by NSF award 1617197 and a Facebook research award.

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Notes

  1. 1.

    Appending the index of the hash function is helpful for dealing with edge cases like \(h_1(x)=h_2(x)\), which happen with non-negligible probability.

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Authors and Affiliations

  1. Oregon State University, Corvallis, USA

    Gayathri Garimella, Mike Rosulek & Jaspal Singh

  2. Facebook, Madison, USA

    Payman Mohassel

  3. Security Compass, Toronto, Canada

    Saeed Sadeghian

Authors
  1. Gayathri Garimella
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  2. Payman Mohassel
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  3. Mike Rosulek
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  4. Saeed Sadeghian
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  5. Jaspal Singh
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Correspondence to Gayathri Garimella .

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  1. Texas A&M University, College Station, TX, USA

    Juan A. Garay

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Garimella, G., Mohassel, P., Rosulek, M., Sadeghian, S., Singh, J. (2021). Private Set Operations from Oblivious Switching. In: Garay, J.A. (eds) Public-Key Cryptography – PKC 2021. PKC 2021. Lecture Notes in Computer Science(), vol 12711. Springer, Cham. https://doi.org/10.1007/978-3-030-75248-4_21

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  • DOI: https://doi.org/10.1007/978-3-030-75248-4_21

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