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Efficient Circuit-Based PSI with Linear Communication

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Advances in Cryptology – EUROCRYPT 2019 (EUROCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11478))

Abstract

We present a new protocol for computing a circuit which implements the private set intersection functionality (PSI). Using circuits for this task is advantageous over the usage of specific protocols for PSI, since many applications of PSI do not need to compute the intersection itself but rather functions based on the items in the intersection.

Our protocol is the first circuit-based PSI protocol to achieve linear communication complexity. It is also concretely more efficient than all previous circuit-based PSI protocols. For example, for sets of size \(2^{20}\) it improves the communication of the recent work of Pinkas et al. (EUROCRYPT’18) by more than 10 times, and improves the run time by a factor of 2.8x in the LAN setting, and by a factor of 5.8x in the WAN setting.

Our protocol is based on the usage of a protocol for computing oblivious programmable pseudo-random functions (OPPRF), and more specifically on our technique to amortize the cost of batching together multiple invocations of OPPRF.

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Notes

  1. 1.

    https://www.bloomberg.com/news/articles/2018-08-30/google-and-mastercard-cut-a-secret-ad-deal-to-track-retail-sales.

  2. 2.

    Note that outputting the intersection is a non-symmetric function. Therefore in that case the order of the elements must be shuffled. However, it is unclear why a circuit-based protocol should be used for computing the intersection, since there are specialized protocols for this which are much more efficient, e.g. [KKRT16, PSZ18].

  3. 3.

    We require that each element in T is uniformly random but the elements may be correlated.

  4. 4.

    In the actual implementation we use a more general variant of Cuckoo hashing with a parameter \(K\in \{2,3\}\) where each item is stored in K locations in the table. The size of the hint will be \(K\cdot n\).

  5. 5.

    In that case either not all items are stored in the stash – resulting in the protocol ignoring part of the input and potentially computing the wrong output, or \(P_{\mathrm 1}\) needs to inform \(P_{\mathrm 2}\) that it uses a stash larger than s – resulting in a privacy breach.

  6. 6.

    Our implementation is available at https://github.com/encryptogroup/OPPRF-PSI.

  7. 7.

    This OPRF protocol has communication that is higher by 10% to 15% than the communication of the OPRF protocol of [KKRT16]. But since OPRF requires less than 3% of the total communication, this additional cost is negligible in our protocol.

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Acknowledgements

We thank Ben Riva and Udi Wieder for valuable discussions about this work. This work has been co-funded by the DFG within project E4 of the CRC CROSSING and by the BMBF and the HMWK within CRISP, by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Ministers Office, and by a grant from the Israel Science Foundation.

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Authors and Affiliations

  1. Bar-Ilan University, Ramat Gan, Israel

    Benny Pinkas & Avishay Yanai

  2. TU Darmstadt, Darmstadt, Germany

    Thomas Schneider & Oleksandr Tkachenko

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  1. Benny Pinkas
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  2. Thomas Schneider
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Correspondence to Benny Pinkas .

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  1. Technion, Haifa, Israel

    Yuval Ishai

  2. COSIC Group, KU Leuven, Heverlee, Belgium

    Vincent Rijmen

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Pinkas, B., Schneider, T., Tkachenko, O., Yanai, A. (2019). Efficient Circuit-Based PSI with Linear Communication. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11478. Springer, Cham. https://doi.org/10.1007/978-3-030-17659-4_5

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