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Faster Unbalanced Private Set Intersection

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Financial Cryptography and Data Security (FC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10957))

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Abstract

Protocols for Private Set Intersection (PSI) are important cryptographic primitives that perform joint operations on datasets in a privacy-preserving way. They allow two parties to compute the intersection of their private sets without revealing any additional information beyond the intersection itself. Unfortunately, PSI implementations in the literature do not usually employ the best possible cryptographic implementation techniques. This results in protocols presenting computational and communication complexities that are prohibitive, particularly in the case when one of the participants is a low-powered device and there are bandwidth restrictions. This paper builds on modern cryptographic engineering techniques and proposes optimizations for a promising one-way PSI protocol based on public-key cryptography. For the case when one of the parties holds a set much smaller than the other (a realistic assumption in many scenarios) we show that our improvements and optimizations yield a protocol that outperforms the communication complexity and the run time of previous proposals by around one thousand times.

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Notes

  1. 1.

    Throughout this paper, the client set is always the smaller one.

  2. 2.

    In constrained scenarios, like 1 Mbps of network bandwidth, our optimized protocol remains a good choice for balanced one-way PSI. See Table 4 in the full version of this paper [40].

  3. 3.

    https://signal.org/blog/contact-discovery/.

  4. 4.

    https://medium.com/@davidbyttow/demystifying-secret-12ab82fda29f#.5433o6e8h.

  5. 5.

    https://signal.org/blog/private-contact-discovery/.

  6. 6.

    https://www.wired.com/2014/12/oracle-buys-data-collection-company-datalogix/.

  7. 7.

    https://support.twitter.com/articles/20170410.

  8. 8.

    The protocol presented in [39] uses asymmetric operations [31] to generate the OT bases. However, the cost of these operations is negligible when the number of elements evaluated is substantially greater than the value of \(\kappa \).

  9. 9.

    These values may change if the FPR changes. Here we set \(\epsilon _{max} = 0.009155\%\).

  10. 10.

    https://bench.cr.yp.to.

  11. 11.

    Average of \(2^{20}\) exponentiations performed on our Haswell machine.

  12. 12.

    In the communication column of Table 2, the protocol [7] can have 2 different values, because according to the networking setting it is better that operations take more time and generate less data than taking less time but producing more data. This trade-off can be changed in FHE by adjusting the system parameters.

  13. 13.

    The filter in the client side from [23] has \(\epsilon = 0.1\%\) and \(\epsilon = 10^{-7}\%\), respectively.

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Acknowledgements

This work was in part supported by the Intel/FAPESP grant 14/50704-7, project “Secure Execution of Cryptographic Algorithms”. We thank Anderson Nascimento and Fabian Monrose for discussion and comments on an earlier version.

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Authors and Affiliations

  1. Institute of Computing, University of Campinas (UNICAMP), Campinas, Brazil

    Amanda C. Davi Resende & Diego F. Aranha

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  1. Amanda C. Davi Resende
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  2. Diego F. Aranha
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Correspondence to Amanda C. Davi Resende .

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  1. Department of Computer Science, University College London, London, UK

    Sarah Meiklejohn

  2. Security Research Laboratories, NEC, Kawasaki, Japan

    Kazue Sako

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Resende, A.C.D., Aranha, D.F. (2018). Faster Unbalanced Private Set Intersection. In: Meiklejohn, S., Sako, K. (eds) Financial Cryptography and Data Security. FC 2018. Lecture Notes in Computer Science(), vol 10957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58387-6_11

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  • DOI: https://doi.org/10.1007/978-3-662-58387-6_11

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