Private Identity Agreement for Private Set Functionalities

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12238)


Private set intersection and related functionalities are among the most prominent real-world applications of secure multiparty computation. While such protocols have attracted significant attention from the research community, other functionalities are often required to support a PSI application in practice. For example, in order for two parties to run a PSI over the unique users contained in their databases, they might first invoke a support functionality to agree on the primary keys to represent their users.

This paper studies a secure approach to agreeing on primary keys. We introduce and realize a functionality that computes a common set of identifiers based on incomplete information held by two parties, which we refer to as private identity agreement, and we prove the security of our protocol in the honest-but-curious model. We explain the subtleties in designing such a functionality that arise from privacy requirements when intending to compose securely with PSI protocols. We also argue that the cost of invoking this functionality can be amortized over a large number of PSI sessions, and that for applications that require many repeated PSI executions, this represents an improvement over a PSI protocol that directly uses incomplete or fuzzy matches.


Private set intersection Private identity agreement Garbled circuits 



We would like thank Samee Zahur for his assistance with the Obliv-C compiler and Jack Doerner for his assistance with Absentminded Crypto Kit.


  1. 1.
    Agrawal, R., Evfimievski, A., Srikant, R.: Information sharing across private databases. In: Proceedings of the 2003 ACM SIGMOD International Conference on Management of Data, SIGMOD 2003, pp. 86–97. ACM, New York (2003).
  2. 2.
    Asharov, G., Komargodski, I., Lin, W.K., Nayak, K., Peserico, E., Shi, E.: Optorama: optimal oblivious ram. Cryptology ePrint Archive, Report 2018/892 (2018).
  3. 3.
    Batcher, K.E.: Sorting networks and their applications. In: Proceedings of the April 30-May 2, 1968, Spring Joint Computer Conference, pp. 307–314. ACM (1968)Google Scholar
  4. 4.
    Beauquier, B., Darrot, É.: On arbitrary size waksman networks and their vulnerability. Parallel Process. Lett. 12(03n04), 287–296 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. Cryptology ePrint Archive, Report 2012/265 (2012).
  6. 6.
    Buddhavarapu, P., Knox, A., Mohassel, P., Sengupta, S., Taubeneck, E., Vlaskin, V.: Private matching for compute. Cryptology ePrint Archive, Report 2020/599 (2020).
  7. 7.
    Chmielewski, L., Hoepman, J.H.: Fuzzy private matching. In: Third International Conference on Availability, Reliability and Security, ARES 2008, pp. 327–334. IEEE (2008)Google Scholar
  8. 8.
    Ciampi, M., Orlandi, C.: Combining private set-intersection with secure two-party computation. In: Catalano, D., De Prisco, R. (eds.) SCN 2018. LNCS, vol. 11035, pp. 464–482. Springer, Cham (2018). Scholar
  9. 9.
    Dachman-Soled, D., Malkin, T., Raykova, M., Yung, M.: Efficient robust private set intersection. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 125–142. Springer, Heidelberg (2009). Scholar
  10. 10.
    De Cristofaro, E., Kim, J., Tsudik, G.: Linear-complexity private set intersection protocols secure in malicious model. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 213–231. Springer, Heidelberg (2010). Scholar
  11. 11.
    Doerner, J.: Absentminded crypto kit (2017)Google Scholar
  12. 12.
    Dong, C., Chen, L., Wen, Z.: When private set intersection meets big data: an efficient and scalable protocol. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security, CCS 2013, pp. 789–800. ACM, New York (2013).
  13. 13.
    Falk, B.H., Noble, D., Ostrovsky, R.: Private set intersection with linear communication from general assumptions. Cryptology ePrint Archive, Report 2018/238 (2018).
  14. 14.
    Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004). Scholar
  15. 15.
    Gamal, T.E.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31(4), 469–472 (1985)MathSciNetCrossRefGoogle Scholar
  16. 16.
    He, X., Machanavajjhala, A., Flynn, C., Srivastava, D.: Composing differential privacy and secure computation: a case study on scaling private record linkage. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, pp. 1389–1406. ACM, New York (2017).
  17. 17.
    Huang, Y., Evans, D., Katz, J.: Private set intersection: are garbled circuits better than custom protocols? In: 19th Annual Network and Distributed System Security Symposium, NDSS 2012, San Diego, California, USA, 5–8 February 2012 (2012).
  18. 18.
    Huberman, B.A., Franklin, M., Hogg, T.: Enhancing privacy and trust in electronic communities. In: Proceedings of the 1st ACM Conference on Electronic Commerce, pp. 78–86. ACM (1999)Google Scholar
  19. 19.
    Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pp. 604–613. ACM (1998)Google Scholar
  20. 20.
    Ion, M., Kreuter, B., Nergiz, E., Patel, S., Saxena, S., Seth, K., Shanahan, D., Yung, M.: Private intersection-sum protocol with applications to attributing aggregate ad conversions. Technical report, Cryptology ePrint Archive, Report 2017/738 (2017)Google Scholar
  21. 21.
    Lambæk, M.: Breaking and fixing private set intersection protocols. Technical report, Cryptology ePrint Archive, Report 2016/665 (2016).
  22. 22.
    Larsen, K.G., Nielsen, J.B.: Yes, there is an oblivious RAM lower bound!. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 523–542. Springer, Cham (2018). Scholar
  23. 23.
    Pinkas, B., Schneider, T., Segev, G., Zohner, M.: Phasing: private set intersection using permutation-based hashing. In: 24th USENIX Security Symposium (USENIX Security 2015), pp. 515–530. USENIX Association, Washington, D.C. (2015).
  24. 24.
    Pinkas, B., Schneider, T., Tkachenko, O., Yanai, A.: Efficient circuit-based psi with linear communication. Cryptology ePrint Archive, Report 2019/241 (2019),
  25. 25.
    Pinkas, B., Schneider, T., Weinert, C., Wieder, U.: Efficient circuit-based psi via cuckoo hashing. Cryptology ePrint Archive, Report 2018/120 (2018).
  26. 26.
    Pinkas, B., Schneider, T., Zohner, M.: Faster private set intersection based on ot extension. Usenix Secur. 14, 797–812 (2014)Google Scholar
  27. 27.
    Rindal, P., Rosulek, M.: Improved private set intersection against malicious adversaries. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 235–259. Springer, Cham (2017). Scholar
  28. 28.
    Segal, A., Ford, B., Feigenbaum, J.: Catching bandits and only bandits: privacy-preserving intersection warrants for lawful surveillance. In: FOCI (2014)Google Scholar
  29. 29.
    Waksman, A.: A permutation network. J. ACM (JACM) 15(1), 159–163 (1968)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Wen, Z., Dong, C.: Efficient protocols for private record linkage. In: Proceedings of the 29th Annual ACM Symposium on Applied Computing, pp. 1688–1694. ACM (2014)Google Scholar
  31. 31.
    Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, SFCS 1982, pp. 160–164. IEEE Computer Society, Washington, DC (1982).
  32. 32.
    Zahur, S., Evans, D.: Obliv-C: a language for extensible data-oblivious computation. IACR Cryptology ePrint Archive 2015, 1153 (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.GoogleNew YorkUSA
  2. 2.UC Santa BarbaraSanta BarbaraUSA

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