Skip to main content
SpringerLink
Log in

Combining Private Set-Intersection with Secure Two-Party Computation

  • Conference paper
  • First Online:
Security and Cryptography for Networks (SCN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11035))

Included in the following conference series:

Abstract

Private Set-Intersection (PSI) is one of the most popular and practically relevant secure two-party computation (2PC) tasks. Therefore, designing special-purpose PSI protocols (which are more efficient than generic 2PC solutions) is a very active line of research. In particular, a recent line of work has proposed PSI protocols based on oblivious transfer (OT) which, thanks to recent advances in OT-extension techniques, is nowadays a very cheap cryptographic building block. Unfortunately, these protocols cannot be plugged into larger 2PC applications since in these protocols one party (by design) learns the output of the intersection. Therefore, it is not possible to perform secure post-processing of the output of the PSI protocol. In this paper we propose a novel and efficient OT-based PSI protocol that produces an “encrypted” output that can therefore be later used as an input to other 2PC protocols. In particular, the protocol can be used in combination with all common approaches to 2PC including garbled circuits, secret sharing and homomorphic encryption. Thus, our protocol can be combined with the right 2PC techniques to achieve more efficient protocols for computations of the form \(z=f(X\cap Y)\) for arbitrary functions f.

This research received funding from: COST Action IC1306; the Danish Independent Research Council under Grant-ID DFF-6108-00169 (FoCC); the European Union’s Horizon 2020 research and innovation programme under grant agreements No 731583 (SODA) and No 780477 (PRIViLEDGE); “GNCS - INdAM”. The work of 1st author has been done in part while visiting Aarhus University, Denmark.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Some apps do not transfer the contact list in cleartext, but a hashed version instead. However, since the domain space of phone numbers is small enough to allow for brute forcing of the hashes, this does not guarantee any real privacy guarantee.

  2. 2.

    Unfortunately, the Signal team has concluded that current PSI protocols are too inefficient for their application scenario and relied on trusted-hardware instead, in the style of [41]. See https://signal.org/blog/private-contact-discovery/ for more details on this.

  3. 3.

    The complexity of the protocols proposed in [37] depends upon parameters that are also related to the used hash function. In order to make our comparison fair, we have set these parameters as showed in the first column in Table 10 of [37]. More precisely, the authors of [37] show in that table which parameters are adopted for their empirical efficiency comparison for the case where one set is much greater than the other set (which is exactly the case of PSM).

  4. 4.

    http://www.ethereum.org.

  5. 5.

    The exact format of the “encryption” \(E(\cdot )\) would depend on the subsequent 2PC protocol and is irrelevant for this high-level description.

  6. 6.

    Sets can always be padded with dummy elements, but the complexity of the protocol can match M that in practice can be \(M\approx 2^{m-1}\).

  7. 7.

    We can assume \(\lambda \) to be smaller than the (statistical) security parameter \(s\) and we will denote the bit decomposition of x by \(x=x_{\lambda }\ldots x_1\). Otherwise before running the protocol the parties can hash their input down and run the protocol with inputs h(x) and \(h(Y)=\{h(y_1),\ldots ,h(y_M)\}\). Clearly if \(x=y_i\) then \(h(x)=h(y_i)\), and for correctness we need that \(Pr[h(x) \in h(Y) \wedge x\not \in Y]<2^{-s}\).

  8. 8.

    Here we use \(\oplus \)-secret sharing without loss of generality. Any 2-out-2 secret sharing would work here.

  9. 9.

    In abuse of notation we refer to a vertex using the key represented by the vertex itself.

  10. 10.

    The key \(k^\star _\lambda \) could not exists; e.g. if Y contains all the strings of \(\lambda \) bits.

  11. 11.

    The only exception is the first OT execution where just two keys are used as input.

  12. 12.

    We observe that if Y is not empty (like in our case) then there exists at most one bit b s.t. \(b\in \mathsf {Prefix}(Y,1)\).

  13. 13.

    In this step, as well as in the step 1.5 of this stage, the function \(\delta \) is used to compute the right amount of fake encryption to be added to the list that will we used as input of \({\mathsf {R}_{\mathcal {OT}}}\).

  14. 14.

    The following three steps are equal to the previous three steps (1.1, 1.2 and 1.3), the only difference is that t||1 is considered instead of t||0.

  15. 15.

    We assume this only to simplify the protocol description, indeed our protocol can be easily instantiated when the two sets have different size.

References

  1. Asharov, G., Lindell, Y., Schneider, T., Zohner, M.: More efficient oblivious transfer and extensions for faster secure computation. In: 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS 2013, Berlin, Germany, 4–8 November 2013, pp. 535–548 (2013)

    Google Scholar 

  2. Asharov, G., Lindell, Y., Schneider, T., Zohner, M.: More efficient oblivious transfer extensions with security for malicious adversaries. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 673–701. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_26

    Chapter  Google Scholar 

  3. Baldi, P., Baronio, R., Cristofaro, E.D., Gasti, P., Tsudik, G.: Countering GATTACA: efficient and secure testing of fully-sequenced human genomes. In: Proceedings of the 18th ACM Conference on Computer and Communications Security, CCS 2011, Chicago, Illinois, USA, 17–21 October 2011, pp. 691–702 (2011)

    Google Scholar 

  4. Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, Baltimore, Maryland, USA, 13–17 May 1990, pp. 503–513 (1990)

    Google Scholar 

  5. Chen, H., Laine, K., Rindal, P.: Fast private set intersection from homomorphic encryption. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, Dallas, TX, USA, 30 October–03 November 2017, pp. 1243–1255. ACM (2017)

    Google Scholar 

  6. Chor, B., Gilboa, N., Naor, M.: Private information retrieval by keywords. IACR Cryptology ePrint Archive 1998, 3 (1998). Appeared in the Theory of Cryptography Library

    Google Scholar 

  7. Ciampi, M., Orlandi, C.: Combining private set-intersection with secure two-party computation. Cryptology ePrint Archive, Report 2018/105 (2018). https://eprint.iacr.org/2018/105

  8. De Cristofaro, E., Tsudik, G.: Practical private set intersection protocols with linear complexity. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 143–159. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14577-3_13

    Chapter  Google Scholar 

  9. De Cristofaro, E., Tsudik, G.: Experimenting with fast private set intersection. In: Katzenbeisser, S., Weippl, E., Camp, L.J., Volkamer, M., Reiter, M., Zhang, X. (eds.) Trust 2012. LNCS, vol. 7344, pp. 55–73. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30921-2_4

    Chapter  Google Scholar 

  10. Dahl, M., Ning, C., Toft, T.: On secure two-party integer division. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 164–178. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32946-3_13

    Chapter  Google Scholar 

  11. Falk, B.H., Noble, D., Ostrovsky, R.: Private set intersection with linear communication from general assumptions. IACR Cryptology ePrint Archive 2018, 238 (2018)

    Google Scholar 

  12. Freedman, M.J., Ishai, Y., Pinkas, B., Reingold, O.: Keyword Search and Oblivious Pseudorandom Functions. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 303–324. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_17

    Chapter  Google Scholar 

  13. 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). https://doi.org/10.1007/978-3-540-24676-3_1

    Chapter  Google Scholar 

  14. Garay, J., Schoenmakers, B., Villegas, J.: Practical and secure solutions for integer comparison. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 330–342. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71677-8_22

    Chapter  Google Scholar 

  15. Goldreich, O., Micali, S., Wigderson, A.: How to play ANY mental game or a completeness theorem for protocols with honest majority. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing, New York, USA, pp. 218–229 (1987)

    Google Scholar 

  16. Hallgren, P., Orlandi, C., Sabelfeld, A.: Privatepool: privacy-preserving ridesharing. In: IEEE 30th Computer Security Foundations Symposium, CSF 2017, Santa Barbara, CA, USA, 21–25 August 2017, pp. 276–291 (2017)

    Google Scholar 

  17. Hazay, C., Lindell, Y.: Efficient protocols for set intersection and pattern matching with security against malicious and covert adversaries. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 155–175. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_10

    Chapter  Google Scholar 

  18. Hazay, C., Venkitasubramaniam, M.: Scalable multi-party private set-intersection. In: Fehr, S. (ed.) PKC 2017. LNCS, vol. 10174, pp. 175–203. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54365-8_8

    Chapter  Google Scholar 

  19. 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)

    Google Scholar 

  20. Ion, M., et al.: Private intersection-sum protocol with applications to attributing aggregate ad conversions. Cryptology ePrint Archive, Report 2017/738 (2017)

    Google Scholar 

  21. Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending oblivious transfers efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_9

    Chapter  Google Scholar 

  22. Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_31

    Chapter  Google Scholar 

  23. Jarecki, S., Liu, X.: Fast secure computation of set intersection. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 418–435. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15317-4_26

    Chapter  Google Scholar 

  24. Kamara, S., Mohassel, P., Raykova, M., Sadeghian, S.: Scaling private set intersection to billion-element sets. In: Christin, N., Safavi-Naini, R. (eds.) FC 2014. LNCS, vol. 8437, pp. 195–215. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45472-5_13

    Chapter  Google Scholar 

  25. Keller, M., Orsini, E., Scholl, P.: Actively secure OT extension with optimal overhead. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 724–741. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_35

    Chapter  Google Scholar 

  26. Kolesnikov, V., Kumaresan, R.: Improved OT extension for transferring short secrets. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 54–70. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_4

    Chapter  Google Scholar 

  27. Kolesnikov, V., Kumaresan, R., Rosulek, M., Trieu, N.: Efficient batched oblivious PRF with applications to private set intersection. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria, 24–28 October 2016, pp. 818–829 (2016)

    Google Scholar 

  28. Lindell, Y., Pinkas, B.: A proof of security of yao’s protocol for two-party computation. J. Cryptol. 22(2), 161–188 (2009)

    Article  MathSciNet  Google Scholar 

  29. Lipmaa, H., Toft, T.: Secure equality and greater-than tests with sublinear online complexity. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013. LNCS, vol. 7966, pp. 645–656. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39212-2_56

    Chapter  MATH  Google Scholar 

  30. Meadows, C.A.: A more efficient cryptographic matchmaking protocol for use in the absence of a continuously available third party. In: Proceedings of the 1986 IEEE Symposium on Security and Privacy, Oakland, California, USA, 7–9 April 1986, pp. 134–137 (1986)

    Google Scholar 

  31. Mohassel, P., Niksefat, S.: Oblivious decision programs from oblivious transfer: efficient reductions. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 269–284. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32946-3_20

    Chapter  Google Scholar 

  32. Nagaraja, S., Mittal, P., Hong, C., Caesar, M., Borisov, N.: BotGrep: finding P2P bots with structured graph analysis. In: Proceedings of the 19th USENIX Security Symposium, Washington, DC, USA, 11–13 August 2010, pp. 95–110 (2010)

    Google Scholar 

  33. Orrù, M., Orsini, E., Scholl, P.: Actively secure 1-out-of-N OT extension with application to private set intersection. In: Handschuh, H. (ed.) CT-RSA 2017. LNCS, vol. 10159, pp. 381–396. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-52153-4_22

    Chapter  Google Scholar 

  34. Pinkas, B., Schneider, T., Segev, G., Zohner, M.: Phasing: private set intersection using permutation-based hashing. In: 24th USENIX Security Symposium, USENIX Security 15, Washington, D.C., USA, 12–14 August 2015, pp. 515–530 (2015)

    Google Scholar 

  35. Pinkas, B., Schneider, T., Weinert, C., Wieder, U.: Efficient circuit-based PSI via Cuckoo hashing. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 125–157. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_5

    Chapter  Google Scholar 

  36. Pinkas, B., Schneider, T., Zohner, M.: Faster private set intersection based on OT extension. In: Proceedings of the 23rd USENIX Security Symposium, San Diego, CA, USA, 20–22 2014, pp. 797–812 (2014)

    Google Scholar 

  37. Pinkas, B., Schneider, T., Zohner, M.: Scalable private set intersection based on OT extension. Cryptology ePrint Archive, Report 2016/930 (2016)

    Google Scholar 

  38. 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). https://doi.org/10.1007/978-3-319-56620-7_9

    Chapter  Google Scholar 

  39. Rindal, P., Rosulek, M.: Malicious-secure private set intersection via dual execution. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, CCS 2017, Dallas, TX, USA, 30 October–03 November 2017, pp. 1229–1242. ACM (2017)

    Google Scholar 

  40. Shamir, A.: On the power of commutativity in cryptography. In: de Bakker, J., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 582–595. Springer, Heidelberg (1980). https://doi.org/10.1007/3-540-10003-2_100

    Chapter  Google Scholar 

  41. Tamrakar, S., Liu, J., Paverd, A., Ekberg, J., Pinkas, B., Asokan, N.: The circle game: scalable private membership test using trusted hardware. In: Proceedings of the 2017 ACM on Asia Conference on Computer and Communications Security, AsiaCCS 2017, Abu Dhabi, United Arab Emirates, 2–6 April 2017, pp. 31–44 (2017)

    Google Scholar 

  42. Toft, T., et al.: Primitives and applications for multi-party computation. Ph.D. thesis, University of Aarhus, Denmark (2007)

    Google Scholar 

  43. Yao, A.C.: Protocols for secure computations (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, USA, 3–5 November 1982, pp. 160–164 (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Edinburgh, Edinburgh, UK

    Michele Ciampi

  2. Aarhus University, Aarhus, Denmark

    Claudio Orlandi

Authors
  1. Michele Ciampi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claudio Orlandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michele Ciampi .

Editor information

Editors and Affiliations

  1. University of Catania, Catania, Italy

    Dario Catalano

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ciampi, M., Orlandi, C. (2018). Combining Private Set-Intersection with Secure Two-Party Computation. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-98113-0_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-98112-3

  • Online ISBN: 978-3-319-98113-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation