Skip to main content
SpringerLink
Log in

Finding One Common Item, Privately

  • Conference paper
  • First Online:
Security and Cryptography for Networks (SCN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13409))

Included in the following conference series:

  • 662 Accesses

Abstract

Private set intersection (PSI) allows two parties, who each hold a set of items, to learn which items they have in common, without revealing anything about their other items. Some applications of PSI would be better served by revealing only one common item, rather than the entire set of all common items. In this work we develop simple special-purpose protocols for privately finding one common item (FOCI) from the intersection of two sets. The protocols differ in how that item is chosen—e.g., uniformly at random from the intersection; the “best” item in the intersection according to one party’s ranking; or the “best” item in the intersection according to the sum of both party’s scores. All of our protocols are proven secure against semi-honest adversaries, under the Decisional Diffie-Hellman (DDH) assumption and assuming a random oracle. All of our protocols leak a small amount of information (e.g., the cardinality of the intersection), which we precisely quantify.

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 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
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.

    All protocols for computing functions of the intersection can be readily augmented to support data associated with the items, e.g., scores/ranks.

  2. 2.

    There are some situations where Alice could use this leakage to deduce some information about the intersection and about Bob’s ranks. For example, suppose Alice assigns ranks \(r_1< r_2 < \cdots \) to her items \(x_1, x_2, \ldots \), respectively, and then she later learns that the intersection contains an item with combined rank \(r^*\). If \(r^* < r_2\) (and all ranks are nonnegative), she can deduce that item \(x_1\) is in the intersection, and that Bob must have assigned rank \(r^* - r_1\) to that item.

References

  1. Boneh, D.: The decision Diffie-Hellman problem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 48–63. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054851. Invited paper

  2. Boneh, D., Lewi, K., Raykova, M., Sahai, A., Zhandry, M., Zimmerman, J.: Semantically secure order-revealing encryption: multi-input functional encryption without obfuscation. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 563–594. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_19

    Chapter  Google Scholar 

  3. Chase, M., Miao, P.: Private set intersection in the internet setting from lightweight oblivious PRF. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020, Part III. LNCS, vol. 12172, pp. 34–63. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56877-1_2

    Chapter  Google Scholar 

  4. 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). https://doi.org/10.1007/978-3-642-01957-9_8

    Chapter  Google Scholar 

  5. 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). https://doi.org/10.1007/978-3-642-17373-8_13

    Chapter  MATH  Google Scholar 

  6. 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 

  7. Garimella, G., Mohassel, P., Rosulek, M., Sadeghian, S., Singh, J.: Private set operations from oblivious switching. In: Garay, J.A. (ed.) PKC 2021, Part II. LNCS, vol. 12711, pp. 591–617. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-75248-4_21

    Chapter  Google Scholar 

  8. Hazay, C.: Oblivious polynomial evaluation and secure set-intersection from algebraic PRFs. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 90–120. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_4

    Chapter  Google Scholar 

  9. Huang, Y., Evans, D., Katz, J.: Private set intersection: are garbled circuits better than custom protocols? In: NDSS 2012. The Internet Society (2012)

    Google Scholar 

  10. Huberman, B.A., Franklin, M., Hogg, T.: Enhancing privacy and trust in electronic communities. In: ACM Conference on Electronic Commerce. ACM (1999)

    Google Scholar 

  11. Ion, M., et al.: On deploying secure computing commercially: private intersection-sum protocols and their business applications. Cryptology ePrint Archive, Report 2019/723 (2019). https://eprint.iacr.org/2019/723

  12. 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 

  13. Kissner, L., Song, D.: Privacy-preserving set operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_15

    Chapter  Google Scholar 

  14. Kolesnikov, V., Kumaresan, R., Rosulek, M., Trieu, N.: Efficient batched oblivious PRF with applications to private set intersection. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) ACM CCS 2016, pp. 818–829. ACM Press (2016). https://doi.org/10.1145/2976749.2978381

  15. Lewi, K., Wu, D.J.: Order-revealing encryption: new constructions, applications, and lower bounds. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) ACM CCS 2016, pp. 1167–1178. ACM Press (2016). https://doi.org/10.1145/2976749.2978376

  16. Meadows, C.: A more efficient cryptographic matchmaking protocol for use in the absence of a continuously available third party. In: 1986 IEEE Symposium on Security and Privacy, pp. 134–134 (1986). https://doi.org/10.1109/SP.1986.10022

  17. Pinkas, B., Rosulek, M., Trieu, N., Yanai, A.: SpOT-light: lightweight private set intersection from sparse OT extension. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 401–431. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_13

    Chapter  Google Scholar 

  18. Pinkas, B., Rosulek, M., Trieu, N., Yanai, A.: PSI from PaXoS: fast, malicious private set intersection. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part II. LNCS, vol. 12106, pp. 739–767. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_25

    Chapter  Google Scholar 

  19. Pinkas, B., Schneider, T., Segev, G., Zohner, M.: Phasing: private set intersection using permutation-based hashing. In: Jung, J., Holz, T. (eds.) USENIX Security 2015, pp. 515–530. USENIX Association (2015)

    Google Scholar 

  20. Pinkas, B., Schneider, T., Tkachenko, O., Yanai, A.: Efficient circuit-based PSI with linear communication. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part III. LNCS, vol. 11478, pp. 122–153. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_5

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  22. Pinkas, B., Schneider, T., Zohner, M.: Faster private set intersection based on OT extension. In: Fu, K., Jung, J. (eds.) USENIX Security 2014, pp. 797–812. USENIX Association (2014)

    Google Scholar 

  23. Rindal, P., Raghuraman, S.: Blazing fast psi from improved OKVS and subfield vole. Cryptology ePrint Archive, Report 2022/320 (2022). https://ia.cr/2022/320

  24. Rindal, P., Rosulek, M.: Malicious-secure private set intersection via dual execution. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 1229–1242. ACM Press (2017). https://doi.org/10.1145/3133956.3134044

  25. Rosulek, M., Trieu, N.: Compact and malicious private set intersection for small sets. In: Vigna, G., Shi, E. (eds.) ACM CCS 2021, pp. 1166–1181. ACM Press (2021). https://doi.org/10.1145/3460120.3484778

Download references

Acknowledgements

The first two authors are supported by NSF award DMS-1757995. We are grateful to anonymous SCN referees for the improvements they suggested to the manuscript.

Author information

Authors and Affiliations

  1. Truman State University, Kirksville, MO, USA

    Tyler Beauregard

  2. Massachussetts Institute of Technology, Cambridge, MA, USA

    Janabel Xia

  3. Oregon State University, Corvallis, OR, USA

    Mike Rosulek

Authors
  1. Tyler Beauregard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Janabel Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mike Rosulek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mike Rosulek .

Editor information

Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

  2. University of California at Irvine, Irvine, CA, USA

    Stanislaw Jarecki

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Beauregard, T., Xia, J., Rosulek, M. (2022). Finding One Common Item, Privately. In: Galdi, C., Jarecki, S. (eds) Security and Cryptography for Networks. SCN 2022. Lecture Notes in Computer Science, vol 13409. Springer, Cham. https://doi.org/10.1007/978-3-031-14791-3_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-14791-3_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-14790-6

  • Online ISBN: 978-3-031-14791-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation