Skip to main content
Springer Nature Link
Log in

An Efficient Toolkit for Computing Third-Party Private Set Intersection

  • Conference paper
  • First Online:
Progress in Cryptology – INDOCRYPT 2024 (INDOCRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15495))

Included in the following conference series:

  • 187 Accesses

Abstract

Third-party private set intersection (PSI) allows two parties to compute the intersection of their private input sets without revealing any more information than the result to an inputless third party. In this work, we leverage homomorphic encryption and oblivious pseudorandom function techniques for the first time to design third-party PSI protocols. We present two highly efficient third-party PSI protocols characterized by linear communication and computational complexity, along with a requirement of only 2 communication rounds. These protocols significantly lower the computational workload compared to prior work. Furthermore, we extend our investigation to third-party PSI cardinality protocols. Our constructions to achieve the cardinality functionality attain linear communication and computational complexity. Finally, we implement our protocols in C++ and perform a comprehensive evaluation, an aspect previously unexplored in third-party PSI research. The results demonstrate that our OPRF-based third-party PSI can obtain a 4.6–13.78 times faster improvement over the HE-based third-party PSI with a single thread in LAN setting. Moreover, the results indicate that our OPRF-based third-party PSI will yield even greater improvements as the set size increases, compared to HE-based third-party PSI.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ben-Efraim, A., Nissenbaum, O., Omri, E., Paskin-Cherniavsky, A.: PSImple: practical multiparty maliciously-secure private set intersection. In: Proceedings of the 2022 ACM on Asia Conference on Computer and Communications Security, pp. 1098–1112 (2022)

    Google Scholar 

  2. Bloom, B.H.: Space/time trade-offs in hash coding with allowable errors. Commun. ACM 13(7), 422–426 (1970)

    Article  Google Scholar 

  3. Bose, P., et al.: On the false-positive rate of bloom filters. Inf. Process. Lett. 108(4), 210–213 (2008)

    Article  MathSciNet  Google Scholar 

  4. Buddhavarapu, P., Knox, A., Mohassel, P., Sengupta, S., Taubeneck, E., Vlaskin, V.: Private matching for compute. Cryptology ePrint Archive (2020)

    Google Scholar 

  5. Chandran, N., Dasgupta, N., Gupta, D., Obbattu, S.L.B., Sekar, S., Shah, A.: Efficient linear multiparty psi and extensions to circuit/quorum psi. In: Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, pp. 1182–1204 (2021)

    Google Scholar 

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

  7. Chen, H., Huang, Z., Laine, K., Rindal, P.: Labeled PSI from fully homomorphic encryption with malicious security. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, pp. 1223–1237 (2018)

    Google Scholar 

  8. Chen, H., Laine, K., Rindal, P.: Fast private set intersection from homomorphic encryption. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, pp. 1243–1255 (2017)

    Google Scholar 

  9. Christensen, K., Roginsky, A., Jimeno, M.: A new analysis of the false positive rate of a bloom filter. Inf. Process. Lett. 110(21), 944–949 (2010)

    Article  MathSciNet  Google Scholar 

  10. Cong, K., et al.: Labeled psi from homomorphic encryption with reduced computation and communication. In: Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, pp. 1135–1150 (2021)

    Google Scholar 

  11. Davidson, A., Cid, C.: An efficient toolkit for computing private set operations. In: Pieprzyk, J., Suriadi, S. (eds.) Information Security and Privacy: 22nd Australasian Conference, ACISP 2017, Auckland, New Zealand, 3–5 July 2017, Proceedings, Part II 22, pp. 261–278. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59870-3_15

  12. De Cristofaro, E., Tsudik, G.: Practical private set intersection protocols with linear complexity. In: Sion, R. (eds.) International Conference on Financial Cryptography and Data Security, pp. 143–159. Springer, Cham (2010). https://doi.org/10.1007/978-3-642-14577-3_13

  13. Devroye, L., Morin, P.: Cuckoo hashing: further analysis. Inf. Process. Lett. 86(4), 215–219 (2003)

    Article  MathSciNet  Google Scholar 

  14. Dittmer, S., et al.: Function secret sharing for PSI-CA: with applications to private contact tracing. arXiv preprint arXiv:2012.13053 (2020)

  15. 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, pp. 789–800 (2013)

    Google Scholar 

  16. Duong, T., Phan, D.H., Trieu, N.: Catalic: delegated PSI cardinality with applications to contact tracing. In: Moriai, S., Wang, H. (eds.) International Conference on the Theory and Application of Cryptology and Information Security, pp. 870–899. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_29

  17. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31(4), 469–472 (1985)

    Article  MathSciNet  Google Scholar 

  18. Flavio, B., et al.: pailliercryptolib (2023)

    Google Scholar 

  19. Fotakis, D., Pagh, R., Sanders, P., Spirakis, P.: Space efficient hash tables with worst case constant access time. Theory Comput. Syst. 38(2), 229–248 (2005)

    Article  MathSciNet  Google Scholar 

  20. 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

  21. 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 

  22. Goldwasser, S., Micali, S.: Probabilistic encryption & how to play mental poker keeping secret all partial information. In: Providing Sound Foundations for Cryptography: on the Work of Shafi Goldwasser and Silvio Micali, pp. 173–201 (2019)

    Google Scholar 

  23. Hallgren, P., Orlandi, C., Sabelfeld, A.: PrivatePool: privacy-preserving ridesharing. In: 2017 IEEE 30th Computer Security Foundations Symposium (CSF), pp. 276–291. IEEE (2017)

    Google Scholar 

  24. Hazay, C., Lindell, Y.: Efficient protocols for set intersection and pattern matching with security against malicious and covert adversaries. In: Canetti, R. (eds.) Theory of Cryptography Conference, pp. 155–175. Springer, Cham (2008). https://doi.org/10.1007/978-3-540-78524-8_10

  25. Hazay, C., Venkitasubramaniam, M.: Scalable multi-party private set-intersection. In: Fehr, S. (eds.) IACR International Workshop on Public Key Cryptography, pp. 175–203. Springer, Cham (2017). https://doi.org/10.1007/978-3-662-54365-8_8

  26. Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: a ring-based public key cryptosystem. In: Buhler, J.P. (eds.) International Algorithmic Number Theory Symposium, pp. 267–288. Springer, Cham (1998). https://doi.org/10.1007/BFb0054868

  27. Hu, J., Chen, J., Dai, W., Wang, H.: Fully homomorphic encryption-based protocols for enhanced private set intersection functionalities. Cryptology ePrint Archive (2023)

    Google Scholar 

  28. 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 (1999)

    Google Scholar 

  29. Ion, M., et al.: On deploying secure computing: private intersection-sum-with-cardinality. In: 2020 IEEE European Symposium on Security and Privacy (EuroS &P), pp. 370–389. IEEE (2020)

    Google Scholar 

  30. Kales, D., Rechberger, C., Schneider, T., Senker, M., Weinert, C.: Mobile private contact discovery at scale. In: 28th USENIX Security Symposium (USENIX Security 2019), pp. 1447–1464 (2019)

    Google Scholar 

  31. 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

  32. Kerschbaum, F.: Outsourced private set intersection using homomorphic encryption. In: Proceedings of the 7th ACM Symposium on Information, Computer and Communications Security, pp. 85–86 (2012)

    Google Scholar 

  33. 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, pp. 818–829 (2016)

    Google Scholar 

  34. Le, P.H., Ranellucci, S., Gordon, S.D.: Two-party private set intersection with an untrusted third party. In: Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, pp. 2403–2420 (2019)

    Google Scholar 

  35. 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. IEEE (1986)

    Google Scholar 

  36. Motwani, R., Raghavan, P.: Randomized algorithms. ACM Comput. Surv. (CSUR) 28(1), 33–37 (1996)

    Article  Google Scholar 

  37. Nagaraja, S., Mittal, P., Hong, C.Y., Caesar, M., Borisov, N.: \(\{\)BotGrep\(\}\): finding \(\{\)P2P\(\}\) bots with structured graph analysis. In: 19th USENIX Security Symposium (USENIX Security 2010) (2010)

    Google Scholar 

  38. 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

  39. Pagh, R., Rodler, F.F.: Cuckoo hashing. J. Algorithms 51(2), 122–144 (2004)

    Article  MathSciNet  Google Scholar 

  40. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_16

    Chapter  Google Scholar 

  41. 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. LNCS, vol. 11694, pp. 401–431. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_13

  42. 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 (2015)

    Google Scholar 

  43. Pinkas, B., Schneider, T., Smart, N.P., Williams, S.C.: Secure two-party computation is practical. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 250–267. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_15

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

  45. 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 

  46. Pinkas, B., Schneider, T., Zohner, M.: Scalable private set intersection based on OT extension. ACM Trans. Privacy Secur. (TOPS) 21(2), 1–35 (2018)

    Article  Google Scholar 

  47. Raab, M., Steger, A.: “Balls into Bins’’—a simple and tight analysis. In: Luby, M., Rolim, J.D.P., Serna, M. (eds.) RANDOM 1998. LNCS, vol. 1518, pp. 159–170. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49543-6_13

    Chapter  Google Scholar 

  48. Rindal, P., Rosulek, M.: Malicious-secure private set intersection via dual execution. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security, pp. 1229–1242 (2017)

    Google Scholar 

  49. Rindal, P., Schoppmann, P.: VOLE-PSI: fast OPRF and Circuit-PSI from Vector-OLE. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12697, pp. 901–930. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77886-6_31

    Chapter  Google Scholar 

  50. Trieu, N., Shehata, K., Saxena, P., Shokri, R., Song, D.: Epione: lightweight contact tracing with strong privacy. arXiv preprint arXiv:2004.13293 (2020)

  51. Wu, M., Yuen, T.H.: Efficient unbalanced private set intersection cardinality and user-friendly privacy-preserving contact tracing. In: 32nd USENIX Security Symposium (USENIX Security 2023), pp. 283–300 (2023)

    Google Scholar 

  52. Yeo, F.Y., Ying, J.H.: Third-party private set intersection. In: 2023 IEEE International Symposium on Information Theory (ISIT), pp. 1633–1638. IEEE (2023)

    Google Scholar 

  53. Yeo, F.Y., Ying, J.H.: A near-linear quantum-safe third-party private set intersection protocol. Cryptology ePrint Archive (2024)

    Google Scholar 

Download references

Acknowledgement

The authors are very appreciate for the reviewers’ valuable comments which are helpful for improving the presentation of the paper. The paper is supported by the National Natural Science Foundation of China under Grant 12371525, and also supported by the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant XDB0690200.

Author information

Authors and Affiliations

  1. Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS, Beijing, China

    Kai Chen, Yongqiang Li & Mingsheng Wang

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Kai Chen, Yongqiang Li & Mingsheng Wang

Authors
  1. Kai Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongqiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingsheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongqiang Li .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology, Kharagpur, West Bengal, India

    Sourav Mukhopadhyay

  2. Naval Postgraduate School, Monterey, CA, USA

    Pantelimon Stănică

Rights and permissions

Reprints and permissions

Copyright information

© 2025 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

Chen, K., Li, Y., Wang, M. (2025). An Efficient Toolkit for Computing Third-Party Private Set Intersection. In: Mukhopadhyay, S., Stănică, P. (eds) Progress in Cryptology – INDOCRYPT 2024. INDOCRYPT 2024. Lecture Notes in Computer Science, vol 15495. Springer, Cham. https://doi.org/10.1007/978-3-031-80308-6_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-80308-6_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-80307-9

  • Online ISBN: 978-3-031-80308-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics