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Hiding the input-size in multi-party private set intersection

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Abstract

Ateniese et al. (PKC 2011) introduced the concept of size-hiding private set intersection (SHI-PSI) and proposed a construction for two parties. The SHI-PSI protocol protects the privacy of input set content and better guarantees the privacy of the client set size. However, more practical protocols in multi-party scenarios have remained a research gap. In this paper, we propose a secure and feasible protocol named size-hiding multi-party private set intersection. Based on the Bloom filter, threshold homomorphic encryption and marking technique, the proposed protocol supports the private set intersection among multiple participants. Meanwhile, the set size privacy of the designated participant is preserved. The proposed protocol is proved to be secure against semi-honest participants under the decisional composite residuosity assumption. Finally, the efficiency of our protocol is illustrated through both performance analyses and comparisons of related work.

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References

  1. Abadi A., Terzis S., Metere R., Dong C.: Efficient delegated private set intersection on outsourced private datasets. IEEE Trans. Depend. Secure Comput. 16(4), 608–624 (2019). https://doi.org/10.1109/TDSC.2017.2708710.

    Article  Google Scholar 

  2. Abadi A., Murdoch S.J., Zacharias T.: Polynomial representation is tricky: maliciously secure private set intersection revisited. In: Bertino E., Shulman H., Waidner M. (eds.) Computer Security–ESORICS 2021, vol. 12973, pp. 721–742. Springer, Darmstadt (2021).

    Chapter  Google Scholar 

  3. Abadi A., Dong C., Murdoch S.J., Terzis S.: Multi-party updatable delegated private set intersection. In: Eyal I., Garay J.A. (eds.) Financial Cryptography and Data Security—FC 2022, Grenada, vol. 13411, pp. 100–119. Springer, Grenada (2022).

    Google Scholar 

  4. Alamati N., Branco P., Döttling N., Garg S., Hajiabadi M., Pu S.: Laconic private set intersection and applications. In: Nissim K., Waters B. (eds.) Theory of Cryptography, TCC 2021, vol. 13044, pp. 94–125. Springer, Raleigh (2021).

    Google Scholar 

  5. Ateniese G., De Cristofaro E., Tsudik G.: (if) size matters: Size-hiding private set intersection. In: Catalano D., Fazio N., Gennaro R., Nicolosi A. (eds.) Public Key Cryptography—PKC 2011, pp. 156–173. Springer, Berlin (2011).

    Chapter  Google Scholar 

  6. Aydin T.S., Metere R., Dong C.: Efficient delegated private set intersection on outsourced private datasets. IEEE Trans. Depend. Secure Comput. 16(4), 608–624 (2019). https://doi.org/10.1109/TDSC.2017.2708710.

    Article  Google Scholar 

  7. Badrinarayanan S., Miao P., Raghuraman S., Rindal P.: Multi-party threshold private set intersection with sublinear communication. In: Garay J.A. (ed.) Public-Key Cryptography—PKC 2021, pp. 349–379. Springer, Cham (2021).

    Chapter  Google Scholar 

  8. Badrinarayanan S., Miao P., Xie T.: Updatable private set intersection. Proc. Privacy Enhanc. Technol. 2022(2), 378–406 (2022). https://doi.org/10.2478/popets-2022-0051.

    Article  Google Scholar 

  9. Bay A., Erkin Z., Hoepman J.-H., Samardjiska S., Vos J.: Practical multi-party private set intersection protocols. IEEE Trans. Inf. Forensics Secur. 17, 1–15 (2022). https://doi.org/10.1109/TIFS.2021.3118879.

    Article  Google Scholar 

  10. Bhowmick A., Boneh D., Myers S., Talwar K., Tarbe K.: The Apple PSI system (2021). https://www.apple.com/child-safety/pdf/Apple_PSI_System_Security_Protocol_and_Analysis.pdf.

  11. Bloom B.H.: Space/time trade-offs in hash coding with allowable errors. Commun. ACM 13(7), 422–426 (1970). https://doi.org/10.1145/362686.362692.

    Article  MATH  Google Scholar 

  12. Bose P., Guo H., Kranakis E., Maheshwari A., Morin P., Morrison J., Smid M., Tang Y.: On the false-positive rate of bloom filters. Inf. Process. Lett. 108(4), 210–213 (2008). https://doi.org/10.1016/j.ipl.2008.05.018.

    Article  MathSciNet  MATH  Google Scholar 

  13. Bradley T., Faber S., Tsudik G.: Bounded size-hiding private set intersection. In: Zikas V., De Prisco R. (eds.) Security and Cryptography for Networks, pp. 449–467. Springer, Cham (2016).

    Google Scholar 

  14. Branco P., Döttling N., Pu S.: Multiparty cardinality testing for threshold private intersection. In: Garay J.A. (ed.) Public-Key Cryptography—PKC 2021, vol. 12711, pp. 32–60. Springer, New York (2021).

    Chapter  Google Scholar 

  15. Cerulli A., De Cristofaro E., Soriente C.: Nothing refreshes like a RePSI: reactive private set intersection. In: Preneel B., Vercauteren F. (eds.) Applied Cryptography and Network Security, pp. 280–300. Springer, Cham (2018).

    Chapter  Google Scholar 

  16. Chase M., Miao P.: Private set intersection in the internet setting from lightweight oblivious PRF. In: Micciancio D., Ristenpart T. (eds.) Advances in Cryptology—CRYPTO 2020, pp. 34–63. Springer, Cham (2020).

    Chapter  Google Scholar 

  17. Chase M., Ostrovsky R., Visconti I.: Executable proofs, input-size hiding secure computation and a new ideal world. In: Oswald E., Fischlin M. (eds.) Advances in Cryptology—EUROCRYPT 2015, pp. 532–560. Springer, Berlin (2015).

    Chapter  Google Scholar 

  18. 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 (CCS ’17), pp. 1243–1255. Association for Computing Machinery, New York (2017).

  19. 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 (CCS ’18), pp. 1223–1237. Association for Computing Machinery, New York (2018).

  20. D’Arco P., González Vasco M.I., Pérez del Pozo A.L., Soriente C.: Size-hiding in private set intersection: existential results and constructions. In: Mitrokotsa, A., Vaudenay, S. (eds.) Progress in Cryptology—AFRICACRYPT 2012, pp. 378–394. Springer, Berlin (2012)

  21. Davidson A., Cid C.: An efficient toolkit for computing private set operations. In: Pieprzyk J., Suriadi S. (eds.) Information Security and Privacy, pp. 261–278. Springer, Cham (2017).

    Chapter  Google Scholar 

  22. Debnath S.K., Stǎnicǎ P., Kundu N., Choudhury T.: Secure and efficient multiparty private set intersection cardinality. Adv. Math. Commun. 15(2), 365–386 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  23. 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 and Communications Security (CCS ’13), pp. 789–800. Association for Computing Machinery, New York, NY, USA (2013).

  24. Fouque P.-A., Poupard G., Stern J.: Sharing decryption in the context of voting or lotteries. In: Frankel Y. (ed.) Financial Cryptography, pp. 90–104. Springer, Berlin (2001).

    Chapter  Google Scholar 

  25. Freedman M.J., Nissim K., Pinkas B.: Efficient private matching and set intersection. In: Cachin C., Camenisch J.L. (eds.) Advances in Cryptology—EUROCRYPT 2004, pp. 1–19. Springer, Berlin (2004).

    Google Scholar 

  26. Garimella G., Pinkas B., Rosulek M., Trieu N., Yanai A.: Oblivious key-value stores and amplification for private set intersection. In: Malkin T., Peikert C. (eds.) Advances in Cryptology—CRYPTO 2021, pp. 395–425. Springer, Cham (2021).

    Chapter  Google Scholar 

  27. Ghosh S., Nilges T.: An algebraic approach to maliciously secure private set intersection. In: Ishai Y., Rijmen V. (eds.) Advances in Cryptology—EUROCRYPT 2019, pp. 154–185. Springer, Cham (2019).

    Chapter  Google Scholar 

  28. Ghosh S., Simkin M.: The communication complexity of threshold private set intersection. In: Boldyreva A., Micciancio D. (eds.) Advances in Cryptology—CRYPTO 2019, pp. 3–29. Springer, Cham (2019).

    Chapter  Google Scholar 

  29. Goldreich O.: Foundations of Cryptography, vol. 2. Cambridge University Press, Cambridge (2004) https://doi.org/10.1017/CBO9780511721656.

    Book  MATH  Google Scholar 

  30. Hazay C., Venkitasubramaniam M.: Scalable multi-party private set-intersection. In: Fehr S. (ed.) Public-Key Cryptography—PKC 2017, pp. 175–203. Springer, Berlin (2017).

    Chapter  Google Scholar 

  31. Ion M., Kreuter B., Nergiz A.E., Patel S., Saxena S., Seth K., Raykova M., Shanahan D., Yung M.: On deploying secure computing: private intersection-sum-with-cardinality. In: 2020 IEEE European Symposium on Security and Privacy (EuroS P), pp. 370–389 (2020)

  32. Kiss Á., Liu J., Schneider T., Asokan N., Pinkas B.: Private set intersection for unequal set sizes with mobile applications. Proceedings on Privacy Enhancing Technologies 2017(4), 177–197 (2017). https://doi.org/10.1515/popets-2017-0044.

    Article  Google Scholar 

  33. Kissner L., Song D.: Privacy-preserving set operations. In: Shoup V. (ed.) Advances in Cryptology—CRYPTO 2005, pp. 241–257. Springer, Berlin (2005).

    Chapter  Google Scholar 

  34. 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.) Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria, October 24–28, 2016, pp. 818–829. ACM, New York (2016).

  35. 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 (CCS ’19), pp. 2403–2420. Association for Computing Machinery, New York (2019).

  36. Lindell Y., Nissim K., Orlandi C.: Hiding the input-size in secure two-party computation. In: Sako K., Sarkar P. (eds.) Advances in Cryptology—ASIACRYPT 2013, pp. 421–440. Springer, Berlin (2013).

    Chapter  MATH  Google Scholar 

  37. 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).

  38. Miao P., Patel S., Raykova M., Seth K., Yung M.: Two-sided malicious security for private intersection-sum with cardinality. In: Micciancio D., Ristenpart T. (eds.) Advances in Cryptology—CRYPTO 2020, pp. 3–33. Springer, Cham (2020).

    Chapter  Google Scholar 

  39. Paillier P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern J. (ed.) Advances in Cryptology—EUROCRYPT ’99, pp. 223–238. Springer, Berlin, Heidelberg (1999).

    Chapter  Google Scholar 

  40. Pinkas B., Schneider T., Tkachenko O., Yanai A.: Efficient circuit-based psi with linear communication. In: Ishai Y., Rijmen V. (eds.) Advances in Cryptology—EUROCRYPT 2019, pp. 122–153. Springer, Cham (2019).

    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.) Advances in Cryptology—CRYPTO 2019, pp. 401–431. Springer, Cham (2019).

    Chapter  Google Scholar 

  42. Pinkas B., Rosulek M., Trieu N., Yanai A.: Psi from Paxos: fast, malicious private set intersection. In: Canteaut A., Ishai Y. (eds.) Advances in Cryptology—EUROCRYPT 2020, pp. 739–767. Springer, Cham (2020).

    Chapter  Google Scholar 

  43. Quach W., Wee H., Wichs D.: Laconic function evaluation and applications. In: Thorup M. (ed.) 59th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2018, pp. 859–870. IEEE Computer Society, Paris, France (2018).

  44. Rindal P., Rosulek M.: Improved private set intersection against malicious adversaries. In: Coron J.-S., Nielsen J.B. (eds.) Advances in Cryptology—EUROCRYPT 2017, pp. 235–259. Springer, Cham (2017).

    Chapter  Google Scholar 

  45. Rindal P., Schoppmann P.: Vole-psi: fast OPRF and circuit-psi from vector-ole. In: Canteaut A., Standaert F.-X. (eds.) Advances in Cryptology—EUROCRYPT 2021, pp. 901–930. Springer, Cham (2021).

    Chapter  Google Scholar 

  46. Ruan O., Wang Z., Mi J., Zhang M.: New approach to set representation and practical private set-intersection protocols. IEEE Access 7, 64897–64906 (2019). https://doi.org/10.1109/ACCESS.2019.2917057.

    Article  Google Scholar 

  47. Ruan O., Huang X., Mao H.: An efficient private set intersection protocol for the cloud computing environments. In: 2020 IEEE 6th International Conference on Big Data Security on Cloud (BigDataSecurity), IEEE International Conference on High Performance and Smart Computing, (HPSC) and IEEE International Conference on Intelligent Data and Security (IDS), pp. 254–259 (2020).

  48. Shinagawa K., Nuida K., Nishide T., Hanaoka G., Okamoto E.: Size-hiding computation for multiple parties. In: Cheon J.H., Takagi T. (eds.) Advances in Cryptology—ASIACRYPT 2016, pp. 937–966. Springer, Berlin, Heidelberg (2016).

    Chapter  Google Scholar 

  49. Shoup V., et al.: NTL: a library for doing number theory (2001). https://www.shoup.net/ntl/.

  50. Wang Y., Huang Q., Li H., Xiao M., Ma S., Susilo W.: Private set intersection with authorization over outsourced encrypted datasets. IEEE Trans. Inf. Forensics Secur. 16, 4050–4062 (2021). https://doi.org/10.1109/TIFS.2021.3101059.

    Article  Google Scholar 

  51. Zhang E., Liu F.-H., Lai Q., Jin G., Li Y.: Efficient multi-party private set intersection against malicious adversaries. In: Proceedings of the 2019 ACM SIGSAC Conference on Cloud Computing Security Workshop, pp. 93–104. Association for Computing Machinery, New York (2019).

  52. Zhang E., Chang J., Li Y.: Efficient threshold private set intersection. IEEE Access 9, 6560–6570 (2021). https://doi.org/10.1109/ACCESS.2020.3048743.

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. U19B2021, 61972457, 62202363, the Key Research and Development Program of Shaanxi under Grant No. 2020ZDLGY08-04, the Innovation Scientists and Technicians Troop Construction Projects of Henan Province, the Youth Innovation Team of Shaanxi Universities, and the Science and Technology on Communication Security Laboratory Foundation (61421030202012103).

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  1. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China

    Yu Zhan, Ziqian Zhang, Qian Liu & Baocang Wang

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  1. Yu Zhan
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Correspondence to Baocang Wang.

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Zhan, Y., Zhang, Z., Liu, Q. et al. Hiding the input-size in multi-party private set intersection. Des. Codes Cryptogr. 91, 2893–2915 (2023). https://doi.org/10.1007/s10623-023-01238-0

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