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Mutual Private Set Intersection with Linear Complexity

  • Myungsun Kim
  • Hyung Tae Lee
  • Jung Hee Cheon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7115)

Abstract

A private set intersection (PSI) protocol allows players to obtain the intersection of their inputs. While in its unilateral version only the client can obtain the intersection, the mutual PSI protocol enables all players to get the desired result. In this work, we construct a mutual PSI protocol that is significantly more efficient than the state-of-the-art in the computation overhead. To the best of our knowledge, our construction is the first result with linear computational complexity in the semi-honest model. For that, we come up with an efficient data representation technique, called prime representation.

Keywords

Mutual Private Set Intersection Prime Representation 

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References

  1. 1.
    Agrawal, M., Kayal, N., Saxena, N.: PRIMES is in P. Annals of Mathematics 160(2), 781–793 (2004)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Agrawal, R., Evfimievski, A., Srikant, R.: Information sharing across private database. In: Halevy, A., Ives, Z., Doan, A. (eds.) SIGMOD, pp. 86–97 (2003)Google Scholar
  3. 3.
    Camenisch, J.: Proof systems for general statements about discrete logarithms. Technical Report TR 260, Dept. of Computer Science, ETH Zurich (1997)Google Scholar
  4. 4.
    Camenisch, J.L., Chaabouni, R., shelat, a.: Efficient Protocols for Set Membership and Range Proofs. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 234–252. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Camenisch, J., Zaverucha, G.M.: Private Intersection of Certified Sets. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 108–127. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R., Sherman, A. (eds.) Advances in Cryptology-Crypto, pp. 199–203 (1982)Google Scholar
  7. 7.
    Cheon, J.H., Jarecki, S., Seo, J.H.: Multi-party privacy-preserving set intersection with quasi-linear complexity. Cryptology ePrint Archive, 2010/512 (2010)Google Scholar
  8. 8.
    Cramer, R., Damgård, I., Nielsen, J.B.: Multiparty Computation from Threshold Homomorphic Encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–299. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    De Cristofaro, E., Tsudik, G.: Practical Private Set Intersection Protocols with Linear Computational and Bandwidth Complexity. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 143–159. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Damgård, I., Jurik, M.: A Generalisation, a Simplification and some Applications of Paillier’s Probabilistic Public-Key System. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  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)CrossRefGoogle Scholar
  15. 15.
    Goldreich, O.: The foundations of cryptography, vol. 2. Cambridge University Press (2004)Google Scholar
  16. 16.
    Hazay, C., Lindell, Y.: Efficient Protocols for Set Intersection and Pattern Matching with Security Against Mailicious and Covert Adversaries. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 155–175. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Hazay, C., Nissim, K.: Efficient Set Operations in the Presence of Malicious Adversaries. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 312–331. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Jarecki, S., Liu, X.: Efficient Oblivious Pseudorandom Function with Applications to Adaptive ot And secure Computation of Set Intersection. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 577–594. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Kissner, L., Song, D.: Privacy-Preserving Set Operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    MacKenzie, P.D., Yang, K.: On Simulation-Sound Trapdoor Commitments. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 382–400. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Mezzour, G., Perrig, A., Gligor, V., Papadimitratos, P.: Privacy-Preserving Relationship Path Discovery in Social Networks. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds.) CANS 2009. LNCS, vol. 5888, pp. 189–208. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: STOC, pp. 245–254 (1999)Google Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    Shoup, V.: Practical Threshold Signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Myungsun Kim
    • 1
  • Hyung Tae Lee
    • 1
  • Jung Hee Cheon
    • 1
  1. 1.ISaC & Dept. of Mathematical SciencesSeoul National UniversitySeoulKorea

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