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Size-Hiding in Private Set Intersection: Existential Results and Constructions

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Progress in Cryptology - AFRICACRYPT 2012 (AFRICACRYPT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7374))

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Abstract

In this paper we focus our attention on private set intersection. We show impossibility and existential results, and we provide some explicit constructions. More precisely, we start by looking at the case in which both parties, client and server, in securely computing the intersection, would like to hide the sizes of their sets of secrets, and we show that:

  • It is impossible to realize an unconditionally secure size-hiding set intersection protocol.

  • In a model where a TTP provides set up information to the two parties and disappears, unconditionally secure size-hiding set intersection is possible.

  • There exist computationally secure size-hiding set intersection protocols.

Then, we provide some explicit constructions for one-sided protocols, where only the client gets the intersection and hides the size of her set of secrets. In the model with the TTP, we design two protocols which are computationally secure under standard assumptions, and two very efficient protocols which are secure in the random oracle model. We close the paper with some remarks and by pointing out several interesting open problems.

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References

  1. 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.) PKC 2011. LNCS, vol. 6571, pp. 156–173. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  2. Bellare, M., Rogaway, P.: The Exact Security of Digital Signatures - How to Sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)

    Google Scholar 

  3. Carter, J.L., Wegman, M.N.: Universal classes of hash functions. Journal of Computer and System Sciences 18, 143–154 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cramer, R.: Introduction to Secure Computation. In: Damgård, I.B. (ed.) Lectures on Data Security. LNCS, vol. 1561, pp. 16–62. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  5. Camenisch, J., Kohlweiss, M., Soriente, C.: An Accumulator Based on Bilinear Maps and Efficient Revocation for Anonymous Credentials. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 481–500. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Camenisch, J., Lysyanskaya, A.: A Signature Scheme with Efficient Protocols. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 268–289. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  9. 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)

    Chapter  Google Scholar 

  10. Dachman-Soled, D., Malkin, T., Raykova, M., Yung, M.: Secure Efficient Multiparty Computing of Multivariate Polynomials and Applications. In: Lopez, J., Tsudik, G. (eds.) ACNS 2011. LNCS, vol. 6715, pp. 130–146. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Even, S., Goldreich, O., Lempel, A.: A Randomized Protocol for Signing Contracts. Communications of the ACM 28(6), 637–647 (1985)

    Article  MathSciNet  Google Scholar 

  12. Frikken, K.: Privacy-Preserving Set Union. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 237–252. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  15. Goldreich, O.: Foundations of Cryptography - Volume II Basic Applications. Cambridge Press (2004)

    Google Scholar 

  16. 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)

    Chapter  Google Scholar 

  17. Ishai, Y., Prabhakaran, M., Sahai, A.: Founding Cryptography on Oblivious Transfer – Efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008)

    Google Scholar 

  18. Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proc. of the 21st Annual ACM Symposium on Theory of Computing, Seattle, Washington, pp. 44–61 (May 1989)

    Google Scholar 

  19. Kissner, L., Song, D.: Privacy-Preserving Set Operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005)

    Google Scholar 

  20. Naor, M., Reingold, O.: Number-theoretic constructions of efficient pseudo-random functions. Journal of the ACM 51(2), 231–262 (2004)

    Article  MathSciNet  Google Scholar 

  21. Paillier, P.: Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–239. Springer, Heidelberg (1999)

    Google Scholar 

  22. Rabin, M.: How to exchange secrets by oblivious transfer, Technical Report TR-81, Aiken Computation Laboratory, Harvard University (1981)

    Google Scholar 

  23. Rivest, R.: Unconditionally Secure Commitment and Oblivious Transfer Schemes Using Private Channels and a Trusted Initializer (August 11, 1999) (unpublished manuscript), http://people.csail.mit.edu/rivest/publications.html

  24. Stinson, D.R.: Universal hash families and the leftover hash lemma, and applications to cryptography and computing. J. Combin. Math. Combin. Comput. 42, 3–31 (2002)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Universitá di Salerno, 84084, Fisciano, SA, Italy

    Paolo D’Arco

  2. Dpto. de Matemática Aplicada, Univ. Rey Juan Carlos, c/ Tulipán, s/n, 28933, Madrid, Spain

    María Isabel González Vasco & Angel L. Pérez del Pozo

  3. Institute of Information Security, ETH Zurich, Switzerland

    Claudio Soriente

Authors
  1. Paolo D’Arco
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  2. María Isabel González Vasco
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  3. Angel L. Pérez del Pozo
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  4. Claudio Soriente
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Editor information

Editors and Affiliations

  1. Ecole Polytechnice Fédérale de Lausanne, IC - LASEC, Bâtiment INF 238, Station 14, 1015, Lausanne, Switzerland

    Aikaterini Mitrokotsa  & Serge Vaudenay  & 

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D’Arco, P., González Vasco, M.I., Pérez del Pozo, A.L., Soriente, C. (2012). Size-Hiding in Private Set Intersection: Existential Results and Constructions. In: Mitrokotsa, A., Vaudenay, S. (eds) Progress in Cryptology - AFRICACRYPT 2012. AFRICACRYPT 2012. Lecture Notes in Computer Science, vol 7374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31410-0_23

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  • DOI: https://doi.org/10.1007/978-3-642-31410-0_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31409-4

  • Online ISBN: 978-3-642-31410-0

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