Multiparty Proximity Testing with Dishonest Majority from Equality Testing

  • Ran Gelles
  • Rafail Ostrovsky
  • Kina Winoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

Abstract

Motivated by the recent widespread emergence of location-based services (LBS) over mobile devices, we explore efficient protocols for proximity-testing. Such protocols allow a group of friends to discover if they are all close to each other in some physical location, without revealing their individual locations to each other. We focus on hand-held devices and aim at protocols with very small communication complexity and a small constant number of rounds.

The proximity-testing problem can be reduced to the private equality testing (PET) problem, in which parties find out whether or not they hold the same input (drawn from a low-entropy distribution) without revealing any other information about their inputs to each other. While previous works analyze the 2-party PET special case (and its LBS application), in this work we consider highly-efficient schemes for the multiparty case with no honest majority. We provide schemes for both a direct-communication setting and a setting with a honest-but-curious mediating server that does not learn the users’ inputs. Our most efficient scheme takes 2 rounds, where in each round each user sends only a couple of ElGamal ciphertexts.

Keywords

Secret Sharing Homomorphic Encryption Oblivious Transfer Honest Party Malicious Adversary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Axel, K.: Location-Based Services: Fundamentals and Operation. John Wiley & Sons, Hoboken (2005)Google Scholar
  2. 2.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC 1988, pp. 1–10 (1988)Google Scholar
  3. 3.
    Boneh, D.: The Decision Diffie-Hellman Problem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 48–63. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Boudot, F., Schoenmakers, B., Traoré, J.: A fair and efficient solution to the socialist millionaires’ problem. Discrete Applied Mathematics 111(1-2), 23–36 (2001)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Canetti, R., Halevi, S., Katz, J., Lindell, Y., MacKenzie, P.: Universally Composable Password-Based Key Exchange. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 404–421. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Fagin, R., Naor, M., Winkler, P.: Comparing information without leaking it. Commun. ACM 39, 77–85 (1996)CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Gelles, R., Ostrovsky, R., Winoto, K.: Multiparty Proximity Testing with Dishonest Majority from Equality Testing. In: Czumaj, A., et al. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 537–548. Springer, Heidelberg (2012)Google Scholar
  10. 10.
    Goldreich, O.: Foundations of cryptography. Basic applications, vol. II. Cambridge University Press, New York (2004)CrossRefMATHGoogle Scholar
  11. 11.
    Goldreich, O., Lindell, Y.: Session-key generation using human passwords only. Journal of Cryptology 19, 241–340 (2006)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Gong, L., Lomas, M., Needham, R., Saltzer, J.: Protecting poorly chosen secrets from guessing attacks. IEEE Journal on Selected Areas in Communications 11(5), 648–656 (1993)CrossRefGoogle Scholar
  13. 13.
    Gruteser, M., Grunwald, D.: Anonymous usage of location-based services through spatial and temporal cloaking. In: MobiSys 2003, pp. 31–42 (2003)Google Scholar
  14. 14.
    Kalnis, P., Ghinita, G., Mouratidis, K., Papadias, D.: Preventing location-based identity inference in anonymous spatial queries. IEEE Transactions on Knowledge and Data Engineering 19(12), 1719–1733 (2007)CrossRefGoogle Scholar
  15. 15.
    Katz, J., Ostrovsky, R., Yung, M.: Efficient Password-Authenticated Key Exchange Using Human-Memorable Passwords. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 475–494. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Katz, J., Yung, M.: Unforgeable Encryption and Chosen Ciphertext Secure Modes of Operation. In: Schneier, B. (ed.) FSE 2000. LNCS, vol. 1978, pp. 284–299. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  17. 17.
    Li, K.A., Sohn, T.Y., Huang, S., Griswold, W.G.: Peopletones: a system for the detection and notification of buddy proximity on mobile phones. In: MobiSys 2008, pp. 160–173 (2008)Google Scholar
  18. 18.
    Lipmaa, H.: Verifiable Homomorphic Oblivious Transfer and Private Equality Test. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 416–433. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: STOC 1999, pp. 245–254 (1999)Google Scholar
  20. 20.
    Narayanan, A., Thiagarajan, N., Lakhani, M., Hamburg, M., Boneh, D.: Location Privacy via Private Proximity Testing. In: NDSS 2011 (2011)Google Scholar
  21. 21.
    Nishide, T., Ohta, K.: Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 343–360. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  22. 22.
    Ostrovsky, R., Skeith III, W.E.: A Survey of Single-Database Private Information Retrieval: Techniques and Applications. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 393–411. Springer, Heidelberg (2007)CrossRefGoogle 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)Google Scholar
  24. 24.
    Pedersen, T.P.: Non-interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)Google Scholar
  25. 25.
    Schnorr, C.P.: Efficient signature generation by smart cards. Journal of Cryptology 4, 161–174 (1991)CrossRefMATHGoogle Scholar
  26. 26.
    Šikšnys, L., Thomsen, J.R., Šaltenis, S., Yiu, M.L., Andersen, O.: A Location Privacy Aware Friend Locator. In: Mamoulis, N., Seidl, T., Pedersen, T.B., Torp, K., Assent, I. (eds.) SSTD 2009. LNCS, vol. 5644, pp. 405–410. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  27. 27.
    Tonicelli, R., David, B.M., de Morais Alves, V.: Universally Composable Private Proximity Testing. In: Boyen, X., Chen, X. (eds.) ProvSec 2011. LNCS, vol. 6980, pp. 222–239. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  28. 28.
    Yao, A.: Protocols for secure computations. In: SFCS 1982, pp. 160–164 (1982)Google Scholar
  29. 29.
    Zhong, G., Goldberg, I., Hengartner, U.: Louis, Lester and Pierre: Three Protocols for Location Privacy. In: Borisov, N., Golle, P. (eds.) PET 2007. LNCS, vol. 4776, pp. 62–76. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ran Gelles
    • 1
  • Rafail Ostrovsky
    • 1
  • Kina Winoto
    • 1
  1. 1.University of CaliforniaLos AngelesUSA

Personalised recommendations