Abstract
We present efficient protocols for private set disjointness tests. We start from an intuition of our protocols that applies Sylvester matrices. Unfortunately, this simple construction is insecure as it reveals information about the cardinality of the intersection. More specifically, it discloses its lower bound. By using the Lagrange interpolation we provide a protocol for the honest-but-curious case without revealing any additional information. Finally, we describe a protocol that is secure against malicious adversaries. The protocol applies a verification test to detect misbehaving participants. Both protocols require O(1) rounds of communication. Our protocols are more efficient than the previous protocols in terms of communication and computation overhead. Unlike previous protocols whose security relies on computational assumptions, our protocols provide information theoretic security. To our knowledge, our protocols are first ones that have been designed without a generic secure function evaluation. More importantly, they are the most efficient protocols for private disjointness tests for the malicious adversary case.
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References
Kiayias, A., Mitrofanova, A.: Testing disjointness and private datasets. In: S. Patrick, A., Yung, M. (eds.) FC 2005. LNCS, vol. 3570, pp. 109–124. Springer, Heidelberg (2005)
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. 1–9. Springer, Heidelberg (2004)
Hohenberger, S., Weis, S.A.: Honest-verifier private disjointness testing without random oracles. In: Danezis, G., Golle, P. (eds.) PET 2006. LNCS, vol. 4258, pp. 277–294. Springer, Heidelberg (2006)
Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: 31st annual ACM Symposium on Theory of Computing (STOC 1999), Atlanta, Georgia, May 1999, pp. 245–254 (1999)
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)
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)
Cramer, R., Gennaro, R., Schoenmakers, B.: A secure and optimally efficient multi-authority election scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997)
Kissner, L., Song, D.: Privacy-preserving set operaitons. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005)
Laur, S., Lipmaa, H., Mielikainen, T.: Private itemset support counting. In: Qing, S., Mao, W., López, J., Wang, G. (eds.) ICICS 2005. LNCS, vol. 3783, pp. 97–111. Springer, Heidelberg (2005)
Kiayias, A., Mitrofanova, A.: Syntax-driven private evaluation of quantified membership queries. In: Zhou, J., Yung, M., Bao, F. (eds.) ACNS 2006. LNCS, vol. 3989, pp. 470–485. Springer, Heidelberg (2006)
Fagin, R., Naor, M., Winkler, P.: Comparing information without leaking it. Communications of the ACM 39(5), 77–85 (1996)
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)
Ye, Q., Wang, H., Tartary, C.: Privacy-preserving distributed set intersection. In: The 2nd Workshop on Advances in Information Security (conjuncted with ARES 2008), Barcelona, Spain, March 2008, pp. 1332–1339. IEEE Computer Society Press, Los Alamitos (2008)
Ye, Q., Wang, H., Pieprzyk, J.: Distributed private matching and set operations. In: ISPEC 2008, April 2008. LNCS, vol. 4991, pp. 347–360. Springer, Heidelberg (2008)
Cramer, R., Damgard, I.: Secure distributed linear algebra in a constant number of rounds. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 119–136. Springer, Heidelberg (2001)
Mohassel, P., Franklin, M.: Efficient polynomial operations in the shared-coefficients setting. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 44–57. Springer, Heidelberg (2006)
von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press, Cambridge (2003)
Bar-Ilan, J., Beaver, D.: Non-cryptographic fault-tolerant computing in a constant number of rounds of interaction. In: 8th ACM Annual Symposium on Principles of Distributed Computing (PODC 1989), pp. 201–209. ACM Press, New York (1989)
Ben-Or, M., Cleve, R.: Computing algebraic formulas using a constant number of registers. In: 20th annual ACM Symposium on Theory of Computing (STOC 1988), pp. 254–257. ACM Press, New York (1988)
Goldreich, O.: The Foundations of Cryptography, vol. 2. Cambridge University Press, Cambridge (2004)
Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. Journal of Symbolic Computing 9, 251–280 (1990)
Kaltofen, E., Villard, G.: On the complexity of computing determinants. Computational Complexity 13(3-4), 91–130 (2005)
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Ye, Q., Wang, H., Pieprzyk, J., Zhang, XM. (2008). Efficient Disjointness Tests for Private Datasets. In: Mu, Y., Susilo, W., Seberry, J. (eds) Information Security and Privacy. ACISP 2008. Lecture Notes in Computer Science, vol 5107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70500-0_12
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DOI: https://doi.org/10.1007/978-3-540-70500-0_12
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