Abstract
Squared Euclidean Distance metric that uses the same equation as the Euclidean distance metric, but does not take the square root (thus clustering with the Squared Euclidean Distance metric is faster than clustering with the regular Euclidean Distance) is an efficient tool for clustering databases. Since there appears to be no previous implementation of secure Squared Euclidean Distance protocols in the malicious model, this paper studies two-party computation of Squared Euclidean Distance protocols in the presence of malicious adversaries based on state-of-the art homomorphic cryptographic primitives without using Yao-style circuit. The security of our protocol is analyzed by comparing what an adversary can do in the a real protocol execution to what it can do in an ideal scenario. We show that the proposed scheme is provably secure against malicious adversary assuming that the underlying homomorphic commitment is statistically hiding and computationally binding and the homomorphic encryption scheme is semantically secure in the common reference string model.
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References
Barak, B., Lindell, Y.: Strict polynomial-time in simulation and extraction. In: STOC 2002, pp. 484–493 (2002)
Boudot, F.: Efficient Proofs that a Committed Number Lies in an Interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic faulttolerant distributed computation. In: Proc. 20th Annual ACM Symposium on Theory of Computing, pp. 1–10 (1988)
Cramer, R., Damgård, I.: Secret-Key Zero-Knowlegde and Non-interactive Verifiable Exponentiation. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 223–237. Springer, Heidelberg (2004)
Damgård, I., Fujisaki, E.: A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 125–142. Springer, Heidelberg (2002)
Damgård, I., Jurik, M.: A Generalisation, a Simplification and Some Applications of Paillier’s Probabilistic Public-Key System. In: Public Key Cryptography 2001, pp. 119–136 (2001)
Damgård, I., Jurik, M.: Client/Server Tradeoffs for Online Elections. In: Proc. of Public Key Cryptography 2002, pp. 125–140. Springer, Heidelberg (2002)
Fagin, R., Naor, M., Winkler, P.: Comparing Information Without Leaking it. Communication of ACM 39, 77–85 (1996)
Fujisaki, E., Okamoto, T.: Statistically zero knowledge protocols to prove modular polynomial relations. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16–30. Springer, Heidelberg (1997)
Goldreich, O.: The Foundations of Cryptography, vol. 2. Cambridge University Press, Cambridge (2004)
Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game: A Completeness Theorem for Protocols with Honest Majority. In: 19th STOC, pp. 218–229 (1987)
Goethals, B., Laur, S., Lipmaa, H., Mielikäinen, T.: On Private Scalar Product Computation for Privacy-Preserving Data Mining. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 104–120. Springer, Heidelberg (2005)
Jagannathan, G., Wright, R.N.: Privacy-preserving distributed k-means clustering over arbitrarily partitioned data. In: ACM-KDD 2005, pp. 593–599 (2005)
Kantarcioglu, M., Clifton, C.: Privacy-preserving distributed mining of association rules on horizontally partitioned data. In: The ACM SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery (DMKD 2002), June 2 (2002)
Lindell, Y.: Composition of Secure Multi-Party Protocols. LNCS, vol. 2815. Springer, Heidelberg (2003)
Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: ACM Conference on Electronic Commerce 1999, pp. 129–139 (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)
Pinkas, B.: Fair Secure Two-Party Computation. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 87–105. Springer, Heidelberg (2003)
Vaidya, J., Clifton, C.: Privacy preserving association rule mining in vertically partitioned data. In: The 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2002), pp. 639–644 (2002)
Yao, A.C.: Protocols for Secure Computations. In: Proc. of the 23rd IEEE Symp. On Foundations of Computer Science, pp. 160–164 (1982)
Yao, A.C.: How to Generate and Exchange Secrets. In: Proc. of the 27th IEEE Symp. On Foundations of Computer Science, pp. 162–167 (1986)
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Mouffron, M., Rousseau, F., Zhu, H. (2008). Secure Two-Party Computation of Squared Euclidean Distances in the Presence of Malicious Adversaries. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds) Information Security and Cryptology. Inscrypt 2007. Lecture Notes in Computer Science, vol 4990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79499-8_12
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