Abstract
Given two or more parties possessing large, confidential datasets, we consider the problem of securely computing the k th-ranked element of the union of the datasets, e.g. the median of the values in the datasets. We investigate protocols with sublinear computation and communication costs. In the two-party case, we show that the k th-ranked element can be computed in log k rounds, where the computation and communication costs of each round are O(log M), where log M is the number of bits needed to describe each element of the input data. The protocol can be made secure against a malicious adversary, and can hide the sizes of the original datasets. In the multi-party setting, we show that the k th-ranked element can be computed in log M rounds, with O(s log M) overhead per round, where s is the number of parties. The multi-party protocol can be used in the two-party case and can also be made secure against a malicious adversary.
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Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: Proc. 22nd Annual ACM Symposium on the Theory of Computing, pp. 503–513 (1990)
Canetti, R.: Security and composition of multiparty cryptographic protocols. Journal of Cryptology 13(1), 143–202 (2000)
Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: Proc. 42nd IEEE Symposium on Foundations of Computer Science, pp. 136–145 (2001)
Canetti, R., Ishai, Y., Kumar, R., Reiter, M., Rubinfeld, R., Wright, R.: Selective private function evaluation with applications to private statistics. In: Proc. of 20th ACM Symposium on Principles of Distributed Computing, pp. 293–304 (2001)
Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two party computation. In: Proc. 34th ACM Symp. on the Theory of Computing, pp. 494–503 (2002)
Feigenbaum, J., Ishai, Y., Malkin, T., Nissim, K., Strauss, M., Wright, R.: Secure multiparty computation of approximations. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 927–938. Springer, Heidelberg (2001)
Fischlin, M.: A cost-effective pay-per-multiplication comparison method for millionaires. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 457–472. Springer, Heidelberg (2001)
Franklin, M., Yung, M.: Communication complexity of secure computation (extended abstract). In: Proc. 24th ACM Symp. on the Theory of Computing, pp. 699–710 (1992)
Gibbons, P., Matias, Y., Poosala, V.: Fast incremental maintenance of approximate histograms. In: Proc. 23rd Int. Conf. Very Large Data Bases, pp. 466–475 (1997)
Goldreich, O.: Secure multi-party computation. In: Theory of Cryptography Library (1998)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or A completeness theorem for protocols with honest majority. In: Proc. 19th Annual ACM Symposium on Theory of Computing, pp. 218–229 (1987)
Jagadish, H., Koudas, N., Muthukrishnan, S., Poosala, V., Sevcik, K., Suel, T.: Optimal histograms with quality guarantees. In: Proc. 24th Int. Conf. Very Large Data Bases, pp. 275–286 (1998)
Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)
Lindell, Y., Pinkas, B.: Privacy preserving data mining. Journal of Cryptology 15(3), 177–206 (2002)
Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: Proc. 33rd Annual ACM Symposium on Theory of Computing, pp. 590–599 (2001)
Poosala, V., Ganti, V., Ioannidis, Y.: Approximate query answering using histograms. IEEE Data Engineering Bulletin 22(4), 5–14 (1999)
Rodeh, M.: Finding the median distributively. Journal of Computer and Systems Sciences 24, 162–166 (1982)
Yao, A.: How to generate and exchange secrets. In: Proc. 27th IEEE Symposium on Foundations of Computer Science, pp. 162–167 (1986)
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Aggarwal, G., Mishra, N., Pinkas, B. (2004). Secure Computation of the k th-Ranked Element. In: Cachin, C., Camenisch, J.L. (eds) Advances in Cryptology - EUROCRYPT 2004. EUROCRYPT 2004. Lecture Notes in Computer Science, vol 3027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24676-3_3
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DOI: https://doi.org/10.1007/978-3-540-24676-3_3
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