Abstract
Differential privacy (DP) is a well-studied notion of privacy that is generally achieved by randomizing outputs to preserve the privacy of the input records. A central problem in differential privacy is how much accuracy must be lost in order to preserve input privacy?
Our work obtains general upper bounds on accuracy for differentially private two-party protocols computing any Boolean function. Our bounds are independent of the number of rounds and the communication complexity of the protocol, and hold with respect to computationally unbounded parties. At the heart of our results is a new general geometric technique for obtaining non-trivial accuracy bounds for any Boolean functionality.
We show that for any Boolean function, there is a constant accuracy gap between the accuracy that is possible in the client-server setting and the accuracy that is possible in the two-party setting. In particular, we show tight results on the accuracy that is achievable for the AND and XOR functions in the two-party setting, completely characterizing which accuracies are achievable for any given level of differential privacy.
Finally, we consider the situation if we relax the privacy requirement to computational differential privacy. We show that to achieve any noticeably better accuracy than what is possible for differentially private two-party protocols, it is essential that one-way functions exist.
Keywords
- Boolean Function
- Random Oracle
- Oblivious Transfer
- Randomize Response Technique
- Secure Function Evaluation
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.
Download conference paper PDF
References
Beaver, D.: Perfect privacy for two-party protocols. In: Feigenbaum, J., Merritt, M. (eds.) Proceedings of DIMACS Workshop on Distributed Computing and Cryptology, vol. 2, pp. 65–77. American Mathematical Society (1989)
Beimel, A., Nissim, K., Omri, E.: Distributed private data analysis: Simultaneously solving how and what. In: Wagner (ed.) [29], pp. 451–468
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: Simon (ed.) [28], pp. 1–10
Canetti, R., Kushilevitz, E., Lindell, Y.: On the limitations of universally composable two-party computation without set-up assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 68–86. Springer, Heidelberg (2003)
Chan, T.-H.H., Shi, E., Song, D.: Optimal lower bound for differentially private multi-party aggregation. In: Epstein, L., Ferragina, P. (eds.) ESA 2012. LNCS, vol. 7501, pp. 277–288. Springer, Heidelberg (2012)
Chaum, D., Crépeau, C., Damgard, I.: Multiparty unconditionally secure protocols. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 11–19. ACM, New York (1988), http://doi.acm.org/10.1145/62212.62214
Chor, B., Kushilevitz, E.: A zero-one law for Boolean privacy. SIAM J. Discrete Math. 4(1), 36–47 (1991)
De, A.: Lower bounds in differential privacy. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 321–338. Springer, Heidelberg (2012)
Dinur, I., Nissim, K.: Revealing information while preserving privacy. In: PODS, pp. 202–210. ACM (2003)
Dwork, C.: Differential privacy. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. Part II, LNCS, vol. 4052, pp. 1–12. Springer, Heidelberg (2006)
Dwork, C., Kenthapadi, K., McSherry, F., Mironov, I., Naor, M.: Our data, ourselves: Privacy via distributed noise generation. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 486–503. Springer, Heidelberg (2006)
Dwork, C., McSherry, F., Nissim, K., Smith, A.: Calibrating noise to sensitivity in private data analysis. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 265–284. Springer, Heidelberg (2006)
Dwork, C., Nissim, K.: Privacy-preserving datamining on vertically partitioned databases. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 528–544. Springer, Heidelberg (2004)
Ghosh, A., Roughgarden, T., Sundararajan, M.: Universally utility-maximizing privacy mechanisms. In: Mitzenmacher, M. (ed.) Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, pp. 351–360. ACM (2009)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: Aho, A.V. (ed.) STOC, pp. 218–229. ACM (1987)
Haitner, I., Omri, E., Zarosim, H.: On the power of random oracles. IACR Cryptology ePrint Archive 2012, 573 (2012)
Hardt, M., Talwar, K.: On the geometry of differential privacy. In: Schulman (ed.) [27], pp. 705–714
Harnik, D., Naor, M., Reingold, O., Rosen, A.: Completeness in two-party secure computation: A computational view. J. Cryptology 19(4), 521–552 (2006)
Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer—efficiently. In: Wagner (ed.) [29], pp. 572–591
Kasiviswanathan, S.P., Rudelson, M., Smith, A., Ullman, J.: The price of privately releasing contingency tables and the spectra of random matrices with correlated rows. In: Schulman (ed.) [27], pp. 775–784
Kilian, J.: Founding cryptography on oblivious transfer. In: Simon (ed.) [28], pp. 20–31
Kilian, J.: A general completeness theorem for two-party games. In: Koutsougeras, C., Vitter, J.S. (eds.) STOC, pp. 553–560. ACM (1991)
Kilian, J.: More general completeness theorems for secure two-party computation. In: STOC, pp. 316–324 (2000)
Kushilevitz, E.: Privacy and communication complexity. In: FOCS, pp. 416–421 (1989)
McGregor, A., Mironov, I., Pitassi, T., Reingold, O., Talwar, K., Vadhan, S.P.: The limits of two-party differential privacy. In: FOCS, pp. 81–90. IEEE Computer Society (2010)
Mironov, I., Pandey, O., Reingold, O., Vadhan, S.: Computational differential privacy. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 126–142. Springer, Heidelberg (2009)
Schulman, L.J. (ed.): Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, Cambridge, Massachusetts, USA, June 5-8. ACM (2010)
Simon, J. (ed.): Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, USA, May 2-4. ACM (1988)
Wagner, D. (ed.): CRYPTO 2008. LNCS, vol. 5157. Springer, Heidelberg (2008)
Yao, A.C.C.: Protocols for secure computations (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science (FOCS 1982), pp. 160–164. IEEE (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 International Association for Cryptologic Research
About this paper
Cite this paper
Goyal, V., Mironov, I., Pandey, O., Sahai, A. (2013). Accuracy-Privacy Tradeoffs for Two-Party Differentially Private Protocols. In: Canetti, R., Garay, J.A. (eds) Advances in Cryptology – CRYPTO 2013. CRYPTO 2013. Lecture Notes in Computer Science, vol 8042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40041-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-40041-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40040-7
Online ISBN: 978-3-642-40041-4
eBook Packages: Computer ScienceComputer Science (R0)