Abstract
In a distributed network, computing a function privately requires that no participant gains any additional knowledge other than the value of the function.We study this problem for incomplete networks and establish a tradeoff between connectivity properties of the network and the amount of randomness needed. First, a general lower bound on the number of random bits is shown. Next, for every k ≥2 we design a quite efficient (with respect to randomness) protocol for symmetric functions that works in arbitrary k-connected networks. Finally, for directed cycles that compute threshold functions privately almost matching lower and upper bounds for the necessary amount of randmoness are proven.
On leave from Instytut Informatyki, Uniwersytet Wroc,lawski, Wroc,law, Poland.
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References
J. Bar-Ilan, D. Beaver, Non-Cryptographic Fault-Tolerant Computing in Constant Number of Rounds of Interaction, Proc. 8. PODC, 1989, 201–209.
M. Bläser, A. Jakoby, M. Liśkiewicz, and B. Siebert, Private Computation-kconnected versus 1-connected Networks, Proc. 22. CRYPTO, 2002, 194–209.
C. Blundo, A. De Santis, G. Persiano, U. Vaccaro, On the Number of Random Bits in Totally Private Computation, Proc. 22. ICALP, 1995, 171–182.
M. Ben-Or, S. Goldwasser, A. Wigderson, Completeness Theorem for Non cryptographic Fault-tolerant Distributed Computing, Proc. 20. STOC, 1988, 1–10.
D. Chaum, C. Crépeau, I. Damgård, Multiparty unconditionally secure protocols, Proc. 20. STOC, 1988, 11–19.
B. Chor, M. Geréb-Graus, E. Kushilevitz, Private Computations Over the Integers, SIAM J. Computing 24, 1995, 376–386.
B. Chor, E. Kushilevitz, A Communication-Privacy Tradeo. for Modular Addition, Information Processing Letters 45, 1993, 205–210.
R. Canetti, R. Ostrovsky, Secure Computation with Honest-Looking Parties: What if nobody is truly honest?, Proc. 31. STOC, 1999, 35–44.
Y. Egawa, R. Glas, S. C. Locke, Cycles and paths through specified vertices in kconnected graphs, Journal of Combinatorial Theory Series B 52, 1991, 20–29.
M. Franklin, M. Yung, Secure hypergraphs: privacy from partial broadcast (Extended Abstract), Proc. 27. STOC, 1995, 36–44.
A. Gál, A. Rosén, A Theorem on Sensitivity and Applications in Private Computation, Proc. 31. STOC, 1999, 348–357.
O. Goldreich, S. Micali, A. Wigderson, How to Play any Mental Game or a Completeness Theorem for Protocols with Honest Majority, 28. FOCS, 1987, 218–229.
E. Kushilevitz, R. Ostrovsky, A. Rosén, Characterizing Linear Size Circuits in Terms of Privacy, Proc. 28. STOC, 1996, 541–550.
E. Kushilevitz, Y. Mansour, Randomness in Private Computations, SIAM J. Discrete Math 10, 1997, 647–661.
E. Kushilevitz, A. Rosén, A Randomness-Rounds Tradeo. in Private Computation, SIAM J. Discrete Math 11, 1998, 61–80.
E. Kushilevitz, Privacy and Communication Complexity, SIAM J. Discrete Math 5, 1992, 273–284.
A. C. Yao, Protocols for Secure Computations, Proc. 23. FOCS, 1982, 160–164.
A. C. Yao, How to generate and exchange secrets, Proc. 27. FOCS, 1986, 162–167.
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Jakoby, A., Liśkiewicz, M., Reischuk, R. (2003). Private Computations in Networks: Topology versus Randomness. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_12
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DOI: https://doi.org/10.1007/3-540-36494-3_12
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