Private Computations in Networks: Topology versus Randomness
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.
Unable to display preview. Download preview PDF.
- 1.J. Bar-Ilan, D. Beaver, Non-Cryptographic Fault-Tolerant Computing in Constant Number of Rounds of Interaction, Proc. 8. PODC, 1989, 201–209.Google Scholar
- 2.M. Bläser, A. Jakoby, M. Liśkiewicz, and B. Siebert, Private Computation-kconnected versus 1-connected Networks, Proc. 22. CRYPTO, 2002, 194–209.Google Scholar
- 3.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.Google Scholar
- 4.M. Ben-Or, S. Goldwasser, A. Wigderson, Completeness Theorem for Non cryptographic Fault-tolerant Distributed Computing, Proc. 20. STOC, 1988, 1–10.Google Scholar
- 5.D. Chaum, C. Crépeau, I. Damgård, Multiparty unconditionally secure protocols, Proc. 20. STOC, 1988, 11–19.Google Scholar
- 8.R. Canetti, R. Ostrovsky, Secure Computation with Honest-Looking Parties: What if nobody is truly honest?, Proc. 31. STOC, 1999, 35–44.Google Scholar
- 10.M. Franklin, M. Yung, Secure hypergraphs: privacy from partial broadcast (Extended Abstract), Proc. 27. STOC, 1995, 36–44.Google Scholar
- 11.A. Gál, A. Rosén, A Theorem on Sensitivity and Applications in Private Computation, Proc. 31. STOC, 1999, 348–357.Google Scholar
- 12.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.Google Scholar
- 13.E. Kushilevitz, R. Ostrovsky, A. Rosén, Characterizing Linear Size Circuits in Terms of Privacy, Proc. 28. STOC, 1996, 541–550.Google Scholar
- 17.A. C. Yao, Protocols for Secure Computations, Proc. 23. FOCS, 1982, 160–164.Google Scholar
- 18.A. C. Yao, How to generate and exchange secrets, Proc. 27. FOCS, 1986, 162–167.Google Scholar