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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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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