2014 | OriginalPaper | Buchkapitel
On the Communication Complexity of Secure Computation
verfasst von : Deepesh Data, Manoj M. Prabhakaran, Vinod M. Prabhakaran
Erschienen in: Advances in Cryptology – CRYPTO 2014
Verlag: Springer Berlin Heidelberg
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Information theoretically secure multi-party computation (MPC) is a central primitive of modern cryptography. However, relatively little is known about the communication complexity of this primitive.
In this work, we develop powerful information theoretic tools to prove lower bounds on the communication complexity of MPC. We restrict ourselves to a concrete setting involving 3-parties, in order to bring out the power of these tools without introducing too many complications. Our techniques include the use of a data processing inequality for
residual information
— i.e., the gap between mutual information and Gács-Körner common information, a new
information inequality
for 3-party protocols, and the idea of
distribution switching
by which lower bounds computed under certain worst-case scenarios can be shown to apply for the general case.
Using these techniques we obtain tight bounds on communication complexity by MPC protocols for various interesting functions. In particular, we show concrete functions that have “communication-ideal” protocols, which achieve the minimum communication simultaneously on all links in the network. Also, we obtain the first
explicit
example of a function that incurs a higher communication cost than the input length in the secure computation model of Feige, Kilian and Naor [17], who had shown that such functions exist. We also show that our communication bounds imply tight lower bounds on the amount of randomness required by MPC protocols for many interesting functions.