Almost-Everywhere Secure Computation

13 years 6 months ago

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Secure multi-party computation (MPC) is a central problem in cryptography. Unfortunately, it is well known that MPC is possible if and only if the underlying communication network has very large connectivity -- in fact, (t), where t is the number of potential corruptions in the network. This impossibility result renders existing MPC results far less applicable in practice, since many deployed networks have in fact a very small degree. In this paper, we show how to circumvent this impossibility result and achieve meaningful security guarantees for graphs with small degree (such as expander graphs and several other topologies). In fact, the notion we introduce, which we call almost-everywhere MPC, building on the notion of almosteverywhere agreement due to Dwork, Peleg, Pippenger and Upfal, allows the degree of the network to be much smaller than the total number of allowed corruptions. In essence, our definition allows the adversary to implicitly wiretap some of the good nodes by corru...

Juan A. Garay, Rafail Ostrovsky

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