Network-Faithful Secure Computation

We investigate privacy-preserving computation under a very general model for message-passing protocols over large networks. Our goal is to construct secure versions of such protocolswhile preserving the property of highly distributed, local computation. We present a general“compiler” that turns any message-passing protocol into one computing the same functionality ina way that is secure against single-party adversaries. We then give a simulation-based definitionof what it means for a secure protocol to be “faithful” to the original protocol and networkstructure, and prove that our compiler produces extremely faithful 1-private protocols. Finally,we show that there is an inherent trade-off between faithfulness and security against coalitions.In particular, for certain functionalities, any highly faithful protocol must be vulnerable tocollusion by small coalitions, thus proving the optimality of our compiler with respect to thistrade-off.