Brief announcement: realizing secure multiparty computation on incomplete networks

We consider a recently proposed model for secure computation appropriate to the setting of low degree networks called almost everywhere secure computation. This model of multiparty computation allows a few honest parties to not achieve the canonical guarantees of Correctness and Privacy. Such honest parties may not be able to communicate reliably or securely with other honest parties in the network due to lack of infrastructure. We explain why a straightforward hybrid argument employed in the previous work can be used to realize privacy only when honest-but-curious type passive corruptions are considered. We further note that the notion of almost everywhere secure computation is theoretically challenging and practically relevant only when malicious corruptions are allowed. We argue and emphasize why simulation based reduction approach taken by the author is the only way to meaningfully realize privacy of almost everywhere secure computation. We present such an approach and show how to realize a.e.s.c. for general Byzantine corruptions, resolving the principle open problem in this line of research. Finally, we note several technical and conceptual improvements to the results given in previous work.