Asynchronous secure communication tolerating mixed adversaries

We study the problem of secure communication tolerating generalized mixed, adversaries across an underlying completely asynchronous incomplete network. We explore the interplay between the minimal network connectivity required and the degree of security attainable, and completely characterize the network requirements for attaining perfect and unconditional (with negligible error) security. We also consider networks with additional broadcast capabilities and prove that unconditionally secure communication can be achieved with much lesser connectivity if the network assures the broadcast primitive.