עמוס ביימל

Reliable communication between parties in a network is a basic requirement for executing any protocol. Dolev and Dolev et al. showed that reliable communication is possible if and only if the communication network is sufficiently connected. Beimel and Franklin showed that the connectivity requirement can be relaxed if some pairs of parties share authentication keys. That is, costly communication links can be replaced by authentication keys. In this work, we continue this line of research. We consider the scenario where there is a specific sender and a specific receiver. In this case, the protocol of has n^O(n) rounds even if there is a single Byzantine processor. We present a more efficient protocol with round complexity of (n/t) ^O(t) where n is the number of processors in the network and t is an upper bound on the number of Byzantine processors in the network. Specifically, our protocol is polynomial when the number of Byzantine processors is O(1), and for every t its round complexity is bounded by 2^O(n). The same improvements hold for reliable and private communication. The improved protocol is obtained by analyzing the properties of a "communication and authentication graph" that characterizes reliable communication.