Exact Consensus under Global Asymmetric Byzantine Links

Fault-tolerant distributed consensus is an important primitive in many large-scale distributed systems and applications. The consensus problem has been investigated under various fault models in the literature since the seminal work by Lamport et al. in 1982. In this paper, we study the exact consensus problem in a new faulty link model, namely global asymmetric Byzantine (GAB) link model. Our link-fault model is simple, yet to our surprise, not studied before.In our system, all the nodes are fault-free and each pair of nodes can communicate directly with each other. In the GAB link model, up to f directed links may become Byzantine, and have arbitrary behavior. Non-faulty links deliver messages reliably. In our model, it is possible that the link from node a to node b is faulty, but the link from node b to node a is fault-free. Unlike some prior models with a local constraint, which enforced a local upper bound on the number of failure links attached to each node, we adopt the global constraint, which allows any link to be corrupted in the GAB model. These global and asymmetric features distinguish our model from all prior faulty link models.In our GAB model, we study the consensus problem in both synchronous and asynchronous systems. We show that 2f + 1 nodes is both necessary and sufficient for solving synchronous consensus, whereas 2f+2 nodes is the tight condition on resilience for solving asynchronous consensus. We also study the models where faulty links are mobile (or transient), i.e., the set of faulty links might change from round to round. We show that 2f + 3 nodes is necessary and sufficient for a family of algorithms that update local state in an iterative fashion.