On Self-stabilizing Synchronous Actions Despite Byzantine Attacks

Abstract

Consider a distributed network of n nodes that is connected to a global source of “beats”. All nodes receive the “beats” simultaneously, and operate in lock-step. A scheme that produces a “pulse” every Cycle beats is shown. That is, the nodes agree on “special beats”, which are spaced Cycle beats apart. Given such a scheme, a clock synchronization algorithm is built. The “pulsing” scheme is self-stabilized despite any transient faults and the continuous presence of up to $f < \frac{n}{3}$ Byzantin nodes. Therefore, the clock synchronization built on top of the “pulse” is highly fault tolerant. In addition, a highly fault tolerant general stabilizer algorithm is constructed on top of the “pulse” mechanism. Previous clock synchronization solutions, operating in the exact same model as this one, either support $f < \frac{n}{4}$ and converge in linear time, or support $f < \frac{n}{3}$ and have exponential convergence time that also depends on the value of max-clock (the clock wrap around value). The proposed scheme combines the best of both worlds: it converges in linear time that is independent of max-clock and is tolerant to up to $f < \frac {n}{3}$ Byzantin nodes. Moreover, considering problems in a self-stabilizing, Byzantin tolerant environment that require nodes to know the global state (clock synchronization, token circulation, agreement, etc.), the work presented here is the first protocol to operate in a network that is not fully connected.