Optimal resiliency against mobile faults

We consider a model where malicious agents can corrupt hosts and move around in a network of processors. We consider a family of mobile fault models MF(t/n-1,/spl rho/). In MF(t/n-1,/spl rho/) there are a total of n processors, the maximum number of mobile faults is t, and their roaming pace is /spl rho/ (for example, /spl rho/=3 means that it takes an agent at least 3 rounds to "hop" to the next host). We study in these models the classical testbed problem for fault tolerant distributed computing: Byzantine agreement. It has been shown that if /spl rho/=1, then agreement cannot be reached in the presence of even one fault, unless one of the processors remains uncorrupted for a certain amount of time. Subject to this proviso, we present a protocol for MF(/sup 1///sub 3/,1), which is optimal. The running time of the protocol is O(n) rounds, also optimal for these models.<>