Optimal Storage under Unsynchrononized Mobile Byzantine Faults

In this paper we prove lower and matching upper bounds for the number of servers required to implement a regular shared register that tolerates unsynchronized Mobile Byzantine failures. We consider the strongest model of Mobile Byzantine failures to date: agents are moved arbitrarily by an omniscient adversary from a server to another in order to deviate their computation in an unforeseen manner. When a server is infected by an Byzantine agent, it behaves arbitrarily until the adversary decides to move the agent to another server. Previous approaches considered asynchronous servers with synchronous mobile Byzantine agents (yielding impossibility results), and synchronous servers with synchronous mobile Byzantine agents (yielding optimal solutions for regular register implementation, even in the case where servers and agents periods are decoupled). We consider the remaining open case of synchronous servers with unsynchronized agents, that can move at their own pace, and change their pace during the execution of the protocol. Most of our findings relate to lower bounds, and characterizing the model parameters that make the problem solvable. It turns out that unsynchronized mobile Byzantine agent movements requires completely new proof arguments, that can be of independent interest when studying other problems in this model. Additionally, we propose a generic server-based algorithm that emulates a regular register in this model, that is tight with respect to the number of mobile Byzantine agents that can be tolerated. Our emulation spans two awareness models: servers with and without self-diagnose mechanisms. In the first case servers are aware that the mobile Byzantine agent has left and hence they can stop running the protocol until they recover a correct state while in the second case, servers are not aware of their faulty state and continue to run the protocol using an incorrect local state

Resilient Consensus Against Mobile Malicious Agents

This paper addresses novel consensus problems in the presence of adversaries that can move within the network and induce faulty behaviors in the attacked agents. By adopting several mobile adversary models from the computer science literature, we develop protocols which can mitigate the influence of such malicious agents. The algorithms follow the class of mean subsequence reduced (MSR) algorithms, under which agents ignore the suspicious values received from neighbors during their state updates. Different from the static adversary models, even after the adversaries move away, the infected agents may remain faulty in their values, whose effects must be taken into account. We develop conditions on the network structures for both the complete and non-complete graph cases, under which the proposed algorithms are guaranteed to attain resilient consensus. Extensive simulations are carried out over random graphs to verify the effectiveness of our approach under uncertainties in the systems