Section: New Results

Byzantine Resilience in autonomous networks

Participant : Sébastien Tixeuil.

We studied [22] the problem of Byzantine-robust topology discovery in an arbitrary asynchronous network. We formally stated the weak and strong versions of the problem. The weak version requires that either each node discovers the topology of the network or at least one node detects the presence of a faulty node. The strong version requires that each node discovers the topology regardless of faults. We focused on non-cryptographic solutions to these problems. We explored their bounds. We proved that the weak topology discovery problem is solvable only if the connectivity of the network exceeds the number of faults in the system. Similarly, we showed that the strong version of the problem is solvable only if the network connectivity is more than twice the number of faults. We presented solutions to both versions of the problem. Our solutions match the established graph connectivity bounds. The programs are terminating, they do not require the individual nodes to know either the diameter or the size of the network. The message complexity of both programs is low polynomial with respect to the network size.

Given a set of robots with arbitrary initial location and no agreementon a global coordinate system, convergence requires that allrobots asymptotically approach the exact same, but unknown beforehand,location. Robots are oblivious— they do not recall the pastcomputations — and are allowed to move in a one-dimensionalspace. Additionally, robots cannot communicate directly, instead theyobtain system related information only via visual sensors. We draw in [32] a connection between the convergence problem in robotnetworks, and the distributed approximate agreement problem(that requires correct processes to decide, for some constant , values distance apart and within the range ofinitial proposed values). Surprisingly, even though specifications are similar,the convergence implementation in robot networks requires specific assumptions about synchrony and Byzantine resilience. In more details, we proved necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being Byzantine (i.e. they can exhibit arbitrary behavior). Additionally, we proposed a deterministic convergence algorithm for robot networks and analyze its correctness and complexity in various synchrony settings.The proposed algorithm tolerates f Byzantine robots for (2f + 1) -sized robot networks in fully synchronous networks, (3f + 1) -sized in semi-synchronous networks and (4f + 1) -sized in asynchronous networks. The bounds obtained for the ATOM model are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots. We proposed in [33] the first deterministic algorithm that tolerates up to f byzantine faults in 3f + 1 -sized networks and performs in the asynchronous CORDA model. Our solution matches the previously established lower bound for the semi-synchronous ATOM model on the number of tolerated Byzantine robots. Our algorithm works under bounded scheduling assumptions for oblivious robots moving in a uni-dimensional space. We also studied [31] the convergence problem in fully asynchronous, uni-dimensional robot networks that are prone to Byzantine (i.e. malicious) failures. We proposed a deterministic algorithm that solves the problem in the most generic settings: fully asynchronous robots that operate in the non-atomic CORDA model. Our algorithm provides convergence in 5f + 1 -sized networks where f is the upper bound on the number of Byzantine robots. Additionally, we proved that 5f + 1 is a lower bound whenever robot scheduling is fully asynchronous. This constrasts with previous results in partially synchronous robots networks, where 3f + 1 robots are necessary and sufficient.