Bounding the Impact of Unbounded Attacks in Stabilization

Abstract

Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. Combining these two properties proved difficult: it is impossible to contain the spatial impact of Byzantine nodes in a self-stabilizing context for global tasks such as tree orientation and tree construction.We present and illustrate a new concept of Byzantine containment in stabilization. Our property, called Strong Stabilization enables to contain the impact of Byzantine nodes if they actually perform too many Byzantine actions. We derive impossibility results for strong stabilization and present strongly stabilizing protocols for tree orientation and tree construction that are optimal with respect to the number of Byzantine nodes that can be tolerated in a self-stabilizing context.

Communicating Reliably in Multihop Dynamic Networks Despite Byzantine Failures

“…This is useful for problems where information from remote nodes is unimportant (such as vertex coloring, link coloring, or dining philosophers). Timelocal algorithms [12], [13], [14], [15], [23] try to limit over time the effect of Byzantine faults. Time-local algorithms presented so far can tolerate the presence of at most a single Byzantine node, and are unable to mask the effect of Byzantine actions.…”

Containing Byzantine Failures with Control Zones

“…A notable class of algorithms tolerates Byzantine failures with either space [17], [22], [25] or time [6], [7], [8], [9], [16] locality. Space local algorithms try to contain the fault as close to its source as possible.…”

Maximum Metric Spanning Tree Made Byzantine Tolerant

“…Strong stabilization To circumvent such impossibility results, [7] defines a weaker notion than the strict stabilization. Here, the requirement to the containment radius is relaxed, i.e.…”

“…As many problems are not local, it turns out that it is impossible to provide strict stabilization for those. To circumvent impossibility results, the weaker notion of strong stabilization was proposed [13,7]: here, correct nodes outside the containment radius may be perturbated by the actions of Byzantine node, but only a finite number of times.…”