The Impact of Topology on Byzantine Containment in Stabilization

Abstract

Self-stabilization is an 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 system that permits to cope with arbitrary malicious behaviors.We consider the well known problem of constructing a maximum metric tree in this context. Combining these two properties prove difficult: we demonstrate that it is impossible to contain the impact of Byzantine nodes in a self-stabilizing context for maximum metric tree construction (strict stabilization). We propose a weaker containment scheme called topology-aware strict stabilization, and present a protocol for computing maximum metric trees that is optimal for this scheme with respect to impossibility result.

Maximum Metric Spanning Tree Made Byzantine Tolerant

“…Moreover, [5] proves that the algorithm introduced for the maximum metric spanning tree construction in [9] performed this optimal containment area. More formally, [5] proves the following results. …”

“…To circumvent this impossibility result, we describe here another weaker notion than the strict stabilization: the topology-aware strict stabilization (denoted by TA strict stabilization for short) introduced by [5]. Here, the requirement to the containment radius is relaxed, i.e.…”

“…Following discussion of Section 2, it is obvious that there exists no strictly stabilizing protocol for this problem. If we consider the weaker notion of topology-aware strict stabilization, [5] defines the best containment area as:…”

“…If we focus on the protocol provided by [5] (which is (S B , n − 1)-TA strictly stabilizing), we can prove that this protocol does not satisfy our constraints since we have the following result.…”

“…Proof To prove this result, it is sufficient to construct an execution of the protocol of [5] for a given metric M which contains an infinite number of S * B -TA disruptions with two Byzantine processes.…”