A Scalable Byzantine Grid

Modern networks assemble an ever growing number of nodes. However, it remains difficult to increase the number of channels per node, thus the maximal degree of the network may be bounded. This is typically the case in grid topology networks, where each node has at most four neighbors. In this paper, we address the following issue: if each node is likely to fail in an unpredictable manner, how can we preserve some global reliability guarantees when the number of nodes keeps increasing unboundedly ? To be more specific, we consider the problem or reliably broadcasting information on an asynchronous grid in the presence of Byzantine failures -- that is, some nodes may have an arbitrary and potentially malicious behavior. Our requirement is that a constant fraction of correct nodes remain able to achieve reliable communication. Existing solutions can only tolerate a fixed number of Byzantine failures if they adopt a worst-case placement scheme. Besides, if we assume a constant Byzantine ratio (each node has the same probability to be Byzantine), the probability to have a fatal placement approaches 1 when the number of nodes increases, and reliability guarantees collapse. In this paper, we propose the first broadcast protocol that overcomes these difficulties. First, the number of Byzantine failures that can be tolerated (if they adopt the worst-case placement) now increases with the number of nodes. Second, we are able to tolerate a constant Byzantine ratio, however large the grid may be. In other words, the grid becomes scalable. This result has important security applications in ultra-large networks, where each node has a given probability to misbehave.Comment: 17 page

Parameterizable Byzantine Broadcast in Loosely Connected Networks

We consider the problem of reliably broadcasting information in a multihop asynchronous network, despite the presence of Byzantine failures: some nodes are malicious and behave arbitrarly. We focus on non-cryptographic solutions. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the good information), but require a highly connected network. A probabilistic approach was recently proposed for loosely connected networks: the Byzantine failures are randomly distributed, and the correct nodes deliver the good information with high probability. A first solution require the nodes to initially know their position on the network, which may be difficult or impossible in self-organizing or dynamic networks. A second solution relaxed this hypothesis but has much weaker Byzantine tolerance guarantees. In this paper, we propose a parameterizable broadcast protocol that does not require nodes to have any knowledge about the network. We give a deterministic technique to compute a set of nodes that always deliver authentic information, for a given set of Byzantine failures. Then, we use this technique to experimentally evaluate our protocol, and show that it significantely outperforms previous solutions with the same hypotheses. Important disclaimer: these results have NOT yet been published in an international conference or journal. This is just a technical report presenting intermediary and incomplete results. A generalized version of these results may be under submission

Dining philosophers with masking tolerance to crash faults

We examine the tolerance of dining philosopher algorithms subject to process crash faults in arbitrary conflict graphs. This classic problem is unsolvable in asynchronous message-passing systems subject to even a single crash fault. By contrast, dining can be solved in synchronous systems capable of implementing the perfect failure detector P (from the Chandra-Toueg hierarchy). We show that dining is also solvable in weaker timing models using a combination of the trusting detector T and the strong detector S; Our approach extends and composes two currents of previous research. First, we define a parametric generalization of Lynch’s classic algorithm for hierarchical resource allocation. Our construction converts any mutual exclusion algorithm into a valid dining algorithm. Second, we consider the fault-tolerant mutual exclusion algorithm (FTME) of Delporte-Gallet, et al., which uses T and the strong detector S to mask crash faults in any environment. We instantiate our dining construction with FTME, and prove that the resulting dining algorithm guarantees masking tolerance to crash faults. Our contribution (1) defines a new construction for transforming mutual exclusion algorithms into dining algorithms, and (2) demonstrates a better upper-bound on the fault-detection capabilities necessary to mask crash faults in dining philosophers

The Weakest Failure Detector for Solving Wait-Free, Eventually Bounded-Fair Dining Philosophers

This dissertation explores the necessary and sufficient conditions to solve a variant of the dining philosophers problem. This dining variant is defined by three properties: wait-freedom, eventual weak exclusion, and eventual bounded fairness. Wait-freedom guarantees that every correct hungry process eventually enters its critical section, regardless of process crashes. Eventual weak exclusion guarantees that every execution has an infinite suffix during which no two live neighbors execute overlapping critical sections. Eventual bounded fairness guarantees that there exists a fairness bound k such that every execution has an infinite suffix during which no correct hungry process is overtaken more than k times by any neighbor. This dining variant (WF-EBF dining for short) is important for synchronization tasks where eventual safety (i.e., eventual weak exclusion) is sufficient for correctness (e.g., duty-cycle scheduling, self-stabilizing daemons, and contention managers). Unfortunately, it is known that wait-free dining is unsolvable in asynchronous message-passing systems subject to crash faults. To circumvent this impossibility result, it is necessary to assume the existence of bounds on timing properties, such as relative process speeds and message delivery time. As such, it is of interest to characterize the necessary and sufficient timing assumptions to solve WF-EBF dining. We focus on implicit timing assumptions, which can be encapsulated by failure detectors. Failure detectors can be viewed as distributed oracles that can be queried for potentially unreliable information about crash faults. The weakest detector D for WF-EBF dining means that D is both necessary and sufficient. Necessity means that every failure detector that solves WF-EBF dining is at least as strong as D. Sufficiency means that there exists at least one algorithm that solves WF-EBF dining using D. As such, our research goal is to characterize the weakest failure detector to solve WF-EBF dining. We prove that the eventually perfect failure detector 3P is the weakest failure detector for solving WF-EBF dining. 3P eventually suspects crashed processes permanently, but may make mistakes by wrongfully suspecting correct processes finitely many times during any execution. As such, 3P eventually stops suspecting correct processes

Case Studies of Modeling Distributed Algorithms in ABS

This thesis presents four case studies in which well known distributed algorithms are implemented in the abstract behavioral language ABS. These algorithms are the Dining Philosophers problem, the Paxos consensus algorithm, the Kademlia distributed hash table, and the Rarest piece algorithm of the BitTorrent protocol. The implemented models form the basis of an evaluation of the ABS language and its suitability for modeling such algorithms. The different selected algorithms require different strategies for synchronization, and it is shown that the ABS language copes well with this