Byzantine vector consensus in complete graphs

Vaidya, Nitin H.; Garg, Vijay K.

doi:10.1145/2484239.2484256

Cited by 53 publications

(91 citation statements)

References 23 publications

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“…Considering Byzantine failures and asynchronous message-passing systems, ǫ-approximate agreement has very recently been generalized to the case where the proposed values are points in an m-dimensional space R m [26,33]. A decided value (point) must then belong to the convex hull of the points proposed by the non-faulty processes (validity), and the Euclidean distance between any pair of values -points -decided by non-faulty processes has to be upper bounded by a predefined constant.…”

Section: B2 Related Workmentioning

confidence: 99%

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Computing in the Presence of Concurrent Solo Executions

Herlihy

Rajsbaum

Raynal

et al. 2014

LATIN 2014: Theoretical Informatics

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In a wait-free model any number of processes may crash. A process runs solo when it computes its local output without receiving any communication from other processes, either because they crashed or they are too slow. While in wait-free shared-memory models at most one process may run solo in an execution, any number of processes may have to run solo in an asynchronous wait-free message-passing model. This paper is on the computability power of models in which several processes may concurrently run solo. It first introduces a family of round-based wait-free models, called the d-solo models, 1 ≤ d ≤ n, where up to d processes may run solo. The paper gives then a characterization of the colorless tasks that can be solved in each d-solo model. These results establish for the first time a hierarchy of wait-free models weaker than the basic read/write model, that are nevertheless still strong enough to solve many tasks. The new failure model, based on taking into account solo executions, has message passing as well as shared-memory instantiations. Key-words:Approximate agreement, Asynchronous system, Communication object, Distributed computability, Message-passing, Read/write shared memory, Solo execution, System partitioning, Task solvability, Topology, Waitfreedom Calcul en présence d'exécutions solo concurrentesRésumé : Dans un modèle wait-free, un nombre quelconque de processus peut s'arrêter de fonctionner de façon inopinée. Un processus s'exécute en solo lorsqu'il calcule sa valeur de sortie sans communiquer avec les autres processus. Dans les modèles wait-free dans lesquels les processus communiquent via une mémoire partagée, au plus un processus peut s'exécuter en solo, alors que dans les modèles wait-free dans lesquels la communication se fait par échange de messages, un nombre quelconque d'entre eux peut avoir à s'exécuter en solo. Cet article étudie la calculabilité dans des modèles intermédiaires, appelés d-solo modèles, modèles dans lesquels jusqu'à d processus s'exécutent en solo. Mots clés :Accord approché, système asynchrone, objet de communication, calculabilité distribuée, système à passage de messages, mémoire partagée, exécution en solo, partitionnement de système, solvabilité d'une tâche, topologie, synchronisation sans attente.

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Section: B2 Related Workmentioning

confidence: 99%

“…Thus, (1, ǫ)-solo approximate agreement problem in R m is essentially the problem that has been recently considered in the context of t Byzantine failures and asynchronous message-passing systems [26,33], where it is shown that it can be solved iff n > t(m + 2).…”

Section: Introductionmentioning

confidence: 99%

Computing in the Presence of Concurrent Solo Executions

Herlihy

Rajsbaum

Raynal

et al. 2014

LATIN 2014: Theoretical Informatics

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“…Due to this correspondence, we use the terms point and vector interchangeably. Recent work [9,12] has addressed Byzantine vector consensus, and presented algorithms with optimal fault tolerance in complete graphs. The correctness conditions for Byzantine vector consensus (elaborated below) cannot be satisfied by independently performing consensus on each element of the input vectors; therefore, new algorithms are necessary [9,12].…”

Section: Introductionmentioning

confidence: 99%

“…The input vector at each process may also be viewed as a point in the d-dimensional Euclidean space R d , where d > 0 is a finite integer. Recent work [9,12] has addressed Byzantine vector consensus, and presented algorithms with optimal fault tolerance in complete graphs. This paper considers Byzantine vector consensus in incomplete graphs using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations.…”

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confidence: 99%

Iterative Byzantine Vector Consensus in Incomplete Graphs

Vaidya

2014

Lecture Notes in Computer Science

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Abstract. This work addresses Byzantine vector consensus, wherein the input at each process is a d-dimensional vector of reals, and each process is required to decide on a decision vector that is in the convex hull of the input vectors at the fault-free processes [9,12]. The input vector at each process may also be viewed as a point in the d-dimensional Euclidean space R d , where d > 0 is a finite integer. Recent work [9,12] has addressed Byzantine vector consensus, and presented algorithms with optimal fault tolerance in complete graphs. This paper considers Byzantine vector consensus in incomplete graphs using a restricted class of iterative algorithms that maintain only a small amount of memory across iterations. For such algorithms, we prove a necessary condition, and a sufficient condition, for the graphs to be able to solve the vector consensus problem iteratively. We present an iterative Byzantine vector consensus algorithm, and prove it correct under the sufficient condition. The necessary condition presented in this paper for vector consensus does not match with the sufficient condition for d > 1; thus, a weaker condition may potentially suffice for Byzantine vector consensus.

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“…A widely studied model of consensus under attack is the byzantine consensus problem [18], [19], [20], in which a number of processors have to agree on a value even if some processors may report a false value to influence the consensus. In our work the processors are the regions, but the attack is fundamentally different; its goal is to impede the convergence of the distributed state estimation, and the mitigation scheme we propose not only provides convergence but it also allows to localize the attack.…”

Section: Related Workmentioning

confidence: 99%

Security of Fully Distributed Power System State Estimation: Detection and Mitigation of Data Integrity Attacks

Vuković

Dán

2014

IEEE J. Select. Areas Commun.

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Abstract-State estimation plays an essential role in the monitoring and supervision of power systems. In today's power systems state estimation is typically done in a centralized or in a hierarchical way, but as power systems will be increasingly interconnected in the future smart grid, distributed state estimation will become an important alternative to centralized and hierarchical solutions. As the future smart grid may rely on distributed state estimation, it is essential to understand the potential vulnerabilities that distributed state estimation may have. In this paper, we show that an attacker that compromises the communication infrastructure of a single control center in an interconnected power system can successfully perform a denial of service attack against state-of-the-art distributed state estimation, and consequently it can blind the system operators of every region. As a solution to mitigate such a denial of service attack, we propose a fully distributed algorithm for attack detection. Furthermore, we propose a fully distributed algorithm that identifies the most likely attack location based on the individual regions' beliefs about the attack location, isolates the identified region, and then reruns the distributed state estimation. We validate the proposed algorithms on the IEEE 118 bus benchmark power system.

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Byzantine vector consensus in complete graphs

Cited by 53 publications

References 23 publications

Computing in the Presence of Concurrent Solo Executions

Computing in the Presence of Concurrent Solo Executions

Iterative Byzantine Vector Consensus in Incomplete Graphs

Security of Fully Distributed Power System State Estimation: Detection and Mitigation of Data Integrity Attacks

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