D. Malkhi, M. Reiter, A. Wool, and R. Wright. Probabilistic Byzantine Quorum Systems. Proc. PODC 98.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....failures. They present fault tolerant variants of stacks, lists and trees. They give a fault tolerant tree with the property that if r adversarial faults occur, no more than O(r) of the data in the tree is lost. This fault tolerant tree is based on the use of expander graphs. Quorum systems ([8, 13, 14]) are an e#cient, robust way to read and write to a variable which is shared among n servers. Many of these systems are resistant up to some number b n 4 of Byzantine faults. The key idea in such systems is to create subsets of the servers called quorums in such a way that any two quorums ....

....keep only that value which has the most recent time stamp and is returned by at least b 1 servers. For quorum systems that are resistant to #(n) faults the load on the servers can be high. In particular, #(n) servers will be involved in a constant fraction of the queries. Recently Malkhi et al. [14] have introduced a probabilistic quorum system. This new system relaxes the constraint that there must be 2b 1 servers shared between any two quoroms and remains resistant to Byzantine faults only with high probability. The load on servers in the probabilistic system is less than the load in the ....

Dahlia Malkhi, Michael Reiter, Avishai Wool, and Rebecca N. Wright. Probabilistic byzantine quorum systems. In Symposium on Principles of Distributed Computing, 1998.

....failures. They present fault tolerant variants of stacks, lists and trees. They give a fault tolerant tree with the property that if r adversarial faults occur, no more than O(r) of the data in the tree is lost. This fault tolerant tree is based on the use of expander graphs. Quorum systems ([8, 13, 14]) are an ecient, robust way to read and write to a variable which is shared among n servers. Many of these systems are resistant up to some number b n=4 of Byzantine faults. The key idea in such systems is to create subsets of the servers called quorums in such a way that any two quorums contain ....

....only that value which has the most recent time stamp and is returned by at least b 1 servers. For quorum systems that are resistant to (n) faults the load on the servers can be high. In particular, n) servers will be involved in a constant fraction of the queries. Recently Malkhi et al. [14] have introduced a probabilistic quorum system. This new system relaxes the constraint that there must be 2b 1 servers shared between any two quoroms and remains resistant to Byzantine faults only with high probability. The load on servers in the probabilistic system is less than the load in the ....

Dahlia Malkhi, Michael Reiter, Avishai Wool, and Rebecca N. Wright. Probabilistic byzantine quorum systems. In Symposium on Principles of Distributed Computing, 1998.

....case memory failures. They present fault tolerant variants of stacks. lists and trees. They give a fault tolerant tree which has the property that if r adversarial faults occur, no more than O(r) of the data is lost. This fault tolerant tree is based on the use of expander graphs. Quorum systems ([7, 14, 13]) are an ecient, robust way to read and write to a variable which is shared among n servers. Many of these systems are resistant up to some number b n=4 of 4 Figure 1: The butter y network of supernodes. Figure 2: The expander graphs between supernodes. Byzantine faults. The key idea in such ....

....keep only that value which has the most recent time stamp and is returned by at least b 1 servers. For quorum systems that are resistant to (n) faults the load on the servers can be high. In particular, n) servers will be involved in a constant fraction of the queries. Recently Malkhi et al. [13] have introduced a probabilistic quorum system. This new system relaxes the constraint that there must be 2b 1 servers shared between any two quoroms and remains resistant to Byzantine faults only with high probability. The load on servers in the probabilistic system is less than the load in the ....

Dahlia Malkhi, Michael Reiter, Avishai Wool, and Rebecca N. Wright. Probabilistic byzantine quorum systems. In Symposium on Principles of Distributed Computing, 1998.

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D. Malkhi, M. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Technical Report 98.7, AT&T Research, 1998.

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D. Malkhi, M. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Technical Report 98.7, AT&T Research, 1998.

....we address the problem of detecting the presence (and to an extent, the identity) of servers that respond to queries with incorrect data. Our techniques are speci cally designed for asynchronous systems replicated using Byzantine quorum systems [MR98] and probabilistic Byzantine quorum systems [MRWW98], although our general approach may shed light on Byzantine failure detection in other settings. A Byzantine quorum system as de ned in [MR98] is designed to mask any failure scenario (set of faulty servers) contained within a failure assumption B 2 speci ed as a parameter to the quorum ....

....in which each server holds a copy of some replicated variable Z, on which clients can execute write and read operations to change or observe its value, respectively. The protocols for writing and reading Z employ a masking quorum system [MR98, MRW99] or the probabilistic variations thereof [MRWW98]. De nition 3 A masking quorum system for a failure assumption B is a set Q 2 subsets of servers such that 8Q 1 ; Q 2 2 Q, 8B 1 ; B 2 2 B : Q 1 Q 2 ) n B 1 6 B 2 Intuitively, if each read and write is performed at a quorum of servers, then the use of a masking quorum system ensures ....

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D. Malkhi, M. K. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Brief announcement in Proceedings of the 17th ACM Symposium on Principles of Distributed Computing, page 321, June 1998. Full version submitted for publication.

....servers that respond to queries with corrupt or fabricated data. Our techniques are particularly well suited to size based Byzantine quorum systems, including Uniform masking quorum systems and Uniform dissemination quorum systems, as well as the probabilistic threshold masking quorum systems of [MRWW98]. We will use Uniform masking quorum systems, which have been the primary focus of this dissertation, as the basis for our examples. Our approach can also be adapted to other types of quorum systems, however; see Appendix A.2. In addition, the methods we describe may shed light on Byzantine ....

....in use. Here we demonstrate this for a size based quorum construction, where a quorum consists of q servers chosen uniformly at random from a universe of n servers. This template includes the Uniform construction of [MR98] Section 2.2. 1) where q = 2 , the probabilistic construction of [MRWW98], where q = b and 2 n=b, and the dissemination threshold structure, where q = n b 1 2 . For such quorum systems, rather than computing highreject directly using (5.1) it is simpler to compute highreject conservatively to be the maximum value such that f) 5.2) 50 since ....

D. Malkhi, M. K. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Brief announcement in Proceedings of the 17th ACM Symposium on Principles of Distributed Computing, page 321, June 1998. Full version submitted for publication.

....path of data operations. In this way, the system can still efficiently guarantee strict consistency in case a full quorum is accessed, but can additionally provide relaxed consistency guarantees when only local information is used. Another variation on quorum systems, probabilistic quorum systems [MRW97, MRWW98], stands to benefit from properly designed message diffusion in different ways than above. Probabilistic quorum systems are a means for gaining dramatically in performance and resilience over traditional (strict) quorum systems by allowing a marginal, controllable probability of inconsistency for ....

D. Malkhi, M. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Technical Report 98.7, AT&T Research, 1998.

.... substantial body of knowledge on quorum systems and their uses, which was initiated in [6, 16] for a survey of quorum systems work, see [12] More specifically, our methods are designed for Byzantine quorum based replication, which was introduced in [13] and further investigated in various works [3, 15, 14]. Our consideration of Byzantine faults makes our treatment fundamentally different from most prior works on dynamic quorum reconfiguration with benign failures only. In [5, Ch. 8, missing writes protocol] and [7, 10] a quorum system is reconfigured by forming a write quorum in such a way that ....

D. Malkhi, M. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Technical Report 98.7, AT&T Research, 1998.

.... substantial body of knowledge on quorum systems and their uses, which was initiated in [6, 16] for a survey of quorum systems work, see [12] More specifically, our methods are designed for Byzantine quorum based replication, which was introduced in [13] and further investigated in various works [3, 15, 14]. Our consideration of Byzantine faults makes our treatment fundamentally different from most prior works on dynamic quorum reconfiguration with benign failures only. In [5, Ch. 8, missing writes protocol] and [7, 10] a quorum system is reconfigured by informing a write quorum such that ....

D. Malkhi, M. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Technical Report 98.7, AT&T Research, 1998. Available from http://www.research.att.com/library/trs/ TRs/98/98.7/98.7.1.body.ps.gz.

.... substantial body of knowledge on quorum systems and their uses, which was initiated in [6, 16] for a survey of quorum systems work, see [12] More specifically, our methods are designed for Byzantine quorum based replication, which was introduced in [13] and further investigated in various works [3, 15, 14]. Our consideration of Byzantine faults makes our treatment fundamentally different from most prior works on dynamic quorum reconfiguration with benign failures only. In [5, Ch. 8, missing writes protocol ] and [7, 10] a quorum system is reconfigured by forming a write quorum in such a way that ....

D. Malkhi, M. Reiter, A. Wool, and R. N. Wright. Probabilistic Byzantine quorum systems. Technical Report 98.7, AT&T Research, 1998.

....paper [31] is devoted to constructions of masking quorum systems for the special case of a threshold of faulty servers. Bazzi [6] explored a variation of our quorum systems for synchronous systems. Probabilistic constructions for dissemination and masking quorum systems are explored in [32] and [33], respectively. A practical effort for building a large scale survivable data repository using Byzantine quorums is described in [29] and the construction of a survivable consensus object in this context is described in [30] 3 Preliminaries 3.1 System model We assume a universe U of servers, ....

D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic Byzantine Quorum Systems. Brief Announcement in Proceedings of the 17th ACM Symposium on Principles of Distributed Computing (PODC), 1998, to be published. Full version submitted for publication.

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D. Malkhi, M. Reiter, A. Wool, and R. Wright. Probabilistic Byzantine Quorum Systems. Proc. PODC 98.

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