Danny Dolev. The byzantine generals strike again. Journal of Algorithms, 3(1):14--30, Mar 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....broadcast communications. Most of their results are related to the interplay of network connectivity and secure communications. Their results also show that in a communication network, if we use broadcast channels, then we may achieve better results for reliability and privacy. For example, Dolev [4] and Dolev et al. 5] showed that, in the case of k Byzantine faults, reliable communication is achievable only if the systems s network is 2k 1 connected. Hadzilacos [15] has shown that even in the absence of malicious failures connectivity k 1 is required to achieve reliable communication in ....

D. Dolev. The Byzantine generals strike again. J. of Algorithms, 3:14--30, 1982.

....the size of the network graph by providing protocols that achieve private and reliable communication without the need for the parties to start with secret keys. The interplay of network connectivity and secure communication has been studied extensively (see, e.g. 1 4, 10] For example, Dolev [3] and Dolev et al. 4] showed that, in the case of k Byzantine faults, reliable communication is achievable only if the system s network is 2k 1 connected. They also showed that if all the paths are one way, then 3k 1 connectivity is necessary and su#cient for reliable and private ....

D. Dolev. The Byzantine generals strike again. J. of Algorithms, 3:14--30, 1982.

....Networks Amos Beimel Ben Gurion University, Beer Sheva 84105, Israel. beimel cs.bgu.ac.il Lior Malka Ben Gurion University, Beer Sheva 84105, Israel. liorma cs.bgu.ac.il ABSTRACT Reliable communication between parties in a network is a basic requirement for executing any protocol. Dolev [4] and Dolev et al. 5] showed that reliable communication is possible if and only if the communication network is sufficiently connected. Beimel and Franklin [1] showed that the connectivity requirement can be relaxed if some pairs of parties share authentication keys. That is, costly communication ....

....of a communication and authentication graph that characterizes reliable communication. 1. INTRODUCTION Suppose that some processors are connected by a network of reliable channels. All of the processors cooperate to execute some protocol, but some of them are maliciously faulty. Dolev [4] and Dolev et al. 5] proved that if there are t faulty processors, then every pair of processors can communicate reliably if and only if the network is (2t 1) connected. Beimel and Franklin [1] showed that the connectivity requirement can be relaxed if some pairs of parties share authentication ....

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D. Dolev. The Byzantine generals strike again. J. of Algorithms, 3:14--30, 1982.

....for establishing a pairwise key based on the desired level of security. Threshold Secret Sharing Since it was first proposed by Shamir [24] there has been a great deal of research on threshold secret sharing. Using threshold secret sharing, Franklin and Wright [9] Desmedt and Wang [6] and Dolev [5] have studied the interplay of network connectivity and secure and reliable communications. For example, Doleve [5] has shown that in the case of k Byzantine faults (one in each disjoint path) between two nodes in a network, reliable and private communication is achievable only if there are 2k 1 ....

....proposed by Shamir [24] there has been a great deal of research on threshold secret sharing. Using threshold secret sharing, Franklin and Wright [9] Desmedt and Wang [6] and Dolev [5] have studied the interplay of network connectivity and secure and reliable communications. For example, Doleve [5] has shown that in the case of k Byzantine faults (one in each disjoint path) between two nodes in a network, reliable and private communication is achievable only if there are 2k 1 disjoint two way paths between the two nodes. In another related work, Gong [11] proposed an approach in which ....

D. Dolev. The Byzantine generals strike again. In J. of Algorithms, 3:14-30, 1982.

....while in CA only links fail by destroying messages; also, in BA, there is a bound on the number of failures, while in CA, all links can be faulty. There does not appear to be any way to reduce CA to BA or vice versa. Later variants of the consensus problem considered network connectivity (e.g. [5, 9]) link failures and sendomission failures (e.g. 18] in which some of the messages sent by a process can be lost. Clearly consensus with an arbitrary number of send omission faults would be identical to CA; as far as we know, the work on send omission faults also assumes a bound on the number of ....

D. Dolev, The Byzantine generals strike again. J. Algor. 3, 14#30 (1982).

....on. Perhaps there are other impossibility proofs con taining explicit constructions of bad executions that could be made more understandable by describing the bad executions implicitly, by a simple way of gener ating them. A related impossibility result for low connectivity networks appears in [39]; it says that at least 2t 1 network connectivity is required to tolerate t faults. The proof is essentially another scenario argument similar to the one above (using a different scenario a) Lamport also proved another impossibility result for 3 processes and i fault, this time for a weaker ....

D. Dolev. 'The Byzantine generals strike again. Journal of Algorithms, 3:14-30, 1982.

....our main lower bound result. Section 7 contains an im portant open question. The reader is urged to read [4. and [5] for discussion of the practical importance of assuring interactive consistency, and [7] for additional re sults not immediately relevant to this paper. Other related papers are [2] and [3] 2. Motivation for the definitions A general model for solving the interactive consistency problem might consist of n processors (automata) communicating by means of n 2 one way communication channels . Each channel can be formalized as a shared variable which can be mod ified by ....

D. Dolev, The Byzantine generals strike again, J. Algo- rithms 3 (1982).

....known, with proofs of this same general form. Our proofs differ from the earlier proofs in the technique we use to construct the set of behaviors. Our technique is simpler, and applies to more general models of distributed computation. For Byzantine agreement, both bounds were already known [12, 5]. The 3m l node lower bound in [12] was proved only for a particular synchronous model of computation. Although carefully done, the proof is somewhat complicated and not as intuitive as one might like. In contrast, our proof is simple and transparent, and applies to general models of computation. ....

....model of computation. Although carefully done, the proof is somewhat complicated and not as intuitive as one might like. In contrast, our proof is simple and transparent, and applies to general models of computation. A proof of the 2 m 1 connectivity lower bound was presented informally in [5]; we prove that bound more formally and for more general models. For weak Byzantine agreement, the requirement of 3m 1 nodes was known [9] but was proved using a complicated construction. The new proof is easy and extends to more general models (although not as general as those for Byzantine ....

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Dolev D (1982) The byzantine generals strike again. J Algorithms 3:14-30

....lower bound result. Section 7 contains an important open question. The reader is urged to read [LSP] and [L] for discussion of the practical importance of assuring interactive consistency, and [IdSL] for additional results not immediately relevant to this paper. Other related papers are [DW] and [D]. 2. Motivation for the Definitions A general model for solving the interactive consistency problem might consist of n processors (automata) communicating by means of n 2 one way communication channels . Each channel can be formalized as a shared variable which can be modified by exactly one ....

Dolev, D. The Byzantine Generals Strike Again. To appear.

....much connectivity is needed for the Byzantine Generals Problem to be solvable. IC2 requires that a loyal lieutenant obey a loyal commander. This is clearly impossible if the commander cannot communicate with the lieutenant. In particular, if every message from the 3 A recent algorithm of Dolev [2] requires less connectivity. ACM Transactions on Programming Languages and Systems, Vol. 4, No. 3, July 1982. commander to the lieutenant must be relayed by traitors, then there is no way to guarantee that the lieutenant gets the commander s order. Similarly, IC1 cannot be guaranteed if there ....

DOLEV, D. The Byzantine generals strike again. J. Algorithms 3, I (Jan. 1982).

....don t reduce precision because the estimator maps these to a potentially correct value. 6 Agreements to accomplish this because of the number of rounds required. Instead, every processor uses a cheaper Crusaders Agreement to disseminate its value to other processors. A Crusaders Agreement [D82] allows a designated processor, called the transmitter, to disseminate a value in such a way that: CRU1: All correct processors that do not know that the transmitter is faulty agree on the same value. CRU2: If the transmitter is correct then all correct processors agree on its value. Thus, ....

....is faulty, and those that are correct and have agreed among themselves on a value from among those the transmitter sent. Crusaders Agreement is simple and inexpensive to implement in a network where N 3m 1 and our reliable communications assumption holds. A 2 round protocol is given in [D82]: 1) The transmitter sends its value to all other processors. 2) Each processor sends the value it has received from the transmitter to all processors (including itself) 3) Each processor sifts through the values it received in step (2) to identify a set of at most m suspicious processors ....

Dolev, D. The byzantine generals strike again. J. of Algorithms 3, 14-30 (1982).

....if they are within l p (proc ) l q (proc ) where p first converted c x to a triple and q reconstructs c x . Values are therefore approximately equal if they are within 2L. Recall, L is the maximum value of l a (b ) for any processors a and b . 5.1. Crusader s Agreement Crusader s Agreement [Dolev 82] allows a designated processor, called the transmitter, to disseminate a value in such a way that: CRU1: All correct processors that do not know that the transmitter is faulty agree on the same value. CRU2: If the transmitter is correct, then all correct processors agree on its value. Thus, ....

Dolev, D. The Byzantine Generals strike again. Journal of Algorithms 3 (1982), 14-30.

....satisfy RTS1. Second, use of an agreement protocol to disseminate each processor s clock can ensure that arguments in corresponding positions in evaluations of CF performed by different processors are equal, thereby enhancing the precision of CF and helping to satisfy RTS2. Crusader s Agreement [Dolev 82] allows a designated processor, called the transmitter, to disseminate a value in such a way that: CRUI: All correct processors that do not know that the transmitter is faulty agree on the same value. CRU2: If the transmitter is correct then all correct processors agree on its value. Thus, ....

Dolev, D. TI.e Byzantine Generals strike again. Journal ofAlgorithrr 3 (1982), 14-30.

....of a fail stop processor approximation. This serves two purposes: First, it gives a feel for the cost and complexity of implementing fail stop processors. Comparison of protocols that assume fail stop processors with protocols that make weaker assumptions (e.g. Byzantine Agreement protocols [1, 8, 10, 11]) is then possible. Secondly, our fail stop processor approximation is a first step toward a practical realization of fail stop processors. We must be content with only an approximation of a fail stop processor because it is impossible to implement a completely fault tolerant computing system ....

....T on its clock, then, since all processes in p(FSP) are running the same program, the same request is made by each other nonfaulty p process at time T on its local clock. A number of protocols for establishing IC1 and IC2 called interactive consistency or Byzantine Agreement have been developed [1, 8, 10, 11]. In these protocols, is based on message delivery time and on maximum difference in the clock speeds of any two correctly functioning processors running s processes. At least f 1 processors are required to handle up to f faults when messages can be authenticated [2] Since our implementation ....

DOLEV, D. The Byzantine Generals strike again. J. Algorithms 3, (1982), 14-30.

....on its clock then since all processes in p (FSP ) are running the same program, the same request is made by each other non faulty p process at time T on its local clock. A number of protocols to establish IC1 and IC2 called interactive consistency or Byzantine Agreement have been developed [Dolev 82] Lamport et al. 82] Lynch et al. 82] Pease et al. 79] In those protocols, d is based on message delivery time and maximum difference in the clock speeds of any two correctly functioning processors running s processes. At least f 1 processors are required to handle up to f faults when ....

Dolev, D. The Byzantine Generals Strike Again. Journal of Algorithms 3, 14-30 (1982).

....and Yung [5] were able to reduce the size of the network graph by providing protocols that achieve private and reliable communication without the need for the parties to start with secret keys. The interplay of network connectivity and secure communication has been studied extensively (see, e.g. [1, 2, 4, 5, 11]) For example, Dolev [4] and Dolev et al. 5] showed that, in the case of k Byzantine faults, reliable communication is achievable only if the system s network is 2k 1 connected. They also showed that if all the paths are one way, then 3k 1 connectivity is necessary and sucient for reliable ....

....size of the network graph by providing protocols that achieve private and reliable communication without the need for the parties to start with secret keys. The interplay of network connectivity and secure communication has been studied extensively (see, e.g. 1, 2, 4, 5, 11] For example, Dolev [4] and Dolev et al. 5] showed that, in the case of k Byzantine faults, reliable communication is achievable only if the system s network is 2k 1 connected. They also showed that if all the paths are one way, then 3k 1 connectivity is necessary and sucient for reliable and private ....

D. Dolev. The Byzantine generals strike again. J. of Algorithms, 3:14-30, 1982.

....cited above solve the consensus problem taking m 1 rounds and sending a number of message bits that is exponential in m. Unauthenticated protocols using more than m 1 rounds of information exchange but using only polynomially (in n and m) many message bits have subsequently been presented [Dolev et al. 1982]. Protocols taking only m 1 rounds and using polynomially (in n and m) many messages have also been presented for authenticated byzantine failures [Dolev Strong 1983] and for crash failures [Tzeng Siu 1995] particularly, in [Tzeng Siu 1995] a message optimal protocol is presented ....

....sufficient conditions to solve the consensus problem in more general networks. A graph representing a network is k connected if, for every pair of vertices (processes) v and w, there are k paths between v and w such that no vertex (except v and w) appears on more than one path. It has been shown [Dolev 1982] that the consensus problem in a synchronous system with reliable links and arbitrary process failures is solvable if and only if m l(n 1) 3J and m l(k 1) 2J, where k represents the connectivity of the network, that is, agreement is achievable if and only if the number of faulty processes in ....

D. Dolev, "The Byzantine Generals Strike Again", Journal of Algorithms, 3 (1), pp.14-30, March 1982.

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Danny Dolev. The byzantine generals strike again. Journal of Algorithms, 3(1):14--30, Mar 1982.

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DOLEV, D. The byzantine generals strike again. In Journal of Algorithms (1982), pp. 14--30. 11

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Danny Dolev. The Byzantine generals strike again. Journal of Algorithms, 3:14--30, 1982.

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D. Dolev, "The Byzantine generals strike again," Journal of Algorithms,Vol.3, 1982, pp. 14-30.

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Danny Dolev. The Byzantine generals strike again. Journal of Algorithms, 3(1):14--30, March 1982.

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D. Dolev. The Byzantine generals strike again. J. Algorithms, 3(1):14--30, Mar. 1982.

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Danny Dolev. The Byzantine generals strike again. J. Algorithms, 3(1), pages 14--30, March 1982.

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Danny Dolev. The Byzantine gener- als strike again. Journal of Algorithms, 3(1):14-30, March 1982.

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