I have long felt that, because it was posed as a cute problem about philosophers seated around a table, Dijkstra’s dining philosopher’s problem received much more attention than it deserves. (For example, it has probably received more attention in the theory community than the readers/writers problem, which illustrates the same principles and has much more practical importance.) I believed that the problem introduced in [41] was very important and deserved the attention of computer scientists. The popularity of the dining philosophers problem taught me that the best way to attract attention to a problem is to present it in terms of a story. There is a problem in distributed computing that is sometimes called the Chinese Generals Problem, in which two generals have to come to a common agreement on whether to attack or retreat, but can communicate only by sending messengers who might never arrive. I stole the idea of the generals and posed the problem in terms of a group of generals, some of whom may be traitors, who have to reach a common decision. I wanted to assign the generals a nationality that would not offend any readers. At the time, Albania was a completely closed society, and I felt it unlikely that there would be any Albanians around to object, so the original title of this paper was The Albanian Generals Problem. Jack Goldberg was smart enough to realize that there were Albanians in the world outside Albania, and Albania might not always be a black hole, so he suggested that I find another name. The obviously more appropriate Byzantine generals then occurred to me. The main reason for writing this paper was to assign the new name to the problem. But a new paper needed new results as well. I came up with a simpler way to describe the general 3n+1-processor algorithm. (Shostak’s 4-processor algorithm was subtle but easy to understand; Pease’s generalization was a remarkable tour de force.) We also added a generalization to networks that were not completely connected. (I don’t remember whose work that was.) I also added some discussion of practical implementation details.

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The Byzantine Generals Problem

Recently the use of public key encryption to provide secure network communication has received considerable attention. Such public key systems are usually effective against passive eavesdroppers, who merely tap the lines and try to decipher the message. It has been pointed out, however, that an improperly designed protocol could be vulnerable to an active saboteur, one who may impersonate another user or alter the message being transmitted. Several models are formulated in which the security of protocols can be discussed precisely. Algorithms and characterizations that can be used to determine protocol security in these models are given.

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On the security of public key protocols

Reliable computer systems must handle malfunctioning components that give conflicting information to different parts of the system. This situation can be expressed abstractly in terms of a group of generals of the Byzantine army camped with their troops around an enemy city. Communicating only by messenger, the generals must agree upon a common battle plan. However, one or more of them may be traitors who will try to confuse the others. The problem is to find an algorithm to ensure that the loyal generals will reach agreement. It is shown that, using only oral messages, this problem is solvable if and only if more than two-thirds of the generals are loyal; so a single traitor can confound two loyal generals. With unforgeable written messages, the problem is solvable for any number of generals and possible traitors. Applications of the solutions to reliable computer systems are then discussed.

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The Byzantine generals problem

Large-scale peer-to-peer systems face security threats from faulty or hostile remote computing elements. To resist these threats, many such systems employ redundancy. However, if a single faulty entity can present multiple identities, it can control a substantial fraction of the system, thereby undermining this redundancy. One approach to preventing these "Sybil attacks" is to have a trusted agency certify identities. This paper shows that, without a logically centralized authority, Sybil attacks are always possible except under extreme and unrealistic assumptions of resource parity and coordination among entities.

The Sybil Attack

This paper gives the main definitions relating to dependability, a generic concept including a special case of such attributes as reliability, availability, safety, integrity, maintainability, etc. Security brings in concerns for confidentiality, in addition to availability and integrity. Basic definitions are given first. They are then commented upon, and supplemented by additional definitions, which address the threats to dependability and security (faults, errors, failures), their attributes, and the means for their achievement (fault prevention, fault tolerance, fault removal, fault forecasting). The aim is to explicate a set of general concepts, of relevance across a wide range of situations and, therefore, helping communication and cooperation among a number of scientific and technical communities, including ones that are concentrating on particular types of system, of system failures, or of causes of system failures.

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Basic concepts and taxonomy of dependable and secure computing

The problem addressed here concerns a set of isolated processors, some unknown subset of which may be faulty, that communicate only by means of two-party messages. Each nonfaulty processor has a private value of information that must be communicated to each other nonfaulty processor. Nonfaulty processors always communicate honestly, whereas faulty processors may lie. The problem is to devise an algorithm in which processors communicate their own values and relay values received from others that allows each nonfaulty processor to infer a value for each other processor. The value inferred for a nonfaulty processor must be that processor's private value, and the value inferred for a faulty one must be consistent with the corresponding value inferred by each other nonfaulty processor.It is shown that the problem is solvable for, and only for, n ≥ 3m + 1, where m is the number of faulty processors and n is the total number. It is also shown that if faulty processors can refuse to pass on information but cannot falsely relay information, the problem is solvable for arbitrary n ≥ m ≥ 0. This weaker assumption can be approximated in practice using cryptographic methods.

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Reaching Agreement in the Presence of Faults

SIFT (Software Implemented Fault Tolerance) is an ultrareliable computer for critical aircraft control applications that achieves fault tolerance by the replication of tasks among processing units. The main processing units are off-the-shelf minicomputers, with standard microcomputers serving as the interface to the I/O system. Fault isolation is achieved by using a specially designed redundant bus system to interconnect the proeessing units. Error detection and analysis and system reconfiguration are performed by software. Iterative tasks are redundantly executed, and the results of each iteration are voted upon before being used. Thus, any single failure in a processing unit or bus can be tolerated with triplication of tasks, and subsequent failures can be tolerated after reconfiguration. Independent execution by separate processors means that the processors need only be loosely synchronized, and a novel fault-tolerant synchronization method is described. The SIFT software is highly structured and is formally specified using the SRI-developed SPECIAL language. The correctness of SIFT is to be proved using a hierarchy of formal models. A Markov model is used both to analyze the reliability of the system and to serve as the formal requirement for the SIFT design. Axioms are given to characterize the high-level behavior of the system, from which a correctness statement has been proved. An engineering test version of SIFT is currently being built.

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SIFT: Design and analysis of a fault-tolerant computer for aircraft control

A wireless communication system has a central computer, one or more wireless access points and one or more personal badges that communicate wirelessly with the one or more wireless access points. The badges provide the user with a communications device that permits the user to initiate telephone calls and conferences, receive telephone calls, receive pages and be located within a particular environment.

Robert E. Shostak

Papers

The Byzantine Generals Problem

The Byzantine generals problem

Reaching Agreement in the Presence of Faults

SIFT: Design and analysis of a fault-tolerant computer for aircraft control

Voice-controlled wireless communications system and method