The incremental agreement

To achieve reliable distributed systems, the fault-tolerance must be studied. One of the most important problems of fault-tolerance issues lies in the Byzantine Agreement (BA) problem. The primary issue surrounding BA is that fault-free processors must obtain common agreement even in cases where faults persist. In this field, the fault diagnosis protocol has been proposed so that each fault-free processor detects/locates a common set of faulty processors. However, in this study, the incremental agreement is invoked to make each processor able to agreement upon executing the fault diagnosis protocol using minimal rounds of message exchange in the presence of dual failure characteristics of processors.     

Reaching Agreement among Virtual Subnets in Hybrid Failure Mode

Fault-tolerance is an important research topic in the study of distributed systems. To cope with the influence of faulty components, reaching a common agreement in the presence of faults before performing certain tasks is essential. However, the Byzantine Agreement (BA) problem is a fundamental problem in fault-tolerant distributed systems. In previous studies, protocols dealing with the BA problem focused on static networks; however, these do not perform well in dynamically changing mobile networks. The most well known mobile network is the Mobile Ad-hoc Network (MANET). To enhance fault-tolerance and MANET reliability, the BA problem in virtual subnets of MANET is revisited in this paper. The proposed protocol is called the Hybrid Agreement Protocol (HAP). It achieves agreement on a common value among all functional mobile processors in a minimal number of message exchange rounds, and can tolerate a maximal number of allowable faulty components in the virtual subnet of MANET.     

Byzantine Agreement under dual failure mobile network

Networks are trending towards wireless systems that provide support for mobile computing. The Byzantine Agreement (BA) protocols used in static networks do not perform well in a dynamically changing mobile environment. Mobile commerce and related applications are necessary for wireless networks. There are numerous properties in a wireless network that play important roles. For example, the processors in a wireless network have highly mobile capabilities. Processors can immigrate into or move away from the network at any time. Although mobile technology has brought greater convenience, it is comparatively more dangerous. Wireless systems are susceptible to security flaws such as attacks by hackers. The number of allowable faulty components within the system is also decreased. To increase the number of allowable faulty components and ensure network security, a simple, secure and efficient protocol, BAM, is proposed to handle the BA problem. The fault symptoms include malicious and dormant faults. Furthermore, the proposed protocol uses the minimum number of message exchange rounds to make all healthy processors agree on a common value and can tolerate the maximum number of allowable faulty components. The proposed method will also ensure message security and increase the system's fault tolerant capability.     

The anatomy study of consensus agreement in MANETs

Reliability is an important research topic of distributed systems. To achieve fault-tolerance in the distributed systems, healthy processors need to reach a common agreement before performing certain special tasks, even if faults exist in many circumstances. This problem is called as the Byzantine Agreement (BA) problem and it must be addressed. In general, the traditional BA problem is solved in well-defined networks. However, the MANETs (Mobile Ad-hoc Network) are increasing in popularity and its network topology is dynamic in nature. In this paper, the BA problem is re-examined in MANETs. Our protocol uses the minimum number of message exchanges to reach an agreement within the distributed system while tolerating the maximum number of faulty processors in MANETs.     

A new solution for the Byzantine agreement problem

Reliability is an important research topic in distributed computing systems consisting of a large number of processors. To achieve reliability, the fault-tolerance scheme of the distributed computing system must be revised. This kind of problem is known as a Byzantine agreement (BA) problem. It requires all fault-free processors to agree on a common value, even if some components are corrupt. Consequently, there have been significant studies of this agreement problem in distributed systems. However, the traditional BA protocols focus on running ⌊(n−1)/3⌋+1 rounds of message exchange continuously to make each fault-free processor reach an agreement. In other words, since having a large number of messages results in a large protocol overhead, those protocols are inefficient and unreasonable, especially for some network environments which have large number of processors. In this study, we propose a novel and efficient protocol to reduce the number of messages. Our protocol can collect, compare and replace the received values to find the reliable processors and replace the values sent by the unreliable processors. Subsequently, each processor can agree on a common value through three rounds of message exchange. Furthermore, the proposed protocol can use the minimum number of messages to tolerate the maximum number of faulty components in a distributed system.     

Eventual strong consensus with fault detection in the presence of dual failure mode on processors under dynamic networks

The fault tolerance capability and reliability of a distributed system can be enhanced if the Strong Consensus (SC) problem can be properly addressed. Most of the extant SC protocols are designed for static networks. Besides, the number of rounds of message exchange required by all of the extant SC protocols is determined by the total number of processors in the network rather than by the actual number of faulty processors in the network. Even if there is only a few or no faulty processor in the network, the SC protocols may waste a lot of time and memory space on many unnecessary rounds of message exchange. Thus, this paper revisits the SC problem in dynamic networks and uses two rules, Detection Rule for Malicious fault in dynamic network (DRM_dyn) and Early Stopping Rule for Strong Consensus protocol in dynamic networks (ESRSC_dyn), to reduce the time consumption and space complexity of SC protocols. DRM_dyn is a rule that detects malicious processors, and ESRSC_dyn is a rule that determines whether the messages collected are enough for reaching a strong consensus. To be succinct, the proposed SC protocol can not only work in dynamic networks consisting of both dormant processors and malicious processors (dual failure mode) but also ensure that all correct processors reach a SC value within fewer rounds of message exchange than required by the extant SC protocols.     

Byzantine agreement in the presence of mixed faults on processorsand links

In early stage, the Byzantine agreement (BA) problem was studied with single faults on processors in either a fully connected network or a nonfully connected network. Subsequently, the single fault assumption was extended to mixed faults (also referred to as hybrid fault model) on processors. For the case of both processor and link failures, the problem has been examined in a fully connected network with a single faulty type, namely an arbitrary fault. To release the limitations of a fully connected network and a single faulty type, the problem is reconsidered in a general network. The processors and links in such a network can both be subjected to different types of fault simultaneously. The proposed protocol uses the minimum number of message exchanges and can tolerate the maximum number of allowable faulty components to make each fault-free processor reach an agreement     

Visiting Byzantine Agreement underlying Ad Hoc environment

The Mobile Ad Hoc Network (MANET) has become more popular because the MANET is a self-organizing, self-configuring, and an instantly deployable multi-hop wireless network that responds to application needs without any fixed infrastructure. Moreover, the MANET is fault-tolerant and reliable. A mechanism is needed in the MANET that allows a set of nodes to agree on a common value. The distributed Byzantine Agreement (BA) problem is one of the most important issues in designing a fault-tolerant system. In many cases, reaching a common agreement among fault-free nodes in coping with the influence from faulty components is crucial in a fault-tolerant system. When a common agreement is achieved, all fault-free nodes in the system can produce stable results without any influence from the faulty components. In this study, the BA problem is visited in a MANET, in which the components are subject to a malicious fault. The proposed protocol can tolerate the maximum number of allowable faulty nodes using a minimum number of message exchange rounds. Each fault-free node can reach a common agreement value for the BA problem in a MANET. The text was submitted by the authors in English.     

Modular construction of an efficient 1-bit Byzantine agreement protocol

This paper presents a new Byzantine agreement protocol that toleratest processor faults usingO(t·logt) processors,t + 1 rounds,O(t ² +o·t) total message bits (whereo is the number of processors that must decide), and messages of maximum size 1 bit. It is the first Byzantine agreement protocol that is simultaneously optimal in rounds, message bits, and message size. The new Byzantine agreement protocol is actually a protocol for the (slightly) more general Byzantine relay problem—a problem which we formulate in this paper. The Byzantine relay protocol is the result of a general recursive construction. Each step of the construction combines two smaller (in terms of number of faults tolerated) Byzantine relay protocols into one larger Byzantine relay protocol. The base case is a collection of very simple Byzantine relay protocols, each tolerant of a small constant number of processor faults. A key new feature of the protocol construction technique presented in this paper is that it does not add unproductive overhead rounds: given two constituent protocols that are optimal in the number of rounds, the composite protocol that is constructed is also optimal in the number of rounds.The work of Jennifer Welch was supported in part by NSF Grant CCR-9010730 and an IBM Faculty Development Award. This work was done while she was at the University of North Carolina at Chapel Hill.     

Byzantine Agreement in a generalized connected network

Traditionally, the Byzantine Agreement (BA) problem is studied either in a fully connected network or in a broadcast network. A generalized network model for BA is proposed in this paper. A fully-connected network or a broadcast network is a special case of the new network architecture. Under the new generalized network model, the BA problem is reexamined with the assumption of malicious faults on both processors and transmission medium (TM), as opposed to previous studies which consider malicious faults on processors only. The proposed algorithm uses the minimum number of message exchanges, and can tolerate the maximum number of allowable faulty components to make each healthy processor reach a common agreement for the cases of processor failures, TM failures, or processor/TM failures. The results can also be used to solve the interactive consistency problem and the consensus problem     

Grouping Byzantine Agreement

The reliability of the distributed system has always been an important topic of research. Byzantine Agreement (BA) protocol, which allows the fault-free processors to agree on a common value, is one of the most fundamental problems studied in a distributed system. In previous works, the problem was visited in a fully connected network or an unfully connected network with fallible processors. In this paper, the BA problem is reexamined in a group-oriented network, which has the feature of grouping, and the network topology does not have to be fully connected. We also enlarge the fault tolerant capability by allowing dormant faults and malicious faults (also called as the dual failure mode) to exist in a group-oriented network simultaneously. The proposed protocol is more efficient than the traditional BA protocols and can tolerate the maximum number of tolerable faulty processors.     

An optimal solution for byzantine agreement under a hierarchical cluster-oriented mobile ad hoc network

Mobile ad hoc NETworks (MANETs) are becoming more popular due to the advantage that they do not require any fixed infrastructure, and that communication among processors can be established quickly. For this reason, potential MANET applications include military uses, search and rescue and meetings or conferences. Therefore, the fault-tolerance and reliability of the MANET is an important issue, which needs to be considered. The problem of reaching agreement in the distributed system is one of the most important areas of research to design a fault-tolerant system. With an agreement, each correct processor can cope with the influence from other faulty components in the network to provide a reliable solution. In this research, a potential MANET with a dual failure mode is considered. The proposed protocol can use the minimum number of rounds of message exchange to reach a common agreement and can tolerate a maximum number of allowable faulty components to induce all correct processors to reach a common agreement within the MANET.     

The anatomy study of server-initial agreement for general hierarchy wired/wireless networks

The Byzantine Agreement (BA) plays a key role in fault-tolerant distributed system design. A number of solutions to the BA problem based on various network model assumptions have been proposed. However, most existing BA protocols are designed for pure wired or pure wireless networks. In practice, most current networks are combined wired and wireless environments. In this paper, we extend the BA problem over a combined wired/wireless network, consisting of both powerful computing stationary processor and low-power mobile processor. The communication overhead of BA protocol is inherently large and secure group communications are important. The protocols proposed in this paper use the hierarchical model concept to reduce the communication overhead and provide secure group communications well suited for combined wired/wireless networks.     

Optimal agreement protocol in malicious faulty processors andfaulty links

Traditionally, the problems of Byzantine agreement, consensus, and interactive consistency are studied in a fully connected network with processors in malicious failure only. Such problems are reexamined with the assumption of malicious faults on both processors and links. The proposed protocols use the minimum number of message exchanges and can tolerate the maximum number of allowable faulty components to make each fault-free processor reach a common agreement for the cases of processor failure, link failure, or processor and link failure     

A note on consensus on dual failure modes

F.J. Meyer and D.K. Pradhan (1991) proposed the MS (for “mixed-sum”) algorithm to solve the Byzantine Agreement (BA) problem with dual failure modes: arbitrary faults (Byzantine faults) and dormant faults (essentially omission faults and timing faults). Our study indicates that this algorithm uses an inappropriate method to eliminate the effects of dormant faults and that the bound on the number of allowable faulty processors is overestimated. This paper corrects the algorithm and gives a new bound for the allowable faulty processors     

Performance study of Byzantine Agreement Protocol with artificial neural network

Since 1982, numerous Byzantine Agreement Protocols (BAPs) have been developed to solve arbitrary faults in the Byzantine Generals Problem (BGP). A novel BAP, using an artificial neural network (ANN), was proposed by Wang and Kao. It requires message exchange rounds similar to the traditional BAP and its suitability, in the context of network size, has not been investigated. In the present study, we propose to adopt Nguyen-Widrow initialization in ANN training, which modifies message communication and limits the message exchange rounds to three rounds. This modified approach is referred to as BAP-ANN. The BAP-ANN performs better than the traditional BAP, when the network size n is greater than nine. We also evaluate the message exchange matrix (MEM) constructed during the message exchange stage. For a fixed number of faulty nodes and remainder cases of (n mod 3), the study shows that the mean epoch for ANN training decreases as the network size increases, which indicates better fault tolerance.     

A self-adjusting algorithm for byzantine agreement

Summary Byzantine Agreement is important both in the theory and practice of distributed computing. However, protocols to reach Byzantine Agreement are usually expensive both in the time required as well as in the number of messages exchanged. In this paper, we present a self-adjusting approach to the problem. The Mostly Byzantine Agreement is proposed as a more restrictive agreement problem that requires that in the consecutive attempts to reach agreement, the number of disagreements (i.e., failures to reach Byzantine Agreement) is finite. Fort faulty processes, we give an algorithm that has at mostt disagreements for 4t or more processes. Another algorithm is given forn3t+1 processes with the number of disagreements belowt ²/2. Both algorithms useO(n ³) message bits for binary value agreement. Yi Zhao is currently working on his Ph.D. degree in Computer Science at University of Houston. His research interests include fault tolerance, distributed computing, parallel computation and neural networks. He obtained his M.S. from University of Houston in 1988 and B.S. from Beijing University of Aeronautics and Astronautics in 1984, both in computer science. Farokh B. Bastani received the B. Tech. degree in electrical engineering from the Indian Institute of Technology, Bombay, India, and the M.S. and Ph.D. degrees in electrical engineering and computer science from the University of California, Berkeley. He joined the University of Houston in 1980, where he is currently an Associate Professor of Computer Science. His research interests include software design and validation techniques, distributed systems, and fault-tolerant systems. He is a member of the ACM and the IEEE and is on the editorial board of theIEEE Transactions on Software Engineering.     

Optimal asynchronous agreement and leader election algorithm for complete networks with Byzantine faulty links

Summary.  We consider agreement and leader election on asynchronous complete networks when the processors are reliable, but some of the channels are subject to failure. Fischer, Lynch, and Paterson have already shown that no deterministic algorithm can solve the agreement problem on asynchronous networks if any processor fails during the execution of the algorithm. Therefore, we consider only channel failures. The type of channel failure we consider in this paper is Byzantine failure, that is, channels fail by altering messages, sending false information, forging messages, losing messages at will, and so on. There are no restrictions on the behavior of a faulty channel. Therefore, a faulty channel may act as an adversary who forges messages on purpose to prevent the successful completion of the algorithm. Because we assume an asynchronous network, the channel delays are arbitrary. Thus, the faulty channels may not be detectable unless, for example, the faulty channels cause garbage to be sent. We present the first known agreement and leader election algorithm for asynchronous complete networks in which the processors are reliable but some channels may be Byzantine faulty. The algorithm can tolerate up to [n−22] faulty channels, where n is the number of processors in the network. We show that the bound on the number of faulty channels is optimal. When the processors terminate their corresponding algorithms, all the processors in the network will have the same correct vector, where the vector contains the private values of all the processors. Received: May 1994/Accepted: July 1995     

The optimal generalized Byzantine Agreement in Cluster-based Wireless Sensor Networks

A Wireless Sensor Network (WSN) is a wireless network consisting of spatially distributed autonomous devices using sensor nodes in a wide range of applications in various domains. In the future, WSNs are expected to be integrated into the “Internet of Things” (IoT), where sensor nodes join the Internet dynamically, and use them to collaborate and accomplish their tasks. Because of the communications of WSN will produce a broadcast storm, the Cluster-based Wireless Sensor Network (CWSN) was proposed to ameliorate the broadcast storm. However, the capability of the fault-tolerance and reliability of CWSNs must be carefully investigated and analyzed. To cope with the influence of faulty components, reaching a common agreement in the presence of faults before performing certain tasks is essential. Byzantine Agreement (BA) problem is a fundamental problem in fault-tolerant distributed systems. To enhance fault-tolerance and reliability of CWSN, the BA problem in CWSN is revisited in this paper. In this paper, a new BA protocol is proposed that adapts to the CWSN and derives its limit of allowable faulty components, while maintaining the minimum number of message exchanges.     

Connectivity requirements for Byzantine agreement under restricted types of failures

We investigate the problem of reaching Byzantine Agreement in arbitrary networks where both processors and communication links are subject to omission or stopping faults. For the case of deterministic, synchronous algorithms we give a necessary and sufficient condition relating the solvability of the problem to the connectivity of the network. In particular, we show that an algorithm resilient to at mostt faulty processors andk faulty links subject to omission or stopping faults exist, if and only if the network has a connectivity pair (t, k)>(t, k).Vassos Hadzilacos received his BSE from Princeton in 1980 and his PhD from Harvard in 1984, both in Computer Science. He is presently an Assistant Professor at University of Toronto. His research interests are synchronisation and reliability in distributed computing. He is a co-author of a book on Concurrency Control and Reliability in Database Systems.