There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper describes a new replication algorithm that is able to tolerate Byzantine faults. We believe that Byzantinefault-tolerant algorithms will be increasingly important in the future because malicious attacks and software errors are increasingly common and can cause faulty nodes to exhibit arbitrary behavior. Whereas previous algorithms assumed a synchronous system or were too slow to be used in practice, the algorithm described in this paper is practical: it works in asynchronous environments like the Internet and incorporates several important optimizations that improve the response time of previous algorithms by more than an order of magnitude. We implemented a Byzantine-fault-tolerant NFS service using our algorithm and measured its performance. The results show that our service is only 3% slower than a standard unreplicated NFS.

/pdf/practical-byzantine-fault-tolerance-58gb0de0hd.pdf

Practical Byzantine fault tolerance

Fabric is a modular and extensible open-source system for deploying and operating permissioned blockchains and one of the Hyperledger projects hosted by the Linux Foundation (www.hyperledger.org). Fabric is the first truly extensible blockchain system for running distributed applications. It supports modular consensus protocols, which allows the system to be tailored to particular use cases and trust models. Fabric is also the first blockchain system that runs distributed applications written in standard, general-purpose programming languages, without systemic dependency on a native cryptocurrency. This stands in sharp contrast to existing block-chain platforms that require "smart-contracts" to be written in domain-specific languages or rely on a cryptocurrency. Fabric realizes the permissioned model using a portable notion of membership, which may be integrated with industry-standard identity management. To support such flexibility, Fabric introduces an entirely novel blockchain design and revamps the way blockchains cope with non-determinism, resource exhaustion, and performance attacks. This paper describes Fabric, its architecture, the rationale behind various design decisions, its most prominent implementation aspects, as well as its distributed application programming model. We further evaluate Fabric by implementing and benchmarking a Bitcoin-inspired digital currency. We show that Fabric achieves end-to-end throughput of more than 3500 transactions per second in certain popular deployment configurations, with sub-second latency, scaling well to over 100 peers.

https://dl.acm.org/doi/pdf/10.1145/3190508.3190538

Hyperledger fabric: a distributed operating system for permissioned blockchains

Our growing reliance on online services accessible on the Internet demands highly available systems that provide correct service without interruptions. Software bugs, operator mistakes, and malicious attacks are a major cause of service interruptions and they can cause arbitrary behavior, that is, Byzantine faults. This article describes a new replication algorithm, BFT, that can be used to build highly available systems that tolerate Byzantine faults. BFT can be used in practice to implement real services: it performs well, it is safe in asynchronous environments such as the Internet, it incorporates mechanisms to defend against Byzantine-faulty clients, and it recovers replicas proactively. The recovery mechanism allows the algorithm to tolerate any number of faults over the lifetime of the system provided fewer than 1/3 of the replicas become faulty within a small window of vulnerability. BFT has been implemented as a generic program library with a simple interface. We used the library to implement the first Byzantine-fault-tolerant NFS file system, BFS. The BFT library and BFS perform well because the library incorporates several important optimizations, the most important of which is the use of symmetric cryptography to authenticate messages. The performance results show that BFS performs 2p faster to 24p slower than production implementations of the NFS protocol that are not replicated. This supports our claim that the BFT library can be used to build practical systems that tolerate Byzantine faults.

/pdf/practical-byzantine-fault-tolerance-and-proactive-recovery-41bx19pxe1.pdf

Practical byzantine fault tolerance and proactive recovery

Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the networks geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -including point process theory, percolation theory, and probabilistic combinatorics-have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.

/pdf/stochastic-geometry-and-random-graphs-for-the-analysis-and-1e671n4af3.pdf

Stochastic geometry and random graphs for the analysis and design of wireless networks

Since the introduction of the concept of failure detectors, several consensus and atomic broadcast algorithms based on these detectors have been published. The performance of these algorithms is often affected by a trade-off between the number of communication steps and the number of messages needed to reach a decision. Some algorithms reach decisions in few communication steps but require more messages to do so. Others save messages at the expense of an additional communication step to diffuse the decision to all processes in the system. This trade-off is heavily influenced by the network latency and the message processing times. Performance evaluations of these algorithms, both in simulated or in real environments, have been published. These evaluations often consider a symmetrical setup : all processes are on the same network and have identical peer-to-peer latencies. In this paper, we evaluate the performance of three consensus and atomic broadcast algorithms using failure detectors in several wide area networks. We specifically focus on the case of a system with three processes, two of which are on a local area network and the third on a distant site and examine how this setting affects the performance of all three algorithms.

Comparing Atomic Broadcast Algorithms in High Latency Networks

/pdf/erratum-early-consensus-in-an-asynchronous-system-with-a-4jl71fz8y7.pdf

Erratum: early consensus in an asynchronous system with a weak failure detector

Transmission faults allow us to reason about permanent and transient value faults in a uniform way. However, all existing solutions to consensus in this model are either in the synchronous system, or require strong conditions for termination, that exclude the case where all messages of a process can be corrupted. In this paper we introduce eventual consistency in order to overcome this limitation. Eventual consistency denotes the existence of rounds in which processes receive the same set of messages. We show how eventually consistent rounds can be simulated from eventually synchronous rounds, and how eventually consistent rounds can be used to solve consensus. Depending on the nature and number of permanent and transient transmission faults, we obtain different conditions on $$n$$
 , the number of processes, in order to solve consensus in our weak model.

/pdf/tolerating-permanent-and-transient-value-faults-3grbkts9iq.pdf

Tolerating permanent and transient value faults

Group communication is nowadays a well established topic in distributed computing. It emerged over the years as a topic with a strong synergy between theory and practice: group communication is highly relevant for building distributed systems, and is also of theoretical importance, because of the difficult problems it addresses. The paper presents an - inevitably subjective - retrospective of the main milestones that led to our current understanding of group communication, with the focus on theoretical contributions of practical relevance. Some open issues are discussed at the end of the paper.

/pdf/practical-impact-of-group-communication-theory-vewmwjis1a.pdf

Practical impact of group communication theory

Comparing the Performance of Two Consensus Algorithms with Centralized and Decentralized Communication Schemes Peter Urban and Andre Schiper Protocols that solve agreement problems are essential building blocks for fault tolerant distributed systems While many protocols have been published, little has been done to analyze their performance, especially the performance of their fault tolerance mechanisms In this paper, we compare two consensus algorithms with different communication schemes: one is centralized and the other decentralized The elements of the simulation study form a generic methodology for evaluating consensus algorithms The results show that the centralized algorithm performs better in some environments, in spite of the fact that the decentralized algorithm finishes in fewer communication steps The reason is that it generates less contention Keywords: simulation tools and techniques, Java-based simulation, distributed consensus, benchmarks

André Schiper

Papers

Comparing Atomic Broadcast Algorithms in High Latency Networks

Erratum: early consensus in an asynchronous system with a weak failure detector

Tolerating permanent and transient value faults

Practical impact of group communication theory

Comparing the Performance of Two Consensus Algorithms with Centralized and Decentralized Communication Schemes