Fault tolerant consensus protocols usually involve ordered rounds of voting between a collection of processes. In this paper, we derive a general specification of fault tolerant asynchronous consensus protocols and present a class of consensus protocols that refine this specification without using rounds. Crash-tolerant protocols in this class use 3f+1 processes, while Byzantine-tolerant protocols use 5f+1 processes.
This document describes a new consensus algorithm which is asynchronous and uses gossip based message dissemination between nodes. The current version of the algorithm does not cover the case of a node failure or significantly delayed response. This is the subject of further research of the algorithm. An outline of a new design for trust-less payment system is given in appendices.
This report contains two related sets of results with different assumptions on synchrony. The first part is about iterative algorithms in synchronous systems. Following our previous work on synchronous iterative approximate Byzantine consensus (IABC) algorithms, we provide a more intuitive tight necessary and sufficient condition for the existence of such algorithms in synchronous networks1. We believe this condition and the previous results also hold in partially asynchronous algorithmic model. In the second part of the report, we explore the problem in asynchronous networks. While the tradit…
In this work, we study the approximate consensus problem in asynchronous message-passing networks where some nodes may become Byzantine faulty. We answer an open problem raised by Tseng and Vaidya, 2012, proposing the first algorithm of optimal resilience for directed networks. Interestingly, our results show that the tight condition on the underlying communication networks for asynchronous Byzantine approximate consensus coincides with the tight condition for synchronous Byzantine exact consensus. Our results can be viewed as a non-trivial generalization of the algorithm by Abraham et al., 20…
The FLP result shows that crash-tolerant consensus is impossible to solve in asynchronous systems, and several solutions have been proposed for crash-tolerant consensus under alternative (stronger) models. One popular approach is to augment the asynchronous system with appropriate failure detectors, which provide (potentially unreliable) information about process crashes in the system, to circumvent the FLP impossibility. In this paper, we demonstrate the exact mechanism by which (sufficiently powerful) asynchronous failure detectors enable solving crash-tolerant consensus. Our approach, which…
This paper defines a new consensus problem, convex consensus. Similar to vector consensus [13, 20, 19], the input at each process is a d-dimensional vector of reals (or, equivalently, a point in the d-dimensional Euclidean space). However, for convex consensus, the output at each process is a convex polytope contained within the convex hull of the inputs at the fault-free processes. We explore the convex consensus problem under crash faults with incorrect inputs, and present an asynchronous approximate convex consensus algorithm with optimal fault tolerance that reaches consensus on an optimal…
In this work we look at Byzantine consensus in asynchronous systems under the local broadcast model. In the local broadcast model, a message sent by any node is received identically by all of its neighbors in the communication network, preventing a faulty node from transmitting conflicting information to different neighbors. Our recent work has shown that in the synchronous setting, network connectivity requirements for Byzantine consensus are lower under the local broadcast model as compared to the classical point-to-point communication model. Here we show that the same is not true in the asy…
In this paper we propose Aleph, a leaderless, fully asynchronous, Byzantine fault tolerant consensus protocol for ordering messages exchanged among processes. It is based on a distributed construction of a partially ordered set and the algorithm for reaching a consensus on its extension to a total order. To achieve the consensus, the processes perform computations based only on a local copy of the data structure, however, they are bound to end with the same results. Our algorithm uses a dual-threshold coin-tossing scheme as a randomization strategy and establishes the agreement in an expected …
We study two fundamental problems of distributed computing, consensus and approximate agreement, through a novel approach for proving lower bounds and impossibility results, that we call the asynchronous speedup theorem. For a given $n$-process task $Π$ and a given computational model $M$, we define a new task, called the closure of $Π$ with respect to $M$. The asynchronous speedup theorem states that if a task $Π$ is solvable in $t\geq 1$ rounds in $M$, then its closure w.r.t. $M$ is solvable in $t-1$ rounds in $M$. We prove this theorem for iterated models, as long as the model allows solo e…
This paper describes a simple and efficient asynchronous Binary Byzantine faulty tolerant consensus algorithm. In the algorithm, non-faulty nodes perform an initial broadcast followed by a executing a series of rounds each consisting of a single message broadcast plus the computation of a global random coin using threshold signatures. Each message is accompanied by a cryptographic proof of its validity. Up to one third of the nodes can be faulty and termination is expected in a constant number of rounds. An optimization is described allowing the round message plus the coin message to be combin…
Most modern asset transfer systems use consensus to maintain a totally ordered chain of transactions. It was recently shown that consensus is not always necessary for implementing asset transfer. More efficient, asynchronous solutions can be built using reliable broadcast instead of consensus. This approach has been originally used in the closed (permissioned) setting. In this paper, we extend it to the open (permissionless) environment. We present Pastro, a permissionless and asynchronous asset-transfer implementation, in which quorum systems, traditionally used in reliable broadcast, are rep…
The famous Fischer, Lynch, and Paterson impossibility proof shows that it is impossible to solve the consensus problem in a natural model of an asynchronous distributed system if even a single process can fail. Since its publication, two decades of work on fault-tolerant asynchronous consensus algorithms have evaded this impossibility result by using extended models that provide (a) randomization, (b) additional timing assumptions, (c) failure detectors, or (d) stronger synchronization mechanisms than are available in the basic model. Concentrating on the first of these approaches, we illustra…
This work performs an experimental evaluation of four asynchronous binary Byzantine consensus algorithms [11,16,18] in various configurations. In addition to being asynchronous these algorithms run in rounds, tolerate up to one third of faulty nodes, use $O(n^2)$ messages, and use randomized common coins to terminate in an expected constant number of rounds. Each of the four algorithms have different requirements for the random coin, for the number of messages needed per round, whether or not cryptographic signatures are needed, among other details. Two different non-interactive threshold comm…
The problem of multivalued consensus is fundamental in the area of fault-tolerant distributed computing since it abstracts a very broad set of agreement problems in which processes have to uniformly decide on a specific value v in V, where |V| >1. Existing solutions (that tolerate process failures) reduce the multivalued consensus problem to the one of binary consensus, e.g., Mostefaoui-Raynal-Tronel and Zhang-Chen. Our study aims at the design of an even more reliable solution. We do so through the lenses of self-stabilization -- a very strong notion of fault-tolerance. In addition to node an…
This paper presents a new framework, namely \emph{\onlay}, for scalable asynchronous distributed systems. In this framework, we propose a consensus protocol $L_ϕ$, which is based on the Lachesis protocol~\cite{lachesis01}. At the core of $L_ϕ$ protocol, it introduces to use layering algorithm to achieve practical Byzantine fault tolerance (pBFT) in leaderless asynchronous Directed Acyclic Graph (DAG). Further, we present new online layering algorithms for the evolutionary DAGs across the nodes. Our new protocol achieves determistic scalable consensus in asynchronous pBFT by using assigned laye…
We study distributed plurality consensus among $n$ nodes, each of which initially holds one of $k$ opinions. The goal is to eventually agree on the initially dominant opinion. We consider an asynchronous communication model in which each node is equipped with a random clock. Whenever the clock of a node ticks, it may open communication channels to a constant number of other nodes, chosen uniformly at random or from a list of constantly many addresses acquired in previous steps. The tick rates and the delays for establishing communication channels (channel delays) follow some probability distri…
This work describes two randomized, asynchronous, round based, Binary Byzantine faulty tolerant consensus algorithms based on the algorithms of [25] and [26]. Like the algorithms of [25] and [26] they do not use signatures, use $O(n^2)$ messages per round (where each message is composed of a round number and a constant number of bits), tolerate up to one third failures, and have expected termination in constant number of rounds. The first, like [26], uses a weak common coin (i.e. one that can return different values at different processes with a constant probability) to ensure termination. The…
Many blockchain-based protocols, such as Bitcoin, implement a decentralized asset transfer (or exchange) system. As clearly stated in the original paper by Nakamoto, the crux of this problem lies in prohibiting any participant from engaging in double-spending. There seems to be a common belief that consensus is necessary for solving the double-spending problem. Indeed, whether it is for a permissionless or a permissioned environment, the typical solution uses consensus to build a totally ordered ledger of submitted transfers. In this paper we show that this common belief is false: consensus is…
Consider a point-to-point message-passing network. We are interested in the asynchronous crash-tolerant consensus problem in incomplete networks. We study the feasibility and efficiency of approximate consensus under different restrictions on topology knowledge and the relay depth, i.e., the maximum number of hops any message can be relayed. These two constraints are common in large-scale networks, and are used to avoid memory overload and network congestion respectively. Specifically, for different values of integers k, k , we consider that each node knows all its neighbors of at most k-hop d…
We give a protocol for Asynchronous Distributed Key Generation (A-DKG) that is optimally resilient (can withstand $f<\frac{n}{3}$ faulty parties), has a constant expected number of rounds, has $\tilde{O}(n^3)$ expected communication complexity, and assumes only the existence of a PKI. Prior to our work, the best A-DKG protocols required $Ω(n)$ expected number of rounds, and $Ω(n^4)$ expected communication. Our A-DKG protocol relies on several building blocks that are of independent interest. We define and design a Proposal Election (PE) protocol that allows parties to retrospectively agree on …
Consensus protocols for asynchronous networks are usually complex and inefficient, leading practical systems to rely on synchronous protocols. This paper attempts to simplify asynchronous consensus by building atop a novel threshold logical clock abstraction, which enables upper layers to operate as if on a synchronous network. This approach yields an asynchronous consensus protocol for fail-stop nodes that may be simpler and more robust than Paxos and its leader-based variants, requiring no common coins and achieving consensus in a constant expected number of rounds. The same approach can be …
In this paper we present an open source, fully asynchronous, leaderless algorithm for reaching consensus in the presence of Byzantine faults in an asynchronous network. We prove the algorithm's correctness provided that less than a third of participating nodes are faulty. We also present a way of applying the algorithm to a network with dynamic membership, i.e. a network in which nodes can join and leave at will. The core contribution of this paper is an optimal model in the definition of an asynchronous BFT protocol, and which is resilient to 1/3 byzantine nodes. This model matches an agreeme…
Weighted voting is a conventional approach to improving the performance of replicated systems based on commonly-used majority quorum systems in heterogeneous environments. In long-lived systems, a weight reassignment protocol is required to reassign weights over time in order to accommodate performance variations accordingly. The weight reassignment protocol should be consensus-free in asynchronous failure-prone systems because of the impossibility of solving consensus in such systems. This paper presents an efficient consensus-free weight reassignment protocol for atomic storage systems in he…
We consider the problem of filling an unknown area represented by an arbitrary connected graph of $n$ vertices by mobile luminous robots. In this problem, the robots enter the graph one-by-one through a specific vertex, called the Door, and they eventually have to cover all vertices of the graph while avoiding collisions. The robots are anonymous and make decisions driven by the same local rule of behavior. They have limited persistent memory and limited visibility range. We investigate the Filling problem in the asynchronous model. We assume that the robots know an upper bound $Δ$ on the maxi…
Consider a network of n processes each of which has a d-dimensional vector of reals as its input. Each process can communicate directly with all the processes in the system; thus the communication network is a complete graph. All the communication channels are reliable and FIFO (first-in-first-out). The problem of Byzantine vector consensus (BVC) requires agreement on a d-dimensional vector that is in the convex hull of the d-dimensional input vectors at the non-faulty processes. We obtain the following results for Byzantine vector consensus in complete graphs while tolerating up to f Byzantin…
In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate consensus is solvable if and only if the communication graph in each round has a rooted spanning tree, i.e., there is a coordinator at each time. The striking point in this result is that the coordinator is not required to be unique and can change arbitrarily from round to round. Interestingly, the class of averaging algorithms, which are memoryless and require no p…
This paper describes a simple and efficient Binary Byzantine faulty tolerant consensus algorithm using a weak round coordinator and the partial synchrony assumption to ensure liveness. In the algorithm, non-faulty nodes perform an initial broadcast followed by a executing a series of rounds consisting of a single message broadcast until termination. Each message is accompanied by a cryptographic proof of its validity. In odd rounds the binary value 1 can be decided, in even round 0. Up to one third of the nodes can be faulty and termination is ensured within a number of round of a constant fac…
We study the consensus problem in a synchronous distributed system of $n$ nodes under an adaptive adversary that has a slightly outdated view of the system and can block all incoming and outgoing communication of a constant fraction of the nodes in each round. Motivated by a result of Ben-Or and Bar-Joseph (1998), showing that any consensus algorithm that is resilient against a linear number of crash faults requires $\tilde Ω(\sqrt{n})$ rounds in an $n$-node network against an adaptive adversary, we consider a late adaptive adversary, who has full knowledge of the network state at the beginnin…
An urgent demand of deploying BFT consensus over the Internet is raised for implementing blockchain services. The deterministic (partial) synchronous protocols can be simple and fast in good network conditions, but are subject to denial-of-service when synchrony assumption fails. Asynchronous protocols, on the contrary, are robust against the adversarial network, but are substantially more complicated and slower for the inherent use of randomness. Facing the issues, optimistic asynchronous atomic broadcast ( Kursawe-Shoup, 2002; Ramasamy-Cachin, 2005) was proposed to improve the normal-case pe…
Consider an asynchronous system where each node begins with some point in $\mathbb{R}^m$. Given some fixed $ε> 0$, we wish to have every nonfaulty node eventually output a point in $\mathbb{R}^m$, where all outputs are within distance $ε$ of each other, and are within the convex hull of the original nonfaulty inputs. This problem, when some of the nodes are adversarial, is known as the ``Byzantine Asynchronous Multidimensional Approximate Agreement'' problem. Previous landmark work by Mendes et al. and Vaidya et al. presented two solutions to the problem. Both of these solutions require expone…
With the emergence of cross-organization attack-prone byzantine fault-tolerant (BFT) systems, so-called Blockchains, providing asynchronous state machine replication (SMR) solutions is no longer a theoretical concern. This paper introduces ACE: a general framework for the software design of fault-tolerant SMR systems. We first propose a new leader-based-view (LBV) abstraction that encapsulates the core properties provided by each view in a partially synchronous consensus algorithm, designed according to the leader-based view-by-view paradigm (e.g., PBFT and Paxos). Then, we compose several LBV…
This paper introduces a new family of consensus protocols, namely \emph{Lachesis-class} denoted by $\mathcal{L}$, for distributed networks with guaranteed Byzantine fault tolerance. Each Lachesis protocol $L$ in $\mathcal{L}$ has complete asynchrony, is leaderless, has no round robin, no proof-of-work, and has eventual consensus. The core concept of our technology is the \emph{OPERA chain}, generated by the Lachesis protocol. In the most general form, each node in Lachesis has a set of $k$ neighbours of most preference. When receiving transactions a node creates and shares an event block with …
Message-passing models of distributed computing vary along numerous dimensions: degree of synchrony, kind of faults, number of faults... Unfortunately, the sheer number of models and their subtle distinctions hinder our ability to design a general theory of message-passing models. One way out of this conundrum restricts communication to proceed by round. A great variety of message-passing models can then be captured in the Heard-Of model, through predicates on the messages sent in a round and received during or before this round. Then, the issue is to find the most accurate Heard-Of predicate …
This work considers a point-to-point network of n nodes connected by directed links, and proves tight necessary and sufficient conditions on the underlying communication graphs for achieving consensus among these nodes under crash faults. We identify the conditions in both synchronous and asynchronous systems
It is commonly held that asynchronous consensus is much more complex, difficult, and costly than partially-synchronous algorithms, especially without using common coins. This paper challenges that conventional wisdom with que sera consensus QSC, an approach to consensus that cleanly decomposes the agreement problem from that of network asynchrony. QSC uses only private coins and reaches consensus in $O(1)$ expected communication rounds. It relies on "lock-step" synchronous broadcast, but can run atop a threshold logical clock (TLC) algorithm to time and pace partially-reliable communication at…
We consider operation of blockchain-based cryptocurrency in case of partitioning. We define the Partitionable Blockchain Consensus Problem. The problem may have an interesting solution if the partitions proceed independently by splitting accounts. We prove that this problem is not solvable in the asynchronous system. The peers in the two partitions may not agree on the last jointly mined block or, alternatively, on the starting point of independent concurrent computation. We introduce a family of detectors that enable a solution. We establish the relationship between detectors. We present the …
Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the pr…
This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model proposed by Garay '94 -- in the model, an omniscient adversary can corrupt up to $f$ nodes in each round, and at the beginning of each round, faults may "move" in the system (i.e., different sets of nodes may become faulty in different rounds). Recent work by Bonomi et al. '16 proposed a simple iterative approximate consensus algorithm which requires at least …
Consensus is one of the fundamental tasks studied in distributed computing. Processors have input values from some set $V$ and they have to decide the same value from this set. If all processors have the same input value, then they must all decide this value. We study the task of consensus in a Multiple Access Channel (MAC) prone to faults, under a very weak communication model called the $\mathit{beeping\ model}$. Communication proceeds in synchronous rounds. Some processors wake up spontaneously, in possibly different rounds decided by an adversary. In each round, an awake processor can eith…
Modular methods to transform Byzantine consensus protocols into ones that are fast and communication efficient in the common cases are presented. Small and short protocol segments called layers are custom designed to optimize performance in the common case. When composed with a Byzantine consensus protocol of choice, they allow considerable control over the tradeoff in the combined protocol's behavior in the presence of failures and its performance in their absence. When runs are failure free in the common case, the resulting protocols decide in two rounds and require $2nt$ bits of communicati…
Distributed consensus, the ability to reach agreement in the face of failures, is a fundamental primitive for constructing reliable distributed systems. The Paxos algorithm is synonymous with consensus and widely utilized in production. Paxos uses two phases: phase one and phase two, each requiring a quorum of acceptors, to reach consensus during a round of the protocol. Traditionally, Paxos requires that all quorums, regardless of phase or round, intersect and majorities are often used for this purpose. Flexible Paxos proved that it is only necessary for phase one quorum of a given round to i…
Much of the past work on asynchronous approximate Byzantine consensus has assumed scalar inputs at the nodes [3, 7]. Recent work has yielded approximate Byzantine consensus algorithms for the case when the input at each node is a d-dimensional vector, and the nodes must reach consensus on a vector in the convex hull of the input vectors at the fault-free nodes [8, 12]. The d-dimensional vectors can be equivalently viewed as points in the d-dimensional Euclidean space. Thus, the algorithms in [8, 12] require the fault-free nodes to decide on a point in the d-dimensional space. In this paper, we…
We tackle the problem of a set of agents achieving resilient consensus in the presence of attacked agents. We present a discrete-time reputation-based consensus algorithm for synchronous and asynchronous networks by developing a local strategy where, at each time, each agent assigns a reputation (between zero and one) to each neighbor. The reputation is then used to weigh the neighbors' values in the update of its state. Under mild assumptions, we show that: (i) the proposed method converges exponentially to the consensus of the regular agents; (ii) if a regular agent identifies a neighbor as …
Institut de Recherche en Informatique Fondamentale (IRIF) CNRS and Université Paris Cité（基础信息学研究所（IRIF）法国国家科学研究中心与巴黎西岱大学）；Tel Aviv University（特拉维夫大学）；Instituto de Matemáticas, Universidad Nacional Autónoma de México（墨西哥国立自治大学数学研究所）
