Abstract Many blockchain-based algorithms, such as Bitcoin, implement a decentralized asset transfer system, often referred to as a cryptocurrency. As stated in the original paper by Nakamoto, at the heart of these systems lies the problem of preventing double-spending; this is usually solved by achieving consensus on the order of transfers among the participants. In this paper, we treat the asset transfer problem as a concurrent object and determine its consensus number, showing that consensus is, in fact, not necessary to prevent double-spending. We first consider the problem as defined by Nakamoto, where only a single process—the account owner—can withdraw from each account. Safety and liveness need to be ensured for correct account owners, whereas misbehaving account owners might be unable to perform transfers. We show that the consensus number of an asset transfer object is 1. We then consider a more general k-shared asset transfer object where up to k processes can atomically withdraw from the same account, and show that this object has consensus number k. We establish our results in the context of shared memory with benign faults, allowing us to properly understand the level of difficulty of the asset transfer problem. We also translate these results in the message passing setting with Byzantine players, a model that is more relevant in practice. In this model, we describe an asynchronous Byzantine fault-tolerant asset transfer implementation that is both simpler and more efficient than state-of-the-art consensus-based solutions. Our results are applicable to both the permissioned (private) and permissionless (public) setting, as normally their differentiation is hidden by the abstractions on top of which our algorithms are based.

We address the problem of online payments, where users can transfer funds among themselves. We introduce Astro, a system solving this problem efficiently in a decentralized, deterministic, and completely asynchronous manner. Astro builds on the insight that consensus is unnecessary to prevent double-spending. Instead of consensus, Astro relies on a weaker primitive---Byzantine reliable broadcast---enabling a simpler and more efficient implementation than consensus-based payment systems. In terms of efficiency, Astro executes a payment by merely broadcasting a message. The distinguishing feature of Astro is that it can maintain performance robustly, i.e., remain unaffected by a fraction of replicas being compromised or slowed down by an adversary. Our experiments on a public cloud network show that Astro can achieve near-linear scalability in a sharded setup, going from 10K payments/sec (2 shards) to 20K payments/sec (4 shards). In a nutshell, Astro can match VISA-level average payment throughput, and achieves a 5× improvement over a state-of-the-art consensus-based solution, while exhibiting sub-second 95^th percentile latency.

Reliable broadcast is a communication primitive guaranteeing, intuitively, that all processes in a distributed system deliver the same set of messages. The reason why this primitive is appealing is twofold: (i) we can implement it deterministically in a completely asynchronous environment, unlike stronger primitives like consensus and total-order broadcast, and yet (ii) reliable broadcast is powerful enough to implement important applications like payment systems. The problem we tackle in this paper is that of dynamic reliable broadcast, i.e., enabling processes to join or leave the system. This property is desirable for long-lived applications (aiming to be highly available), yet has been precluded in previous asynchronous reliable broadcast protocols. We study this property in a general adversarial (i.e., Byzantine) environment. We introduce the first specification of a dynamic Byzantine reliable broadcast (DBRB) primitive that is amenable to an asynchronous implementation. We then present an algorithm implementing this specification in an asynchronous network. Our DBRB algorithm ensures that if any correct process in the system broadcasts a message, then every correct process delivers that message unless it leaves the system. Moreover, if a correct process delivers a message, then every correct process that has not expressed its will to leave the system delivers that message. We assume that more than $2/3$ of processes in the system are correct at all times, which is tight in our context. We also show that if only one process in the system can fail---and it can fail only by crashing---then it is impossible to implement a stronger primitive, ensuring that if any correct process in the system broadcasts or delivers a message, then every correct process in the system delivers that message---including those that leave.

SBFT is a state of the art Byzantine fault tolerant state machine replication system that addresses the challenges of scalability, decentralization and global geo-replication. SBFT is optimized for decentralization and is experimentally evaluated on a deployment of more than 200 active replicas withstanding a malicious adversary controlling f=64 replicas. Our experiments show how the different algorithmic ingredients of SBFT contribute to its performance and scalability. The results show that SBFT simultaneously provides almost 2x better throughput and about 1.5x better latency relative to a highly optimized system that implements the PBFT protocol. To achieve this performance improvement, SBFT uses a combination of four ingredients: using collectors and threshold signatures to reduce communication to linear, using an optimistic fast path, reducing client communication and utilizing redundant servers for the fast path. SBFT is the first system to implement a correct dual-mode view change protocol that allows to efficiently run either an optimistic fast path or a fallback slow path without incurring a view change to switch between modes.

Many blockchain-based algorithms, such as Bitcoin, implement a decentralized asset transfer system, often referred to as a cryptocurrency. As stated in the original paper by Nakamoto, at the heart of these systems lies the problem of preventing double-spending ; this is usually solved by achieving consensus on the order of transfers among the participants. By treating the asset transfer problem as a concurrent object and determining its consensus number, we show that consensus is not necessary to prevent double-spending. We first consider the problem as defined by Nakamoto, where only a single process---the account owner---can withdraw from each account. Safety and liveness need to be ensured for correct account owners, whereas misbehaving account owners might be unable to perform transfers. We show that the consensus number of an asset transfer object is 1. We then consider a more general k-shared asset transfer object where up to k processes can atomically withdraw from the same account, and show that this object has consensus number k. We first establish these these results in the context of shared memory with benign faults, in order to properly understand the level of difficulty of the asset transfer problem. Then, we translate our result in the more practically relevant message passing setting with Byzantine players. We describe an asynchronous Byzantine fault-tolerant asset transfer implementation that is both simpler and more efficient than state-of-the-art consensus-based solutions. Our results are applicable to both the permissioned (private) and permissionless (public) setting, as normally their differentiation is hidden by the abstractions on top of which our algorithms are based.

Byzantine reliable broadcast is a powerful primitive that allows a set of processes to agree on a message from a designated sender, even if some processes (including the sender) are Byzantine. Existing broadcast protocols for this setting scale poorly, as they typically build on quorum systems with strong intersection guarantees, which results in linear per-process communication and computation complexity. We generalize the Byzantine reliable broadcast abstraction to the probabilistic setting, allowing each of its properties to be violated with a fixed, arbitrarily small probability. We leverage these relaxed guarantees in a protocol where we replace quorums with stochastic samples. Compared to quorums, samples are significantly smaller in size, leading to a more scalable design. We obtain the first Byzantine reliable broadcast protocol with logarithmic per-process communication and computation complexity. We conduct a complete and thorough analysis of our protocol, deriving bounds on the probability of each of its properties being compromised. During our analysis, we introduce a novel general technique that we call adversary decorators. Adversary decorators allow us to make claims about the optimal strategy of the Byzantine adversary without imposing any additional assumptions. We also introduce Threshold Contagion, a model of message propagation through a system with Byzantine processes. To the best of our knowledge, this is the first formal analysis of a probabilistic broadcast protocol in the Byzantine fault model. We show numerically that practically negligible failure probabilities can be achieved with realistic security parameters.