Sybil attacks, in which a large number of adversary-controlled nodes join a network, are a concern for many peer-to-peer database systems, necessitating expensive countermeasures such as proof-of-work. However, there is a category of database applications that are, by design, immune to Sybil attacks because they can tolerate arbitrary numbers of Byzantine-faulty nodes. In this paper, we characterize this category of applications using a consistency model we call Byzantine Eventual Consistency (BEC). We introduce an algorithm that guarantees BEC based on Byzantine causal broadcast, prove its correctness, and demonstrate near-optimal performance in a prototype implementation.
Peer sampling is a first-class abstraction used in distributed systems for overlay management and information dissemination. The goal of peer sampling is to continuously build and refresh a partial and local view of the full membership of a dynamic, large-scale distributed system. Malicious nodes under the control of an adversary may aim at being over-represented in the views of correct nodes, increasing their impact on the proper operation of protocols built over peer sampling. State-of-the-art Byzantine resilient peer sampling protocols reduce this bias as long as Byzantines are not overly p…
We consider the problem of Byzantine fault-tolerance in the peer-to-peer (P2P) distributed gradient-descent method -- a prominent algorithm for distributed optimization in a P2P system. In this problem, the system comprises of multiple agents, and each agent has a local cost function. In the fault-free case, when all the agents are honest, the P2P distributed gradient-descent method allows all the agents to reach a consensus on a solution that minimizes their aggregate cost. However, we consider a scenario where a certain number of agents may be Byzantine faulty. Such faulty agents may not fol…
Federated learning (FL) is a privacy-friendly type of machine learning where devices locally train a model on their private data and typically communicate model updates with a server. In decentralized FL (DFL), peers communicate model updates with each other instead. However, DFL is challenging since (1) the training data possessed by different peers is often non-i.i.d. (i.e., distributed differently between the peers) and (2) malicious, or Byzantine, attackers can share arbitrary model updates with other peers to subvert the training process. We address these two challenges and present Bristl…
Recent years have witnessed a slew of coding techniques custom designed for networked storage systems. Network coding inspired regenerating codes are the most prolifically studied among these new age storage centric codes. A lot of effort has been invested in understanding the fundamental achievable trade-offs of storage and bandwidth usage to maintain redundancy in presence of different models of failures, showcasing the efficacy of regenerating codes with respect to traditional erasure coding techniques. For practical usability in open and adversarial environments, as is typical in peer-to-p…
In this paper we analyse the correctness of Istanbul BFT (IBFT), which is a Byzantine-fault-tolerant (BFT) proof-of-authority (PoA) blockchain consensus protocol that ensures immediate finality. We show that the IBFT protocol does not guarantee Byzantine-fault-tolerant consistency and liveness when operating in an eventually synchronous network, and we propose modifications to the protocol to ensure both Byzantine-fault-tolerant consistency and liveness in eventually synchronous settings.
We explore the property of equivocation tolerance for Conflict-Free Replicated Data Types (CRDTs). We show that a subclass of CRDTs is equivocation-tolerant and can thereby cope with any number of Byzantine faults: Without equivocation detection, prevention or remediation, they still fulfill strong eventual consistency (SEC). We also conjecture that there is only one operation-based CRDT design supporting non-commutative operations that fulfills SEC in Byzantine environments with any number of faults.
Byzantine agreement algorithms typically assume implicit initial state consistency and synchronization among the correct nodes and then operate in coordinated rounds of information exchange to reach agreement based on the input values. The implicit initial assumptions enable correct nodes to infer about the progression of the algorithm at other nodes from their local state. This paper considers a more severe fault model than permanent Byzantine failures, one in which the system can in addition be subject to severe transient failures that can temporarily throw the system out of its assumption b…
Byzantine-Fault-Tolerant (BFT) systems are rapidly emerging as a viable technology for production-grade systems, notably in closed consortia deployments for nancial and supply-chain applications. Unfortunately, most algorithms proposed so far to coordinate these systems suffer from substantial scalability issues, and lack important features to implement Internet-scale governance mechanisms. In this paper, we observe that many application workloads offer little concurrency, and propose PnyxDB, an eventually-consistent Byzantine Fault Tolerant replicated datastore that exhibits both high scalabi…
University of Louisville（路易斯维尔大学）；North Carolina State University（北卡罗来纳州立大学）；University of Wisconsin-Whitewater（威斯康星大学怀特沃特分校）；Wayne State University（韦恩州立大学）；The Ohio State University（俄亥俄州立大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Duke University（杜克大学）
The Byzantine agreement problem requires a set of $n$ processes to agree on a value sent by a transmitter, despite a subset of $b$ processes behaving in an arbitrary, i.e. Byzantine, manner and sending corrupted messages to all processes in the system. It is well known that the problem has a solution in a (an eventually) synchronous message passing distributed system iff the number of processes in the Byzantine subset is less than one third of the total number of processes, i.e. iff $n > 3b+1$. The rest of the processes are expected to be correct: they should never deviate from the algorithm a…
The Bitcoin system only provides eventual consistency. For everyday life, the time to confirm a Bitcoin transaction is prohibitively slow. In this paper we propose a new system, built on the Bitcoin blockchain, which enables strong consistency. Our system, PeerCensus, acts as a certification authority, manages peer identities in a peer-to-peer network, and ultimately enhances Bitcoin and similar systems with strong consistency. Our extensive analysis shows that PeerCensus is in a secure state with high probability. We also show how Discoin, a Bitcoin variant that decouples block creation and t…
Blockchain systems benefit from lessons in prior art such as fault tolerance, distributed systems, peer-to-peer systems, and game theory. In this paper we argue that blockchain algorithms should tolerate both rational (self-interested) users and Byzantine (malicious) ones, rather than assuming all non-Byzantine users are altruistic and follow the protocols blindly. Such algorithms are called BAR-tolerant [1]. To design a BAR-tolerant system, one can follow these three steps: clearly define the utility function for the rational users, prove the algorithm is such that there is no benefit from un…
Traditional Byzantine resilient algorithms use 2f+1 vertex disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. Distributed algorithms for topology discovery cope with a never ending task, dealing with frequent changes in the network topology and unpredictable transient faults. Therefore, algorithms for topology discovery should be self-stabilizing to ensure convergence of the topology information following any such unpredictable sequence of events. We pr…
The ``Pulse Synchronization'' problem can be loosely described as targeting to invoke a recurring distributed event as simultaneously as possible at the different nodes and with a frequency that is as regular as possible. This target becomes surprisingly subtle and difficult to achieve when facing both transient and permanent failures. In this paper we present an algorithm for pulse synchronization that self-stabilizes while at the same time tolerating a permanent presence of Byzantine faults. The Byzantine nodes might incessantly try to de-synchronize the correct nodes. Transient failures mig…
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…
We consider the gathering task by a team of $m$ synchronous mobile robots in a graph of $n$ nodes. Each robot has an identifier (ID) and runs its own deterministic algorithm, i.e., there is no centralized coordinator. We consider a particularly challenging scenario: there are $f$ Byzantine robots in the team that can behave arbitrarily, and even have the ability to change their IDs to any value at any time. There is no way to distinguish these robots from non-faulty robots, other than perhaps observing strange or unexpected behaviour. The goal of the gathering task is to eventually have all no…
UNESCO Chair in Data Privacy（联合国教科文组织数据隐私教席）；CYBERCAT-Center for Cybersecurity Research of Catalonia（CYBERCAT-加泰罗尼亚网络安全研究中心）；Universitat Rovira i Virgili（罗维拉-威尔吉利大学）
The decentralized nature of federated learning, that often leverages the power of edge devices, makes it vulnerable to attacks against privacy and security. The privacy risk for a peer is that the model update she computes on her private data may, when sent to the model manager, leak information on those private data. Even more obvious are security attacks, whereby one or several malicious peers return wrong model updates in order to disrupt the learning process and lead to a wrong model being learned. In this paper we build a federated learning framework that offers privacy to the participati…
We give fault-tolerant algorithms for establishing synchrony in distributed systems in which each of the $n$ nodes has its own clock. Our algorithms operate in a very strong fault model: we require self-stabilisation, i.e., the initial state of the system may be arbitrary, and there can be up to $f<n/3$ ongoing Byzantine faults, i.e., nodes that deviate from the protocol in an arbitrary manner. Furthermore, we assume that the local clocks of the nodes may progress at different speeds (clock drift) and communication has bounded delay. In this model, we study the pulse synchronisation problem, w…
Recent works have proposed new Byzantine consensus algorithms for blockchains based on epidemics, a design which enables highly scalable performance at a low cost. These methods however critically depend on a secure random peer sampling service: a service that provides a stream of random network nodes where no attacking entity can become over-represented. To ensure this security property, current epidemic platforms use a Proof-of-Stake system to select peer samples. However such a system limits the openness of the system as only nodes with significant stake can participate in the consensus, le…
Interactive consistency is the problem in which n nodes, where up to t may be byzantine, each with its own private value, run an algorithm that allows all non-faulty nodes to infer the values of each other node. This problem is relevant to critical applications that rely on the combination of the opinions of multiple peers to provide a service. Examples include monitoring a content source to prevent equivocation or to track variability in the content provided, and resolving divergent state amongst the nodes of a distributed system. Previous works assume a fully synchronous system, where one ca…
Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is to eventually have all correct nodes labeling the pulses with increasing values modulo $c$ in agreement. Thus, we are considering algorithms that are self-stabilising despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have optimal resilience, (3) have a linear stabilisation tim…
