Byzantine Fault Research Articles

Byzantine fault tolerance in distributed machine learning: a survey

ABSTRACT Byzantine Fault Tolerance (BFT) is crucial for ensuring the resilience of Distributed Machine Learning (DML) systems during training under adversarial conditions. Among the rising corpus of research on BFT in DML, there is no comprehensive classification of techniques or broad analysis of different approaches. This paper provides an in-depth survey of recent advancements in BFT for DML, with a focus on first-order optimisation methods, particularly, the popular one Stochastic Gradient Descent (SGD) during the training phase. We offer a novel classification of BFT approaches based on characteristics such as the communication process, optimisation method, and topology setting. This classification aims to enhance the understanding of various BFT methods and guide future research in addressing open challenges in the field. This work provides the foundations for developing robust BFT systems, using a variety of optimisation methods to strengthen resilience.

Blockchain Consensus Mechanisms: A Bibliometric Analysis (2014–2024) Using VOSviewer and R Bibliometrix

Blockchain consensus mechanisms play a critical role in ensuring the security, decentralization, and integrity of distributed networks. As blockchain technology expands beyond cryptocurrencies into broader applications such as supply chain management and healthcare, the importance of efficient and scalable consensus algorithms has grown significantly. This study provides a comprehensive bibliometric analysis of blockchain and consensus mechanism research from 2014 to 2024, using tools such as VOSviewer and R’s Bibliometrix package. The analysis traces the evolution from foundational mechanisms like Proof of ork (PoW) to more advanced models such as Proof of Stake (PoS) and Byzantine Fault Tolerance (BFT), with particular emphasis on Ethereum’s “The Merge” in 2022, which marked the historic shift from PoW to PoS. Key findings highlight emerging themes, including scalability, security, and the integration of blockchain with state-of-the-art technologies like artificial intelligence (AI), the Internet of Things (IoT), and energy trading. The study also identifies influential authors, institutions, and countries, emphasizing the collaborative and interdisciplinary nature of blockchain research. Through thematic analysis, this review uncovers the challenges and opportunities in decentralized systems, underscoring the need for continued innovation in consensus mechanisms to address efficiency, sustainability, scalability, and privacy concerns. These insights offer a valuable foundation for future research aimed at advancing blockchain technology across various industries.

Blockchain Scalability with Proof of Descriptor

Blockchain networks use consensus mechanisms so that participants can exchange transactions without the need to rely on a trusted third party. Consensus mechanisms using Proof of Work burn significant energy to select a block miner, and this delay limits performance. Other consensus mechanisms such as Proof of Stake or Practical Byzantine Fault Tolerance still designate a single validator to append a block to the chain, preventing blocks from being built and published in parallel. In this paper we introduce a new consensus mechanism, Proof of Descriptor, enabling clients to work together to publish blockchain transactions using a descriptor object which stores information on the cooperative parallel execution of transactions. Proof of Descriptor consensus allows commutative transactions to be mined concurrently. It does not require a single leader to append transactions to the ledger, enabling clients to cooperate on publishing transactions. We also propose a novel graph-based ledger with multiple entry points to facilitate the scalability of Proof of Descriptor, as well as a secure hashing scheme to resist long-range-attacks. We demonstrate that our approach is as secure as related works with respect to a malicious leader, 51% attack, and other known blockchain vulnerabilities. Furthermore, our experimental evaluation shows that our approach scales with the size of the network, experiencing up to a 4x improvement in throughput over the fastest sequential blockchain, Solana .

BRFL: A blockchain-based byzantine-robust federated learning model

With the increasing importance of machine learning, the privacy and security of training data have become a concern. Federated learning, which stores data in distributed nodes and shares only model parameters, has gained significant attention for addressing this concern. However, a challenge arises in federated learning due to the byzantine attack problem, where malicious local models can compromise the global model's performance during aggregation. This article proposes the Blockchain-based Byzantine-Robust Federated Learning (BRFL) model, which combines federated learning with blockchain technology. We improve the robustness of federated learning by proposing a new consensus algorithm and aggregation algorithm for blockchain-based federated learning. Meanwhile, we modify the block saving rules of the blockchain to reduce the storage pressure of the nodes. Experimental results on public datasets demonstrate the superior byzantine robustness of our secure aggregation algorithm compared to other baseline aggregation methods, and reduce the storage pressure of the blockchain nodes.

Reputation-Based Self-Differential Sequential Mechanism for Collaborative Spectrum Sensing Against Byzantine Attack in Cognitive Wireless Sensor Networks

Reputation-Based Self-Differential Sequential Mechanism for Collaborative Spectrum Sensing Against Byzantine Attack in Cognitive Wireless Sensor Networks

Trustworthy V2G scheduling and energy trading: A blockchain-based framework

The rapid growth of electric vehicles (EVs) and the deployment of vehicle-to-grid (V2G) technology pose significant challenges for distributed power grids, particularly in fostering trust and ensuring effective coordination among stakeholders. Establishing a trustworthy V2G operation environment is crucial for enabling large-scale EV user participation and realizing V2G’s potential in real-world applications. In this paper, an integrated scheduling and trading framework is developed to conduct transparent and efficacious coordination in V2G operations. In blockchain implementation, a cyber-physical blockchain architecture is proposed to enhance transaction efficiency and scalability by leveraging smart charging points (SCPs) for rapid transaction validation through a fast-path practical byzantine fault tolerance (fast-path PBFT) consensus mechanism. From the energy dispatching perspective, a game-theoretical pricing strategy is employed and smart contracts are utilized for autonomous decision-making between EVs and operators, aiming to optimize the trading process and maximize economic benefits. Numerical evaluation of blockchain consensus shows the effect of the fast-path PBFT consensus in improving systems scalability with a balanced trade-off in robustness. A case study, utilizing real-world data from the Southern University of Science and Technology (SUSTech), demonstrates significant reductions in EV charging costs and the framework’s potential to support auxiliary grid services.

Sublinear message bounds of authenticated implicit Byzantine agreement

This paper studies the message complexity of authenticated Byzantine agreement (BA) in synchronous, fully-connected distributed networks under an honest majority. We focus on the so-called implicit Byzantine agreement problem where each node starts with an input value and at the end a non-empty subset of the honest nodes should agree on a common input value by satisfying the BA properties (i.e., there can be undecided nodes)3. We show that a sublinear (in n, number of nodes) message complexity BA protocol under honest majority is possible in the standard PKI model when the nodes have access to an unbiased global coin and hash function. In particular, we present a randomized Byzantine agreement algorithm which, with high probability achieves implicit agreement, uses O˜(n) messages, and runs in O˜(1) rounds while tolerating (1/2−ϵ)n Byzantine nodes for any fixed ϵ>0, the notation O˜ hides a O(polylogn) factor4. The algorithm requires standard cryptographic setup PKI and hash function with a static Byzantine adversary. The algorithm works in the CONGEST model and each node does not need to know the identity of its neighbors, i.e., works in the KT0 model. The message complexity (and also the time complexity) of our algorithm is optimal up to a polylog n factor, as we show a Ω(n) lower bound on the message complexity. We further extend the result to Byzantine subset agreement, where a non-empty subset of nodes should agree on a common value. Lastly, we analyze several relevant results that follow from the construction of the main result.To the best of our knowledge, this is the first sublinear message complexity result of Byzantine agreement. A quadratic message lower bound is known for any deterministic BA protocol (due to Dolev-Reischuk [JACM 1985]). The existing randomized BA protocols have at least quadratic message complexity in the honest majority setting. Our result shows the power of a global coin in achieving significant improvement over the existing results. It can be viewed as a step towards understanding the message complexity of randomized Byzantine agreement in distributed networks with PKI.

An innovative NSGA-II-based Byzantine Fault Tolerant solution for software defined network environments

Byzantine fault tolerance (BFT) of the control plane in Software Defined Networking (SDN) is achieved by mapping each switch to 3f+1 number of controllers, where f represents the number of faulty controllers that can be tolerated at a time. A BFT approach protects the data plane from any potential malicious activity at the control plane by detecting the inconsistency among the response messages from multiple controllers. To compute the optimal mapping of switches to the controller, the existing literature does not consider some important parameters. This paper proposes a novel approach, named NBFT-SDN, that extends an artificial intelligence algorithm (i.e. NSGA-II) to solve a new formulated multi-objective optimization problem associated with this mapping. NBFT-SDN considers the very important parameters link reliability and link load along with switch-to-controller minimum delay, switch-to-controllers maximum reliability, controller-to-controller minimum delay, minimum link load, minimum hop count, and controller load balancing when mapping the switches to the controllers in optimum manner. The performance of our proposed approach is evaluated in comparison to a state-of-art approach using real network traces with network topologies of diverse sizes. Our proposed approach NBFT-SDN show improved network performance in terms of reliability, delay, hop count, load balancing and link load.

Efficient Lightweight Blockchain with Hybridized Consensus Algorithm for IoT Networks

Blockchain (BC) technology has attracted a lot of interest due to its excellent security and privacy features as well as its immutability. While BC can address security and privacy challenges in IoT, it is often computationally expensive, suffers from limited scalability, and introduces bandwidth overheads and delays, making it unsuitable for IoT applications. This paper proposes a novel lightweight and scalable blockchain (LIGHT-SB) designed specifically for IoT environments. In a smart IoT ecosystem, low-resource devices benefit from a centralized manager that handles communication keys and manages requests. LIGHT-SB enhances decentralization while maintaining robust privacy and security through a hybrid consensus algorithm combining permissionless proof-of-capacity and permissioned Byzantine fault tolerance (PoC-PBFT). Secure message delivery is achieved using SHA-256 and RSA cryptographic techniques. IoT device authentication, communication, and storage are safeguarded within the network. Distributed throughput management is implemented to monitor and adjust BC usage, ensuring it remains efficient. Qualitative evaluations demonstrate that LIGHT-SB effectively mitigates several security threats.

A Prototype Model of Zero Trust Architecture Blockchain with EigenTrust-Based Practical Byzantine Fault Tolerance Protocol to Manage Decentralized Clinical Trials

The COVID-19 pandemic necessitated the emergence of decentralized Clinical Trials (DCTs) due to patient retention, accelerate trials, improve data accessibility, enable virtual care, and facilitate seamless communication through integrated systems. However, integrating systems in DCTs exposes clinical data to potential security threats, making them susceptible to theft at any stage, a high risk of protocol deviations, and monitoring issues. To mitigate these challenges, blockchain technology serves as a secure framework, acting as a decentralized ledger, creating an immutable environment by establishing a zero-trust architecture, where data are deemed untrusted until verified. In combination with Internet of Things (IoT)-enabled wearable devices, blockchain secures the transfer of clinical trial data on private blockchains during DCT automation and operations. This paper proposes a prototype model of the Zero-Trust Architecture Blockchain (z-TAB) to integrate patient-generated clinical trial data during DCT operation management. The EigenTrust-based Practical Byzantine Fault Tolerance (T-PBFT) algorithm has been incorporated as a consensus protocol, leveraging Hyperledger Fabric. Furthermore, the Internet of Things (IoT) has been integrated to streamline data processing among stakeholders within the blockchain platforms. Rigorous evaluation has been done for immutability, privacy and security, mutual consensus, transparency, accountability, tracking and tracing, and temperature‒humidity control parameters.

FedCut: A Spectral Analysis Framework for Reliable Detection of Byzantine Colluders.

This paper proposes a general spectral analysis framework that thwarts a security risk in federated Learning caused by groups of malicious Byzantine attackers or colluders, who conspire to upload vicious model updates to severely debase global model performances. The proposed framework delineates the strong consistency and temporal coherence between Byzantine colluders' model updates from a spectral analysis lens, and, formulates the detection of Byzantine misbehaviours as a community detection problem in weighted graphs. The modified normalized graph cut is then utilized to discern attackers from benign participants. Moreover, the Spectral heuristics is adopted to make the detection robust against various attacks. The proposed Byzantine colluder resilient method, i.e., FedCut, is guaranteed to converge with bounded errors. Extensive experimental results under a variety of settings justify the superiority of FedCut, which demonstrates extremely robust model accuracy (MA) under various attacks. It was shown that FedCut's averaged MA is 2.1% to 16.5% better than that of the state of the art Byzantine-resilient methods. In terms of the worst-case model accuracy (MA), FedCut is 17.6% to 69.5% better than these methods.

Resilient Cruise Control of Heterogeneous Platoons Against Byzantine Attacks: Theory and Experiment.

This article studies the problem of the resilient cruise control in heterogeneous vehicle platoons against f -local Byzantine attacks (BAs). Agents under BAs become traitors of the swarm, who try to mislead its neighbors while adopting wrong inputs. Thus, BAs are extremely challenging to be suppressed. This study introduces a novel hierarchical protocol characterized by a virtual twin layer (TL), motivated by the rationale of digital twin. This protocol separates the defense scheme against f -local BAs into two parts: one defense scheme against Byzantine edge attacks (BEAs) via the TL and another scheme against Byzantine node attacks (BNAs) via the cyber-physical layer (CPL). The TL employs a trusted-edge strategy, enhancing the network resilience by incorporating a minimal fraction of the key edges. It is rigorously proven that a TL topology meeting strong (2f+1) -robustness is sufficient for achieving distributed resilient estimation against BEAs. On the CPL, a series of decentralized chattering-free controllers is proposed, guaranteeing the resilient cruise tracking of heterogeneous platoons against exponentially unbounded BNAs. Besides, these controllers can achieve uniformly ultimately bounded convergence. The theoretical results' effectiveness and practicality are validated through a numerical simulation example and an unmanned ground vehicle experiment involving heterogeneous platoons against f -local BAs.

Beta Distribution Function for Cooperative Spectrum Sensing against Byzantine Attack in Cognitive Wireless Sensor Networks

In order to explore more spectrum resources to support sensors and their related applications, cognitive wireless sensor networks (CWSNs) have emerged to identify available channels being underutilized by the primary user (PU). To improve the detection accuracy of the PU signal, cooperative spectrum sensing (CSS) among sensor paradigms is proposed to make a global decision about the PU status for CWSNs. However, CSS is susceptible to Byzantine attacks from malicious sensor nodes due to its open nature, resulting in wastage of spectrum resources or causing harmful interference to PUs. To suppress the negative impact of Byzantine attacks, this paper proposes a beta distribution function (BDF) for CSS among multiple sensors, which includes a sequential process, beta reputation model, and weight evaluation. Based on the sequential probability ratio test (SPRT), we integrate the proposed beta reputation model into SPRT, while improving and reducing the positive and negative impacts of reliable and unreliable sensor nodes on the global decision, respectively. The numerical simulation results demonstrate that, compared to SPRT and weighted sequential probability ratio test (WSPRT), the proposed BDF has outstanding effects in terms of the error probability and average number of samples under various attack ratios and probabilities.

A novel Raft consensus algorithm combining comprehensive evaluation partitioning and Byzantine fault tolerance

A novel Raft consensus algorithm combining comprehensive evaluation partitioning and Byzantine fault tolerance

Serein: A parallel pipeline‐based DAG schema for consensus in blockchain

AbstractAs the core technology of blockchain, consensus mechanisms play a crucial role in ensuring the consistency and reliability of blockchain systems. In a decentralized and open system environment like blockchain, traditional consensus algorithms are often unsuitable due to their inability to tolerate arbitrary faults such as malicious node behaviour. Consequently, Byzantine fault tolerance consensus algorithms have become a focal point in blockchain systems. However, as Byzantine fault tolerance consensus algorithms have evolved, they still face significant challenges, particularly in addressing issues related to network latency and throughput. This paper proposes a parallel pipeline‐based DAG schema for consensus in blockchain, Serein. Firstly, the Serein algorithm achieves functional partitioning of nodes, enhancing their scalability. Secondly, it employs a pipeline structure, allowing each block to proceed without waiting for the previous block's result, thereby reducing block generation latency. Lastly, the Serein algorithm leverages the advantages of the DAG block structure to achieve concurrent block ordering and submission, improving system throughput. Experimental results demonstrate that the proposed Serein algorithm maintains robust performance under conditions of high transaction volume with multiple nodes, effectively enhancing consensus efficiency while ensuring Byzantine fault‐tolerant security.

Robust Distributed Learning Against Both Distributional Shifts and Byzantine Attacks.

In distributed learning systems, robustness threat may arise from two major sources. On the one hand, due to distributional shifts between training data and test data, the trained model could exhibit poor out-of-sample performance. On the other hand, a portion of working nodes might be subject to Byzantine attacks, which could invalidate the learning result. In this article, we propose a new research direction that jointly considers distributional shifts and Byzantine attacks. We illuminate the major challenges in addressing these two issues simultaneously. Accordingly, we design a new algorithm that equips distributed learning with both distributional robustness and Byzantine robustness. Our algorithm is built on recent advances in distributionally robust optimization (DRO) as well as norm-based screening (NBS), a robust aggregation scheme against Byzantine attacks. We provide convergence proofs in three cases of the learning model being nonconvex, convex, and strongly convex for the proposed algorithm, shedding light on its convergence behaviors and endurability against Byzantine attacks. In particular, we deduce that any algorithm employing NBS (including ours) cannot converge when the percentage of Byzantine nodes is [Formula: see text] or higher, instead of [Formula: see text] , which is the common belief in current literature. The experimental results verify our theoretical findings (on the breakpoint of NBS and others) and also demonstrate the effectiveness of our algorithm against both robustness issues, justifying our choice of NBS over other widely used robust aggregation schemes. To the best of our knowledge, this is the first work to address distributional shifts and Byzantine attacks simultaneously.

Byzantine-robust Federated Learning via Cosine Similarity Aggregation

Federated Learning (FL) is proposed to train a machine learning model for clients with different training data. During the training of FL, a centralized server is usually employed to aggregate local models from clients iteratively. The aggregation process suffers from Byzantine attacks, where clients’ models could be maliciously modified by attackers to degrade the training performance. Existing defense aggregation solutions use distances or angles between different gradients to identify and eliminate malicious models from clients. However, they do not work well due to the high dimensional property of the machine learning model. Distance-based solutions cannot effectively identify attackers when the gradient direction of the model is maliciously tampered with. Angle-based solutions face the issue of low model accuracy for large models. In this paper, we propose Convolutional Kernel Angle-based Defense Aggregation (CKADA) to improve defense performance under various Byzantine attacks. The key of CKADA is to use the angle between convolutional kernels as the attack detection metric because the obtuse angle indicates the wrong training direction. CKADA calculates the angle between a client’s convolutional kernel gradients and the server’s convolutional kernel gradients as the attacker detection metric and eliminates convolutional kernel gradients of clients that create an obtuse angle to mitigate the impact of attackers on the model. We evaluate the performance of CKADA using AlexNet, ResNet-50, and GoogLeNet under two typical attacks. Simulation results show that CKADA mitigates the impact of Byzantine attacks and outperforms existing angle-based solutions and distance-based solutions by improving inference accuracy up to 67% and 89% respectively.

Experimental quantum Byzantine agreement on a three-user quantum network with integrated photonics.

Quantum communication networks are crucial for both secure communication and cryptographic networked tasks. Building quantum communication networks in a scalable and cost-effective way is essential for their widespread adoption. Here, we establish a complete polarization entanglement-based fully connected network, which features an ultrabright integrated Bragg reflection waveguide quantum source, managed by an untrusted service provider, and a streamlined polarization analysis module, which requires only one single-photon detector for each user. We perform a continuously working quantum entanglement distribution and create correlated bit strings between users. Within the framework of one-time universal hashing, we provide the experimental implementation of source-independent quantum digital signatures using imperfect keys circumventing the necessity for private amplification. We further beat the 1/3 fault tolerance bound in the Byzantine agreement, achieving unconditional security without relying on sophisticated techniques. Our results offer an affordable and practical route for addressing consensus challenges within the emerging quantum network landscape.

Exploring Scalability of BFT Blockchain Protocols through Network Simulations

Novel Byzantine fault-tolerant (BFT) state machine replication protocols improve scalability for their practical use in distributed ledger technology, where hundreds of replicas must reach consensus. Evaluating the performance of BFT protocol implementations requires careful evaluation. We propose a new methodology using scalable network simulations to predict BFT protocol performance. Our simulation architecture allows for the integration of existing BFT implementations without modification or re-implementation, offering a cost-effective alternative to large-scale cloud experiments. We validate our method by comparing simulation results with real-world cloud deployments, showing that simulations can accurately predict performance at larger scales when network limitations dominate. In our study, we applied this methodology to assess the performance of several “blockchain-generation” BFT protocols, including HotStuff, Kauri, Narwhal & Tusk, and Bullshark, under realistic network conditions (with constrained 25 Mbit/s bandwidth) and induced faults. Kauri emerges as the top performer, achieving 6742 operations per second (op/s) with 128 replicas, outperforming BullShark (2318 op/s) and Tusk (1952 op/s). HotStuff, using secp256k1 and BLS signatures, reaches 494 op/s and 707 op/s, respectively, demonstrating the efficiency of BLS-signature aggregation for saving bandwidth. This study demonstrates that state-of-the-art asynchronous BFT protocols can achieve competitive throughput in large-scale, real-world scenarios.

Improved Fast-Response Consensus Algorithm Based on HotStuff.

Recent Byzantine Fault-Tolerant (BFT) State Machine Replication (SMR) protocols increasingly focus on scalability and security to meet the growing demand for Distributed Ledger Technology (DLT) applications across various domains. Current BFT consensus algorithms typically require a single leader node to receive and validate votes from the majority process and broadcast the results, a design challenging to scale in large systems. We propose a fast-response consensus algorithm based on improvements to HotStuff, aimed at enhancing transaction ordering speed and overall performance of distributed systems, even in the presence of faulty copies. The algorithm introduces an optimistic response assumption, employs a message aggregation tree to collect and validate votes, and uses a dynamically adjusted threshold mechanism to reduce communication delay and improve message delivery reliability. Additionally, a dynamic channel mechanism and an asynchronous leader multi-round mechanism are introduced to address multiple points of failure in the message aggregation tree structure, minimizing dependence on a single leader. This adaptation can be flexibly applied to real-world system conditions to improve performance and responsiveness. We conduct experimental evaluations to verify the algorithm's effectiveness and superiority. Compared to the traditional HotStuff algorithm, the improved algorithm demonstrates higher efficiency and faster response times in handling faulty copies and transaction ordering.