Byzantine Fault Research Articles

Resource analysis for quantum-aided Byzantine agreement with the four-qubit singlet state

In distributed computing, a Byzantine fault is a condition where a component behaves inconsistently, showing different symptoms to different components of the system. Consensus among the correct components can be reached by appropriately crafted communication protocols even in the presence of byzantine faults. Quantum-aided protocols built upon distributed entangled quantum states are worth considering, as they are more resilient than traditional ones. Based on earlier ideas, here we establish a parameter-dependent family of quantum-aided weak broadcast protocols. We compute upper bounds on the failure probability of the protocol, and define and illustrate a procedure that minimizes the quantum resource requirements. Following earlier work demonstrating the suitability of noisy intermediate scale quantum (NISQ) devices for the study of quantum networks, we experimentally create our resource quantum state on publicly available quantum computers. Our work highlights important engineering aspects of the future deployment of quantum communication protocols with multi-qubit entangled states.

AdoB: Bridging Benign and Byzantine Consensus with Atomic Distributed Objects

Achieving consensus is a challenging and ubiquitous problem in distributed systems that is only made harder by the introduction of malicious byzantine servers. While significant effort has been devoted to the benign and byzantine failure models individually, no prior work has considered the mechanized verification of both in a generic way. We claim this is due to the lack of an appropriate abstraction that is capable of representing both benign and byzantine consensus without either losing too much detail or becoming impractically complex. We build on recent work on the atomic distributed object model to fill this void with a novel abstraction called AdoB. In addition to revealing important insights into the essence of consensus, this abstraction has practical benefits for easing distributed system verification. As a case study, we proved safety and liveness properties for AdoB in Coq, which are the first such mechanized proofs to handle benign and byzantine consensus in a unified manner. We also demonstrate that AdoB faithfully models real consensus protocols by proving it is refined by standard network-level specifications of Fast Paxos and a variant of Jolteon.

Performance of PBFT Consensus under Voting by Groups

Practical Byzantine Fault Tolerance (PBFT) is the protocol of choice for many applications that require distributed consensus between a number of participant nodes. While PBFT assumes a single voting committee, many applications recognize different groups of participants that need to reach a consensus separately before accepting a proposal. To this end, we propose to count the votes by separate groups or committees of participating nodes, instead of all together as in the original PBFT. We then investigate the performance impact of this approach on the mean time to accept a data block and the number of nodes involved in making the final decision. Our results indicate that the proposed solutions impose a slight performance penalty which may be countermanded by reducing the quorum numbers needed in different subsets of the original committee.

Research on evolutionary game of digital twin data information sharing based on blockchain technology

Due to the significant characteristics of decentralization and tamper resistance of blockchain technology, it helps to solve the problems of timeliness and slow permission control in traditional information sharing. However, most researchers are committed to exploring how to improve the efficiency, reliability, and privacy security of digital twin data. There is a lack of research on issues such as blockchain participants free-riding and not actively participating in information sharing, and how to promote information sharing through incentives. Therefore, this paper designs a distance grouping based practical byzantine fault tolerance consensus algorithm to address the credibility issue of transmitted data, thereby improving the efficiency of negotiation. The feasibility of the algorithm is verified through cases analysis. In addition, for the problem of low subjective willingness of information sharing, this paper designs an information sharing incentive strategy based on blockchain intelligent contracts, establishes digital twin data sharing evolutionary game models with reputation incentives and non-reputation incentives, so as to explore the impact of reputation incentive on evolutionary stability strategies. Finally, simulation analysis is conducted on the evolutionary game model of digital twin data sharing. The impact of several key indicators such as data complementarity, trust, positive incentive coefficient, and data sharing cost on the evolution process of information sharing are considered, and corresponding management insights are obtained.

Improvement of Practical Byzantine Fault Tolerance Consensus Algorithm Based on DIANA in Intellectual Property Environment Transactions

In response to the shortcomings of the consensus algorithm for intellectual property transactions, such as high communication overhead, random primary node selection, and prolonged consensus time, a Practical Byzantine Fault Tolerance (PBFT) improvement algorithm based on Divisive Analysis (DIANA) D-PBFT algorithm is proposed. Firstly, the algorithm adopts the hierarchical clustering mechanism of DIANA to cluster nodes based on similarity, enhancing node partition accuracy and reducing the number of participating consensus nodes. Secondly, it designs a reward and punishment system based on node ranking, to achieve consistency between node status and permissions, timely evaluation, and feedback on node behaviours, thereby enhancing node enthusiasm. Then, the election method of the primary node is improved by constructing proxy and alternate nodes and adopting a majority voting strategy to achieve the selection and reliability of the primary node. Finally, the consistency protocol is optimised to perform consensus once within the cluster and once between all primary nodes, to ensure the accuracy of the consensus results. Experimental results demonstrate that the D-PBFT algorithm shows a better performance, in terms of communication complexity, throughput, and latency.

Double‐layer Byzantine fault‐tolerant grouping consensus algorithm based on raft

AbstractAddressing the scalability issues, excessive communication overhead, and challenges in adapting to large‐scale network node environments faced by the Practical Byzantine Fault Tolerance (PBFT) consensus algorithm currently employed in consortium blockchains, this paper proposes a Double Layer Consensus Algorithm Based on RAFT and PBFT Consensus Algorithms (DLCA_R_P). The nodes in the blockchain are initially divided into several groups to form the lower‐layer consensus network. Subsequently, the leaders of these groups constitute the upper‐layer consensus network, creating a dual‐layer consensus network structure. Within the lower‐layer consensus network, the PBFT consensus algorithm is employed for consensus among the groups, while the primary accountants form the upper‐layer RAFT consensus network. The algorithm incorporates a supervision mechanism and a reputation mechanism to enhance the security of the consensus network. Additionally, a grouping mechanism is introduced to transform the consensus network into a dynamic structure. Experimental results analysis demonstrates that compared to traditional PBFT consensus algorithms, DLCA_R_P reduces consensus latency by two orders of magnitude and improves throughput by one order of magnitude in a scenario with 100 nodes. Furthermore, it exhibits significant advantages over other improved algorithms. Thus, the DLCA_R_P consensus algorithm exhibits excellent scalability and can be widely applied in various scenarios within consortium blockchains.

The Bitcoin Backbone Protocol: Analysis and Applications

Bitcoin is the first and most popular decentralized cryptocurrency to date. In this work, we extract and analyze the core of the Bitcoin protocol, which we term the Bitcoin backbone , and prove three of its fundamental properties which we call Common Prefix , Chain Quality and Chain Growth in the static setting where the number of players remains fixed. Our proofs hinge on appropriate and novel assumptions on the “hashing power” of the protocol participants and their interplay with the protocol parameters and the time needed for reliable message passing between honest parties in terms of computational steps. A takeaway from our analysis is that, all else being equal, the protocol’s provable tolerance in terms of the number of adversarial parties (or, equivalently, their “hashing power” in our model) decreases as the duration of a message passing round increases. Next, we propose and analyze applications that can be built “on top” of the backbone protocol, specifically focusing on Byzantine agreement (BA) and on the notion of a public transaction ledger. Regarding BA, we observe that a proposal due to Nakamoto falls short of solving it, and present a simple alternative which works assuming that the adversary’s hashing power is bounded by 1/3. The public transaction ledger captures the essence of Bitcoin’s operation as a cryptocurrency, in the sense that it guarantees the liveness and persistence of committed transactions. Based on this notion we describe and analyze the Bitcoin system as well as a more elaborate BA protocol and we prove them secure assuming the adversary’s hashing power is strictly less than 1/2. Instrumental to this latter result is a technique we call 2-for-1 proof-of-work (PoW) that has proven to be useful in the design of other PoW-based protocols.

Byzantine Fault-Tolerant Federated Learning Based on Trustworthy Data and Historical Information

Federated learning (FL) is a highly promising collaborative machine learning method that preserves privacy by enabling model training on client nodes (e.g., mobile phones, Internet-of-Things devices) without sharing raw data. However, FL is vulnerable to Byzantine nodes, which can disrupt model performance, render training ineffective, or even manipulate the model by transmitting harmful gradients. In this paper, we propose a Byzantine fault-tolerant FL algorithm called federated learning with trustworthy data and historical information (FLTH). It utilizes a small trusted training dataset at the parameter server to filter out gradient updates from suspicious client nodes during model training, which provides both Byzantine resilience and convergence guarantee. It further introduces a historical information-based credibility assessment scheme such that the client nodes performing poorly over the long-term have a lower impact on the aggregation of gradients, thereby enhancing fault tolerance capability. Additionally, FLTH does not compromise the training efficiency of FL because of its low time complexity. Extensive simulation results show that FLTH achieves higher model accuracy compared to state-of-the-art methods under typical kinds of attack.

Byzantine Agreement with Optimal Resilience via Statistical Fraud Detection

Since the mid-1980s it has been known that Byzantine Agreement can be solved with probability 1 asynchronously, even against an omniscient, computationally unbounded adversary that can adaptively corrupt up to f < n/3 parties. Moreover, the problem is insoluble with f ≥ n/3 corruptions. However, Bracha’s [ 13 ] 1984 protocol (see also Ben-Or [ 8 ]) achieved f < n/3 resilience at the cost of exponential expected latency 2 Θ ( n ) , a bound that has never been improved in this model with f = ⌊ (n-1)/3 ⌋ corruptions. In this article, we prove that Byzantine Agreement in the asynchronous, full information model can be solved with probability 1 against an adaptive adversary that can corrupt f < n/3 parties, while incurring only polynomial latency with high probability . Our protocol follows an earlier polynomial latency protocol of King and Saia [ 33 , 34 ], which had suboptimal resilience, namely f ≈ n /10 9 [ 33 , 34 ]. Resilience f = (n-1)/3 is uniquely difficult, as this is the point at which the influence of the Byzantine and honest players are of roughly equal strength. The core technical problem we solve is to design a collective coin-flipping protocol that eventually lets us flip a coin with an unambiguous outcome. In the beginning, the influence of the Byzantine players is too powerful to overcome, and they can essentially fix the coin’s behavior at will. We guarantee that after just a polynomial number of executions of the coin-flipping protocol, either (a) the Byzantine players fail to fix the behavior of the coin (thereby ending the game) or (b) we can “blacklist” players such that the blacklisting rate for Byzantine players is at least as large as the blacklisting rate for good players. The blacklisting criterion is based on a simple statistical test of fraud detection .

Improving byzantine fault tolerance based on stake evaluation and consistent hashing

Improving byzantine fault tolerance based on stake evaluation and consistent hashing

Byzantine Machine Learning: A Primer

The problem of Byzantine resilience in distributed machine learning, a.k.a. Byzantine machine learning , consists of designing distributed algorithms that can train an accurate model despite the presence of Byzantine nodes—that is, nodes with corrupt data or machines that can misbehave arbitrarily. By now, many solutions to this important problem have been proposed, most of which build upon the classical stochastic gradient descent scheme. Yet, the literature lacks a unified structure of this emerging field. Consequently, the general understanding on the principles of Byzantine machine learning remains poor. This article addresses this issue by presenting a primer on Byzantine machine learning. In particular, we introduce three pillars of Byzantine machine learning, namely the concepts of breakdown point , robustness , and gradient complexity , to curate the efficacy of a solution. The introduced systematization enables us to (i) bring forth the merits and limitations of the state-of-the-art solutions, and (ii) pave a clear path for future advancements in this field.

A blockchain-based data storage architecture for Internet of Vehicles: Delay-aware consensus and data query algorithms

The recent development of the Internet of Vehicles (IoV) relies heavily on the secure store and analysis of reliable driving data. Blockchain technology has been widely used in the IoV field due to its security advantages, where consensus and query algorithms are two key modules determining its performance. However, existing solutions do not perform well enough in terms of delay performance, thus limiting their ability to support IoV environments with ultra-low-latency requirements. To address this challenge, we design a blockchain-based data storage architecture, focusing on the design of delay-aware consensus and data query algorithms. Specifically, to reduce the consensus delay, we propose a reputation-assisted and grouping-simplified Practical Byzantine Fault Tolerant (RGS-PBFT) algorithm. First, we develop a novel node credit value evaluation model by combining the behavior and configuration reputation to select the primary node with both high security and high computing capacity. Second, after determining the primary node, we reduce the communication complexity of traditional PBFT from O(Z2) to O(Z43) by establishing a grouping-simplified consensus structure. These contributions effectively reduce the consensus delay. To reduce the query delay and index construction time, we propose an index query algorithm based on the data tracking chain (DTC-Index query). By introducing the LevelDB database, it establishes a transaction index chain coupled to vehicle ID in the blockchain. This approach avoids the time-consuming block traversal during data querying. Experimental results demonstrate that the proposed algorithms outperform existing solutions, achieving significant improvements in both consensus delay and query time reduction. Notably, our solutions offer exceptional delay performance, making them well-suited for IoV environments.

Gaussian Mixture Model-Based Anomaly Detection for Defense Against Byzantine Attack in Cooperative Spectrum Sensing

Gaussian Mixture Model-Based Anomaly Detection for Defense Against Byzantine Attack in Cooperative Spectrum Sensing

Enabling intrinsic intelligence, ubiquitous learning and blockchain empowerment for trust and reliability in 6G network evolution

This study investigates the 6th Generation (6G) wireless communication network as a vital component of Ubiquitous Learning, which makes it possible to build trustworthy relationships and accurate intelligence in a variety of contexts. The important significance of blockchain technology is recognized, and its potential to improve the performance of the 6G network is investigated. Blockchain technology powers Ubiquitous Learning as a decentralized tool. But in Ubiquitous Learning contexts, problems arise when varied communication settings, information asymmetry, and resource limits confront wireless-connected devices functioning as blockchain consensus nodes. To solve these difficulties, which are critical for Ubiquitous Learning, a blockchain sharding and incentive system is presented. The purpose of this technique is to improve the learning process in the 6G network by cultivating reliable intelligence. A sharding architecture that integrates a contract theory-based incentive mechanism and a realistic Byzantine fault tolerance mechanism, particularly tailored for Ubiquitous Learning settings, is described. This model analyses the useful Byzantine consensus mechanism and block broadcast characteristics in wireless networks. This study finds the best contract combination for both completely symmetric and asymmetric information scenarios, optimizing block rewards for customers that seek blockchain services.

Resilient Output Formation-Tracking of Heterogeneous Multiagent Systems Against General Byzantine Attacks: A Twin-Layer Approach.

This work solves the countermeasure design problems of distributed resilient output time-varying formation-tracking (TVFT) of heterogeneous multiagent systems (MASs) against general Byzantine attacks (GBAs). Inspired by the concept of Digital Twin, a hierarchical protocol equipped with a twin layer (TL) is proposed, which decouples the above problem into the defense against Byzantine edge attacks (BEAs) on the TL and the defense against Byzantine node attacks (BNAs) on the cyber-physical layer (CPL). First, a secure TL with respect to (w.r.t.) the high-order leader dynamics is designed, which achieves resilient estimation against BEAs. A trusted-node strategy against BEAs is proposed, which promotes network resilience by protecting almost the smallest fraction of crucial nodes on the TL. It is proven that strongly (2f+1) -robustness w.r.t. the above trusted nodes is sufficient for the resilient estimation performance of the TL. Second, a decentralized adaptive and chattering-free controller against potentially unbounded BNAs is designed on the CPL. This controller has the merit of uniformly ultimately bounded (UUB) convergence and an assignable exponential decay rate when converging into the above UUB bound. To the best of our knowledge, this article is the first to achieve resilient output TVFT against GBAs, rather than under GBAs. Finally, the practicability and validity of this new hierarchical protocol are illustrated via a simulation example.

DIGITAL ASSETS MARKET HUB

Block chain technology, non-fungible tokens (NFTs), and cryptocurrency have all contributed to the explosive rise of the digital assets sector. The dynamic and cutting-edge digital asset marketplace shown in this abstract is intended to satisfy the various demands of traders, investors, and enthusiasts in the digital asset market. The marketplace offers a user-friendly and safe platform for purchasing, selling, and managing different digital assets, and it is distinguished by its user-centric approach. It offers real-time market data, order book information, and robust analytical capabilities for well-informed decision-making, all with an intuitive interface that streamlines asset transactions. The ability to move assets seamlessly between blockchain networks, multi factor authentication, cold storage, and complex trading algorithms that optimise trading tactics are some of the key characteristics. ----------------------------------------------------------------------------------------------------------------------------------- Keywords Blockchain, Smart Contract, Ethereum, Transparency, Data sharing, Privacy, Byzantine fault tolerance, decentralized systems.

Defending dominant cooperative probabilistic attack in CRNs by JS-divergence-based improved reputation algorithm

Rapid advances in wireless communication services has made limited spectrum resources increasingly scarce. One promising solution for enhancing spectrum utilization is cooperative spectrum sensing (CSS) in cognitive radio networks (CRNs). However CSS is vulnerable to Byzantine attack. Current researches show that Byzantine attack is easily defended for their fixed attack probability. In this context, we propose an improved attack model called the dominated cooperative probabilistic attack (DCPA) model in the actual situation, building upon the generalized collaborative probabilistic Byzantine attack model. This DCPA model contains auxiliary cooperative attackers (ACAs) who launch attacks and a dominant attacker (DA) who determines ACAs’ attack probability intervals based on their respective credibility. The DCPA model allows ACAs to flexibly launch attacks, without being identified by the traditional reputation defense algorithm, significantly compromising the sensing performance of CSS. To successfully resist the threat posed by the DCPA model to CSS, we propose a JS-divergence-based improved reputation algorithm that can distinguish honest users (HUs) from attackers. This algorithm analyzes two consecutive sensing reports to identify differences in sensing behavior between HUs and attackers. Through Python simulation analysis, we demonstrate that, compared to the generalized cooperative probabilistic attack (CPA) model and the attack-free CSS (AFC) model, the proposed DCPA model is more concealed and significantly more disruptive to the performance of traditional reputation defense algorithms. Furthermore, our approach greatly enhances the performance of CSS by promoting the participation of HUs and suppressing attackers during the final data fusion. And also compared with the PAM2 algorithm, the conventional voting rule (CVR) algorithm and the traditional reputation defense algorithm, our proposed algorithm improves the detection performance by at least 7%, 15% and 50%.

PIoT-blockchain-enabled security framework for strengthening IoT device identity and data access

The Internet of Things (IoT) connects billions of devices, but concerns about data security and device identification have grown. This study introduces Proof of IoT (PIoT), a novel consensus method using blockchain-based smart contracts to ensure secure data transfer and device authentication in IoT networks. PIoT employs NuCypher-based security computations for authentication and data updating, ensuring only authorized parties access blockchain-recorded information. A reward-based filtering mechanism identifies malicious nodes, bolstering consensus integrity. Simulations demonstrate PIoT's superior performance compared to conventional methods, showing a 74.7% and 96.8% improvement over LPBFT and DAC4SH Consensus, respectively. PIoT enhances blockchain security under IoT by 15% compared to DAC4SH. Beyond facilitating secure IoT device communication, this approach mitigates various IoT attacks, offering a comprehensive solution to emerging IoT security challenges. ABBREVIATION: DAC4SH, Data access control scheme for smart home; DDoS, Distributed denial of service; DoS, Denial of Service; DTLS, Datagram Transport Layer Security; IoT, Internet of Things; LPBFT, Lightweight Particle Byzantine fault tolerance; MAC, Message authentication code; MITM, Man in the Middle; PBFT, Practical Byzantine Fault Tolerance; PIoT, Proof of IoT; TLS, Transport Layer Security

CG-PBFT: an efficient PBFT algorithm based on credit grouping

Because of its excellent properties of fault tolerance, efficiency and availability, the practical Byzantine fault tolerance (PBFT) algorithm has become the mainstream consensus algorithm in blockchain. However, current PBFT algorithms have problems such as inadequate security of primary node selection, high communication overhead and network delay in the process of consensus. To address these problems, we design a novel efficient Byzantine fault tolerance algorithm based on credit grouping, called CG-PBFT. First, we propose a new credit evaluation model to obtain nodes’ credit values and introduce an optimized three-way quick sorting algorithm to divide nodes into the master-node group, the consensus-node group and the observation-node group, which have different privileges. The nodes in the observation-node group are restricted from participating in consensus, which reduces the communication overhead and improves consensus efficiency. Second, we propose an optimized selection method for the primary node based on a voting mechanism whereby the consensus-node group and observation-node group vote to produce the primary node, which reduces the probability of malicious nodes acting as the primary node and improves the security of primary node selection. Finally, the identity conversion mechanism between node groups is designed, and the actual behavior of nodes within different groups is given credit rewards or punishment, so as to keep an incentive for nodes to participate in appropriate system behavior and improve the working enthusiasm of nodes. The experimental simulation results show that compared with existing PBFT algorithms, the CG-PBFT algorithm improves the average throughput by 51.3% and reduces the average delay by 64.5%; it greatly improves the operating efficiency of the system and can be more suitable for application in the consortium blockchain scenarios.

Byzantine-Robust Decentralized Learning via Remove-then-Clip Aggregation

We consider decentralized learning over a network of workers with heterogeneous datasets, in the presence of Byzantine workers. Byzantine workers may transmit arbitrary or malicious values to neighboring workers, leading to degradation in overall performance. The heterogeneous nature of the training data across various workers complicates the identification and mitigation of Byzantine workers. To address this complex problem, we introduce a resilient decentralized learning approach that combines the gradient descent algorithm with a novel robust aggregator. Specifically, we propose a remove-then-clip aggregator, whereby each benign worker meticulously filters the neighbors' values and subsequently projects the remaining values to a sphere centered at its local value, with an appropriately selected radius. We prove that our proposed method converges to a neighborhood of a stationary point for non-convex objectives under standard assumptions. Furthermore, empirical evaluations are provided to demonstrate the superior performance of our method in comparison to existing algorithms, under various Byzantine attack models.