Byzantine broadcast (BB) and Byzantine agreement (BA) are two most fundamental problems and essential building blocks in distributed computing, and improving their efficiency is of interest to both theoreticians and practitioners. In this paper, we study extension protocols of BB and BA, i.e., protocols that solve BB/BA with long inputs of $l$ bits using lower costs than $l$ single-bit instances. We present new protocols with improved communication complexity in almost all settings: authenticated BA/BB with $t<n/2$, authenticated BB with $t<(1-ε)n$, unauthenticated BA/BB with $t<n/3$, and asynchronous reliable broadcast and BA with $t<n/3$. The new protocols are advantageous and significant in several aspects. First, they achieve the best-possible communication complexity of $Θ(nl)$ for wider ranges of input sizes compared to prior results. Second, the authenticated extension protocols achieve optimal communication complexity given the current best available BB/BA protocols for short messages. Third, to the best of our knowledge, our asynchronous and authenticated protocols in the setting are the first extension protocols in that setting.
This paper studies the {\em good-case latency} of {\em unauthenticated} Byzantine fault-tolerant broadcast, which measures the time it takes for all non-faulty parties to commit given a non-faulty broadcaster. For both asynchrony and synchrony, we show that $n\geq 4f$ is the tight resilience threshold that separates good-case 2 rounds and 3 rounds. For asynchronous Byzantine reliable broadcast (BRB), we also investigate the {\em bad-case latency} for all non-faulty parties to commit when the broadcaster is faulty but some non-faulty party commits. We provide matching upper and lower bounds on …
This paper explores the problem good-case latency of Byzantine fault-tolerant broadcast, motivated by the real-world latency and performance of practical state machine replication protocols. The good-case latency measures the time it takes for all non-faulty parties to commit when the designated broadcaster is non-faulty. We provide a complete characterization of tight bounds on good-case latency, in the authenticated setting under synchrony, partial synchrony and asynchrony. Some of our new results may be surprising, e.g., 2-round PBFT-style partially synchronous Byzantine broadcast is possib…
We consider the problem of reliably broadcasting information in a multihop asynchronous network that is subject to Byzantine failures. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the authentic message and nothing else), but they require a highly connected network. An approach giving only probabilistic guarantees (correct nodes deliver the authentic message with high probability) was recently proposed for loosely connected networks, such as grids and tori. Yet, the proposed solution requires a specific initialization (that includes global k…
Fault tolerance of a blockchain is often characterized by the fraction $f$ of "adversarial power" that it can tolerate in the system. Despite the fast progress in blockchain designs in recent years, existing blockchain systems can still only tolerate $f$ below $0.5$. Can practically usable blockchains tolerate a malicious majority, i.e., $f$ above $0.5$? This work presents a positive answer to this question. We first note that the well-known impossibility of {\em byzantine consensus} for $f$ above $0.5$ does not carry over to blockchains. To tolerate $f$ above $0.5$, we use {\em byzantine broa…
This paper investigates the problem \textit{good-case latency} of Byzantine agreement, broadcast and state machine replication in the synchronous authenticated setting. The good-case latency measure captures the time it takes to reach agreement when all non-faulty parties have the same input (or in BB/SMR when the sender/leader is non-faulty). Previous result implies a lower bound showing that any Byzantine agreement or broadcast protocol tolerating more than $n/3$ faults must have a good-case latency of at least $Δ$, where $Δ$ is the assumed maximum message delay bound. Our first result is a …
We consider the problem of reliably broadcasting information in a multihop asynchronous network in the presence of Byzantine failures: some nodes may exhibit unpredictable malicious behavior. We focus on completely decentralized solutions. Few Byzantine-robust algorithms exist for loosely connected networks. A recent solution guarantees reliable broadcast on a torus when D > 4, D being the minimal distance between two Byzantine nodes. In this paper, we generalize this result to 4-connected planar graphs. We show that reliable broadcast can be guaranteed when D > Z, Z being the maximal number o…
The spectacular success of Bitcoin and Blockchain Technology in recent years has provided enough evidence that a widespread adoption of a common cryptocurrency system is not merely a distant vision, but a scenario that might come true in the near future. However, the presence of Bitcoin's obvious shortcomings such as excessive electricity consumption, unsatisfying transaction throughput, and large validation time (latency) makes it clear that a new, more efficient system is needed. We propose a protocol in which a set of nodes maintains and updates a linear ordering of transactions that are be…
We present new protocols for Byzantine state machine replication and Byzantine agreement in the synchronous and authenticated setting. The celebrated PBFT state machine replication protocol tolerates $f$ Byzantine faults in an asynchronous setting using $3f+1$ replicas, and has since been studied or deployed by numerous works. In this work, we improve the Byzantine fault tolerance threshold to $n=2f+1$ by utilizing a relaxed synchrony assumption. We present a synchronous state machine replication protocol that commits a decision every 3 rounds in the common case. The key challenge is to ensure…
In this paper we extend the \emph{Multidimensional Byzantine Agreement (MBA) Protocol}, a {leaderless} Byzantine agreement for lists of arbitrary values, into a protocol suitable for wide gossiping networks: \emph{Cob}. This generalization allows the consensus process to be run by an incomplete network of nodes provided with (non-synchronized) same-speed clocks. Not all nodes are active in every step, so the network size does not hamper the efficiency, as long as the gossiping broadcast delivers the messages to every node in reasonable time. These network assumptions model more closely real-li…
In this paper, we challenge the conventional approach of state machine replication systems to design deterministic agreement protocols in the eventually synchronous communication model. We first prove that no such protocol can guarantee bounded communication cost before the global stabilization time and propose a different approach that hopes for the best (synchrony) but prepares for the worst (asynchrony). Accordingly, we design an optimistic byzantine agreement protocol that first tries an efficient deterministic algorithm that relies on synchrony for termination only, and then, only if an a…
In this paper we will present the Multidimensional Byzantine Agreement (MBA) Protocol, a leaderless Byzantine agreement protocol defined for complete and synchronous networks that allows a network of nodes to reach consensus on a vector of relevant information regarding a set of observed events. The consensus process is carried out in parallel on each component, and the output is a vector whose components are either values with wide agreement in the network (even if no individual node agrees on every value) or a special value $\bot$ that signals irreconcilable disagreement. The MBA Protocol is…
This paper introduces Flexible BFT, a new approach for BFT consensus solution design revolving around two pillars, stronger resilience and diversity. The first pillar, stronger resilience, involves a new fault model called alive-but-corrupt faults. Alive-but-corrupt replicas may arbitrarily deviate from the protocol in an attempt to break safety of the protocol. However, if they cannot break safety, they will not try to prevent liveness of the protocol. Combining alive-but-corrupt faults into the model, Flexible BFT is resilient to higher corruption levels than possible in a pure Byzantine fau…
Byzantine fault tolerant protocols enable state replication in the presence of crashed, malfunctioning, or actively malicious processes. Designing such protocols without the assistance of verification tools, however, is remarkably error-prone. In an adversarial environment, performance and flexibility come at the cost of complexity, making the verification of existing protocols extremely difficult. We take a different approach and propose a formally verified consensus protocol designed for a specific use case: secure logging. Our protocol allows each node to propose entries in a parallel subro…
The surging interest in blockchain technology has revitalized the search for effective Byzantine consensus schemes. In particular, the blockchain community has been looking for ways to effectively integrate traditional Byzantine fault-tolerant (BFT) protocols into a blockchain consensus layer allowing various financial institutions to securely agree on the order of transactions. However, existing BFT protocols can only scale to tens of nodes due to their $O(n^2)$ message complexity. In this paper, we propose FastBFT, a fast and scalable BFT protocol. At the heart of FastBFT is a novel message …
The decentralized cryptocurrency Bitcoin has experienced great success but also encountered many challenges. One of the challenges has been the long confirmation time. Another challenge is the lack of incentives at certain steps of the protocol, raising concerns for transaction withholding, selfish mining, etc. To address these challenges, we propose Solida, a decentralized blockchain protocol based on reconfigurable Byzantine consensus augmented by proof-of-work. Solida improves on Bitcoin in confirmation time, and provides safety and liveness assuming the adversary control less than (roughly…
Byzantine fault-tolerant (BFT) state machine replication (SMR) has been studied for over 30 years. Recently it has received more attention due to its application in permissioned blockchain systems. A sequence of research efforts focuses on improving the commit latency of the SMR protocol in the common good case, including PBFT with $3$-round latency and $n\geq 3f+1$ and FaB with $2$-round latency and $n\geq 5f+1$. In this paper, we propose an authenticated protocol that solves $2$-round BFT SMR with only $n\geq 5f-1$ replicas, which refutes the optimal resiliency claim made in FaB for needing …
The problem of Authenticated Byzantine Generals (ABG) aims to simulate a virtual reliable broadcast channel from the General to all the players via a protocol over a real (point-to-point) network in the presence of faults. We propose a new model to study the self-composition of ABG protocols. The central dogma of our approach can be phrased as follows: Consider a player who diligently executes (only) the delegated protocol but the adversary steals some private information from him. Should such a player be considered faulty? With respect to ABG protocols, we argue that the answer has to be no. …
Byzantine Agreement (BA) is one of the most fundamental problems in distributed computing, and its communication complexity is an important efficiency metric. It is well known that quadratic communication is necessary for BA in the worst case due to a lower bound by Dolev and Reischuk. This lower bound has been shown to be tight for the unauthenticated setting with $f < n/3$ by Berman et al. but a considerable gap remains for the authenticated setting with $n/3 \le f < n/2$. This paper provides two results towards closing this gap. Both protocols have a quadratic communication complexity and h…
Byzantine general problem is the core problem of the consensus algorithm, and many protocols are proposed recently to improve the decentralization level, the performance and the security of the blockchain. There are two challenging issues when the blockchain is operating in practice. First, the outcomes of the consensus algorithm are usually related to the incentive model, so whether each participant's value has an equal probability of being chosen becomes essential. However, the issues of fairness are not captured in the traditional security definition of Byzantine agreement. Second, the bloc…
Secure networks rely upon players to maintain security and reliability. However not every player can be assumed to have total loyalty and one must use methods to uncover traitors in such networks. We use the original concept of the Byzantine Generals Problem by Lamport, and the more formal Byzantine Agreement describe by Linial, to nd traitors in secure networks. By applying general fault-tolerance methods to develop a more formal design of secure networks we are able to uncover traitors amongst a group of players. We also propose methods to integrate this system with insecure channels. This n…
In this paper we propose a protocol of quantum communication to achieve Byzantine agreement among multiple parties. The striking feature of our proposal in comparison to the existing protocols is that we do not use entanglement to achieve the agreement. There are two stages in our protocol. In the first stage, a list of numbers that satisfies some special properties is distributed to every participant by a group of semi-honest list distributors via quantum secure communication. Then, in the second stage those participants exchange some information to reach agreement.
We propose Byzantine-robust federated learning protocols with nearly optimal statistical rates. In contrast to prior work, our proposed protocols improve the dimension dependence and achieve a tight statistical rate in terms of all the parameters for strongly convex losses. We benchmark against competing protocols and show the empirical superiority of the proposed protocols. Finally, we remark that our protocols with bucketing can be naturally combined with privacy-guaranteeing procedures to introduce security against a semi-honest server. The code for evaluation is provided in https://github.…
We proposed a framework of quantum-enhanced logic-based blockchain, which improves the efficiency and power of quantum-secured blockchain. The efficiency is improved by using a new quantum honest-success Byzantine agreement protocol to replace the classical Byzantine agreement protocol, while the power is improved by incorporating quantum protection and quantum certificate into the syntax of transactions. Our quantum-secured logic-based blockchain can already be implemented by the current technology. The cryptocurrency created and transferred in our blockchain is called qulogicoin. Incorporati…
We present a device-independent quantum scheme for the {\em Byzantine Generals} problem. The protocol is for three parties. Party $C$ is to send two identical one bit messages to parties $A$ and $B$. The receivers $A$ and $B$ may exchange two one bit messages informing the other party on the message received from $C$. A bit flipping error in one of the transmissions, does not allow the receiving parties to establish what was the message of $C$. Our quantum scheme has the feature that if the messages of the Byzantine protocol are readable (that is give an unambiguous bit value for any of the re…
Network coding achieves optimal throughput in multicast networks. However, throughput optimality \emph{relies} on the network nodes or routers to code \emph{correctly}. A Byzantine node may introduce junk packets in the network (thus polluting downstream packets and causing the sinks to receive the wrong data) or may choose coding coefficients in a way that significantly reduces the throughput of the network. Most prior work focused on the problem of Byzantine nodes polluting packets. However, even if a Byzantine node does not pollute packets, he can still affect significantly the throughput o…
Increasingly machine learning systems are being deployed to edge servers and devices (e.g. mobile phones) and trained in a collaborative manner. Such distributed/federated/decentralized training raises a number of concerns about the robustness, privacy, and security of the procedure. While extensive work has been done in tackling with robustness, privacy, or security individually, their combination has rarely been studied. In this paper, we propose a secure two-server protocol that offers both input privacy and Byzantine-robustness. In addition, this protocol is communication-efficient, fault-…
The blockchain technology has achieved tremendous success in open (permissionless) decentralized consensus by employing proof-of-work (PoW) or its variants, whereby unauthorized nodes cannot gain disproportionate impact on consensus beyond their computational power. However, PoW-based systems incur a high delay and low throughput, making them ineffective in dealing with real-time applications. On the other hand, byzantine fault-tolerant (BFT) consensus algorithms with better delay and throughput performance have been employed in closed (permissioned) settings to avoid Sybil attacks. In this pa…
