Short Note on Complexity of Multi-Value Byzantine Agreement

Byzantine Agreement, Broadcast and State Machine Replication with Near-optimal Good-case Latency

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 …

Optimal Communication Complexity of Authenticated Byzantine Agreement

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…

Asynchronous Byzantine Agreement in Incomplete Networks [Technical Report]

The Byzantine agreement problem is considered to be a core problem in distributed systems. For example, Byzantine agreement is needed to build a blockchain, a totally ordered log of records. Blockchains are asynchronous distributed systems, fault-tolerant against Byzantine nodes. In the literature, the asynchronous byzantine agreement problem is studied in a fully connected network model where every node can directly send messages to every other node. This assumption is questionable in many real-world environments. In the reality, nodes might need to communicate by means of an incomplete netwo…

认证隐式拜占庭协议的次线性消息界

Sublinear Message Bounds of Authenticated Implicit Byzantine Agreement

本文针对同步全连接网络中的认证隐式拜占庭协议，提出基于PKI、全局硬币与哈希的随机算法，在诚实多数下以$\tilde{O}(\sqrt{n})$消息和$\tilde{O}(1)$轮达成一致，并给出匹配下界。

Byzantine Agreement with Less Communication: Recent Advances

In recent years, Byzantine Agreement is being considered in increasing scales due to the proliferation of blockchains and other decentralized financial technologies. Consequently, a number of works have improved its communication complexity in various network models. In this short paper we survey recent advances and outline some open research questions on the subject.

Juggernaut：高效的密码学无关拜占庭协议

Juggernaut: Efficient Crypto-Agnostic Byzantine Agreement

研究密码学无关拜占庭协议，提出编译器将认证与信息论设置下的协议转换为在密码学被攻破时仍具回退安全性的协议，改进了比特复杂度并保持认证设置下的效率。

次平方多值异步拜占庭协议 WHP

Subquadratic Multivalued Asynchronous Byzantine Agreement WHP

本文填补了拜占庭异步环境下多值共识到二元共识归约的空白，并利用新开发的次平方二元拜占庭协议技术实现了次平方通信复杂度。

A Necessary Condition for Byzantine $k$-Set Agreement

This short paper presents a necessary condition for Byzantine $k$-set agreement in (synchronous or asynchronous) message-passing systems and asynchronous shared memory systems where the processes communicate through atomic single-writer multi-reader registers. It gives a proof, which is particularly simple, that $k$-set agreement cannot be solved $t$-resiliently in an $n$-process system when $n \leq 2t + \frac{t}{k}$. This bound is tight for the case $k=1$ (Byzantine consensus) in synchronous message-passing systems.

Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems

In this paper, we show that the protocol complex of a Byzantine synchronous system can remain $(k - 1)$-connected for up to $\lceil t/k \rceil$ rounds, where $t$ is the maximum number of Byzantine processes, and $t \ge k \ge 1$. This topological property implies that $\lceil t/k \rceil + 1$ rounds are necessary to solve $k$-set agreement in Byzantine synchronous systems, compared to $\lfloor t/k \rfloor + 1$ rounds in synchronous crash-failure systems. We also show that our connectivity bound is tight as we indicate solutions to Byzantine $k$-set agreement in exactly $\lceil t/k \rceil + 1$ sy…

Improved Extension Protocols for Byzantine Broadcast and Agreement

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 asyn…

Correction to Byzantine Agreement in Expected Polynomial Time, JACM 2016

This is a correction by the authors to "Byzantine Agreement in Expected Polynomial Time" which appeared in the Journal of the ACM in 2016. It corrects a failure in the paper to consider the adversary's ability to decide the number of fair coinflips in an iteration, where this number ranges between n(n-t) and n(n-2t).

The Sum of Its Parts: Analysis of Federated Byzantine Agreement Systems

Federated Byzantine Agreement Systems (FBASs) are a fascinating new paradigm in the context of consensus protocols. Originally proposed for powering the Stellar payment network, FBASs can instantiate Byzantine quorum systems without requiring out-of-band agreement on a common set of validators; every node is free to decide for itself with whom it requires agreement. Sybil-resistant and yet energy-efficient consensus protocols can therefore be built upon FBASs, and the "decentrality" possible with the FBAS paradigm might be sufficient to reduce the use of environmentally unsustainable proof-of-…

Byzantine Lattice Agreement in Asynchronous Systems

We study the Byzantine lattice agreement (BLA) problem in asynchronous distributed message passing systems. In the BLA problem, each process proposes a value from a join semi-lattice and needs to output a value also in the lattice such that all output values of correct processes lie on a chain despite the presence of Byzantine processes. We present an algorithm for this problem with round complexity of $O(\log f)$ which tolerates $f < \frac{n}{5}$ Byzantine failures in the asynchronous setting without digital signatures, where $n$ is the number of processes. We also show how this algorithm can…

Not a COINcidence: Sub-Quadratic Asynchronous Byzantine Agreement WHP

King and Saia were the first to break the quadratic word complexity bound for Byzantine Agreement in synchronous systems against an adaptive adversary, and Algorand broke this bound with near-optimal resilience (first in the synchronous model and then with eventual-synchrony). Yet the question of asynchronous sub-quadratic Byzantine Agreement remained open. To the best of our knowledge, we are the first to answer this question in the affirmative. A key component of our solution is a shared coin algorithm based on a VRF. A second essential ingredient is VRF-based committee sampling, which we fo…

Validated Asynchronous Byzantine Agreement with Optimal Resilience and Asymptotically Optimal Time and Word Communication

We provide a new protocol for Validated Asynchronous Byzantine Agreement. Validated (multi-valued) Asynchronous Byzantine Agreement is a key building block in constructing Atomic Broadcast and fault-tolerant state machine replication in the asynchronous setting. Our protocol can withstand the optimal number $f<n/3$ of Byzantine failures and reaches agreement in the asymptotically optimal expected $O(1)$ running time. Honest parties in our protocol send only an expected $O(n^2)$ messages where each message contains a value and a constant number of signatures. Hence our total expected communicat…

Byzantine Agreement with Faulty Majority using Bounded Broadcast

Byzantine Agreement introduced in [Pease, Shostak, Lamport, 80] is a widely used building block of reliable distributed protocols. It simulates broadcast despite the presence of faulty parties within the network, traditionally using only private unicast links. Under such conditions, Byzantine Agreement requires more than 2/3 of the parties to be compliant. [Fitzi, Maurer, 00], constructed a Byzantine Agreement protocol for any compliant majority based on an additional primitive allowing transmission to any two parties simultaneously. They proposed a problem of generalizing these results to wid…

一种使用委员会的高效可验证异步拜占庭共识协议

An efficient validated asynchronous byzantine agreement protocol using committee

本文提出一种基于随机子集委员会的可验证异步拜占庭共识协议，仅让部分参与方广播请求以降低消息和计算开销，并通过理论分析证明其高效性。

Approximate Agreement under Mobile Byzantine Faults

In this paper we address Approximate Agreement problem in the Mobile Byzantine faults model. Our contribution is threefold. First, we propose the the first mapping from the existing variants of Mobile Byzantine models to the Mixed-Mode faults model.This mapping further help us to prove the correctness of class MSR (Mean-Subsequence-Reduce) Approximate Agreement algorithms in the Mobile Byzantine fault model, and is of independent interest. Secondly, we prove lower bounds for solving Approximate Agreement under all existing Mobile Byzantine faults models. Interestingly, these lower bounds are d…

Fair Byzantine Agreements for Blockchains

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…

Asynchronous Byzantine Agreement with Optimal Resilience and Linear Complexity

Given a system with $n > 3t + 1$ processes, where $t$ is the tolerated number of faulty ones, we present a fast asynchronous Byzantine agreement protocol that can reach agreement in $O(t)$ expected running time. This improves the $O(n^2)$ expected running time of Abraham, Dolev, and Halpern [PODC 2008]. Furthermore, if $n = (3 + \varepsilon) t$ for any $\varepsilon > 0$, our protocol can reach agreement in $O (1 / \varepsilon)$ expected running time. This improves the result of Feldman and Micali [STOC 1988] (with constant expected running time when $n > 4 t$).

Byzantine Agreement with Optimal Early Stopping, Optimal Resilience and Polynomial Complexity

We provide the first protocol that solves Byzantine agreement with optimal early stopping ($\min\{f+2,t+1\}$ rounds) and optimal resilience ($n>3t$) using polynomial message size and computation. All previous approaches obtained sub-optimal results and used resolve rules that looked only at the immediate children in the EIG (\emph{Exponential Information Gathering}) tree. At the heart of our solution are new resolve rules that look at multiple layers of the EIG tree.

Byzantine Agreement with Unknown Participants and Failures

A set of mutually distrusting participants that want to agree on a common opinion must solve an instance of a Byzantine agreement problem. These problems have been extensively studied in the literature. However, most of the existing solutions assume that the participants are aware of $n$ -- the total number of participants in the system -- and $f$ -- an upper bound on the number of Byzantine participants. In this paper, we show that most of the fundamental agreement problems can be solved without affecting resiliency even if the participants do not know the values of (possibly changing) $n$ an…

应对拜占庭与反复瞬时故障的自稳定复制状态机

Self-Stabilizing Replicated State Machine Coping with Byzantine and Recurring Transient Faults

本文提出首个同时具备拜占庭容错、反复瞬时容错、准确性和自稳定能力的重复拜占庭协议，可从任意配置恢复一致性，并明确给出多类故障下的容忍界。

Revisiting EZBFT: A Decentralized Byzantine Fault Tolerant Protocol with Speculation

In this note, we revisit EZBFT[2] and present safety, liveness and execution consistency violations in the protocol. To demonstrate these violations, we present simple scenarios, involving only four replicas, two clients, and one or two owner changes. We also note shortcomings of the presented TLA+ specification used to model check the proposed protocol.

Byzantine Preferential Voting

In the Byzantine agreement problem, n nodes with possibly different input values aim to reach agreement on a common value in the presence of t < n/3 Byzantine nodes which represent arbitrary failures in the system. This paper introduces a generalization of Byzantine agreement, where the input values of the nodes are preference rankings of three or more candidates. We show that consensus on preferences, which is an important question in social choice theory, complements already known results from Byzantine agreement. In addition preferential voting raises new questions about how to approximate …

所有拜占庭协议问题都是昂贵的

All Byzantine Agreement Problems are Expensive

本文证明了所有非平凡的拜占庭协议问题在最坏情况下都需要交换Omega(t^2)条消息，通过确定最弱协议问题并运用新颖的不可区分性论证，解决了长期未决的开放问题。

Dandelion: multiplexing Byzantine agreements to unlock blockchain performance

Permissionless blockchain protocols are known to consume an outrageous amount of computing power and suffer from a trade-off between latency and confidence in transaction confirmation. The recently proposed Algorand blockchain protocol employs Byzantine agreements and has shown transaction confirmation latency on the order of seconds. Its strong resilience to Denial-of-Service and Sybil attacks and its low computing power footprint make it a strong candidate for the venue of decentralized economies and business ecosystems across industries. Nevertheless, Algorand's throughput is still far from…

Finding Traitors in Secure Networks Using Byzantine Agreements

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…

Dropbear: Machine Learning Marketplaces made Trustworthy with Byzantine Model Agreement

Marketplaces for machine learning (ML) models are emerging as a way for organizations to monetize models. They allow model owners to retain control over hosted models by using cloud resources to execute ML inference requests for a fee, preserving model confidentiality. Clients that rely on hosted models require trustworthy inference results, even when models are managed by third parties. While the resilience and robustness of inference results can be improved by combining multiple independent models, such support is unavailable in today's marketplaces. We describe Dropbear, the first ML model …

Detectable Quantum Byzantine Agreement for Any Arbitrary Number of Dishonest Parties

Reaching agreement in the presence of arbitrary faults is a fundamental problem in distributed computation, which has been shown to be unsolvable if one-third of the processes can fail, unless signed messages are used. In this paper, we propose a solution to a variation of the original BA problem, called Detectable Byzantine Agreement (DBA), that does not need to use signed messages. The proposed algorithm uses what we call $Q$-correlated lists, which are generated by a quantum source device. Once each process has one of these lists, they use them to reach the agreement in a classical manner. …

Mathematical Analysis and Algorithms for Federated Byzantine Agreement Systems

We give an introduction to federated Byzantine agreement systems (FBAS) with many examples ranging from small "academic" cases to the current Stellar network. We then analyze the main concepts from a mathematical and an algorithmic point of view. Based on work of Lachowski we derive algorithms for quorum enumeration, checking quorum intersection, and computing the intact nodes with respect to a given set of ill-behaved (Byzantine) nodes. We also show that from the viewpoint of the intactness probability of nodes, which we introduce in this paper, a hierarchical setup of nodes is inferior to an…

Byzantine Lattice Agreement in Synchronous Systems

In this paper, we study the Byzantine lattice agreement problem in synchronous systems. The lattice agreement problem in crash failure model has been studied both in synchronous and asynchronous systems, which leads to the current best upper bound of $O(\log f)$ rounds in both systems. However, very few algorithmic results are known for the lattice agreement problem in Byzantine failure model. The paper [Nowak et al., DISC, 2019] first gives an algorithm for a variant of the lattice agreement problem on cycle-free lattices that tolerates up to $f < n/(h(X) + 1)$ Byzantine faults, where $n$ is …

Breaking the O(n^2) Bit Barrier: Scalable Byzantine agreement with an Adaptive Adversary

We describe an algorithm for Byzantine agreement that is scalable in the sense that each processor sends only $\tilde{O}(\sqrt{n})$ bits, where $n$ is the total number of processors. Our algorithm succeeds with high probability against an \emph{adaptive adversary}, which can take over processors at any time during the protocol, up to the point of taking over arbitrarily close to a 1/3 fraction. We assume synchronous communication but a \emph{rushing} adversary. Moreover, our algorithm works in the presence of flooding: processors controlled by the adversary can send out any number of messages.…

Beyond One Third Byzantine Failures

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…

Self-stabilizing Byzantine Agreement

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…

稀疏网络中的全分布式拜占庭协议

Fully-Distributed Byzantine Agreement in Sparse Networks

针对稀疏有界度数网络中仅靠局部知识且需容忍大量拜占庭节点的开放问题，本文提出全分布式拜占庭协议，将容忍上限提升至 O(n/polylog(n))。

带预测的拜占庭协议

Byzantine Agreement with Predictions

研究带预测的拜占庭协议问题，提出在预测准确时提升效率、预测不准时保持最优性能的算法，证明消息复杂度下界并利用分类预测实现最优时间复杂度。

Expected Constant Time Self-stabilizing Byzantine Pulse Resynchronization

In extending fast digital clock synchronization to the bounded-delay model, the expected constant time Byzantine pulse resynchronization problem is investigated. In this problem, the synchronized state of the system should not only be deterministically maintained but be reached from arbitrary states with expected constant time in the presence of Byzantine faults. An intuitive geometric representation of the problem is introduced, with which the classical approximate agreement, randomized Byzantine agreement, and random walk are integrated with some geometric operations. Efficient realizations …

Byzantine Agreement in Polynomial Time with Near-Optimal Resilience

It has been known since the early 1980s that Byzantine Agreement in the full information, asynchronous model is impossible to solve deterministically against even one crash fault [FLP85], but that it can be solved with probability 1 [Ben83], even against an adversary that controls the scheduling of all messages and corrupts up to $f<n/3$ players [Bra87]. The main downside of [Ben83, Bra87] is that they terminate in $2^{Θ(n)}$ rounds in expectation whenever $f=Θ(n)$. King and Saia [KS16, KS18(arXiv:1812.10169)] developed a polynomial protocol (polynomial rounds, polynomial computation) that is …

拜占庭协作学习的近似一致算法

Approximate Agreement Algorithms for Byzantine Collaborative Learning

本文针对拜占庭协作学习中的聚合一致性问题，提出一种基于几何中位数的超盒算法，在集中式和去中心化设置下均能比传统均值方法更好地容忍符号翻转攻击。

随机拜占庭协议轮复杂度的下界

On the Round Complexity of Randomized Byzantine Agreement

本研究证明了随机拜占庭协议在一轮和两轮后停止概率的下界，并指出在合理猜想下，第三轮终止的协议已接近最优，匹配Micali的协议。

Efficient Asynchronous Byzantine Agreement without Private Setups

Efficient asynchronous Byzantine agreement (BA) protocols were mostly studied with private setups, e.g., pre-setup threshold cryptosystem. Challenges remain to reduce the large communication in the absence of such setups. Recently, Abraham et al. (PODC'21) presented the first asynchronous validated BA (VBA) with expected $O(n^3)$ messages and $O(1)$ rounds, relying on only public key infrastructure (PKI) setup, but the design still costs $O(λn^3 \log n)$ bits. Here $n$ is the number of parties, and $λ$ is a cryptographic security parameter. In this paper, we reduce the communication of private…

部分同步是免费的吗？拜占庭协议的新上界

Partial Synchrony for Free? New Upper Bounds for Byzantine Agreement

本文提出通用变换 Oper，将同步确定性拜占庭协议转为部分同步协议，在无密码学、最优容错下达到 O(n^2) 比特复杂度，并证明 Dolev-Reischuk 界在部分同步中仍紧。

OciorCOOL：更快的拜占庭协议与可靠广播

OciorCOOL: Faster Byzantine Agreement and Reliable Broadcast

本文将四阶段拜占庭协议 COOL 减少一个通信轮次，提出 OciorCOOL，并据此构造仅需六轮的最优可靠广播协议。

Validated Byzantine Asynchronous Multidimensional Approximate Agreement

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…

An Almost-Surely Terminating Polynomial Protocol for Asynchronous Byzantine Agreement with Optimal Resilience

Consider an asynchronous system with private channels and $n$ processes, up to $t$ of which may be faulty. We settle a longstanding open question by providing a Byzantine agreement protocol that simultaneously achieves three properties: 1. (optimal) resilience: it works as long as $n>3t$ 2. (almost-sure) termination: with probability one, all nonfaulty processes terminate 3. (polynomial) efficiency: the expected computation time, memory consumption, message size, and number of messages sent are all polynomial in $n$. Earlier protocols have achieved only two of these three properties. In partic…

The Contest Between Simplicity and Efficiency in Asynchronous Byzantine Agreement

In the wake of the decisive impossibility result of Fischer, Lynch, and Paterson for deterministic consensus protocols in the aynchronous model with just one failure, Ben-Or and Bracha demonstrated that the problem could be solved with randomness, even for Byzantine failures. Both protocols are natural and intuitive to verify, and Bracha's achieves optimal resilience. However, the expected running time of these protocols is exponential in general. Recently, Kapron, Kempe, King, Saia, and Sanwalani presented the first efficient Byzantine agreement algorithm in the asynchronous, full information…

Complexity of Multi-Value Byzantine Agreement

In this paper, we consider the problem of maximizing the throughput of Byzantine agreement, given that the sum capacity of all links in between nodes in the system is finite. We have proposed a highly efficient Byzantine agreement algorithm on values of length l>1 bits. This algorithm uses error detecting network codes to ensure that fault-free nodes will never disagree, and routing scheme that is adaptive to the result of error detection. Our algorithm has a bit complexity of n(n-1)l/(n-t), which leads to a linear cost (O(n)) per bit agreed upon, and overcomes the quadratic lower bound (Omega…

Revisiting Fast Practical Byzantine Fault Tolerance

In this note, we observe a safety violation in Zyzzyva and a liveness violation in FaB. To demonstrate these issues, we require relatively simple scenarios, involving only four replicas, and one or two view changes. In all of them, the problem is manifested already in the first log slot.

Synchronous Byzantine Lattice Agreement in ${\cal O}(\log (f))$ Rounds

In the Lattice Agreement (LA) problem, originally proposed by Attiya et al. \cite{Attiya:1995}, a set of processes has to decide on a chain of a lattice. More precisely, each correct process proposes an element $e$ of a certain join-semi lattice $L$ and it has to decide on a value that contains $e$. Moreover, any pair $p_i,p_j$ of correct processes has to decide two values $dec_i$ and $dec_j$ that are comparable (e.g., $dec_i \leq dec_j$ or $dec_j < dec_i$). LA has been studied for its practical applications, as example it can be used to implement a snapshot objects \cite{Attiya:1995} or a rep…

Quantum Byzantine Agreement via Hardy correlations and entanglement swapping

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…

Centrality of nodes in Federated Byzantine Agreement Systems

The federated Byzantine agreement system (FBAS) is a consensus model introduced by Mazières in 2016 where the participating nodes conceptually form a network, with links between them being established by each node individually and thus in a decentralized way. An important question is whether these decentralized decisions lead to an overall decentralized network. The level of (de-)centralization in a network can be assessed using centrality measures. In this paper we consider three different approaches for obtaining centrality measures for the nodes in an FBAS. Two of them are based on adapting…

Gorilla：安全的无许可拜占庭共识

Gorilla: Safe Permissionless Byzantine Consensus

本文提出Gorilla Sandglass，在中本聪式同步无许可模型下实现确定性一致与概率1终止，并通过映射至Sandglass执行证明其拜占庭容错正确性。

Byzantine Generalized Lattice Agreement

The paper investigates the Lattice Agreement (LA) problem in asynchronous systems. In LA each process proposes an element $e$ from a predetermined lattice, and has to decide on an element $e'$ of the lattice such that $e \leq e'$. Moreover, decisions of different processes have to be comparable (no two processes can decide two elements $e$ and $e'$ such that $(e \not\leq e') \land (e' \not\leq e)$). It has been shown that Generalized LA (i.e., a version of LA proposing and deciding on sequences of values) can be used to build a Replicated State Machine (RSM) with commutative update operations.…