Lewis Tseng

Iterative approximate byzantine consensus in arbitrary directed graphs

This paper proves a necessary and sufficient condition for the existence of iterative, algorithms that achieve approximate Byzantine consensus in arbitrary directed graphs, where each directed edge represents a communication channel between a pair of nodes. The class of iterative algorithms considered in this paper ensures that, after each iteration of the algorithm, the state of each fault-free node remains in the convex hull of the states of the fault-free nodes at the end of the previous iteration. The following convergence requirement is imposed: for any ε > 0, after a sufficiently large number of iterations, the states of the fault-free nodes are guaranteed to be within ε of each other. To the best of our knowledge, tight necessary and sufficient conditions for the existence of such iterative consensus algorithms in synchronous arbitrary point-to-point networks in presence of Byzantine faults, have not been developed previously. The methodology and results presented in this paper can also be extended to asynchronous systems.

Iterative Approximate Byzantine Consensus under a Generalized Fault Model

In this work, we consider a generalized fault model [7,9,5] that can be used to represent a wide range of failure scenarios, including correlated failures and non-uniform node reliabilities. Under the generalized fault model, we explore iterative approximate Byzantine consensus (IABC) algorithms [15] in arbitrary directed networks. We prove a tight necessary and sufficient condition on the underlying communication graph for the existence of IABC algorithms.

Fault-Tolerant Consensus in Directed Graphs

Consider a point-to-point network in which nodes are connected by directed links. This paper proves tight necessary and sufficient conditions on the underlying communication graphs for solving the following fault-tolerant consensus problems: Exact crash-tolerant consensus in synchronous systems, Approximate crash-tolerant consensus in asynchronous systems, and Exact Byzantine consensus in synchronous systems. The problem of asynchronous Byzantine consensus in directed graphs remains open. Prior work has developed analogous necessary and sufficient conditions for undirected graphs [11,3,9]. However, the conditions for undirected graphs are not adequate to completely characterize these consensus problems in directed graphs. Moreover, the algorithms for directed graphs presented in this paper are substantially different from those previously developed for undirected graphs. Other prior work on directed graphs has explored somewhat different problems than those solved in this paper.

Characterizing and Adapting the Consistency-Latency Tradeoff in Distributed Key-Value Stores

The CAP theorem is a fundamental result that applies to distributed storage systems. In this article, we first present and prove two CAP-like impossibility theorems. To state these theorems, we present probabilistic models to characterize the three important elements of the CAP theorem: consistency (C), availability or latency (A), and partition tolerance (P). The theorems show the un-achievable envelope, that is, which combinations of the parameters of the three models make them impossible to achieve together. Next, we present the design of a class of systems called Probabilistic CAP (PCAP) that perform close to the envelope described by our theorems. In addition, these systems allow applications running on a single data center to specify either a latency Service Level Agreement (SLA) or a consistency SLA. The PCAP systems automatically adapt, in real time and under changing network conditions, to meet the SLA while optimizing the other C/A metric. We incorporate PCAP into two popular key-value stores: Apache Cassandra and Riak. Our experiments with these two deployments, under realistic workloads, reveal that the PCAP systems satisfactorily meets SLAs and perform close to the achievable envelope. We also extend PCAP from a single data center to multiple geo-distributed data centers.

Broadcast using certified propagation algorithm in presence of Byzantine faults

We explore the correctness of the Certified Propagation Algorithm (CPA) [6,1,8,5] in solving broadcast with locally bounded Byzantine faults. CPA allows the nodes to use only local information regarding the network topology. We provide a tight necessary and sufficient condition on the network topology for the correctness of CPA. We explore using Certified Propagation Algorithm (CPA) to achieve broadcast.The fault model we considered is the locally bounded Byzantine faults.We identify a tight necessary and sufficient condition on the network topology.We also propose extensions of the results.

Iterative Approximate Consensus in the Presence of Byzantine Link Failures

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each directed link of the underlying communication graph represents a communication channel between a pair of nodes. We adopt the transient Byzantine link failure model [15, 16], where an omniscient adversary controls a subset of the directed communication links, but the nodes are assumed to be fault-free.

Asynchronous convex hull consensus in the presence of crash faults

This paper defines a new consensus problem, convex hull consensus. The input at each process is a d-dimensional vector of reals (or, equivalently, a point in the d-dimensional Euclidean space), and the output at each process is a convex polytope contained within the convex hull of the inputs at the fault-free processes. We explore the convex hull consensus problem under crash faults with incorrect inputs, and present an asynchronous approximate convex hull consensus algorithm with optimal fault tolerance that reaches consensus on an optimal output polytope. Convex hull consensus can be used to solve other related problems. For instance, a solution for convex hull consensus trivially yields a solution for vector (multidimensional) consensus. More importantly, convex hull consensus can potentially be used to solve other more interesting problems, such as function optimization.

Recent Results on Fault-Tolerant Consensus in Message-Passing Networks

Fault-tolerant consensus has been studied extensively in the literature, because it is one of the important distributed primitives and has wide applications in practice. This paper surveys important works on fault-tolerant consensus in message-passing networks, and the focus is on results from the past decade. Particularly, we categorize the results into two groups: new problem formulations and practical applications. In the first part, we discuss new ways to define the consensus problem, which include larger input domains, enriched correctness properties, different network models, etc. In the second part, we focus on real-world systems that use Paxos or Raft to reach consensus, and Byzantine Fault-Tolerant (BFT) systems. We also discuss Bitcoin, which can be related to solving Byzantine consensus in anonymous systems, and compare Bitcoin with BFT systems and Byzantine consensus algorithms.

Voting in the Presence of Byzantine Faults

Voting (or election) algorithms are used widely in many safety-critical systems to mask errors. Most systems only tolerate malicious (or Byzantine) voters – these systems assume the existence of a correct and centralized mechanism to collect the votes and propagate the voting output to each voter. However, in many realistic scenarios, such a centralized voting mechanism is not feasible. Thus, we study the Byzantine voting problem – no centralized mechanism exists in the system, and voters may become Byzantine faulty. We first present impossibility results in both synchronous and asynchronous systems. To circumvent the impossibility results presented in this paper, we propose two relaxed voting properties that are achievable and present optimal voting algorithms that satisfy the relaxed properties. Finally, we show that it is possible to design Byzantine voting algorithms that produce the voting output in one communication step under contention-free scenarios.

Bitcoin’s Consistency Property

Bitcoin is the most popular cryptocurrency nowadays. Inspired by the success, both industry and academia seek to apply Bitcoins core technique, Blockchain, to other fields like finance, healthcare and Internet-of-Things. One main application is to use Blockchain as the distributed transaction ledger system, a ledger (or a log) of all transactions that is maintained by anonymous participants in a distributed fashion. For the ledger system, consistency is an important property which specifies how the system orders the transactions. Intuitively, Blockchain is designed to maintain a single ground truth – the chain itself is the order of the transactions that all participants should respect. However, we show that under some circumstances, Bitcoin violates eventual consistency, i.e., participants would not converge to a single chain. Thus, we urge a more thorough study on Bitcoins consistency properties. At the end of the paper, we propose related research directions.