Byzantine Approximate Agreement on Graphs

Consider a distributed system with n processors out of which f can be Byzantine faulty. In the approximate agreement task, each processor i receives an input value x_i and has to decide on an output value y_i such that 1) the output values are in the convex hull of the non-faulty processors\u27 input values, 2) the output values are within distance d of each other. Classically, the values are assumed to be from an m-dimensional Euclidean space, where m >= 1. In this work, we study the task in a discrete setting, where input values with some structure expressible as a graph. Namely, the input values are vertices of a finite graph G and the goal is to output vertices that are within distance d of each other in G, but still remain in the graph-induced convex hull of the input values. For d=0, the task reduces to consensus and cannot be solved with a deterministic algorithm in an asynchronous system even with a single crash fault. For any d >= 1, we show that the task is solvable in asynchronous systems when G is chordal and n > (omega+1)f, where omega is the clique number of G. In addition, we give the first Byzantine-tolerant algorithm for a variant of lattice agreement. For synchronous systems, we show tight resilience bounds for the exact variants of these and related tasks over a large class of combinatorial structures

Multi-hop Byzantine reliable broadcast with honest dealer made practical

We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g., digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment

Byzantine Agreement Given Partial Broadcast

This paper considers unconditionally secure protocols for reliable broadcast among a set of n players, where up to t of the players can be corrupted by a (Byzantine) adversary but the remaining h = n - t players remain honest. In the standard model with a complete, synchronous network of bilateral authenticated communication channels among the players, broadcast is achievable if and only if 2n/h < 3. We show that, by extending this model by the existence of partial broadcast channels among subsets of b players, global broadcast can be achieved if and only if the number h of honest players satisfies 2n/h < b + 1. Achievability is demonstrated by protocols with communication and computation complexities polynomial in the size of the network, i.e., in the number of partial broadcast channels. A respective characterization for the related consensus problem is also give

EESMR: Energy Efficient BFT-SMR for the masses

Modern Byzantine Fault-Tolerant State Machine Replication (BFT-SMR) solutions focus on reducing communication complexity, improving throughput, or lowering latency. This work explores the energy efficiency of BFT-SMR protocols. First, we propose a novel SMR protocol that optimizes for the steady state, i.e., when the leader is correct. This is done by reducing the number of required signatures per consensus unit and the communication complexity by order of the number of nodes n compared to the state-of-the-art BFT-SMR solutions. Concretely, we employ the idea that a quorum (collection) of signatures on a proposed value is avoidable during the failure-free runs. Second, we model and analyze the energy efficiency of protocols and argue why the steady-state needs to be optimized. Third, we present an application in the cyber-physical system (CPS) setting, where we consider a partially connected system by optionally leveraging wireless multicasts among neighbors. We analytically determine the parameter ranges for when our proposed protocol offers better energy efficiency than communicating with a baseline protocol utilizing an external trusted node. We present a hypergraph-based network model and generalize previous fault tolerance results to the model. Finally, we demonstrate our approach's practicality by analyzing our protocol's energy efficiency through experiments on a CPS test bed. In particular, we observe as high as 64% energy savings when compared to the state-of-the-art SMR solution for n=10 settings using BLE.Comment: Appearing in Middleware 202

Fault Tolerance in Networks of Bounded Degree

Achieving processor cooperation in the presence of faults is a major problem in distributed systems. Popular paradigms such as Byzantine agreement have been studied principally in the context of a complete network. Indeed, Dolev [J. Algorithms, 3 (1982), pp. 14–30] and Hadzilacos [Issues of Fault Tolerance in Concurrent Computations, Ph.D. thesis, Harvard University, Cambridge, MA, 1984] have shown that Ω(t) connectivity is necessary if the requirement is that all nonfaulty processors decide unanimously, where t is the number of faults to be tolerated. We believe that in forseeable technologies the number of faults will grow with the size of the network while the degree will remain practically fixed. We therefore raise the question whether it is possible to avoid the connectivity requirements by slightly lowering our expectations. In many practical situations we may be willing to “lose” some correct processors and settle for cooperation between the vast majority of the processors. Thus motivated, we present a general simulation technique by which vertices (processors) in almost any network of bounded degree can simulate an algorithm designed for the complete network. The simulation has the property that although some correct processors may be cut off from the majority of the network by faulty processors, the vast majority of the correct processors will be able to communicate among themselves undisturbed by the (arbitrary) behavior of the faulty nodes. We define a new paradigm for distributed computing, almost-everywhere agreement, in which we require only that almost all correct processors reach consensus. Unlike the traditional Byzantine agreement problem, almost-everywhere agreement can be solved on networks of bounded degree. Specifically, we can simulate any sufficiently resilient Byzantine agreement algorithm on a network of bounded degree using our communication scheme described above. Although we “lose” some correct processors, effectively treating them as faulty, the vast majority of correct processors decide on a common value

Multi-hop Byzantine Reliable Broadcast with Honest Dealer Made Practical

We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g. digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment

Multi-hop Byzantine Reliable Broadcast with Honest Dealer Made Practical

We revisit Byzantine tolerant reliable broadcast with honest dealer algorithms in multi-hop networks. To tolerate Byzantine faulty nodes arbitrarily spread over the network, previous solutions require a factorial number of messages to be sent over the network if the messages are not authenticated (e.g. digital signatures are not available). We propose modifications that preserve the safety and liveness properties of the original unauthenticated protocols, while highly decreasing their observed message complexity when simulated on several classes of graph topologies, potentially opening to their employment

Meeting in a Convex World: Convex Consensus with Asynchronous Fallback

Convex Consensus (CC) allows a set of parties to agree on a value $v$ inside the convex hull of their inputs with respect to a predefined convexity notion, even in the presence of byzantine parties. In this work, we focus on achieving CC in the best-of-both-worlds paradigm, i.e., simultaneously tolerating at most $t_s$ corruptions if communication is synchronous, and at most $t_a \leq t_s$ corruptions if it is asynchronous. Our protocol is randomized, which is a requirement under asynchrony, and we prove that it achieves optimal resilience. In the process, we introduce communication primitives tailored to the best-of-both-worlds model, which we believe to be of independent interest. These are a deterministic primitive, which allows honest parties to obtain intersecting views, and a randomized primitive, leading to identical views (which is impossible to achieve deterministically). Afterwards, we consider achieving consensus using deterministic protocols, for which the agreement condition must be appropriately relaxed depending on the convexity space. For the relevant case of graph convexity spaces, we find that a previous asynchronous approximate agreement protocol for chordal graphs is incorrect, and hereby give a new protocol for the problem designed for the best-of-both-worlds model and achieving tight point-wise resilience bounds. Finally, we show that asynchronous graph approximate agreement remains unsolvable by deterministic protocols even when corruptions are restricted to at most two crashing nodes and the distance agreement threshold is linear in the size of the graph

Locality and Checkability in Wait-free Computing

22 pagesThis paper studies several notions of locality that are inherent to the specification of distributed tasks and independent of the computing environment, and investigates the ability of a shared memory wait-free system to solve tasks satisfying various forms of locality. First, we define a task to be projection-closed if every partial output π(t) for a full input s is also a valid output for the partial input π(s) and prove that projection-closed tasks are precisely those tasks that are wait-free checkable. Our second main contribution is dealing with a stronger notion of lo- cality of topological nature. A task T = (I, O, ∆) is said to be locality- preserving if and only if O is a covering complex of I, that is, each simplex s of I is mapped by ∆ to a set of simplexes of O each isomorphic to s. This topological property yields obstacles for wait-free solvability different in nature from the classical agreement impossibility results. On the other hand, locality-preserving tasks are projection-closed and therefore always wait-free checkable. We provide a classification of locality-preserving tasks in term of their computational power, by establishing a correspondence between locality-preserving tasks and subgroups of the edgepath group of a complex. Using this correspondence, we prove the existence of hierarchies of locality-preserving tasks, each one containing a universal task (induced by the universal covering complex), and at the bottom the trivial identity task

Unconditionally Reliable and Secure Message Transmission in Undirected Synchronous Networks: Possibility, Feasibility and Optimality

We study the interplay of network connectivity and the issues related to the ‘possibility’, ‘feasibility’ and ‘optimality’ for unconditionally reliable message transmission (URMT) and unconditionally secure message transmission (USMT) in an undirected synchronous network, under the influence of an adaptive mixed adversary having unbounded computing power, who can corrupt some of the nodes in the network in Byzantine, omission, fail-stop and passive fashion respectively. We consider two types of adversary, namely threshold and non-threshold. One of the important conclusions we arrive at from our study is that allowing a negligible error probability significantly helps in the ‘possibility’, ‘feasibility’ and ‘optimality’ of both reliable and secure message transmission protocols. To design our protocols, we propose several new techniques which are of independent interest