Hybrid Fault-Tolerant Consensus in Asynchronous and Wireless Embedded Systems

Byzantine fault-tolerant (BFT) consensus in an asynchronous system can only tolerate up to floor[(n-1)/3] faulty processes in a group of n processes. This is quite a strict limit in certain application scenarios, for example a group consisting of only 3 processes. In order to break through this limit, we can leverage a hybrid fault model, in which a subset of the system is enhanced and cannot be arbitrarily faulty except for crashing. Based on this model, we propose a randomized binary consensus algorithm that executes in complete asynchrony, rather than in partial synchrony required by deterministic algorithms. It can tolerate up to floor[(n-1)/2] Byzantine faulty processes as long as the trusted subsystem in each process is not compromised, and terminates with a probability of one. The algorithm is resilient against a strong adversary, i. e. the adversary is able to inspect the state of the whole system, manipulate the delay of every message and process, and then adjust its faulty behaviour during execution. From a practical point of view, the algorithm is lightweight and has little dependency on lower level protocols or communication primitives. We evaluate the algorithm and the results show that it performs promisingly in a testbed consisting of up to 10 embedded devices connected via an ad hoc wireless network

Exploiting replication in distributed systems

Techniques are examined for replicating data and execution in directly distributed systems: systems in which multiple processes interact directly with one another while continuously respecting constraints on their joint behavior. Directly distributed systems are often required to solve difficult problems, ranging from management of replicated data to dynamic reconfiguration in response to failures. It is shown that these problems reduce to more primitive, order-based consistency problems, which can be solved using primitives such as the reliable broadcast protocols. Moreover, given a system that implements reliable broadcast primitives, a flexible set of high-level tools can be provided for building a wide variety of directly distributed application programs

Near Optimal Parallel Algorithms for Dynamic DFS in Undirected Graphs

Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently, Baswana et al. [SODA16] presented a simple algorithm for updating DFS tree of an undirected graph after an edge/vertex update in $\tilde{O}(n)$ time. However, their algorithm is strictly sequential. We present an algorithm achieving similar bounds, that can be adopted easily to the parallel environment. In the parallel model, a DFS tree can be computed from scratch using $m$ processors in expected $\tilde{O}(1)$ time [SiComp90] on an EREW PRAM, whereas the best deterministic algorithm takes $\tilde{O}(\sqrt{n})$ time [SiComp90,JAlg93] on a CRCW PRAM. Our algorithm can be used to develop optimal (upto polylog n factors deterministic algorithms for maintaining fully dynamic DFS and fault tolerant DFS, of an undirected graph. 1- Parallel Fully Dynamic DFS: Given an arbitrary online sequence of vertex/edge updates, we can maintain a DFS tree of an undirected graph in $\tilde{O}(1)$ time per update using $m$ processors on an EREW PRAM. 2- Parallel Fault tolerant DFS: An undirected graph can be preprocessed to build a data structure of size O(m) such that for a set of $k$ updates (where $k$ is constant) in the graph, the updated DFS tree can be computed in $\tilde{O}(1)$ time using $n$ processors on an EREW PRAM. Moreover, our fully dynamic DFS algorithm provides, in a seamless manner, nearly optimal (upto polylog n factors) algorithms for maintaining a DFS tree in semi-streaming model and a restricted distributed model. These are the first parallel, semi-streaming and distributed algorithms for maintaining a DFS tree in the dynamic setting.Comment: Accepted to appear in SPAA'17, 32 Pages, 5 Figure

Parameterizable Byzantine Broadcast in Loosely Connected Networks

We consider the problem of reliably broadcasting information in a multihop asynchronous network, despite the presence of Byzantine failures: some nodes are malicious and behave arbitrarly. We focus on non-cryptographic solutions. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the good information), but require a highly connected network. A probabilistic approach was recently proposed for loosely connected networks: the Byzantine failures are randomly distributed, and the correct nodes deliver the good information with high probability. A first solution require the nodes to initially know their position on the network, which may be difficult or impossible in self-organizing or dynamic networks. A second solution relaxed this hypothesis but has much weaker Byzantine tolerance guarantees. In this paper, we propose a parameterizable broadcast protocol that does not require nodes to have any knowledge about the network. We give a deterministic technique to compute a set of nodes that always deliver authentic information, for a given set of Byzantine failures. Then, we use this technique to experimentally evaluate our protocol, and show that it significantely outperforms previous solutions with the same hypotheses. Important disclaimer: these results have NOT yet been published in an international conference or journal. This is just a technical report presenting intermediary and incomplete results. A generalized version of these results may be under submission

A Scalable Byzantine Grid

Modern networks assemble an ever growing number of nodes. However, it remains difficult to increase the number of channels per node, thus the maximal degree of the network may be bounded. This is typically the case in grid topology networks, where each node has at most four neighbors. In this paper, we address the following issue: if each node is likely to fail in an unpredictable manner, how can we preserve some global reliability guarantees when the number of nodes keeps increasing unboundedly ? To be more specific, we consider the problem or reliably broadcasting information on an asynchronous grid in the presence of Byzantine failures -- that is, some nodes may have an arbitrary and potentially malicious behavior. Our requirement is that a constant fraction of correct nodes remain able to achieve reliable communication. Existing solutions can only tolerate a fixed number of Byzantine failures if they adopt a worst-case placement scheme. Besides, if we assume a constant Byzantine ratio (each node has the same probability to be Byzantine), the probability to have a fatal placement approaches 1 when the number of nodes increases, and reliability guarantees collapse. In this paper, we propose the first broadcast protocol that overcomes these difficulties. First, the number of Byzantine failures that can be tolerated (if they adopt the worst-case placement) now increases with the number of nodes. Second, we are able to tolerate a constant Byzantine ratio, however large the grid may be. In other words, the grid becomes scalable. This result has important security applications in ultra-large networks, where each node has a given probability to misbehave.Comment: 17 page

Echo-CGC: A Communication-Efficient Byzantine-Tolerant Distributed Machine Learning Algorithm in Single-Hop Radio Network

In the past few years, many Byzantine-tolerant distributed machine learning (DML) algorithms have been proposed in the point-to-point communication model. In this paper, we focus on a popular DML framework - the parameter server computation paradigm and iterative learning algorithms that proceed in rounds, e.g., [Gupta and Vaidya, 2020; El-Mhamdi et al., 2020; Chen et al., 2017]. One limitation of prior algorithms in this domain is the high communication complexity. All the Byzantine-tolerant DML algorithms that we are aware of need to send n d-dimensional vectors from worker nodes to the parameter server in each round, where n is the number of workers and d is the number of dimensions of the feature space (which may be in the order of millions). In a wireless network, power consumption is proportional to the number of bits transmitted. Consequently, it is extremely difficult, if not impossible, to deploy these algorithms in power-limited wireless devices. Motivated by this observation, we aim to reduce the communication complexity of Byzantine-tolerant DML algorithms in the single-hop radio network [Alistarh et al., 2010; Bhandari and Vaidya, 2005; Koo, 2004]. Inspired by the CGC filter developed by Gupta and Vaidya, PODC 2020 [Gupta and Vaidya, 2020], we propose a gradient descent-based algorithm, Echo-CGC. Our main novelty is a mechanism to utilize the broadcast properties of the radio network to avoid transmitting the raw gradients (full d-dimensional vectors). In the radio network, each worker is able to overhear previous gradients that were transmitted to the parameter server. Roughly speaking, in Echo-CGC, if a worker "agrees" with a combination of prior gradients, it will broadcast the "echo message" instead of the its raw local gradient. The echo message contains a vector of coefficients (of size at most n) and the ratio of the magnitude between two gradients (a float). In comparison, the traditional approaches need to send n local gradients in each round, where each gradient is typically a vector in a ultra-high dimensional space (d ? n). The improvement on communication complexity of our algorithm depends on multiple factors, including number of nodes, number of faulty workers in an execution, and the cost function. We numerically analyze the improvement, and show that with a large number of nodes, Echo-CGC reduces 80% of the communication under standard assumptions