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

On Byzantine Broadcast in Loosely Connected Networks

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 knowledge) of each node, which may be difficult or impossible to guarantee in self-organizing networks - for instance, a wireless sensor network, especially if they are prone to Byzantine failures. In this paper, we propose a new protocol offering guarantees for loosely connected networks that does not require such global knowledge dependent initialization. In more details, we give a methodology to determine whether a set of nodes will always deliver the authentic message, in any execution. Then, we give conditions for perfect reliable broadcast in a torus network. Finally, we provide experimental evaluation for our solution, and determine the number of randomly distributed Byzantine failures than can be tolerated, for a given correct broadcast probability.Comment: 1

Resilience in Numerical Methods: A Position on Fault Models and Methodologies

Future extreme-scale computer systems may expose silent data corruption (SDC) to applications, in order to save energy or increase performance. However, resilience research struggles to come up with useful abstract programming models for reasoning about SDC. Existing work randomly flips bits in running applications, but this only shows average-case behavior for a low-level, artificial hardware model. Algorithm developers need to understand worst-case behavior with the higher-level data types they actually use, in order to make their algorithms more resilient. Also, we know so little about how SDC may manifest in future hardware, that it seems premature to draw conclusions about the average case. We argue instead that numerical algorithms can benefit from a numerical unreliability fault model, where faults manifest as unbounded perturbations to floating-point data. Algorithms can use inexpensive "sanity" checks that bound or exclude error in the results of computations. Given a selective reliability programming model that requires reliability only when and where needed, such checks can make algorithms reliable despite unbounded faults. Sanity checks, and in general a healthy skepticism about the correctness of subroutines, are wise even if hardware is perfectly reliable.Comment: Position Pape

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

Reliable Communication in a Dynamic Network in the Presence of Byzantine Faults

We consider the following problem: two nodes want to reliably communicate in a dynamic multihop network where some nodes have been compromised, and may have a totally arbitrary and unpredictable behavior. These nodes are called Byzantine. We consider the two cases where cryptography is available and not available. We prove the necessary and sufficient condition (that is, the weakest possible condition) to ensure reliable communication in this context. Our proof is constructive, as we provide Byzantine-resilient algorithms for reliable communication that are optimal with respect to our impossibility results. In a second part, we investigate the impact of our conditions in three case studies: participants interacting in a conference, robots moving on a grid and agents in the subway. Our simulations indicate a clear benefit of using our algorithms for reliable communication in those contexts

A Study of Deep Learning Robustness Against Computation Failures

For many types of integrated circuits, accepting larger failure rates in computations can be used to improve energy efficiency. We study the performance of faulty implementations of certain deep neural networks based on pessimistic and optimistic models of the effect of hardware faults. After identifying the impact of hyperparameters such as the number of layers on robustness, we study the ability of the network to compensate for computational failures through an increase of the network size. We show that some networks can achieve equivalent performance under faulty implementations, and quantify the required increase in computational complexity

Fast Byzantine Leader Election in Dynamic Networks

International audienceWe study the fundamental Byzantine leader election problem in dynamic networks where the topology can change from round to round and nodes can also experience heavy churn (i.e., nodes can join and leave the network continuously over time). We assume the full information model where the Byzantine nodes have complete knowledge about the entire state of the network at every round (including random choices made by all the nodes), have unbounded computational power and can deviate arbitrarily from the protocol. The churn is controlled by an adversary that has complete knowledge and control over which nodes join and leave and at what times and also may rewire the topology in every round and has unlimited computational power, but is oblivious to the random choices made by the algorithm.Our main contribution is an O(log^3 n) round algorithm that achieves Byzantine leader election under the presence of up to O(n^(1/2)−ε) Byzantinenodes (for a small constant ε > 0) and a churn of up to O( √n/ polylog(n)) nodes per round (where n is the stable network size). The algorithm elects a leader with probability at least 1 − n^(−Ω(1)) and guarantees that it is an honest node with probability at least 1 − n^(−Ω(1)); assuming the algorithm succeeds, the leader’s identity will be known to a 1 − o(1) fraction of the honest nodes. Our algorithm is fully-distributed, lightweight, and is simple to implement. It is also scalable, as it runs in polylogarithmic (in n) time and requires nodes to send and receive messages of only polylogarithmic size per round. To the best of our knowledge, our algorithm is the first scalable solution for Byzantine leader election in a dynamic network with a high rate of churn; our protocol can also be used to solve Byzantine agreement in a straightforward way. We also show how to implement an (almost-everywhere) public coin with constant bias in a dynamic network with Byzantine nodes and provide a mechanism for enabling honest nodes to store information reliably in the network, which might be of independent interest