Presence Of Byzantine Attacks Research Articles

High-dimensional M-estimation for Byzantine-robust decentralized learning

In this paper, we focus on robust sparse M-estimation over decentralized networks in the presence of Byzantine attacks. In particular, a decentralized network is modeled as an undirected graph without a central node, while a small fraction of nodes usually behave arbitrarily and send erroneous information due to system breakdowns, cyber attacks and so on. To address the Byzantine issue, some pre-determined robust aggregation rules are applied. Moreover, the gradient tracking and proximal algorithm are combined to ensure convergence and sparsity simultaneously. Theoretically, our proposed algorithms are provably robust against Byzantine attacks and achieve linear convergence rates. The finite-sample performance is studied through numerical experiments under various settings and an application to Communities and Crime Data is also presented.

Byzantine Resilient Joint Localization and Target Tracking of Multi-Vehicle Systems

This work investigates the problem of joint localization and target tracking (JLATT) of multi-vehicle systems (MVSs) in the presence of Byzantine attacks (BAs). For MVSs, there may exist malicious and misbehaving vehicles, called Byzantine vehicles, which act as deceivers and pass false information to their neighbors. For the first time, we formulate a resilient JLATT framework to synthesize the hybrid problems of distributed cooperative localization and flock tracking in the presence of BAs. More specifically, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">covariance weighted mean-subsequence-filter</i> (CW-MSF) algorithm to guarantee that the MVS achieves flock tracking w.r.t a target even in the presence of a certain fraction of Byzantine vehicles. Note that this resilient JLATT scheme does not require global information and thus it is fully distributed. The practicality and validity of this novel JLATT framework are verified via an illustrative numerical simulation example.

Byzantine-Robust Distributed Learning With Compression

Communication between workers and the master node to collect local stochastic gradients is a key bottleneck in a large-scale distributed learning system. Various recent works have proposed to compress the local stochastic gradients to mitigate the communication overhead. However, robustness to malicious attacks is rarely considered in such a setting. In this work, we investigate the problem of Byzantine-robust compressed distributed learning, where the attacks from Byzantine workers can be arbitrarily malicious. We theoretically point out that different to the attacks-free compressed stochastic gradient descent (SGD), its vanilla combination with geometric median-based robust aggregation seriously suffers from the compression noise in the presence of Byzantine attacks. In light of this observation, we propose to reduce the compression noise with gradient difference compression so as to improve the Byzantine-robustness. We also observe the impact of the intrinsic stochastic noise caused by selecting random samples, and adopt the stochastic average gradient algorithm (SAGA) to gradually eliminate the inner variations of regular workers. We theoretically prove that the proposed algorithm reaches a neighborhood of the optimal solution at a linear convergence rate, and the asymptotic learning error is in the same order as that of the state-of-the-art uncompressed method. Finally, numerical experiments demonstrate the effectiveness of the proposed method.

Federated Variance-Reduced Stochastic Gradient Descent With Robustness to Byzantine Attacks

This paper deals with distributed finite-sum optimization for learning over networks in the presence of malicious Byzantine attacks. To cope with such attacks, most resilient approaches so far combine stochastic gradient descent (SGD) with different robust aggregation rules. However, the sizeable SGD-induced stochastic gradient noise makes it challenging to distinguish malicious messages sent by the Byzantine attackers from noisy stochastic gradients sent by the 'honest' workers. This motivates us to reduce the variance of stochastic gradients as a means of robustifying SGD in the presence of Byzantine attacks. To this end, the present work puts forth a Byzantine attack resilient distributed (Byrd-) SAGA approach for learning tasks involving finite-sum optimization over networks. Rather than the mean employed by distributed SAGA, the novel Byrd- SAGA relies on the geometric median to aggregate the corrected stochastic gradients sent by the workers. When less than half of the workers are Byzantine attackers, the robustness of geometric median to outliers enables Byrd-SAGA to attain provably linear convergence to a neighborhood of the optimal solution, with the asymptotic learning error determined by the number of Byzantine workers. Numerical tests corroborate the robustness to various Byzantine attacks, as well as the merits of Byrd- SAGA over Byzantine attack resilient distributed SGD.

Analysis of Byzantine Attacks for Target Tracking in Wireless Sensor Networks.

Herein, the problem of target tracking in wireless sensor networks (WSNs) is investigated in the presence of Byzantine attacks. More specifically, we analyze the impact of Byzantine attacks on the performance of a tracking system. First, under the condition of jointly estimating the target state and the attack parameters, the posterior Cramer–Rao lower bound (PCRLB) is calculated. Then, from the perspective of attackers, we define the optimal Byzantine attack and theoretically find a way to achieve such an attack with minimal cost. When the attacked nodes are correctly identified by the fusion center (FC), we further define the suboptimal Byzantine attack and also find a way to realize such an attack. Finally, in order to alleviate the negative impact of attackers on the system performance, a modified sampling importance resampling (SIR) filter is proposed. Simulation results show that the tracking results of the modified SIR filter can be close to the true trajectory of the moving target. In addition, when the quantization level increases, both the security performance and the estimation performance of the tracking system are improved.

Local Threshold Design for Target Localization Using Error Correcting Codes in Wireless Sensor Networks in the Presence of Byzantine Attacks

In this paper, we revisit the received signal strength (RSS)-based target localization technique presented in Vempaty et al. , where a simple threshold quantizer was employed to quantize the RSS values prior to sending them to the fusion center. It was shown that the probability of misclassification of the distributed classification fusion using error correcting codes scheme vanishes as the number of sensors tends to infinity. This result was obtained based on an intuitive threshold design at the local sensors, and the question of how much a careful design of local thresholds can help improve the overall performance was not addressed. In this paper, we demonstrate the significance of threshold design for accurate and robust target localization in wireless sensor networks, particularly, when the number of sensors is finite. With this objective, we derive an upper bound on the probability of misclassification as a function of RSS thresholds by using the union inequality. The RSS thresholds that algorithmically minimize the derived misclassification error bound are then numerically obtained over a mirror-based homomorphic sensor deployment structure. Simulations over fading wireless links show that the scheme based on newly found optimized RSS thresholds considerably outperforms the previous scheme using the thresholds that are intuitively selected, especially in the presence of Byzantine attacks that severely impact information security.

Processing Delays Do Not Degrade Network Error-Correction Capacity in Directed Networks

This letter considers the network error-correction capacity in the presence of Byzantine attacks. Unlike prior papers, which assume no delay in any part of networks, we consider the effects of processing delays in the nodes. We prove that these processing delays have no impact on the network error-correction capacity region for any directed network.

Asymptotically Optimum Distributed Estimation in the Presence of Attacks

Distributed estimation of a deterministic mean-shift parameter in additive zero-mean noise is studied when using quantized data in the presence of Byzantine attacks. Several subsets of sensors are assumed to be tampered with by adversaries using different attacks such that the compromised sensors transmit fictitious data. First, we consider the task of identifying and categorizing the attacked sensors into different groups according to distinct types of attacks. It is shown that increasing the number K of time samples at each sensor and enlarging the size N of the sensor network can both ameliorate the identification and categorization, but to different extents. As K→∞, the attacked sensors can be perfectly identified and categorized, while with finite but sufficiently large K, as N→∞, it can be shown that the fusion center can also ascertain the number of attacks and obtain an approximate categorization with a sufficiently small percentage of sensors that are misclassified. Next, in order to improve the estimation performance by utilizing the attacked observations, we consider joint estimation of the statistical description of the attacks and the parameter to be estimated after the sensors have been well categorized. When using the same quantization approach successfully employed without attacks, it can be shown that the corresponding Fisher Information Matrix (FIM) is singular. To overcome this, a time-variant quantization approach is proposed, which will provide a nonsingular FIM, provided that K ≥ 2. Furthermore, the FIM is employed to provide necessary and sufficient conditions under which utilizing the compromised sensors in the proposed fashion will lead to better estimation performance when compared to approaches where the compromised sensors are ignored.

Distributed Inference With M-Ary Quantized Data in the Presence of Byzantine Attacks

The problem of distributed inference with M-ary quantized data at the sensors is investigated in the presence of Byzantine attacks. We assume that the Byzantine nodes attack the inference network by modifying the symbol corresponding to the quantized data to one of the other symbols in the quantization alphabet-set and transmitting falsified symbol to the fusion center (FC). In this paper, we find the optimal Byzantine attack that blinds any distributed inference network. As the quantization alphabet size increases, a tremendous improvement in the security performance of the distributed inference network is observed. In addition to the perfect channel case, in Appendix A , we also analyze the optimal Byzantine attack when the channel between the nodes and the FC is noisy and is modelled as a discrete M-ary channel. We also investigate the optimal attack within the restricted space of highly-symmetric attack strategies, that maximally degrades the performance of the inference network in the presence of resource-constrained Byzantine attacks. A reputation-based scheme for identifying malicious nodes is also presented as the network's strategy to mitigate the impact of Byzantine threats on the inference performance of the distributed sensor network. We also provide asymptotic analysis to find the optimal reputation-based scheme as a function of the fraction of compromised nodes in the network.

Collaborative Spectrum Sensing in the Presence of Byzantine Attacks in Cognitive Radio Networks

Cognitive radio (CR) has emerged as a solution to the problem of spectrum scarcity as it exploits transmission opportunities in the under-utilized spectrum bands of primary users. Collaborative (or distributed) spectrum sensing has been shown to have various advantages in terms of spectrum utilization and robustness. The data fusion scheme is a key component of collaborative spectrum sensing. In this paper, we analyze the performance limits of collaborative spectrum sensing under Byzantine Attacks where malicious users send false sensing data to the fusion center leading to increased probability of incorrect sensing results. We show that above a certain fraction of Byzantine attackers in the CR network, data fusion scheme becomes completely incapable and no reputation based fusion scheme can achieve any performance gain. We present optimal attacking strategies for given attacking resources and also analyze the possible counter measures at the fusion center (FC). Based on these analyses, we also propose a novel and easy to implement technique to counter Byzantine attacks in CRNs. In this approach, the FC identifies the attackers and removes them from the data fusion process. Our analysis indicates that the proposed scheme is robust against Byzantine attacks and can successfully remove the Byzantines in a short time span.

Distributed Detection in the Presence of Byzantine Attacks

Distributed detection in the presence of cooperative (Byzantine) attack is considered. It is assumed that a fraction of the monitoring sensors are compromised by an adversary, and these compromised (Byzantine) sensors are reprogrammed to transmit fictitious observations aimed at confusing the decision maker at the fusion center. For detection under binary hypotheses with quantized sensor observations, the optimal attacking distributions for Byzantine sensors that minimize the detection error exponent are obtained using a ldquowater-fillingrdquo procedure. The smallest error exponent, as a function of the Byzantine sensor population, characterizes the power of attack. Also obtained is the minimum fraction of Byzantine sensors that destroys the consistency of detection at the fusion center. The case when multiple measurements are made at the remote nodes is also considered, and it is shown that the detection performance scales with the number of sensors differently from the number of observations at each sensor.