Guessing Based On Length Functions

This paper aims to investigate the security problem of nonlinear cyber-physical systems (CPSs), which poses a challenge to handle compared with linear CPSs. A series of optimization problems for nonlinear CPSs under injection attack are constructed, which are based on a general model of the nonlinear systems with repetitive operation characteristics and a novel introduction of the key technical lemma. These optimization results are more general than the existing injection attack results and the requirements for attackers to obtain system information are relaxed. Also, the form of switching applied to the attack strategy possesses several advantages, including high stealthiness, lower cost, and more flexibility. Therefore, the new optimal injection attack strategies are expected to be more widespread and provide a basis for the design of defense strategies. The key to acquiring the designed optimal attack strategies is to adopt the linear input/output (I/O) data model for these systems via introducing an estimation term of the improved projection estimation method into the linear model. Finally, a networked GLUON-6L3 manipulator example validates the effectiveness of the proposed methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The main purpose of this paper is to study the cyber security of nonlinear cyber-physical systems from the perspective of attackers, which can help defenders fully understand the behavior of attackers. Most of the existing attack strategies aimed at linear systems or have a priori knowledge of the attacked systems. However, there are great limitations and difficulties in practical application. In this paper, the new attack strategies are proposed by combining system identification, iterative learning and control theory, which relaxes the requirement of the attacker’s ability. In detail, the attacker only needs to obtain the control input and output data of the attacked system and design the attack strategy according to it. Among them, the first-in, first-out queue storage method is applied to remove the requirements for the storage capability of the attacker. In practical applications, the attacker does not need to store the I/O data continuously, but only store the initial value and the data of two successive iterations. The mathematical analytic forms of two optimal attack strategies are given, and then their effectiveness are verified on a welding work of a networked six-axis manipulator. In the future, we will investigate the design of attack strategies for nonlinear systems with heterogeneous dynamics and multiple delays.

This paper considers a Denial-of-Service (DoS) attack scheduling problem. Specifically, a sensor employs the wireless link to send the data packet to the remote estimator at each time step, while an energy-constrained attacker launches DoS attacks against the remote state estimation, and designs an optimal attack strategy to maximize damage to the remote estimation quality. The packet will drop if the channel is jammed. In most of the existing works on DoS attacks, it is assumed that the wireless channel is perfect, i.e., the packet dropout never occurs in the absence of attack. However, this is far from the practical situation. To encompass the lossy nature of wireless networks, we study the scenario of lossy networks in which the packet may drop even without attack, and construct the optimal attack strategy that maximizes the average expected estimation error at the remote estimator over lossy networks. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Optimal attack strategy of complex networks based on tabu search

Cyberspace is vulnerable to continuous malicious attacks. Traceability of network attacks is an effective defense means to curb and counter network attacks. In this paper, the evolutionary game model is used to analyze the network attack and defense behavior. On the basis of the quantification of attack and defense benefits, the replication dynamic learning mechanism is used to describe the change process of the selection probability of attack and defense strategies, and finally the evolutionary stability strategies and their solution curves of both sides are obtained. On this basis, the attack behavior is analyzed, and the probability curve of attack strategy and the optimal attack strategy are obtained, so as to realize the effective traceability of attack behavior.

The parallel distributed detection is studied for mobile wireless sensor networks (MWSNs) in the presence of Byzantine attacks in entirely unknown environment or complicated environment from the perspective of the information theory, where we pay most of our attention toward design, analysis, and evaluation of the attack strategy. In particular, the multihop relay network and the harsh wireless communication condition, e.g., the dynamic and entirely unknown channel, are taken into consideration in our configuration. Second, the conditions that the optimal attacking strategy should satisfy is analyzed and developed under different attacking scenarios. Third, the minimum attacking power is developed for the Byzantines to blind the fusion center (FC). Furthermore, the optimal attacking strategies are developed when no prior information of the system is known for the Byzantines. Finally, the traditional four typical attack strategies are evaluated, and we find that the fraction of Byzantines is the only factor that affects the reliable data fusion when the network size and the attacking strategy are fixed. The extensive simulation is conducted to verify our design, analysis, and evaluation of the attack strategy.

This work investigates the attack strategy design problem of the false data injection attack against the cyber-physical system. Distinct from the relevant results which utilise the current intercepted data or additionally consider side information, a more universal attack model is proposed which combines historical data and side information with the current intercepted data to synergistically deteriorate the system estimation performance. In order to quantify the impact resulting from the proposed attack strategy, the optimisation objective is characterised by deriving the error covariance matrix under the attacks, which becomes more intricate since the proposed attack model introduces more decision variables and coupled terms. Take the stealthiness which is characterised by Kullback-Leibler divergence as the constraints, the problem investigated in this work is equivalently transformed into the constrained multi-variable non-convex optimisation problems, which are not able to be solved directly by the methods in the relevant results. By utilising the Lagrange multiplier method, the structural characteristic of the optimal mean and the optimal covariance which only related to the Lagrange multiplier are derived, such that the optimal distribution of the modified innovation is able to be obtained by a simple search procedure. Following that, the design of the optimal attack strategy is completed by using semi-definite programming to derive the optimal attack matrices. Finally, the simulation examples are given such that the validity of the results is verified.

This paper deals with an attrition game on a combat network, where attackers depart from multiple start nodes heading to multiple destination nodes and defenders deploy a limited number of members on arcs to intercept the attackers. Due to conflicts between the attackers and the deployed defenders, both players incur casualties or attrition on arcs. The attackers aim to bring as many members as possible to destination nodes while the defenders desires to minimize the number of surviving attackers. For the two-person zero-sum (TPZS) attrition game, we propose linear programming formulations to derive an optimal attacker's strategy of their attack paths and an optimal defender's strategy of deployment on arcs.

The problem of key generation over wireless fading channels is investigated. First, a joint source-channel approach that combines existing source and channel models for key agreement over wireless fading channels is developed. It is shown that, in general, to fully exploit the resources provided by time-varying channel gains, one needs to combine both the channel model, in which Alice sends a key to Bob over a wireless channel, and the source model, in which Alice and Bob generate a key by exploiting the correlated observations obtained from the wireless fading channel. Asymptotic analyses suggest that in the long coherence time regime, the channel model is asymptotically optimal. On the other hand, in the high power regime, the source model is asymptotically optimal. Second, the framework is extended to the scenario with an active attacker. Assuming that the goal of the attacker is to minimize the key rate that can be generated using the proposed protocol and the attacker will employ such an attack strategy, the attacker's optimal attack strategy is identified and the key rate under this attack model is characterized.

The problem of network disintegration, such as suppressing the epidemic spreading and destabilizing terrorist networks, has broad applications and recently has attracted more attentions. The fundamental purpose of this study is to find the critical nodes whose deficiency could lead to the network collapse. By now, most related works of attack strategy in complex networks use certain properties of the nodes, while little is known about optimal attack strategy for complex networks. In this paper, we presented an optimized attack strategy model for complex networks and introduced the tabu search into the problem. The network performance is quantitatively measured by natural connectivity, which can be used to effectively characterize the robustness of complex networks. Numerical experiments suggest that our solution can identify the 'best' choice for node failure attack.

In this paper, a multiserver retrial system with constant retrial policy is considered. The input is assumed to be a general renewal process, service times are iid with a general distribution and the retrial attempts follow an exponential distribution. The system is described with a regenerative process, and we focus on the logarithmic asymptotics of the large deviation (overflow) probability that the orbit size reaches a high level N within regeneration cycle. To analyze the upper bound of this probability, we interpret the retrial system as a buffered system with service times of a special type. Simulation results show the accuracy of the obtained bound for Weibull/M/2 retrial system.

The privacy of machine learning models has become a significant concern in many emerging Machine-Learning-as- a-Service applications, where prediction services based on well- trained models are offered to users via the pay-per-query scheme. However, the lack of a defense mechanism can impose a high risk on the privacy of the server’s model since an adversary could efficiently steal the model by querying only a few ‘good’ data points. The game between a server’s defense and an adversary’s attack inevitably leads to an arms race dilemma, as commonly seen in Adversarial Machine Learning. To study the fundamental tradeoffs between model utility from a benign user’s view and privacy from an adversary’s view, we develop new metrics to quantify such tradeoffs, analyze their theoretical properties, and develop an optimization problem to understand the optimal adversarial attack and defense strategies. The developed concepts and theory match the empirical findings on the ‘equilibrium’ between privacy and utility. In terms of optimization, the key ingredient that enables our results is a unified representation of the attack-defense problem as a min-max bi-level problem. The developed results are demonstrated by examples and empirical experiments.

We investigate the impact of Byzantine attacks in distributed detection under binary hypothesis testing. It is assumed that a fraction of the transmitted sensor measurements are compromised by the injected data from a Byzantine attacker, whose purpose is to confuse the decision maker at the fusion center. From the perspective of a Byzantine attacker, under the injection energy constraint, an optimization problem is formulated to maximize the asymptotic missed detection error probability, which is based on the Kullback-Leibler divergence. The properties of the optimal attack strategy are analyzed by convex optimization and parametric optimization methods. Based on the derived theoretic results, a coordinate descent algorithm is proposed to search the optimal attack solution. Simulation examples are provided to illustrate the effectiveness of the obtained attack strategy.

One proves theorems on the probabilities of large and moderate deviations for maximum likelihood estimates while for less restrictive assumptions one establishes coarse asymptotics for probabilities of large deviations in the regular case. Similar results are obtained in the case of observations in “white Gaussian noise.”

Cyber-Physical Systems (CPSs) play an increasingly significant role in many critical applications. These valuable applications attract various sophisticated attacks. This paper considers a stealthy estimation attack, which aims to modify the state estimation of the CPSs. The intelligent attackers can learn defense strategies and use clandestine attack strategies to avoid detection. To address the issue, we design a Chi-square detector in a Digital Twin (DT), which is an online digital model of the physical system. We use a Signaling Game with Evidence (SGE) to find the optimal attack and defense strategies. Our analytical results show that the proposed defense strategies can mitigate the impact of the attack on the physical estimation and guarantee the stability of the CPSs. Finally, we use an illustrative application to evaluate the performance of the proposed framework.

The distributed localisation with M ‐ary quantised data at sensor nodes is investigated in the presence of Byzantines from the attacker's perspective. The Byzantine nodes attack the network by transmitting falsified data to the fusion centre (FC) to deteriorate the performance of the distributed target localisation, where the independent and probabilistic Byzantine attack model is considered. By making the determinant of Fisher information matrix be zero, the optimal Byzantine attack strategy, which makes the FC incapable of estimating target location using the data at sensor nodes, is found. Numerical results show that the security performance of the distributed localisation improves sharply as the number of quantisation bits increases. Moreover, the security performance also increases tremendously as the attack probability decreases. Hence, the Byzantine attacker faces a trade‐off between the performance damage and the hazard to be identified.