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One of the most studied forms of attacks on the cyber-physical systems is the replay attack. The statistical similarities of the replay signal and the true observations make the replay attack difficult to detect. In this paper, we have addressed the problem of replay attack detection by adding watermarking to the control inputs and then performed resilient detection using cumulative sum (CUSUM) test on the joint statistics of the innovation signal and the watermarking signal. We derive the expression of the Kullback-Liebler divergence (KLD) between the two joint distributions before and after the replay attack, which is asymptotically inversely proportional to the detection delay. We perform structural analysis of the derived KLD expression and suggest a technique to improve the KLD for the systems with relative degree greater than one. A scheme to find the optimal watermarking signal variance for a fixed increase in the control cost to maximize the KLD under the CUSUM test is presented. We provide various numerical simulation results to support our theory. The proposed method is also compared with a state-of-the-art method.
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In this paper, we investigate the role of a physical watermarking signal in quickest detection of a deception attack in a scalar linear control system where the sensor measurements can be replaced by an arbitrary stationary signal generated by an attacker. By adding a random watermarking signal to the control action, the controller designs a sequential test based on a Cumulative Sum (CUSUM) method that accumulates the log-likelihood ratio of the joint distribution of the residue and the watermarking signal (under attack) and the joint distribution of the innovations and the watermarking signal under no attack. As the average detection delay in such tests is asymptotically (as the false alarm rate goes to zero) upper bounded by a quantity inversely proportional to the Kullback-Leibler divergence(KLD) measure between the two joint distributions mentioned above, we analyze the effect of the watermarking signal variance on the above KLD. We also analyze the increase in the LQG control cost due to the watermarking signal, and show that there is a tradeoff between quick detection of attacks and the penalty in the control cost. It is shown that by considering a sequential detection test based on the joint distributions of residue/innovations and the watermarking signal, as opposed to the distributions of the residue/innovations only, we can achieve a higher KLD, thus resulting in a reduced average detection delay. Numerical results are provided to support our claims.
This paper considers a statistical signal processing problem involving agent based models of financial markets which at a micro-level are driven by socially aware and risk- averse trading agents. These agents trade (buy or sell) stocks by exploiting information about the decisions of previous agents (social learning) via an order book in addition to a private (noisy) signal they receive on the value of the stock. We are interested in the following: (1) Modelling the dynamics of these risk averse agents, (2) Sequential detection of a market shock based on the behaviour of these agents. Structural results which characterize social learning under a risk measure, CVaR (Conditional Value-at-risk), are presented and formulation of the Bayesian change point detection problem is provided. The structural results exhibit two interesting prop- erties: (i) Risk averse agents herd more often than risk neutral agents (ii) The stopping set in the sequential detection problem is non-convex. The framework is validated on data from the Yahoo! Tech Buzz game dataset.
In this paper, we propose and analyze an attack detection scheme for securing the physical layer of a networked control system against attacks where the adversary replaces the true observations with stationary false data. An independent and identically distributed watermarking signal is added to the optimal linear quadratic Gaussian (LQG) control inputs, and a cumulative sum (CUSUM) test is carried out using the joint distribution of the innovation signal and the watermarking signal for quickest attack detection. We derive the expressions of the supremum of the average detection delay (SADD) for a multi-input and multi-output (MIMO) system under the optimal and sub-optimal CUSUM tests. The SADD is asymptotically inversely proportional to the expected Kullback-Leibler divergence (KLD) under certain conditions. The expressions for the MIMO case are simplified for multi-input and single-output systems and explored further to distil design insights. We provide insights into the design of an optimal watermarking signal to maximize KLD for a given fixed increase in LQG control cost when there is no attack. Furthermore, we investigate how the attacker and the control system designer can accomplish their respective objectives by changing the relative power of the attack signal and the watermarking signal. Simulations and numerical studies are carried out to validate the theoretical results.
This paper studies the problem of sequential Gaussian shift-in-mean hypothesis testing in a distributed multi-agent network. A sequential probability ratio test (SPRT) type algorithm in a distributed framework of the emph{consensus}+emph{innovations} form is proposed, in which the agents update their decision statistics by simultaneously processing latest observations (innovations) sensed sequentially over time and information obtained from neighboring agents (consensus). For each pre-specified set of type I and type II error probabilities, local decision parameters are derived which ensure that the algorithm achieves the desired error performance and terminates in finite time almost surely (a.s.) at each network agent. Large deviation exponents for the tail probabilities of the agent stopping time distributions are obtained and it is shown that asymptotically (in the number of agents or in the high signal-to-noise-ratio regime) these exponents associated with the distributed algorithm approach that of the optimal centralized detector. The expected stopping time for the proposed algorithm at each network agent is evaluated and is benchmarked with respect to the optimal centralized algorithm. The efficiency of the proposed algorithm in the sense of the expected stopping times is characterized in terms of network connectivity. Finally, simulation studies are presented which illustrate and verify the analytical findings.
The advances in IC process make future chip multiprocessors (CMPs) more and more vulnerable to transient faults. To detect transient faults, previous core-level schemes provide redundancy for each core separately. As a result, they may leave transient faults in the uncore parts, which consume over 50% area of a modern CMP, escaped from detection. This paper proposes RepTFD, the first core-level transient fault detection scheme with 100% coverage. Instead of providing redundancy for each core separately, RepTFD provides redundancy for a group of cores as a whole. To be specific, it replays the execution of the checked group of cores on a redundant group of cores. Through comparing the execution results between the two groups of cores, all malignant transient faults can be caught. Moreover, RepTFD adopts a novel pending period based record-replay approach, which can greatly reduce the number of execution orders that need to be enforced in the replay-run. Hence, RepTFD brings only 4.76% performance overhead in comparison to the normal execution without fault-tolerance according to our experiments on the RTL design of an industrial CMP named Godson-3. In addition, RepTFD only consumes about 0.83% area of Godson-3, while needing only trivial modifications to existing components of Godson-3.
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