A Comparison of Stealthy Sensor Attacks on Control Systems

As more attention is paid to security in the context of control systems and as attacks occur to real control systems throughout the world, it has become clear that some of the most nefarious attacks are those that evade detection. The term stealthy has come to encompass a variety of techniques that attackers can employ to avoid detection. Here we show how the states of the system (in particular, the reachable set corresponding to the attack) can be manipulated under two important types of stealthy attacks. We employ the chi-squared fault detection method and demonstrate how this imposes a constraint on the attack sequence either to generate no alarms (zero-alarm attack) or to generate alarms at a rate indistinguishable from normal operation (hidden attack)

Characterization of Model-Based Detectors for CPS Sensor Faults/Attacks

A vector-valued model-based cumulative sum (CUSUM) procedure is proposed for identifying faulty/falsified sensor measurements. First, given the system dynamics, we derive tools for tuning the CUSUM procedure in the fault/attack free case to fulfill a desired detection performance (in terms of false alarm rate). We use the widely-used chi-squared fault/attack detection procedure as a benchmark to compare the performance of the CUSUM. In particular, we characterize the state degradation that a class of attacks can induce to the system while enforcing that the detectors (CUSUM and chi-squared) do not raise alarms. In doing so, we find the upper bound of state degradation that is possible by an undetected attacker. We quantify the advantage of using a dynamic detector (CUSUM), which leverages the history of the state, over a static detector (chi-squared) which uses a single measurement at a time. Simulations of a chemical reactor with heat exchanger are presented to illustrate the performance of our tools.Comment: Submitted to IEEE Transactions on Control Systems Technolog

Perturbative quantum analysis and classical limit of the electron scattering by a solenoidal magnetic field

A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non-perturbative methodology should be applied.Comment: To appear in the proceedings of 13th Mexican School of Particles and Fields (MSPF 2008), San Carlos, Sonora, Mexico, 2-11 Oct 2008. 6 pages, 2 Postscript figure

Multifractal analyses of row sum signals of elementary cellular automata

We first apply the WT-MFDFA, MFDFA, and WTMM multifractal methods to binomial multifractal time series of three different binomial parameters and find that the WTMM method indicates an enhanced difference between the fractal components than the known theoretical result. Next, we make use of the same methods for the time series of the row sum signals of the two complementary ECA pairs of rules (90,165) and (150,105) for ten initial conditions going from a single 1 in the central position up to a set of ten 1's covering the ten central positions in the first row. Since the members of the pairs are actually similar from the statistical point of view, we can check which method is the most stable numerically by recording the differences provided by the methods between the two members of the pairs for various important quantities of the scaling analyses, such as the multifractal support, the most frequent Holder exponent, and the Hurst exponent and considering as the better one the method that provides the minimum differences. According to this criterion, our results show that the MFDFA performs better than WT-MFDFA and WTMM in the case of the multifractal support, while for the other two scaling parameters the WT-MFDFA is the best. The employed set of initial conditions does not generate any specific trend in the values of the multifractal parametersComment: 23 pages including an appendix and 11 figures, extended version accepted for publication by Physica