Security is an important aspect of modern large-scale infrastructure networks. In one hand, there has been a significant improvement in the efficiency and reliability of systems due to enhanced interconnection of intelligent devices. On the other hand, this provides an opportunity for strategic adversaries to exploit the vulnerabilities of the network and cause damage. An example of an infrastructure system that is a part of our daily lives, and is vulnerable to adversarial attacks is the power network. Enhancing power grids' security, performance and resilience has been an important research topic in engineering. A significant penetration of information communication technologies (ICT) in modern power systems, renders this network vulnerable to cyber attacks from strategic malicious entities.

According to The North American Electric Reliability Corporation (NERC), every power system should be operated such that failure of a single component should not leave the rest of components heavily loaded. This is called N-1 rule in power networks. However higher order contingency conditions are inevitable due to cooperated cyber attacks or natural calamities. As a result N-k contingency analysis is an important notion of security and resilience of power grids. The central challenge of higher order cyber-physical contingency analysis is the exponential blow-up of the attack surface due to a large number of attack vectors. This gives rise to computational challenges in devising efficient attack mitigation strategies. Due to these challenges, most of the tools are effective in analysing contingencies caused by failure of one or two components in the power network. Moreover, current tools for contingency analysis do not consider the strategic and smart attackers, and consider different attack profiles as faults in the system. However, smart attackers can exploit such naive defense strategies and cause a significant damage to the system.

In this work, we focus on challenges due to higher order contingency conditions resulting from cyber-attacks. Our approach provides efficient tools to consider higher order cyber-physical contingency analysis in a game-theoretic frame work, which enables the operator to exploit the strategic actions of the attacker. Moreover, we provide computationally efficient algorithms to deal with higher order contingency conditions, and find the optimal defense strategies which cannot be exploited by the smart attacker. Our contributions in this thesis are as follows:

\textbf{Cyber-Physical contingency analysis modeling using Game-Theoretic framework:} We develop a game-theoretic model in which different actions of the attacker and the defender lead to different contingency conditions. We formulate the problem as a security game. First, we consider a zero-sum scenario and provide the best algorithm (in terms of computational complexity) to compute the Saddle-Point strategies for the players. Moreover, we generalize the zero-sum model to a general-sum security model, in which the pay-off for the players are different, and provide a computationally efficient algorithms to compute the Nash Equilibrium in general scenarios. Our results for this part appeared in \cite{emadi2019security}

\textbf{Structural properties of the solutions:} We present structural properties of the optimal attacker and defender strategies in terms of the parameters (impact) of the problem. This helps us to identify the most important targets that need to be protected against an adversarial attack in the face of resource constraints. Moreover, unlike state-of-art algorithms that solve security game which are primarily iterative in nature, our algorithm does not lack of a central tenet and it provides a deep insight the relationship between the parameter of the problem and the optimal solutions. Our results for this part appeared in \cite{emadi2020characterization}.

\textbf{A paradigm for robust network design:} Using the structural properties of the solutions, we address the problem of designing the optimal topology and power generation in power networks to minimize impact in the face of an adversarial attack. To the best of our knowledge, this is first work that explores such design problems in the context of cyber-physical systems.

\textbf{IEEE Case studies and evaluation of the proposed solutions:} In order to evaluate the performance of our algorithms, we validate the efficacy of the proposed solutions through extensive simulations on a number of IEEE standardized power networks. Our results for this part appeared in \cite{emadi2021power}.