In this chapter, we propose game-theoretic models for resource allocation in interference channels with physical layer security. Three two-user interference channel scenarios are studied: the peaceful system with public messages, the case with private messages and forward secrecy, and the case with a public feedback channel. These lead to achievable rate, achievable secrecy, and achievable secret-key regions. Next, the outcome of a strategic game in normal form is computed and it is shown that either there exists an equilibrium in dominant strategies or a Nash equilibrium. Finally, three cooperative game models are applied: the Nash bargaining solution, a strategic bargaining algorithm, and the Walrasian market model. They are applicable to all three interference channel scenarios. Numerical illustrations show the utility regions and the outcomes from the different game models are discussed.
In this chapter, we propose game-theoretic models for resource allocation in interference channels with physical layer security. Three two-user interference channel scenarios are studied: the peaceful system with public messages, the case with private messages and forward secrecy, and the case with a public feedback channel. These lead to achievable rate, achievable secrecy, and achievable secret-key regions. Next, the outcome of a strategic game in normal form is computed and it is shown that either there exists an equilibrium in dominant strategies or a Nash equilibrium. Finally, three cooperative game models are applied: the Nash bargaining solution, a strategic bargaining algorithm, and the Walrasian market model. They are applicable to all three interference channel scenarios. Numerical illustrations show the utility regions and the outcomes from the different game models are discussed.
This dissertation investigates the physical layer security of wireless communication networks using game-theoretic and optimization models. Considered is a wireless network of parallel channels that may be under eavesdropping attack. Game models are played between a friendly interferer (he) who can broadcast artificial noise and a strategic eavesdropper (she). The friendly interferer wants to maximize the secrecy level of the wireless communication network by decreasing the eavesdropper's listening capability with intentionally generated noise signals, while the eavesdropper wants to maximize her own capability and avoid interference. The game-theoretic models reflect the strategic confrontation between the friendly interferer and the eavesdropper in different communication environments. These models address some of the limitations in literature. Most existing resource allocation strategies for friendly interference adopt the conservative assumption that all parallel channels are under attack. Game-theoretic approaches provide more efficient strategies to the friendly interferer by anticipating the channels to be attacked by the eavesdropper. The first model considers the case in which the friendly interferer can flexibly allocate cooperative jamming power to all communication channels in the network under a total power constraint. When all channels used for secret communication are under the threat of eavesdropping attacks, the optimal power allocation policy results from solving a convex optimization problem. In this case, the optimal policy is unique and can be obtained via a water-filling scheme. When the eavesdropper can not attack all channels, the eavesdropper should behave strategically and may select the targets probabilistically. In this case, a non-zero-sum game helps the friendly interferer predict and concentrate on the targets selected by the eavesdropper. When the eavesdropper can only attack a single channel, an analytical form of the NE strategies is presented; while an iterative numerical method that guarantees the convergence to NE strategies is proposed if the eavesdropper can attack multiple channels. Compared to naive power allocation strategies, such as splitting the power equally to each channel, the game-theoretic power allocation strategy always delivers better expected total secrecy capacity. Next, an extension of the power allocation game for cooperative jamming models the case in which the state information of the eavesdropping channels may not be known completely. New utility functions for the friendly interferer and the eavesdropper are designed to include the distributional information of eavesdropping channels' state information. A non-zero sum game using the new utility functions is analyzed between the friendly interferer and the strategic eavesdropper who can only attack a limited number of channels. Note that the friendly interferer may not have the capability to send cooperative jamming signals to multiple channels simultaneously. For such a friendly interferer, a probabilistic cooperative jamming scheme is devised such that the defender focuses on protecting randomly selected channels. In the mean time, the eavesdropper selects the most vulnerable channels to attack. A linearly constrained non-zero-sum bimatrix game models the competition between the defender and the eavesdropper. The Nash equilibrium is shown to be equivalent to the solution of a quadratic programming problem. A closed form solution is derived for the special case in which the eavesdropper can only attack a single channel. We show that there exists a cut-off index determining the set of channels that will be covered in the equilibrium strategies. Furthermore, the adverse effect of the interference signal plays an important role in the value of the cut-off index and it represents the vulnerability of wireless communication networks against eavesdroppers Wireless communication networks of parallel channels actually share a lot of similarities with general cyber networks. Thus, the final model in this dissertation is a cost-efficient network security game for defensive resource allocation in a heterogeneous cyber network of N nodes. A defender, by allocating defensive resources to a networked node, can decrease the node's vulnerabilities. At the same time, the cost of using defensive resources is taken into consideration. Two non-zero-sum Nash games model the competition between the defender and two types of attackers, respectively. The first type tries to maximize damage based on the value of security assets related to networked nodes, while the second type aims at infiltrating the network. Consideration of the case that the defender does not know the attacker's type leads to a Bayesian game. For all three games, we derive conditions for the existence of a unique Nash equilibrium (NE), and obtain the equilibria and the value functions in closed form.
Secret key establishment leveraging the physical layer as a source of common randomness has been investigated in a range of settings. We investigate the problem of establishing, in an information-theoretic sense, a secret key between a user and a base-station (BS) (more generally, part of a wireless infrastructure), but for two such user-BS pairs attempting the key establishment simultaneously. The challenge in this novel setting lies in that a user can eavesdrop another BS-user communications. It is thus paramount to ensure the two keys are established with no leakage to the other user, in spite the interference across neighboring cells. We model the system with BS-user communication through an interference channel and user-BS communication through a public channel. We find the region including achievable secret key rates for the general case that the interference channel (IC) is discrete and memoryless. Our results are examined for a Gaussian IC. In this setup, we investigate the performance of different transmission schemes for power allocation. The chosen transmission scheme by each BS essentially affects the secret key rate of the other BS-user. Assuming base stations are trustworthy but that they seek to maximize the corresponding secret key rate, a game-theoretic setting arises to analyze the interaction between the base stations. We model our key agreement scenario in normal form for different power allocation schemes to understand performance without cooperation. Numerical simulations illustrate the inefficiency of the Nash equilibrium outcome and motivate further research on cooperative or coordinated schemes.
A secure communication game is considered for the two-user MISO Gaussian interference channel with confidential messages, where each transmitter aims to maximize the difference between its secrecy rate and the secrecy rate of the other transmitter. In this novel problem, the weaker link tries to minimize the extra secret information obtained by its adversary, while the stronger link attempts to maximize it. We provide an information theoretic formulation for this non-cooperative zero-sum game scenario and determine that, under the assumption of Gaussian signaling at the transmitters, there exists a unique Nash equilibrium solution for the proposed problem. Moreover, we obtain in closed-form the optimal strategies (beamformers) at the transmitters that result in the Nash equilibrium. While the NE strategies are achievable in one shot when full channel state information is available at the transmitters (CSIT), we also propose an iterative step-by-step algorithm that converges to the NE point, but only requires limited CSIT. Numerical results are presented to illustrate the analytical findings and to study the role of different channel parameters on the NE strategies.
Physical layer security has emerged as a promising technique to safeguard the information security in wireless networks. In this paper, we investigate the physical layer security issue for a wireless network where there coexist multiple users with security concerns. Specifically, we tackle the problem from a distributed perspective and formulate the secure transmissions at different users as a non-cooperative game. Consider the practical situation that the legitimate transmitter may not always have the perfect information regarding the channel state information of the eavesdropper, we adopt the robust secrecy rate to combat the potential worst cases. Accordingly, the robust Nash equilibrium is employed as the solution to the resource competition game among the users. Further, we analyze properties of the equilibrium and derive the optimal transmission strategy for each individual user to maximize its own robust secrecy rate, following which the distributed algorithm is proposed for the network-wide competition to reach the equilibrium. Finally, simulation results are provided to corroborate our theoretical findings.
The information theoretic description of secrecy capacities and secrecy capacity regions (Liang et al., 2009) is an important research area to support a better understanding of security on the physical layer. Based on the secrecy capacity expressions or achievable secrecy rates, the transmit strategies, including power allocation, beamforming and subcarrier allocation, are optimized in order to choose a certain operating point. In this chapter, we focus on the optimization of the physical layer transmit strategies for typical wireless communication scenarios. In single-user scenarios, the system design is more complicated with additional secrecy constraints, since the secrecy capacity expressions are in general not concave or convex in the transmit strategies. The secrecy rate terms usually consist of a difference of two parts. The first one corresponds to the amount of data that can be reliably transmitted to the intended user and it is therefore concave in the transmit strategies. The second one corresponds to the amount of data that is overheard by the eavesdropper and it is thus also concave in the transmit strategies. The resulting transmit optimization problems are non-convex optimization problems since the difference of two concave functions is not necessarily convex or concave. However, in the multi-carrier case, the problem can be reduced to a convex optimization problem that can be efficiently computed. We conjecture that also the multiple antenna (MIMO) scenario will be completely solved in the very next future. In multi-user scenarios, the secrecy rate regions of all four elements of network information theory, the broadcast, the multiple access, the relay, and the interference channel were recently studied. The attacker models of the MAC and the relay case are more difficult than the wellmotivated ones of the broadcast and the interference channel. Therefore, we focus on the broadcast and interference channel. The resource allocation for the parallel broadcast channel without secrecy is involved due to a hard combinatorial problem the matching of carriers to users. Interestingly, with secrecy constraints, the resulting programming problem is much simpler and the optimal power and resource allocation can be solved efficiently. A similar
The growth of wireless networks has been considerable over the last decades. Due to the broadcast nature of these networks, security issues have taken a critical role in today’s communications. A promising direction towards achieving secure communications is information theoretic secrecy, which is an approach exploiting the randomness of the channels to ensure secrecy. Based on this approach, there has been a recent surge of interest in a potential cooperation between users to enhance the secrecy of communications. In this thesis we investigate the interaction between cooperation and secrecy. In particular the contributions of the thesis can be divided into two parts. In the first part, we study cooperative strategies for secrecy for wireless channels. Our goal is to evaluate the effect of fading and limited CSI on the eavesdropper’s channels. In that purpose we consider a scenario where a helper aims at increasing the secrecy of the communication between a source and destination in the presence of an eavesdropper. Several strategies are discussed for the helper, namely decode-and-forward, amplify-and-forward, and cooperative jamming. We introduce the secrecy outage probability, the conditional secrecy outage probability and the secure throughput as secrecy measures. For each measure, we investigate and compare the secrecy performance of cooperation. We furthermore elaborate a system optimization in terms of strategy selection, node positioning, power allocation and rate design. In the second part, we consider cooperation in the 4-node scenario against a more sophisticated adversary: an active eavesdropper, which can either passively eavesdrop, or jam the transmission. A game-theoretic perspective is a natural way to analyze the competitive interaction between the helper and the eavesdropper. Therefore we define several secrecy games, for which we find the Nash and Stackelberg equilibria as well as the corresponding secrecy rate outcomes. Another important consideration in this scenario is the interaction between the source and the helper, which we model and solve as a Stackelberg game, and we illustrate its impact on the achievable secrecy rates.