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IEEE Transactions on Information Forensics and Security

Power Allocation for Cooperative Jamming Against a Strategic Eavesdropper Over Parallel Channels

Zhifan Xu, Melike Baykal‐Gürsoy

Published Dec 12, 2022• 12 citations
Publisher

Abstract

This paper considers a friendly interferer allocating jamming power to eavesdropping channels to increase the level of secrecy of a wireless network. The friendly interferer has access to limited power, while the eavesdropper may not have the ability to attack all channels simultaneously. 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 targets probabilistically. We propose a non-zero-sum game that helps the friendly interferer predict and concentrate on the targets selected by the eavesdropper. Under certain conditions, we prove that there exists a unique Nash equilibrium (NE) strategy pair, which has a threshold type structure. We provide conditions under which the eavesdropper’s equilibrium strategy is deterministic. We devise a strategy iteration algorithm to compute an equilibrium power allocation strategy. We present examples showing that the game-theoretic power allocation strategy performs better than the conservative power allocation strategy that assumes every channel to be under attack.

DOI
10.1109/tifs.2022.3228520

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This paper considers a friendly interferer allocating jamming power to eavesdropping channels to increase the level of secrecy of a wireless network. The friendly interferer has access to limited power, while the eavesdropper may not have the ability to attack all channels simultaneously. 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 targets probabilistically. We propose a non-zero-sum game that helps the friendly interferer predict and concentrate on the targets selected by the eavesdropper. Under certain conditions, we prove that there exists a unique Nash equilibrium (NE) strategy pair, which has a threshold type structure. We provide conditions under which the eavesdropper’s equilibrium strategy is deterministic. We devise a strategy iteration algorithm to compute an equilibrium power allocation strategy. We present examples showing that the game-theoretic power allocation strategy performs better than the conservative power allocation strategy that assumes every channel to be under attack.
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.
We investigate optimal power allocation strategies over a OFDM Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and a jammer-who acts as unfriendly to both the legitimate parties and the eavesdropper. In particular, we formulate a zero-sum power allocation game between the transmitter and the jammer where the payoff function is the secrecy rate. We characterize the optimal power allocation strategies as well as the Nash equilibrium in some asymptotic regimes. We also provide a set of results that cast further insight into the problem.
We consider a multi-link interference network that is tapped by an external eavesdropper. To conceal information from the eavesdropper, legitimate links are equipped with transmitter-based friendly jamming (TxFJ) and receiver-based friendly jamming (RxFJ). Each link seeks to maximize its secrecy rate by determining the best power assignment (PA) for the information, TxFJ, and RxFJ signals. Joint optimization of these parameters is a non-convex problem. Hence, we seek sub-optimal solutions. Specifically, we find a lower bound on the allocated power to TxFJ above which positive secrecy is achievable for a given link. Once positive secrecy is achieved, the secrecy rate becomes monotonically increasing in the power at the transmitter (Alice). Therefore, the rest of Alice's power is allocated to the information signal. Despite its sub-optimality, such an approach precludes the possibility of employing successive interference cancellation by the eavesdropper. The RxFJ PA of a link is adjusted using an on-off PA that depends only on the link's local channel state information (CSI). With every link following such a strategy, we model this interaction as a non-cooperative game. We derive sufficient conditions for the uniqueness of the resulting Nash equilibrium. We then propose an algorithm to implement the PA game. Lastly, we relax knowledge of eavesdropper's CSI (E-CSI) and propose a framework that is robust to unknown E-CSI. Our results indicate that this robust framework performs close to when E-CSI is fully known to legitimate links. Moreover, empirically it is shown that the secrecy sum-rate scales with the power budget of transmitters.
This paper investigates optimal power allocation strategies over a bank of independent parallel Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and an unfriendly jammer. In particular, we formulate a zero-sum power allocation game between the transmitter and the jammer where the payoff function is the secrecy rate. We characterize the optimal power allocation strategies as well as the Nash equilibrium in some asymptotic regimes. We also provide a set of results that cast further insight into the problem. Our scenario, which is applicable to current OFDM communications systems, demonstrates that transmitters that adapt to jammer experience much higher secrecy rates than non-adaptive transmitters.
In this paper, we investigate a cooperative wireless network with jamming-based secure communications, where a friendly jammer can transmit jamming signals to interfere the malicious eavesdropper. We find that the secrecy rate of the source-destination link can be effectively improved with the help of the friendly jammer, and each source intends to obtain optimal jamming power from the friendly jammer to maximize its secrecy rate for data transmission. We then formulate this power allocation problem as an auction game and propose two distributively auction-based power allocation schemes, which are power allocation using Traditional Ascending Clock Auction (ACA-T) and power allocation using Alternative Ascending Clock Auction (ACA-A), considering the friendly jammer as the auctioneer and the sources as the bidders. In addition, we prove that both the proposed schemes can converge in a finite number of iterations. We also prove that the ACA-A scheme is cheat-proof while the ACA-T scheme is not. Finally, simulation results are presented to demonstrate the efficiency of the proposed auction-based schemes in improving secrecy rate of wireless networks.
In this paper, we propose efficient power allocation techniques using both convex optimization (using Lagrange multiplier method) and a soft evolutionary approach (using Differential Evolution (DE) algorithm) to optimize both the relay and jammer powers in addition to an increase in the system performance in terms of secrecy rate. Here, we consider a cooperative wireless network with control jamming comprising of a source-destination pair with a set of relay nodes in the presence of single and multiple eavesdroppers. Optimal relay node is selected based on the SNR received at each relay, which transmits the data to the destination using decode and forward strategy. Amongst the remaining nodes, selection of jammer is done based on the SNR value of the relay to eavesdropper link. The proposed power allocation schemes are compared with equal power allocation policy for using the Monte-Carlo simulation study and these schemes are found to be superior in terms of average secrecy rate.