Optimal Defense Strategy Research Articles

Solution of a Game-Theoretical Model of Resource Allocation

We consider a game-theoretical model of defense in which the opponents use several types of infinitelydivisible attack and defense weapons. The defender (first player) payoff is the probability of destroying each attack weapon by at least one of the defense weapons. It is assumed that defense deploys at least one unit of each type of weapons. The optimal defense strategy is a pure maximin strategy, and the optimal mixed attack strategy involves choosing only one of the available attack weapons with certain probabilities. The search for optimal player strategies is reduced to the solution of linear programs.

Security Management of Process Plants by a Bayesian Network Methodology

Before the tragedy of 9/11, the perception of risk in process plants was mainly focused on accidental events caused by technical failures, human errors or natural events. However, since then, the risk of deliberate actions against process facilities - also known as security risk - has also become a concern. Security risk assessment of engineering systems and infrastructures constitutes a complex task since a significant multitude of technical and socio-political information is needed to reasonably predict the risk of intentional malevolent acts. In the present study, a methodology based on Bayesian network (BN) has been applied to increase the security of critical infrastructures via cost-effective allocation of security measures. Using the probability updating feature of BN, the proposed methodology can be employed to investigate the effect of vulnerabilities on adversaries' preferences while planning security scenarios. Moreover, the proposed methodology is capable of efficiently identifying an optimal defensive strategy given a security scenario (i.e., an attack) through maximizing defenders' expected utility.

A Differential Game Based Approach Against Objective Function Attack in Cognitive Networks

We study the problem of defense strategy against Objective function attack (OFA) in Cognitive networks (CNs), where the network can be operated at the optimal state by adapting the parameters of its objective function. An OFA attacker can disrupt the parameter adaptation by interfering measures, which results in some operating parameters of the objective function deviating from their optimal settings. We first model the interactive process between the OFA attacker and defense system using differential game theory, and propose a defense strategy by introducing a new metric, namely, threat factor. Then, we obtain the optimal defense strategy by proving the existence of the saddle point of the proposed model. Moreover, this defense strategy is scale-free such that it can conquer a large number of OFAs in a decentralized way. Finally, we conduct extensive simulations to show that the proposed approach is effective.

Intrusion detection model of wireless sensor networks based on game theory and an autoregressive model

An effective security strategy for Wireless Sensor Networks (WSNs) is imperative to counteract security threats. Meanwhile, energy consumption directly affects the network lifetime of a wireless sensor. Thus, an attempt to exploit a low-consumption Intrusion Detection System (IDS) to detect malicious attacks makes a lot of sense. Existing Intrusion Detection Systems can only detect specific attacks and their network lifetime is short due to their high energy consumption. For the purpose of reducing energy consumption and ensuring high efficiency, this paper proposes an intrusion detection model based on game theory and an autoregressive model. The paper not only improves the autoregressive theory model into a non-cooperative, complete-information, static game model, but also predicts attack pattern reliably. The proposed approach improves on previous approaches in two main ways: (1) it takes energy consumption of the intrusion detection process into account, and (2) it obtains the optimal defense strategy that balances the system’s detection efficiency and energy consumption by analyzing the model’s mixed Nash equilibrium solution. In the simulation experiment, the running time of the process is regarded as the main indicator of energy consumption of the system. The simulation results show that our proposed IDS not only effectively predicts the attack time and the next targeted cluster based on the game theory, but also reduces energy consumption.

Optimal Denial-of-Service Attack Scheduling With Energy Constraint Over Packet-Dropping Networks

The recent years have seen a surge of security issues of cyber-physical systems (CPS). In this paper, denial-of-service (DoS) attack scheduling is investigated in depth. Specifically, we consider a system where a remote estimator receives the data packet sent by a sensor over a wireless network at each time instant, and an energy-constrained attacker that cannot launch DoS attacks all the time designs the optimal DoS attack scheduling to maximize the attacking effect on the remote estimation performance. Most of the existing works concerning DoS attacks focus on the ideal scenario in which data packets can be received successfully if there is no DoS attack. To capture the unreliability nature of practical networks, we study the packet-dropping network in which packet dropouts may occur even in the absence of attack. We derive the optimal attack scheduling scheme that maximizes the average expected estimation error, and the one which maximizes the expected terminal estimation error over packet-dropping networks. We also present some countermeasures against DoS attacks, and discuss the optimal defense strategy, and how the optimal attack schedule can serve for more effective and resource-saving countermeasures. We further investigate the optimal attack schedule with multiple sensors. The optimality of the theoretical results is demonstrated by numerical simulations.

Optimal control of networks in the presence of attackers and defenders.

We consider the problem of a dynamical network whose dynamics is subject to external perturbations ("attacks") locally applied at a subset of the network nodes. We assume that the network has an ability to defend itself against attacks with appropriate countermeasures, which we model as actuators located at (another) subset of the network nodes. We derive the optimal defense strategy as an optimal control problem. We see that the network topology as well as the distribution of attackers and defenders over the network affect the optimal control solution and the minimum control energy. We study the optimal control defense strategy for several network topologies, including chain networks, star networks, ring networks, and scale free networks.

Policy Learning for Continuous Space Security Games Using Neural Networks

A wealth of algorithms centered around (integer) linear programming have been proposed to compute equilibrium strategies in security games with discrete states and actions. However, in practice many domains possess continuous state and action spaces. In this paper, we consider a continuous space security game model with infinite-size action sets for players and present a novel deep learning based approach to extend the existing toolkit for solving security games. Specifically, we present (i) OptGradFP, a novel and general algorithm that searches for the optimal defender strategy in a parameterized continuous search space, and can also be used to learn policies over multiple game states simultaneously; (ii) OptGradFP-NN, a convolutional neural network based implementation of OptGradFP for continuous space security games. We demonstrate the potential to predict good defender strategies via experiments and analysis of OptGradFP and OptGradFP-NN on discrete and continuous game settings.

A Bayesian network methodology for optimal security management of critical infrastructures

Security management of critical infrastructures is a complex task as a great variety of technical and socio-political information is needed to realistically predict the risk of intentional malevolent acts. In the present study, a methodology based on Limited Memory Influence Diagram (LIMID) has been developed for the protection of critical infrastructures via cost-effective allocation of security measures. LIMID is an extension of Bayesian network (BN) intended for decision-making, allowing for efficient modelling of complex systems while accounting for interdependencies and interaction of system components. The probability updating feature of BN has been used to investigate the effect of vulnerabilities on adversaries’ preferences when planning attacks. Moreover, the proposed methodology has been shown to be able to identify an optimal defensive strategy given an attack through maximizing defenders’ expected utility. Despite being demonstrated via a chemical facility, the methodology can easily be tailored to a wide variety of critical infrastructures.

A Game-theoretic Approach for Channel Security Against Active Time-Varying attacks Based on Artificial Noise.

To penetrate sensitive communication systems, attackers can attack the channel using an Active Time-Varying(ATV) way, which will lead to a great information loss. The conventional approach is to encrypt the original signal making it difficult for attackers to get information. However, this technology is constrained by the limited wireless terminal equipment. In this paper, we choose to insert artificial noise into the channel, which aims at disturbing the attackers and reducing the loss of the system once attacks occur. However this technology has some side effects and tradeoffs. In this paper, we deal with this issue and propose a game-theoretic framework to minimize the total losses. We model the problem as a defender-attacker Stackelberg security game where the communication system plays a defender role. Furthermore we propose a novel binary search based algorithm to efficiently compute the Strong Stackelberg Equilibrium which is the optimal defense strategy. This algorithm reduces a M-dimensional problem to M 1-dimensional problems so that the complexity is lowered. The experimental results show that our proposed algorithm significantly outperforms other non-strategic strategies in terms of decreasing the total losses against ATV attacks.

Optimal Network Defense Strategy Selection Based on Incomplete Information Evolutionary Game

The issue of selecting the optimal defense strategy in the dynamic adversarial network is difficult. To solve this problem, we start from the realistic bounded rationality of both the attacker and the defender. First, we build the Bayesian attack-defense evolutionary game model combining with incomplete information game scenario. Specifically, we convert the uncertainty of the strategy payoffs of attackers and defenders to the uncertainty of their related types. Meanwhile, both the set of player types and the set of game strategies can be expanded to n in our model. Furthermore, we improve the replicator dynamics equation by adding the selecting intensity factor to depict the noise effect. This reflects the randomness of decision making for players due to their bounded learning capacities. In this way, the static analysis in the traditional game is extended as a dynamic process. On this basis, we summarize the evolutions of different player types with different strategies. Finally, by calculating the evolutionary stable equilibrium, we give the algorithm of selecting optimal defense strategy and depict the evolutionary track of this strategy selected by the defender with time going by. Our method provides decision support for the network proactive defense toward moderate security. Moreover, the dynamic analysis efficiency of defense decision making is improved, and the predicting ability of the defense situation is enhanced. Experimental results verify the scientificity and availability of the proposed model and method.

Markov Differential Game for Network Defense Decision-Making Method

While network attack and defense are experiencing a rapid change, the current research achievements of network security based on traditional game theory fail to characterize the real-time performance of the actual network attack–defense process accurately. Furthermore, all kinds of disturbance and accidental factors would affect the evolution of the network security state. Therefore, to tackle with the randomness of network security state and the high dynamic of network defense decision making, we analyzed the attack–defense behaviors from the perspectives of dynamic and real-time confrontation. Then we constructed the Markov attack–defense differential game model for the dynamic analysis to predict multi-stage continuous attack–defense process by combining differential game models and the Markov decision-making method. In addition, according to the discounted total payoffs of attack–defense game, we designed the objective function of the game. Based on previous statements, we proposed the multi-stage game equilibrium solution and designed the optimal defense strategy selection algorithm. Finally, we conducted simulations to demonstrate that the proposed model and method could shed some light to the real-time interplay of decision making between attack and defense.

Immune Signaling Networks: Sources of Robustness and Constrained Evolvability during Coevolution.

Defense against infection incurs costs as well as benefits that are expected to shape the evolution of optimal defense strategies. In particular, many theoretical studies have investigated contexts favoring constitutive versus inducible defenses. However, even when one immune strategy is theoretically optimal, it may be evolutionarily unachievable. This is because evolution proceeds via mutational changes to the protein interaction networks underlying immune responses, not by changes to an immune strategy directly. Here, we use a theoretical simulation model to examine how underlying network architectures constrain the evolution of immune strategies, and how these network architectures account for desirable immune properties such as inducibility and robustness. We focus on immune signaling because signaling molecules are common targets of parasitic interference but are rarely studied in this context. We find that in the presence of a coevolving parasite that disrupts immune signaling, hosts evolve constitutive defenses even when inducible defenses are theoretically optimal. This occurs for two reasons. First, there are relatively few network architectures that produce immunity that is both inducible and also robust against targeted disruption. Second, evolution toward these few robust inducible network architectures often requires intermediate steps that are vulnerable to targeted disruption. The few networks that are both robust and inducible consist of many parallel pathways of immune signaling with few connections among them. In the context of relevant empirical literature, we discuss whether this is indeed the most evolutionarily accessible robust inducible network architecture in nature, and when it can evolve.

Security as a Service for Cloud-Enabled Internet of Controlled Things Under Advanced Persistent Threats: A Contract Design Approach

In this paper, we aim to establish a holistic framework that integrates the cyber-physical layers of a cloud-enabled Internet of Controlled Things (IoCT) through the lens of contract theory. At the physical layer, the device uses cloud services to operate the system. The quality of cloud services is unknown to the device, and hence the device designs a menu of contracts to enable a reliable and incentive-compatible service. Based on the received contracts, the cloud service provider (SP) serves the device by determining its optimal cyber defense strategy. A contract-based FlipCloud game is used to assess the security risk and the cloud quality of service (QoS) under advanced persistent threats. The contract design approach creates a pricing mechanism for on-demand security as a service for cloud-enabled IoCT. By focusing on high and low QoS types of cloud SPs, we find that the contract design can be divided into two regimes (regimes I and II) with respect to the provided cloud QoS. Specifically, the physical devices whose optimal contracts are in regime I always request the best possible cloud security service. In contrast, the device only asks for a cloud security level that can stabilize the system when the optimal contracts lie in regime II. We illustrate the obtained results via case studies of a cloud-enabled smart home.

Multi-objective Stackelberg game model for water supply networks against interdictions with incomplete information

Water supply networks are infrastructures pivotal to economic development and living standards, of which the increasing complexity and interdependencies have brought challenges for the protection and enhancement of water supplies. We address the problem on how to defend water supply networks with hydraulic characteristics against an interdictor by building a multi-objective Stackelberg game model with incomplete information. In this model, the defender and the interdictor, both considered as rational players, choose a subset of network components to defend or interdict based on their payoffs. The defender, with incomplete information on the interdictor's efforts, initiates to trade off the two objectives of maximizing the expected network satisfaction rate and of minimizing defense efforts, whereas the interdictor, with no information on network operational capacity, follows to trade off the objectives of minimizing the expected network efficiency and of minimizing interdiction efforts. The algorithm of determining the final optimal defense strategies is presented, which consists of three steps: (1) develop the strategy sets by the assessments of network vulnerability and resilience; (2) analyze the equilibrium through a nested heuristic genetic algorithm; and (3) determine the final optimal defense strategy based on the minimax regret approach. A case study of D-town water supply network demonstrates the practical significance of the proposed approach. Furthermore, the impacts of the incomplete information are analyzed to provide suggestions on the defense strategy making.

A game theoretic method to model and analyze attack‐defense strategy of resource service in cloud application

SummaryCloud computing has attracted much attention recently in both industry field and academic research area. More and more Internet applications are moving to the cloud environment. However, it is difficult to construct perfectly secure mechanisms facing up with complex and various attacks in cloud computing, the efficient attack‐defense strategy is highly demanded. In this paper, a stochastic game model is proposed based on combining stochastic Petri nets with game theory, which is used to describe the attack‐defense behaviors in cloud computing. The physical machine, attack‐defense behavior, and their attributes are also modeled by stochastic game model thus forming the attack‐defense game model of cloud computing. On this basis, the Nash equilibrium of attack‐defense process in physical machine is computed to get the optimal defense strategy. The related theories of Petri nets and the reachable states of attack‐defense game model are used to formally verify the correctness and effectiveness of the proposed method. The enforcement algorithm is proposed to make cloud computing dynamically evaluate and select the defense strategy to against attack behavior as quickly as possible. Both case study and simulation results show that the proposed method can adapt quickly to the changes in cloud application thus improving the security of cloud computing.

Designing game-theoretic security strategies for large public events

High-profile, large-scale public events may be attractive targets for terrorist attacks. The security challenge for such events is exacerbated by their dynamic nature: the impact of an attack on different `targets, such as studio entrances, changes over time. In addition, the defender can relocate security resources among potential attack targets at any time, while the attacker may act at any time during the event. This study focuses on developing efficient patrolling algorithms for such dynamic domains, with continuous strategy spaces for both the defender and attacker. We propose SCOUT-A, which makes assumptions regarding relocation costs, exploits payoff representation, and computes optimal solutions efficiently. We furthermore propose SCOUT-C, to compute the exact optimal defender strategy for general cases despite the continuous strategy spaces. The experimental results demonstrate that our algorithms significantly outperform existing strategies.

When to Reset Your Keys: Optimal Timing of Security Updates via Learning

Cybersecurity is increasingly threatened by advanced and persistent attacks. As these attacks are often designed to disable a system (or a critical resource, e.g., a user account) repeatedly, it is crucial for the defender to keep updating its security measures to strike a balance between the risk of being compromised and the cost of security updates. Moreover, these decisions often need to be made with limited and delayed feedback due to the stealthy nature of advanced attacks. In addition to targeted attacks, such an optimal timing policy under incomplete information has broad applications in cybersecurity. Examples include key rotation, password change, application of patches, and virtual machine refreshing. However, rigorous studies of optimal timing are rare. Further, existing solutions typically rely on a pre-defined attack model that is known to the defender, which is often not the case in practice. In this work, we make an initial effort towards achieving optimal timing of security updates in the face of unknown stealthy attacks. We consider a variant of the influential FlipIt game model with asymmetric feedback and unknown attack time distribution, which provides a general model to consecutive security updates.The defender's problem is then modeled as a time associative bandit problem with dependent arms. We derive upper confidence bound based learning policies that achieve low regret compared with optimal periodic defense strategies that can only be derived when attack time distributions are known.

Optimal Personalized Defense Strategy Against Man-In-The-Middle Attack

The Man-In-The-Middle (MITM) attack is one of the most common attacks employed in the network hacking. MITM attackers can successfully invoke attacks such as denial of service (DoS) and port stealing, and lead to surprisingly harmful consequences for users in terms of both financial loss and security issues. The conventional defense approaches mainly consider how to detect and eliminate those attacks or how to prevent those attacks from being launched in the first place. This paper proposes a game-theoretic defense strategy from a different perspective, which aims at minimizing the loss that the whole system sustains given that the MITM attacks are inevitable. We model the interaction between the attacker and the defender as a Stackelberg security game and adopt the Strong Stackelberg Equilibrium (SSE) as the defender's strategy. Since the defender's strategy space is infinite in our model, we employ a novel method to reduce the searching space of computing the optimal defense strategy. Finally, we empirically evaluate our optimal defense strategy by comparing it with non-strategic defense strategies. The results indicate that our game-theoretic defense strategy significantly outperforms other non-strategic defense strategies in terms of decreasing the total losses against MITM attacks.

Generalized Engage or Retreat Differential Game With Escort Regions

This paper is motivated by the desire to develop optimal defensive control strategies that discourage an attacker from engaging in attack while simultaneously encouraging retreat. We develop a general, two-player, differential game in which one player represents an attacker and the opposing player represents the defender. The attacker possesses superior dynamics such that it is capable of terminating the game either in engagement or retreat as it so chooses. The defender is incapable of directly preventing engagement. Instead, the defender uses the manipulation of the attacker's utility function as a form of indirect control in an attempt to make retreat a more attractive option over engagement. The solution to the overall engage or retreat differential game is found by solving two related optimization problems: the differential game of engagement and the optimal constrained retreat. The equilibrium open-loop control strategies and resulting game values of the attack or retreat game are expressed in terms of the solutions to these subproblems. Within the optimal constrained retreat problem, a value function constraint is imposed in order to prevent the attacker from moving into regions where engagement becomes optimal. This leads to regions of constrained retreat which we refer to as escort regions.

Markov Evolutionary Games for Network Defense Strategy Selection

Since the characteristics of opposite objectives, non-cooperation relationship, and dependent strategies of network attack and defense are highly consistent with game theory, researching the decision-making methods of network defense and applying the game models to analyze the network attack–defense behaviors has been of concern in recent years. However, most of the research achievements regarding to the game models are based on the hypothesis that both the two sides’ players are completely rational, which is hard to meet. Therefore, we combined the evolutionary game theory and Markov decision-making process to construct a multi-stage Markov evolutionary game model for network attack–defense analysis, in view of the bounded rationality constraint. The model, based on the non-cooperative evolutionary game theory, could accomplish dynamic analysis and deduction for the multi-stage and multi-state network attack–defense process. In addition, an objective function with discounted total payoffs was designed by analyzing payoff characteristics of the multi-stage evolutionary game, which is more consistent with the reality of network attack and defense. Besides, the solving method for multi-stage game equilibrium was proposed on the basis of calculating the single-stage evolutionary game equilibrium. In addition, an algorithm for optimal defense strategy of the multi-stage evolutionary games was given. Finally, the experiments showed the high effectiveness and validity of the model and method that has a guiding significance for the network attack and defense.