Cyber-physical Security Analysis of Smart Grids With Bayesian Sequential Game Models
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摘要: 智能电网是利用信息技术优化从供应者到消费者的电力传输和配电网络.作为一种信息物理系统（Cyber-physical system，CPS），智能电网由物理设备和负责数据计算与通信的网络组成.智能电网的诸多安全问题会出现在通信网络和物理设备这两个层面，例如注入坏数据和收集客户隐私信息的网络攻击，攻击电网物理设备的物理攻击等.本文主要研究了智能电网的系统管理员（防护者）如何确定攻击者类型，从而选择最优防护策略的问题.提出了一种贝叶斯序贯博弈模型以确定攻击者的类型，根据序贯博弈树得到博弈双方的均衡策略.首先，对类型不确定的攻击者和防护者构建静态贝叶斯博弈模型，通过海萨尼转换将不完全信息博弈转换成完全信息博弈，得到贝叶斯纳什均衡解，进而确定攻击者的类型.其次，考虑攻击者和防护者之间的序贯博弈模型，它能够有效地帮助防护者进行决策分析.通过逆向归纳法分别对两种类型的攻击者和防护者之间的博弈树进行分析，得到博弈树的均衡路径，进而得到攻击者的最优攻击策略和防护者的最优防护策略.分析表明，贝叶斯序贯博弈模型能够使防护者确定攻击者的类型，并且选择最优防护策略，从而为涉及智能电网信息安全的相关研究提供参考.Abstract: A smart grid is a network which uses communication and information technologies to optimize the transmission and distribution of power from suppliers to consumers. As a kind of cyber-physical system (CPS), a smart grid consists of the network part of data computing and communication and the physical part of all devices. Many security issues arise in both components of the grid, such as injecting bad data, collecting customer privacy information (cyber attacks) and attacking the grid physical devices (physical attacks). In this paper, we study how the system administrator (defender) can determine the type of attack and make optimal protection strategy. We propose a Bayesian sequential game model to defermine the type of attack, and analyze the equilibrium strategy of both game sides according to the sequential game tree. Firstly, we construct a static Bayesian game model between the attacker of an indeterminate type and the defender. We transform the incomplete information game into a complete information game through Harsanyi transformation, and analyze the Bayesian Nash equilibrium to determine the type of attacker. Secondly, we consider the sequential game model between attackers and defenders, which can effectively help defender to make decision in dynamic networks. Through the backward induction, the game tree is analyzed between two types of attackers and defenders, respectively. Then we obtain the equilibrium path of the game tree and make the optimal strategies for both players. It is shown that the defender can determine the type of attacker and make the optimal strategy by the Bayesian sequential game model, which provides a reference for the security research on smart grids.1) 本文责任编委 孙秋野
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表 1 攻击者类型为网络攻击
Table 1 The type of attacker is a cyber attack
防护 不防护 攻击 (1-2α)ω-cic, (2α-1)ω-cd ω-cic; -ω 不攻击 0, -βω-cd 0, 0 
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表 2 攻击者类型为物理攻击
Table 2 The type of attacker is a physical attack
防护 不防护 攻击 (1-2α)ω-cip, (2α-1)ω-cd ω-cip; -ω 不攻击 0, -βω-cd 0, 0
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表 3 行为函数收益
Table 3 The payoff of the behavioral function
$A(S, a, d)$ $a$为攻击者策略 $a$为防护者策略 $S$为攻击者 d×Impact(a) 0 $S$为防护者 $ - Impact(a)^{d}$ d×Impact(a)
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表 4 行为策略$a$的影响函数(网络攻击)
Table 4 The payoff of the behavioral function
行为策略$(a)$ $C(a)$ $I(a)$ $A(a)$ $SF(a)$ $Impact(a)$ $d_{\langle km, jd\rangle}$ $m$ $m$ $l$ $h$ $0.3l + 0.6m + 0.1h$ $a_{ce}$ $h$ $l$ $l$ $m$ $0.7l + 0.1m + 0.2h$ $a_{cj}$ $l$ $h$ $m$ $l$ $0.3l + 0.3m + 0.4h$ $a_{cd}$ $l$ $h$ $m$ $h$ $0.2l + 0.3m + 0.5h$
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表 5 行为策略$a$的影响函数(物理攻击)
Table 5 The payoff of the behavioral function (physical attack)
行为策略$(a)$ $C(a)$ $I(a)$ $A(a)$ $SF(a)$ $Impact(a)$ $d_{\langle ca, mp\rangle}$ $l$ $m$ $m$ $m$ $0.1l + 0.9m$ $a_{ps}$ $m$ $l$ $l$ $m$ $0.8l + 0.2m$ $a_{pn}$ $l$ $m$ $m$ $m$ $0.1l + 0.9m$ $a_{pt}$ $l$ $h$ $h$ $h$ $0.1l + 0.9h$
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