Abstract A particular challenging problem in designing Internet of Things is that howto detect and prevent internal attacks, because all nodes try their best to save their limitednetwork resource. So it is difficult to achieve optimal objectives simultaneously, game theoryprovides an appropriate tool. In this paper, we propose a non-cooperative differential gamemodel, which allows all nodes to choose the optimal amount of network resource to invest ininformation security contingent upon the state of game. In our model, we specifically considerhow the vulnerability of information and the potential loss from such vulnerability affectsthe optimal amount of resources that should be devoted to securing that information. In thepaper, the optimal strategies of selfish nodes and malicious nodes are obtained respectively.The simulation results show that our game model has a good performance in stability of theprobability that the selfish nodes discover the malicious nodes under the optimal strategiesof the selfish and the malicious nodes.
Keywords Internet of things · Security · Differential game · Nash equilibrium
1 Introduction
Recently, Internet of Things is slowly but inevitably becoming part of daily life to provideinterconnection among many heterogeneous devices, such as cars, aircrafts, foods and allkinds of sensors [1]. It has been widely deployed in various environments (e.g., logistics,retail, forest fire detection, surveillance, supply chain management, industrial environment,oil and gas, battlefield environment). Internet of Things has been a very active research field[2,3].
From the standpoint of security and privacy, Internet of Things does not offer adequatesecurity [4]. There are two types of the attackers: outside attackers and insider attackers, where
Y. Ding (B) · X. Zhou · Z. Cheng · F. LinSchool of Computer and Communication Engineering, University of Scienceand Technology Beijing (USTB), Beijing 100083, People’s Republic of Chinae-mail: [email protected]
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the former are not legitimate users who haven’t gained access to use the network resources,while the latter are legitimate and have gained access to the network [5]. In Internet of Things,security mechanisms based on access control and secret communication channels regardingdefending against outside attackers have been studied particularly in [6].
Internal denial of service attacks can occur by malicious nodes [7], generally speaking,there are two types of internal denial of service attacks: passive denial of service attacks andactive denial of service attacks [8]. For passive denial of service attacks, the selfish nodesuse the network, but do not cooperate with other nodes, because they want to save theirlimited network resource, although they do not intend to damage other nodes. For activedenial of service attacks, the malicious nodes aim to damage the network [8]. Protectionagainst external malicious attacks is achieved by cryptographic mechanisms (e.g., encryptionalgorithm, digital signature algorithm) [8].
Because the nodes try their best to save their limited network resource (e.g., storage space,computing power, energy), a particular challenging problem in designing such networks isthat how to detect and prevent internal attacks. Especially, the limitation of energy is the mostsignificant, as technological progress on batteries is much slower than on electronics [9].Analyzing the interaction among a group of nodes who behave strategically is the advantageof game-theoretic models, so game-theoretic approach has been used extensively to modelwireless networks [10].
In [9], the authors proposed a multiplayer game model to prevent distributed denial ofservice attacks in ad hoc networks, where nodes are divided into some groups that decreasethe ability of malicious nodes to cooperate with one another in order to effectively launchdistributed denial of service attacks. When all malicious nodes collude with one another tomake a distributed denial of service attack, the model of [9] may be invalid. In the paper, ourmodel focuses on defending against inside attackers.
The paper presents a differential game model that determines the optimal amount of net-work resource to invest in network security. Accordingly, network security includes varioussecurity goals (e.g., authenticity, availability, non-repudiation, confidentiality and integrityof information). In our model, we specifically consider how the vulnerability of informationand the potential loss from such vulnerability affects the optimal amount of resources thatshould be devoted to securing that information, and malicious behaviors can be discoveredwith a high probability.
The rest of this paper is organized as follows. Related works are presented in Sect. 2.The security differential game model is reviewed in Sect. 3. In Sect. 4, the feedback Nashequilibrium solutions are given. Section 5 concludes the paper.
2 Related Works
Game theory has been proposed to solve security issue for wireless networks against inter-nal attacks [11,12] in the literature. For example, in [11], a game model was proposed toencourage the cooperation of nodes and improve the non-cooperative operation to the levelof cooperative equilibrium. Agah et al. in [12] proposed a repeated game model to preventpassive denial of service attacks for wireless sensor networks.
The authors in [13] proposed a non-cooperative game model, in which each node madeindividual decision regarding its power level or transmission probability. In the model of [13],the selfish nodes tried to maximize own throughput, the malicious nodes pursued destruc-tive objectives such as jamming and denial of service attacks at the media access controllayer.
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In [14], Lin et al. proposed a non-cooperative differential game based efficiency—awaretraffic assignment for multi-path routing in cognitive radio ad hoc networks; the objectiveof [14] was to take further advantage of efficiency of multi-path routing. But they didn’tconsider the optimal amount of network resource to invest in network security.
The authors in [15] presented a game model to consider the problem of distributed con-vergence to a Nash equilibrium, which was obtained by a stochastic extremum seekingalgorithm.
In [16], the authors proposed a notion of hidden puzzle difficulty, where the attacker couldnot determine the difficulty of the puzzle without spending a minimal amount of computingpower, and they showed that a defense mechanism was more effective by using game theory.
Game theory provides a mathematical tool that can be applied to model the interactionbetween selfish nodes and malicious nodes in Internet of Things. Security games and theirequilibrium solutions are used to predict attacker behavior [17]. The application of securitygame theory, especially discrete game theory, is usually studied based on security, trust andprivacy in wireless networks [18–23]. However, up to now, the application of differentialgames (especially, non-cooperative differential games) in Internet of Things security hasbeen researched little. Nevertheless, the non-cooperative differential game allows the nodesto choose the optimal amount of resource that should be devoted to securing that informationcontingent upon the state of the game, may be adaptive and feasible to Internet of Things.
3 Differential Game Model
In this paper, to formally analyze the security issue in an Internet of Things, we model thedynamic interactions between the selfish nodes and the malicious nodes as a differentialgame. We present a security differential game model that was inspired by the works in [24].Sorger in [24] studied the problem of dynamic advertising game with two players, whichallow firms to choose their advertising rates contingent upon the state of the game to optimizetheir payoffs, each player seeks to maximize an objective function. We extend the game modelwith more players.
In our model, the differential game model can be described as having three components,as summarized in Table 1:Players The set of the legitimate nodes in an Internet of Things, which is composed of themalicious nodes who is the abstraction of one or multiple nodes with malicious intent to
compromise the Internet of Things and the selfish nodes defending them,{
P Dnj
}n
j=1and
{PC
mi
}mi=1denote the set of the malicious nodes and the selfish ones, respectively.
Strategy space Assume that an Internet of Things consisting of wireless nodes that arecapable of deciding whether to collaborate with one another or defect. On the one hand, mostof them are selfish and want to preserve their network resource. On the other hand, they haveto forward packets to one another in order to enable multi-hop communications. At the same
Table 1 Components of a security differential game model
Component Description
Players The set of the legitimate wireless nodes
Strategy space The set of the attacks and the defensive measures
Gains Cost and benefit to nodes for each action-reaction
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time, for some malicious nodes, they may advertise false routing information, not forwardpacket correctly, fabricate, modify, or simply drop packets [25], the action set of the nodesis shown as follows
S = {C, D} (1)
where C represents collaboration and D denotes defection.In this paper, x(s) denotes the probability that selfish nodes discover the malicious nodes
at time s. For the selfish nodes, the bigger x(s), the more gains they will obtain. For simplicity,the gain gmi (x(s)) of the selfish node PC
mi is shown as follows
gmi (x(s)) = qmi x(t) (2)
where qmi is a positive parameter.fmi (t) denotes the number of packets that has been scheduled to send and have successfully
arrived at their destinations at time t by the selfish node PCmi . For a collaborate node PC
mi ,if a packet originated from a selfish node can be successfully delivered to its destination,then the node can get gain gmi . For simplicity, rmi ( fmi (t)) represents the packets that havebeen scheduled to send and have successfully arrived at their destinations, which is shownas follows
rmi ( fmi (t)) = fmi (t)gmi (3)
where gmi is a positive parameter.hnj (i, t) denotes that a node P D
nj drops or injects the number of packets, which are trans-
mitted by the node PCmi at time t . It is natural to assure that the nodes are battery limited in
Internet of Things, and they take into account the amount of energy spent. If the packets aredropped or injected by the malicious nodes and are not discovered by the selfish nodes, themalicious node can obtain gains wnj (hnj (i, t)). For simplicity, the gains wnj (hnj (i, t)) of themalicious node P D
nj is shown as follows
wnj (hnj (i, t)) = (1 − x(s))hnj (i, t)c (4)
where c is a positive constant.In the paper, ui (s) denotes the resource consume rate of a node i (i.e., amount of resources)
that is devoted to securing that information at time s, which is a ratio, so its unit is 1.
ui (s) = resource consume at time s
the total o f node i(5)
Assume that the cost paid by the selfish node PCmi is shown as follows
ymi (umi (s)) = cmi
2umi (s)
2 (6)
And the cost paid by the malicious node P Dnj is shown as follows
ynj (unj (s)) = cnj
2unj (s)
2 (7)
The selfish nodes are rational, a selfish node PCmi seek to maximize the instantaneous
probability x(s) and maximize the packets fmi (t) that have been scheduled to send and havesuccessfully arrived at the node PC
mi ’s destinations; and minimize resource consumptionincurred by their actions. Assume that the game is a perfect information game; a selfish nodePC
mi chooses the optimal amount of network resource umi (s) to invest in information security
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contingent upon the state of game in order to maximize the individual gain function Umi .The gain function for the selfish nodes is defined as follows.
Umi =T∫
t0
[qmi x(t) + fmi (t)gmi − cmi
2umi (s)
2]
exp(−r(s − t0))ds
+ exp(−r(T − t0))Smi x(T ) (8)
where r > 0 denotes discount factor, values received t time is discounted by the factor r,and Smi x(T ) denotes the marginal utility of the node PC
mi at time T .The malicious nodes, unlike the selfish nodes, are motivated by the reward for disrupting
or jamming the transmissions of other nodes. Similarly, for a malicious node P Dnj , we can
model the malicious nodes’ gain function as follows
Unj =T∫
t0
[qnj (1 − x(s)) + (1 − x(s))hnj (i, s)c − cnj
2unj (s)
2]
exp(−r(s − t0))ds
+ exp(−r(T − t0))Snj [1 − x(T )] (9)
When x(s) = 1, the selfish nodes’ instantaneous probability that discovers the mali-cious nodes is 100 %, according to our model, the increase of x(s) means increasethe intensity of the defensive countermeasures to against attacks, which may cost theirlarge amounts of resources, so the selfish nodes have to decrease their intensity of thedefensive countermeasures to save their resources. Similarly, assume that x(s) = 0, theprobability that discovers the malicious nodes is 0, the selfish nodes don’t take any defen-sive countermeasure to against attacks, which may threat the network security. So theselfish nodes have to increase their intensity of the defensive countermeasures to againstattacks. For simplicity, the dynamics of the probability x(s) that discovers malicious nodes isgoverned by
dx(s)
ds=
m∑i=1
umi (s)[1 − x(s)]1/2 −n∑
j=1
unj (s)x(s)1/2,
x(0) = x0 (10)
The game takes place in continuous time t with t ∈ [t0, T ]. T − t0 denotes the timeinterval. The objective of the selfish nodes is to maximize Umi , while the objective of themalicious nodes is to maximize Unj .
4 Feedback Nash Equilibrium Solutions
In this section, we give the solution to the non-cooperative game (8), (9) and (10), none ofthe selfish nodes and the malicious nodes make a pre-agreement, so they seek a feedbackNash equilibrium solution. Inspired by [26,27], such feedback Nash equilibrium for the game(8–10) can be characterized as follows.
A feedback Nash solution allows each node i to choose the optimal amount of networkresource ui (s) to invest in information security contingent upon the state of game.
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4.1 The Nash Equilibrium Feedback Solution for the Selfish Nodes
Let u(t0)∗(t, x) = [u(t0)∗m1 (t, x), u(t0)∗
m2 (t, x), . . . , u(t0)∗mm (t, x), u(t0)∗
n1 (t, x), u(t0)∗n2 (t, x), . . . ,
u(t0)∗nn (t, x)], for t ∈ [t0, T ] denotes a set of strategies that provides a feedback Nash
equilibrium solution to the non-cooperative game �(x0, T − t0), and W (t0)i (t, x) :[t0, T ] × Rn → R denotes the value function of the selfish node PC
mi , which satisfiesthe Isaacs-Bellman equation [26].
For the selfish node PCmi , i ∈ {1, 2, . . . , m}, a feedback Nash equilibrium solution to the
game (8), (10) satisfies the following conditions
− V (t0)mit (t, x) = max
umi
⎧⎨⎩
⎡⎣qmi x(t) + fmi (t)gmi − cmi
2umi (t)
2
⎤⎦ exp(−r(t − t0))
+ V mix (t, x)
⎡⎣umi (t)[1 − x(t)]1/2 +
m∑k �=i=1
u∗mk(t)[1 − x(t)]1/2
−n∑
j=1
u∗nj (t, x)x(t)1/2
⎤⎦⎫⎬⎭
V mi (T, x) = exp(−r(T − t0))Smi x, (11)
The Nash equilibrium feedback solution for the selfish nodes by performing the indicatedmaximization in Eq. (11) yields
u(t0)∗mi (t, x) = V mi
x (t, x)
cmi(1 − x)1/2 exp[r(t − t0)] for i ∈ {1, 2, . . . , m} (12)
4.2 The Nash Equilibrium Feedback Solution for the Malicious Nodes
For malicious node P Dnj , j ∈ {1, 2, . . . , n}, a feedback Nash equilibrium solution to the game
(9), (10) has to satisfy the following conditions
− V (t0)njt (t, x)= max
unj
⎧⎨⎩
⎡⎣qnj (1−x(t))+(1−x(t))hnj (i, t)c− cnj
2unj (t)
2
⎤⎦ exp(−r(t − t0))
+ V njx (t, x)
[−unj (t)[x(t)]1/2 +
m∑i=1
u∗mi (t, x)[1 − x(t)]1/2
−n∑
l �= j=1
u∗nl(t, x)x(t)1/2
⎤⎦⎫⎬⎭
V nj (T, x) = exp[−r(T − t0)]Snj (1 − x), (13)
Similarly, the Nash equilibrium feedback solution for the malicious nodes by performingthe indicated maximization in Eq. (13) yields,
where Ami (t), Bmi (t), Anj (t), and Bnj (t) satisfy
Ami (t)
dt= r Ami (t) − qmi + A2
mi (t)
2cmi+
m∑k �=i=1
Ami (t)Amk(t)
cmk+
n∑j=1
Ami (t)Anj (t)
cnj(17)
Ami (T ) = Smi (18)
Bmi (t)
dt= r Bmi (t) − fmi gmi − A2
mi (t)
2cmi−
m∑k �=i=1
Ami (t)Amk(t)
cmk(19)
Bmi (T ) = 0 (20)
Anj (t)
dt= r Anj (t)−qnj −hnj c+ A2
nj (t)
2cnj+
n∑l �= j=1
Anj (t)Anl(t)
cnl+
m∑i=1
Ami (t)Anj (t)
cmi(21)
Anj (T ) = Snj (22)
Bnj (t)
dt= r Bnj (t) − qnj − hnj c +
m∑i=1
Ami (t)Anj (t)
cmi, and (23)
Bnj (T ) = 0. (24)
For the symmetric case, (17) becomes
Ami (t)
dt= r Ami (t) + (m − 1/2)
A2mi (t)
cmi+ n
Ami (t)Anj (t)
cnj− qmi − hnj c (25)
Similarly, we have that
Anj (t)
dt= r Anj (t) − qnj − hnj c +
(n − 1
2
) A2nj (t)
cnj+ m
Ami (t)Anj (t)
cmi(26)
Upon substituting the relevant partial derivatives of V mi (t, x) and V nj (t, x) from (15)and (16) into (12) and (14) yields the feedback Nash equilibrium strategies
u(t0)∗mi (t, x)= Ami (t)
cmi(1 − x)1/2 for the selfish node PC
mi , i ∈ {1, 2, . . . , m} (27)
and u(t0)∗nj (t, x) = Anj (t)
cnjx1/2 for the malicious node P D
j , j ∈ {1, 2, . . . , n}. (28)
Substituting the game equilibrium strategies above into (10) yields the optimal state tra-jectory as
dx(s)ds = −
(m∑
i=1
Ami (t)cmi
+n∑
j=1
Anj (t)cnj
)x(s) +
m∑i=1
Ami (t)cmi
x(0) = x0
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Table 2 The parameter settings for the selfish nodes in the numerical example
qmi fmi cmi gmi Smi (x(T )) r c T
8.7 12 1.8 8 2.5 r > 0 7 [2, 4] hour
Table 3 The parameter settings for the malicious nodes in the numerical example
qnj hnj (i, t) cnj Snj (1 − x(T )) r c T
6.5 3 2.5 1.7 r > 0 7 [2, 4] hour
So,
x∗ (t) = �(t0, t)
⎛⎝
t∫
t0
[m∑
i=1
Ami (t)
cmi
]�−1(t0, s)ds + x0
⎞⎠, for t ∈ [t0, T ]
where �(t0, s) = exp[− ∫ st0
H(τ )dτ ] and H(s) = −(∑m
i=1Ami (t)
cmi+ ∑n
j=1Anj (t)
cnj
)
The feedback Nash equilibrium strategies, u(t0)∗mi (t, x) and u(t0)∗
nj (t, x), which are strat-egy profile for the non-cooperative differential game with the property that no nodes canimprove its gains by altering its strategy unilaterally while the other nodes keep their strate-gies unchanged [26,27].
5 Numerical Results
In this section, we provide a numerical example to evaluate the performance of our proposeddifferential game model. The example below introduces two teams consisting of the selfishnodes and the malicious nodes. In an Internet of Things, the total number of selfish nodes isset to be 1,000 and the total number of malicious nodes is set to be 200. Simply, the start timeof game is denoted 0, i.e., t0 = 0. Table 2 shows the parameter settings for the selfish nodesin the numerical example. Table 3 shows the parameter settings for the malicious nodes inthe numerical example.
In Tables 2 and 3, r > 0 denotes the discount rate, values received t time is discountedby the factor r . And Smi (x(T )) denote the marginal utility of the selfish nodes at time T .Snj (1 − x(T )) denote the marginal utility of the malicious nodes at time T . And T = [2, 4]hours denotes the time interval.
The variation of Ami (t) and Anj (t) varying with time t are shown in Fig. 1, it is shownthat the values of Ami (t) is decreased over time t ∈ [0, 2] hour, and Anj (t) is increased overtime. As shown in (27) and (28), the expected corresponding feedback Nash equilibriumstrategies, u(t0)∗
mi (t, x) and u(t0)∗nj (t, x), are a function of Ami (t) and Anj (t), respectively,
which will significantly affect on the variation of nodes’ optimal strategies, and it means theoptimal amount of network resource to invest in information security or attack the network toeach node in the Internet of Things will be modified with the variation of Ami (t) and Anj (t).
Figure 2 shows the relation between the optimal trajectories unj (t) and umi (t) and gametime t ∈ [0, 2] hour. As the same time, Fig. 2 also shows the optimal amount of networkresource used to invest in information security under the feedback Nash equilibrium strategiesu(t0)∗
mi (t, x) and u(t0)∗nj (t, x). As shown in Fig. 2, the optimal amount of network resource varies
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0 0.22 0.44 0.66 0.88 1.1 1.32 1.54 1.76 20.5
1
1.5
2
2.5
3
t
optim
al tr
ajec
tory
of r
esou
rce
cons
ume
A(t
)
Ami(t)
Anj(t)
Fig. 1 The relation between Ami (t), Anj (t) and game time t
0 0.22 0.44 0.66 0.88 1.1 1.32 1.54 1.76 20.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
t
optim
al tr
ajec
tory
of r
esou
rce
cons
ume
u(t)
umi(t)
unj(t)
Fig. 2 The relation between the optimal trajectories unj (t), umi (t) and game time t ∈ [0, 2] hour
depending on the security mechanisms over t ∈ [0, 2] hour. It can be easily seen that thevalues of umi (t) for the selfish nodes decrease over time t ∈ [0, 2] hour, and the values ofunj (t) for the malicious nodes increase over time t ∈ [0, 2] hour, which will increase theiroverhead. In practical application, the selfish nodes want to save their limited resource; themalicious nodes aim to damage the network while saving limited resource is not their priority.
Assume that the total number of selfish nodes is set to be 1,000 and the total number ofmalicious nodes is set to be 2 in the Internet of Things. In Figs. 3 and 4, under the optimalstrategies unj (t) and umi (t), it is shown that the probability x(t) that the selfish nodes discoverthe malicious nodes increases over time t , which increases from 70 % to almost 100 %.
Assume that the total number of selfish nodes is set to be 1,000 and the total number ofmalicious nodes is set to be 50 in the Internet of Things. In Figs. 5 and 6, under the optimal
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0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.65
0.7
0.75
0.8
0.85
0.9
0.95
1
t
Pro
b
m=1000,n=2
x(t)
Fig. 3 The relation between the probability x(t) that the selfish nodes discover the malicious nodes gametime t ∈ [0, 2] hour with 1,000 selfish nodes, 2 malicious nodes and T = 2 hour
0 0.5 1 1.5 2 2.5 3 3.5 40.65
0.7
0.75
0.8
0.85
0.9
0.95
1
t
m=1000,n=2
x(t)
Fig. 4 The relation between the probability x(t) that the selfish nodes discover the malicious nodes gametime t ∈ [0, 4] hour with 1,000 selfish nodes, 2 malicious nodes, and T = 4 hour
strategies unj (t) and umi (t), it is shown that the probability x(t) that the selfish nodes discoverthe malicious nodes increases over time t .
As shown in Figs. 3 and 4, under a very low number of malicious nodes, the probabilityx(t) that the selfish nodes discover the malicious nodes is growing faster than a very highnumber of malicious nodes as shown in Figs. 5 and 6 when the state is steady. The simulationresult shows that our game model has a good performance in stability of the probability thatthe selfish nodes discover the malicious nodes under the optimal strategies of the selfish andthe malicious nodes.
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0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 20.65
0.7
0.75
0.8
0.85
0.9
0.95
1
t
Pro
b
m=1000,n=50
x(t)
Fig. 5 The relation between the probability x(t) that the selfish nodes discover the malicious nodes gametime t ∈ [0, 2] hour with 1,000 selfish nodes, 50 malicious nodes T = 2 hour
0 0.5 1 1.5 2 2.5 3 3.5 40.65
0.7
0.75
0.8
0.85
0.9
0.95
1
t
m=1000,n=50
x(t)
Fig. 6 The relation between the probability x(t) that the selfish nodes discover the malicious nodes gametime t ∈ [0, 4] hour with 1,000 selfish nodes, 50 malicious nodes and T = 4 hour
6 Conclusions and Future Work
In this paper, a security communication differential game model in Internet of Things wasproposed. We jointly considered optimal amount of network resource to invest in informationsecurity and packet forwarding. The interactions between selfish nodes and malicious nodeswere modeled as a differential game. In our model, we specifically considered how thevulnerability of information and the potential loss from such vulnerability affects the optimalamount of resources that should be devoted to securing that information. Meanwhile, we
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obtained the optimal amount of resources u(t0)∗mi (t, x) and u(t0)∗
nj (t, x), of the selfish nodesand the malicious nodes that should be devoted to securing that information, as shown in(27) and (28). The simulation result shows that malicious behaviors can be discovered witha high probability.
How to better combine our differential game model with Internet of Things environmentwill be studied in our next step works.
Acknowledgments The authors thank the Editor and the anonymous reviewers very much for their veryuseful comments that improved our manuscript. This work is supported by the Foundation for Key Program ofMinistry of Education, People’s Republic of China (No. 311007) and the National Science Foundation Projectof People’s Republic of China (No. 61202079, 61170014 and 61003250).
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Author Biographies
Yan Ding received M.S. degree in Department of Mathematics fromZhengzhou University, China in 2009. At present, he is pursuing hisPh.D. degree in Department of Communication Engineering, School ofComputer and Communication Engineering, University of Science andTechnology Beijing. His research interests include security and privacyof mobile systems, resource allocation of wireless networks, game the-ory, and authentication and secure routing in wireless networks.
Xian-wei Zhou received his B.S. degree in Department of Mathemat-ics from Southwest Teachers’ University in 1986 and his M.S. degree inDepartment of System Science and Mathematics from Zhengzhou Uni-versity in 1992, and in 1999 he obtained the Ph.D. degree in Depart-ment of Transportation Engineering from the Southwest Jiaotong Uni-versity, P. R. China. He was engaged in postdoctor study at School ofElectronic and Information Engineering of Beijing Jiaotong University,P. R. China, from 1999 to 2000. Now, as a professor in Departmentof Communication Engineering, School of Computer and Communi-cation Engineering, University of Science and Technology Beijing, hisresearch interests include security and privacy of mobile systems, nextgeneration networks, mobile IPv6, scheduling theory and game theory.
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Zhi-mi Cheng received M.S. degree in School of Mathematics andStatistics from Lanzhou University, China in 2008. At present, she ispursuing her Ph.D. degree in Department of Communication Engineer-ing, School of Computer and Communication Engineering, Univer-sity of Science and Technology Beijing, China. Her research interestsinclude resource allocation of wireless networks, security and privacyof mobile systems, radio control, and differential game theory.
Fu-hong Lin received his M.S. degree and Ph.D degree from BeijingJiaotong University, Beijing, China, in 2006 and 2010, respectively,both in Electronics Engineering. Now he is a lecturer in departmentof Computer and Communication Engineering, University of Scienceand Technology Beijing, P. R. China. His research interests includewisdom network, social network and peer-to-peer network. Email:[email protected].
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