A mobile offloading game against smart attacks

SPECIAL SECTION ON THEORETICAL FOUNDATIONS FOR BIG DATA APPLICATIONS:
CHALLENGES AND OPPORTUNITIES
Received April 17, 2016, accepted April 21, 2016, date of publication May 9, 2016, date of current version June 3, 2016.
Digital Object Identifier 10.1109/ACCESS.2016.2565198
A Mobile Offloading Game Against Smart Attacks
LIANG XIAO1,2, (Senior Member, IEEE), CAIXIA XIE1, TIANHUA CHEN1,
HUAIYU DAI3, (Senior Member, IEEE), AND H. VINCENT POOR4, (Fellow, IEEE)
1Department of Communication Engineering, Xiamen University, Xiamen 361005, China
2Key Laboratory of Underwater Acoustic Communication and Marine Information Technology Ministry of Education, Xiamen University, Xiamen 361005, China
3Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695, USA
4Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
Corresponding author: L. Xiao (adalittlel@gmail.com)
This work was supported in part by the National Natural Science Foundation of China under Grant 61271242 and in part by the
U.S. National Science Foundation under Grant CMMI-1435778, Grant CNS-1016260, Grant ECCS-1307949,
and Grant EARS-1444009.
ABSTRACT Mobile devices, such as smartphones, can offload applications and data to the cloud via
access points or base stations to reduce energy consumption and improve user experience. However, mobile
offloading is vulnerable to smart attackers that use smart and programmable radio devices, such as universal
software radio peripherals, to perform multiple types of attacks, such as spoofing and jamming, based on the
radio environment and offloading transmissions. In this paper, a mobile offloading game is investigated that
consists of three players: a mobile device that chooses its offloading rate, a smart attacker that determines
its attack mode, and a security agent that decides whether or not to initiate full protection for the serving
access point during the offloading. Nash and Stackelberg equilibria of the offloading game are derived and
their existence conditions are discussed. A Q-learning-based mobile offloading strategy is proposed for
mobile devices that are unaware of system parameters, such as the channel conditions, in dynamic radio
environments. Simulation results show that the proposed offloading strategy can improve the utility of the
mobile device and reduce the attack rate of smart attackers.
INDEX TERMS Mobile offloading, spoofing, jamming, game theory, smart attacks, Q-learning.
I. INTRODUCTION
With the proliferation of cloud-based mobile services, mobile
devices such as smartphones and tablets can offload their
applications and data to the cloud to improve user experi-
ence in terms of longer battery lifetime, larger data storage,
faster processing speed and more powerful security services.
However, data offloading to the cloud via access points (APs)
or base stations (BSs) is vulnerable to various types of attacks,
such as spoofing, eavesdropping and jamming [1]. A smart
attacker can use smart and programmable radio devices such
as Universal Software Radio Peripherals (USRPs) or the
Wireless Open-Access Research Platform (WARP) devel-
oped by Rice University [2] to launch multiple types of
attacks. Compared with traditional single mode attacks,
mobile offloading is more vulnerable to smart attacks, as a
smart attacker flexibly chooses its attack mode and strength
according to the ongoing offloading transmissions and radio
environment. For example, a smart attacker can launch
jamming attacks if it is close to the serving AP and can
efficiently block the offloading, or can send spoofing signals
with the MAC address of the mobile device.
Although the detection of spoofing and jamming attacks
has been well studied [3], [4], mobile devices still suffer from
time and energy loss due to false alarms and security loss
resulting from missed detection of attacks. Security agents at
APs or BSs can apply both physical-layer and higher-layer
security mechanisms [5] to protect the offloading process.
More specifically, the security agent can apply an advanced
security mechanism, possibly by processing the offloading
data again or changing the session keys, at the cost of higher
processing and transmission overhead. The offloading rate of
the mobile device is chosen according to the radio environ-
ment, e.g., a mobile device has to process the data locally
under strong jamming or heavy traffic at the AP or BS [6]–[9].
While game theory has been used to study the interac-
tions between attackers and mobile devices [3], [4], [10],
mobile offloading usually involves three players: a mobile
device, a smart attacker and a security agent. In this paper,
we investigate the secure mobile offloading game, in which
a smart attacker can perform multiple types of attacks,
including spoofing and jamming, a mobile device deter-
mines its offloading rate, and a security agent at the AP
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L. Xiao et al.: Mobile Offloading Game Against Smart Attacks
protects the offloading with two modes: a fast mode that
applies physical-layer security and a safe mode that applies
both physical-layer and higher-layer security mechanisms.
We analyze the Nash equilibria (NEs) of the secure mobile
offloading game, at which none of the three players can
increase its utility by unilaterally choosing a different strat-
egy. The sequential interactions among the mobile device,
the security agent and the attacker can be modeled as a
Stackelberg game, in which the mobile device chooses its
offloading rate first, the smart attacker determines its attack
mode afterwards based on the observed offloading rate,
and finally the security agent chooses its defense mode
(i.e., whether or not to invoke a higher-layer security mecha-
nism) based on both the offloading rate and the attack mode.
We derive the Stackelberg equilibria (SEs) of this game and
discuss the impact of the radio channel gains on the security
of offloading.
A mobile device has difficulty obtaining all the system
parameters, such as the channel condition and transmit pow-
ers of the attacker in dynamic environments needed to derive
the optimal offloading strategy. As an important reinforce-
ment learning technique, Q-learning can be applied by the
mobile device to derive the optimal offloading strategy via tri-
als. Thus, we propose a Q-learning based offloading strategy
for mobile devices to decide their offloading rates based on
the observed state, which consists of the previous actions of
the opponents and the channel gain in dynamic environments.
Our main contributions can be summarized as follows:
• We formulate a secure mobile offloading game to inves-
tigate the interactions among a mobile device, a smart
attacker and a security agent.
• We derive both the NEs and SEs of the secure mobile
offloading game, and provide conditions under which
the equilibria exist.
• We propose a Q-learning based offloading strategy
for dynamic radio environments to improve resistance
against smart attacks.
The rest of this paper is organized as follows. We review
related work in Section II, and present the system model
in Section III. We formulate the secure mobile offloading
game and derive the NEs of the game in Section IV, and
investigate the Stackelberg game in Section V. We present
the Q-learning based offloading strategy and investigate the
dynamic secure offloading game in Section VI. Simulation
results are provided in Section VII. Conclusions are drawn
in Section VIII.
II. RELATED WORK
Mobile offloading has recently attracted extensive research
attention. For example, a mobile offloading algorithm based
on the user’s local load and the availability of intermit-
tently connected cloudlets was proposed in [6] to reduce
the computation and offloading costs of mobile devices.
Task dispatch, transmission and execution for mobile clouds
were investigated in [11], and a semi-Markovian decision
process based mobile offloading method was developed to
achieve a balance between performance and battery life.
A delayed offloading model analyzes the energy-delay trade-
off was developed in [12], which leverages the complemen-
tary strengths of WiFi and cellular networks. Two offloading
strategies for mobile cloud offloading systems based on the
energy-response time weighted product metric were proposed
in [13] to analyze the energy-performance tradeoff. Based
on the time complexity and data sharing information at
the procedure calls, the offloading scheme proposed in [8]
constructs a cost graph and partitions the computational tasks
to save energy. The distributed mobile offloading algorithm
proposed in [14] formulates a revenue maximization prob-
lem for software defined networks. The offloading strategy
designed in [15] applies a hybrid queueing model and quanti-
fies the security attributes and their impact on the offloading
performance.
Privacy and security are critical for mobile offload-
ing [1], [16]. Game theory has been applied to investigate net-
work security, especially for attacks with uncertainties. For
example, the interaction between a wireless transmitter and
a dual-threat attacker that can implement both eavesdropping
and jamming was formulated in [3] as a zero-sum game. The
joint threat from an advanced persistent threat attacker and
insiders was formulated in [4] as a two-player game, and the
NE of the game was provided. A zero-sum game between a
transmitter and an adversary that is either a passive eaves-
dropper or an active jammer was investigated in [17], and
conditions for the existence of an NE of the game were exam-
ined. A stochastic game was studied in [18] to improve the
secrecy and reliability of communication against an adversary
that can implement both jamming and eavesdropping.
A nested two-stage offloading game was formulated in [7],
in which the mobile device judiciously decides whether or
not to offload and chooses the portion of an application to
offload, while the cloud allocates the resources for the mobile
device. A computation offloading game investigated in [9]
can achieve efficient offloading. A Q-learning based malware
detection strategy was proposed in [19] for smartphones with
limited radio bandwidth, in which each smartphone offloads
a portion of its applications to a security server in the cloud
to improve the detection speed and accuracy. We formu-
lated a secure offloading game for the interactions among a
mobile device, a smart attacker and a security agent in [20].
Compared with our previous work in [20], in this paper, we
incorporate radio channel variations in the game model and
investigate the impact of the channel gains on the NEs of the
game. In addition, we formulate a Stackelberg game, in which
the mobile device, attacker and security agent choose their
strategies in sequence based on the observations of the former
player’s actions. We provide the SE of the offloading game
and propose a Q-learning based mobile offloading strategy
for dynamic games.
III. SYSTEM MODEL
We consider the offloading of a mobile device (T ) in the
presence of a smart attacker (E) under the protection of
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FIGURE 1. Illustration of an offloading game consisting of a mobile
device with offloading rate x, a smart attacker with attack mode y, and a
security agent that protects the serving AP in defense mode z.
a security agent (D) at the serving AP. As illustrated in Fig. 1,
the mobile device offloads its applications and data to the
cloud via the AP. The offloading is threatened by the smart
attacker that uses USRPs to perform multiple types of attacks,
e.g., spoofing and jamming. The offloading rate of the mobile
device, denoted by x ∈ [0, 1], is defined as the proportion of
the data that is sent to the serving AP. If x = 0, the mobile
device processes all the data locally, while x = 1 means that
all the data are processed in the cloud. The offloading rate is
chosen as a tradeoff among the fast processing in the cloud,
the radio transmission cost and the risks of being attacked
during offloading.
The smart attacker chooses its attack mode against the
mobile device, denoted by y ∈ {0, 1, 2}, which corresponds to
no attack, spoofing and jamming, respectively. More specif-
ically, the attacker sends spoofing signals with the mobile
device’s identity when y = 1, transmits jamming signals
to block the offloading when y = 2, and keeps silent when
y = 0. The security agent operates in two modes: A safe
mode combining a physical-layer security method such as
the channel-based spoofing detector of [21] and advanced
higher-layer security mechanisms such as the authentication
technique presented in [5] for attack detection at the AP is
used when z = 1; and a fast mode in which only the physical-
layer security mechanism is used if z = 0. The extra cost of
the safe mode over the fast mode, denoted by β, is positive
by definition, and the cost of the fast mode is ignored for
simplicity.
The channel gain between the AP and the mobile device is
modeled as a Markov chain. More specifically, the channel
gain during the offloading at time n, denoted by hn
T ∈ HT =
{Hl
T }1≤l≤NT , is quantized into NT levels, where Hl
T is the l-th
level of the channel gain with Hm
T < Hk
T , ∀1 ≤ m < k ≤ NT .
The transition probability of the channel gain hn
T is defined as
pm,k = Pr(hn+1
T = Hk
T |hn
T = Hm
T ). For simplicity, we assume
that the channel gain only changes to its neighboring states,
as shown in Fig. 2. Similarly, the channel gain between the
attacker and the AP, denoted by hn
E ∈ HE = {H
j
E }1≤j≤NE ,
is modeled as a Markov chain with NE states with transition
probabilities denoted by qm,k = Pr(hn+1
E = Hk
E |hn
E = Hm
E ).
For simplicity of notation, the time index of the channel gain
is omitted if no confusion results. Table 1 summarizes the
notation used in the paper.
IV. SECURE MOBILE OFFLOADING GAME
We consider a static secure mobile offloading game denoted
by G, in which three players make decisions simultaneously
FIGURE 2. Channel model of offloading based on an NT -state Markov
chain, in which pm,k is the transition probability.
TABLE 1. Summary of symbols and notation.
in a time slot: The mobile device chooses its offload-
ing rate, x ∈ [0, 1], the smart attacker determines its
attack mode y ∈ {0, 1, 2}, and the security agent selects
its defense mode during offloading with z ∈ {0, 1}.
Let Cz
y denote the attack cost of the mobile device if the
attacker adopts attack mode y and the security agent protects
the AP via mode z. The cost of an attack to the offloading con-
sists of the loss of the mobile device due to attack y, the cost to
launch the attack, and the penalty to the attacker if caught by
the security agent. For instance, if the penalty of the attacker
after being caught is greater than the user’s loss, Cz
y can be
negative. On the other hand, the attack detection accuracy at
the AP depends on the defense mode of the security agent,
and thus the attack cost depends on z. The attack cost in the
fast mode, in which the security agent uses the physical-layer
security mechanism to protect the serving AP is greater than
that in the safe mode, i.e., C0
y > C1
y , ∀y = 1, 2. If the attacker
keeps silent with y = 0, then the offloading incurs zero attack
cost, i.e., Cz
0 = 0, ∀z = 0, 1. For simplicity, we define the
attack cost matrix C = [C0
0 , C1
0 ; C0
1 , C1
1 ; C0
2 , C1
2 ].
We assume that both the mobile device and the security
agent make decisions to maximize the same utility denoted
by u, which depends on the attack mode, the channel gains,
and the transmit power of the offloading signals denoted
by PT . Without loss of generality, the receiver noise power
is set to be one. More specifically, if the attacker keeps
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silent (y = 0), the mobile device benefits from the channel
capacity minus the transmit cost of the offloading. Thus the
utility of the mobile device is given by
u(x, 0, z) = x (log (1 + PT hT ) − σPT ) − zβ, (1)
where β is the extra cost of the security agent in the safe mode
compared with the fast mode, and σ > 0 is the positive unit
transmission cost.
If the smart attacker sends a spoofing signal without inter-
rupting the ongoing offloading in the time slot (y = 1), the
utility of the mobile device can be defined as
u(x, 1, z) = x (log (1 + PT hT ) − σPT ) − Cz
1 − zβ, (2)
where Cz
1 is the cost of the mobile device under spoofing
attacks in defense mode z.
If the attacker sends jamming signals (y = 2) with
jamming power PE during the offloading, the mobile
device suffers from a low signal-to-interference-plus-noise
ratio (SINR), and its utility can be defined as
u(x, 2, z) = x log 1 +
PT hT
1 + PE hE
− σPT − Cz
2 − zβ.
(3)
In this game, the utility of the attacker denoted by uE is given
by
uE(x, y, z) = −u(x, y, z). (4)
In summary, we consider a three-player secure offload-
ing game, G = {T , E, D}, {x, y, z}, {u, uE, u} , in which
x ∈ [0, 1], y ∈ {0, 1, 2}, and z ∈ {0, 1}. A Nash equilibrium
of the static offloading game G denoted by (x∗, y∗, z∗) is given
by definition as
u(x∗
, y∗
, z∗
) ≥ u(x, y∗
, z∗
), ∀x ∈ [0, 1] (5)
u(x∗
, y, z∗
) ≥ u(x∗
, y∗
, z∗
), ∀y ∈ {0, 1, 2} (6)
u(x∗
, y∗
, z∗
) ≥ u(x∗
, y∗
, z), ∀z ∈ {0, 1}. (7)
No player has motivation to unilaterally deviate from a Nash
equilibrium of a game, as its utility decreases in that case.
Theorem 1: The static offloading game G has an NE
(1, 0, 0), if



C0
1 ≤ 0 (8a)
hT >
2σPT − 1
PT
(8b)
C0
2 ≤ log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
. (8c)
Proof: By Eqs. (1)-(3), if (8a) and (8c) hold, we have
u(1, 0, 0) = log(1 + PT hT ) − σPT
≤ min log(1 + PT hT ) − σPT − C0
1 ,
log 1 +
PT hT
1 + PE hE
− σPT − C0
2
= min {u(1, 1, 0), u(1, 2, 0)}. (9)
If (8b) holds, as x ≤ 1, we have
u(1, 0, 0) = log(1 + PT hT ) − σPT
≥ x (log(1 + PT hT ) − σPT ) = u(x, 0, 0). (10)
Similarly, as β > 0, we have
u(1, 0, 0) = log(1 + PT hT ) − σPT
≥ log(1 + PT hT ) − σPT − β = u(1, 0, 1). (11)
By Eqs. (9)-(11), we see that (5)-(7) hold for (1, 0, 0), which
is an NE of G.
Remark: Under a high penalty of being caught (i.e., (8a)
and (8c)), the smart attacker keeps silent (y = 0). If the
channel gain between the mobile device and the AP is high
(i.e., (8b)), the mobile device chooses a full offloading rate
(x = 1). In this case, the security agent applies the fast
mode at a low cost (z = 0), since the attack motivation is
suppressed.
(1, 1, 0), if (8b) holds and



max 0, log
(1 + PE hE )(1 + PT hT )
1 + PE hE + PT hT
+ C0
2 ≤ C0
1
(12a)
β ≥ C0
1 − C1
1 . (12b)
Proof: By Eqs. (1)-(3), if (12a) holds, we have
u(1, 1, 0) = log(1 + PT hT ) − σPT − C0
1
≤ min log(1 + PT hT ) − σPT ,
log 1 +
PT hT
1 + PE hE
− σPT − C0
2
= min {u(1, 0, 0), u(1, 2, 0)}. (13)
If (8b) holds, as x ≤ 1, we have
u(1, 1, 0) = log(1 + PT hT ) − σPT − C0
1
≥ x (log(1 + PT hT ) − σPT ) − C0
1 = u(x, 1, 0).
(14)
If (12b) holds, we have
u(1, 1, 0) = log(1 + PT hT ) − σPT − C0
1
≥ log(1 + PT hT ) − σPT − C1
1 − β = u(1, 1, 1).
(15)
By Eqs. (13)-(15), we see that (5)-(7) hold for (1, 1, 0), which
is an NE of G.
Remark: If spoofing is more harmful than jamming to the
mobile device (i.e., (12a)), the smart attacker sends spoofing
signals (y = 1). If the channel gain of the mobile device is
high (i.e., (8b)), the mobile device chooses a full offloading
rate (x = 1). The security agent applies the fast mode (z = 0)
because the cost of the safe mode is high (i.e., (12b)).
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(1, 2, 0), if



β ≥ C0
2 − C1
2 (16a)
hT >
2σPT − 1 (1 + PE hE )
PT
(16b)
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
≤ min{C0
2 , C0
2 − C0
1 }. (16c)
Proof: By Eqs. (1)-(3), if (16c) holds, we have
u(1, 2, 0) = log 1 +
PT hT
1 + PE hE
− σPT − C0
2
≤ min{log(1 + PT hT ) − σPT ,
log(1 + PT hT ) − σPT − C0
1 }
= min {u(1, 0, 0), u(1, 1, 0)} . (17)
If (16b) holds, we have
u(1, 2, 0) = log 1 +
PT hT
1 + PE hE
− σPT − C0
2
≥ x log 1 +
PT hT
1 + PE hE
− σPT − C0
2 = u(x, 2, 0).
(18)
If (16a) holds, we have
u(1, 2, 0) = log 1 +
PT hT
1 + PE hE
− σPT − C0
2
≥ log 1 +
PT hT
1 + PE hE
− σPT − C1
2 − β = u(1, 2, 1).
(19)
By Eqs. (17)-(19), we see that Eqs. (5)-(7) hold for (1, 2, 0),
which is an NE of G.
Remark: If jamming is harmful to the mobile device
(i.e., (16c)), the attacker sends jamming signals (y = 2).
The mobile device chooses a full offloading rate (x = 1)
only if the channel gain of the mobile device is high enough
(i.e., (16b)). If the extra cost of the safe mode is high
(i.e., (16a)), the security agent chooses the fast mode (z = 0).
(0, 0, 0), if



max C0
1 , C0
2 ≤ 0 (20a)
hT ≤
2σPT − 1
PT
. (20b)
Proof: Similar to that of Theorem 1.
Remark: If the channel gain of the mobile device is low
(i.e., (20b)), the mobile device processes the data locally
(x = 0). If the penalty of being detected is high, both
C0
1 and C0
2 are negative (i.e., (20a)), and thus the attacker
keeps silent (y = 0). In this case, the security agent applies
the physical-layer security mechanism (z = 0).
Other NEs of the static game are given in the following
theorem.
(0, 1, 0), if (20b) holds and
max{0, C0
2 } ≤ C0
1 < C1
1 + β. (21)
The game G has an NE (0, 1, 1), if (20b) holds and
C1
1 ≥ max{0, C1
2 } (22a)
β < C0
1 − C1
1 . (22b)
The game G has an NE (0, 2, 0), if



hT ≤
2σPT − 1 (1 + PE hE )
PT
(23a)
max{0, C0
1 } ≤ C0
2 < C1
2 + β. (23b)
The game G has an NE (0, 2, 1), if (23a) holds and
C1
2 ≥ max{0, C1
1 } (24a)
β < C0
2 − C1
2 . (24b)
The game G has an NE (1, 2, 1), if (16b) holds and



β < C0
2 − C1
2 (25a)
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
≤ min{C1
2 , C1
2 − C1
1 }. (25b)
The game G has an NE (1, 1, 1), if (8b), (22b) hold and
C1
1 ≥ max 0, log
(1 + PE hE )(1 + PT hT )
1 + PE hE + PT hT
+ C1
2 .
(26)
Remark: The mobile offloading rate depends on the current
channel gain of the mobile device. Take the NE (0,1,0) as an
example. In this case, the mobile device chooses to process
the data locally, as the channel gain is low, as shown in (20b).
The smart attacker sends spoofing signals, if the spoofing
cost is high as indicated by (21). The security agent uses the
physical-layer security mechanism in the fast mode as the
data is processed locally.
Fig. 3 summarizes the NEs of the game, in which
ψ = log
(1 + PE hE )(1 + PT hT )
1 + PE hE + PT hT
. (27)
As shown in Fig. 3 (a), the mobile device chooses a full
offloading rate if Eqs. (8b), (16b) and (26) hold. The attacker
performs spoofing attacks if (12) holds, as the spoofing
signal is difficult to detect by the security agent. If the
cost of a spoofing attack is large, the security agent applies
the safe mode to secure the mobile device. In Fig. 3 (b),
if Eqs. (8b), (16b) and (25b) hold, the mobile device offloads
all the data to the cloud via the AP. The attacker sends jam-
ming signals if (16) and (25) hold, because jamming signals
can significantly decrease the SINR of the offloading signal
at the AP. If the jamming strength is high, the security agent
protects the AP with the safe mode. Fig. 3 (c) corresponds to
the case in which Eqs. (20b), (22a) and (23a) hold and the
mobile device processes the data locally. More specifically,
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FIGURE 3. NEs of the static secure offloading game G, in which the
mobile device applies a full offloading rate (full rate) or processes the
data locally (local), the smart attacker chooses spoofing, jamming or no
attack, and the security agent enters either the fast mode or safe mode.
(a) Conditions (8b), (16b) and (26). (b) Conditions (8b), (16b) and (25b).
(c) Conditions (20b), (23a) and (22a). (d) Conditions (20b), (23a) and (24a).
the smart attacker sends spoofing signals if (22a) holds, and
the security agent applies both the physical-layer and higher-
layer security mechanisms in the safe mode with a low cost.
As shown in Fig. 3 (d), the security agent uses a safe mode
with a low cost (24b), while the smart attacker performs a
jamming attack if the jamming cost to offloading is high (23b)
and (24a), and spoofs if the spoofing cost C0
1 is large (21).
V. MOBILE OFFLOADING STACKELBERG GAME
We consider a mobile offloading Stackelberg game denoted
by G , in which the mobile device chooses its offloading rate x
first, then the smart attacker chooses its attack mode y based
on the observed offloading rate, and finally the security agent
decides whether to start its advanced defense mode according
to both the offloading rate and the attack mode. For simplicity,
each follower is assumed to accurately obtain the action of
a leader. A Stackelberg equilibrium of its offloading game
denoted by (xSE , ySE , zSE ) is given by definition as follows:
zSE
(x, y) = arg max
z∈{0,1}
u(x, y, z) (28)
ySE
(x) = arg min
y∈{0,1,2}
u x, y, zSE
(x, y) (29)
xSE
= arg max
x∈[0,1]
u x, ySE
(x), zSE
(x, y) . (30)
At a Stackelberg equilibrium of the offloading game, the
mobile device as the leader chooses its offloading rate first
to maximize its utility given by (30) considering the response
of the smart attacker as the follower. The attack mode of the
attacker is selected to minimize the utility in (29) based on
the observed offloading rate. The security agent chooses its
defense mode based on both x and y, as shown in (28).
Theorem 6: The static offloading game G has an SE
(1, 0, 0), if (8b) and one of (31)-(34) hold, with



C0
1 ≤ 0 (31a)
β ≥ max C0
y − C1
y , ∀y = 1, 2 (31b)
C0
2 ≤ log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
(31c)



C0
2 − C1
2 ≤ β < min C0
1 − C1
1 , −C1
1 (32a)
C0
2 ≤ log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
(32b)



C0
1 ≤ 0 (33a)
C0
1 − C1
1 ≤ β < min C0
2 − C1
2 ,
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
− C1
2 (33b)
β < min C0
1 − C1
1 , C0
2 − C1
2 , −C1
1 ,
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
− C1
2 . (34)
Proof: By (1), as β > 0, we have
u(x, 0, 0) = x (log(1 + PT hT ) − σPT )
≥ x (log(1 + PT hT ) − σPT ) − β = u(x, 0, 1).
(35)
Thus, (28) holds for (x, 0, 0) and we have zSE (x, 0) = 0.
2286 VOLUME 4, 2016

Similarly, by (2), if β ≥ C0
1 − C1
1 , we have
u(x, 1, 0) = x (log(1 + PT hT ) − σPT ) − C0
1
≥ x (log(1 + PT hT ) − σPT ) − C1
1 − β = u(x, 1, 1).
(36)
Thus, (28) holds for (x, 1, 0), and we have zSE (x, 1) = 0.
Otherwise, if β < C0
1 − C1
1 , we have zSE (x, 1) = 1.
By (3), if β ≥ C0
2 − C1
2 , we have
u(x, 2, 0) = x log 1 +
PT hT
1 + PE hE
− σPT − C0
2
≥ x log 1+
PT hT
1 + PE hE
−σPT −C1
2 − β = u(x, 2, 1),
(37)
indicating that zSE (x, 2) = 0. Otherwise, if β < C0
2 −C1
2 , we
have zSE (x, 1) = 1.
If (31) holds, by (1), (2) and (3), we have
u(x, 0, 0) = x (log(1 + PT hT ) − σPT )
≤ min x (log(1 + PT hT ) − σPT ) − C0
1 ,
x log 1+
PT hT
1 + PE hE
− σPT − C0
2
= min {u(x, 1, 0), u(x, 2, 0)}. (38)
Similarly, if (32) holds, we have
u(x, 0, 0) = x (log(1 + PT hT ) − σPT )
1 − β,
x log 1+
PT hT
1 + PE hE
−σPT −C0
2
= min {u(x, 1, 1), u(x, 2, 0)}. (39)
If (33) holds, we have
u(x, 0, 0) = x (log(1 + PT hT ) − σPT )
1 ,
x log 1 +
PT hT
1 + PE hE
− σPT − C1
2 − β
= min {u(x, 1, 0), u(x, 2, 1)} , (40)
and if (34) holds, we have
u(x, 0, 0) = x (log(1 + PT hT ) − σPT )
1 − β,
x log 1 +
PT hT
1 + PE hE
− σPT − C1
2 − β
= min {u(x, 1, 1), u(x, 2, 1)} . (41)
In summary, (29) holds for (x, 0, 0), thus ySE (x) = 0. By (1),
if (8b) holds, we have
u(0, 0, 0) = 0 < log(1 + PT hT ) − σPT = u(1, 0, 0). (42)
Thus (1, 0, 0) is an SE, if (8b) and one of (31)-(34)
hold.
Remark: In the Stackelberg game G , the security agent
decides its defense mode based on the observed attack strat-
egy y. Under a small cost of the safe mode (i.e., (34)) or the
attack cost (i.e., (31), (32) and (33)), the smart attacker keeps
silent (y = 0), and thus the security agent chooses the fast
mode (z = 0). The mobile device chooses a full offloading
rate (x = 1) if the channel gain is high (i.e., (8b)).
(1, 1, 0), if (8b) holds, and either (43) or (44) holds, where



max 0, log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
+ C0
2 < C0
1
(43a)
β ≥ max{C0
y − C1
y }, ∀y = 1, 2 (43b)
and



C0
1 > 0 (44a)
C0
1 − C1
1 ≤ β < min C0
2 − C1
2 ,
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
− C1
2 + C0
1 . (44b)
Remark: Under a high channel gain (i.e., (8b)), the mobile
device offloads at a full rate (x = 1). If the spoofing attack
is effective (i.e., (43a) and (44a)), the attacker sends spoof-
ing signals (y = 1). If the cost of the safe mode is high
(i.e., (43b) and (44b)), the security agent checks the AP status
in the fast mode (z = 0).
(1, 2, 1), if (16b) holds, and either (45) or (46) holds, where



C0
1 − C1
1 ≤ β ≤ C0
2 − C1
2 (45a)
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
≤ min{C1
2 + β, C1
2 + β − C0
1 } (45b)
and



β < min C0
y − C1
y , ∀y = 1, 2 (46a)
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
≤ min{C1
2 + β, C1
2 − C1
1 }. (46b)
Remark: If the jamming attack is effective
(i.e., (45b) and (46b)), the attacker chooses to jam (y = 2).
If the channel gain of the mobile device is large (i.e., (16b)),
the mobile device chooses a full offloading rate (x = 1).
The security agent applies a safe mode (z = 1) if its cost is
reasonable (i.e., (45a) and (46a)).
With the other two SEs given by Lemma 1 in the appendix,
Fig. 4 summarizes the SEs of the game G . If Eqs. (8b), (16b)
and (46b) hold, the mobile device applies full offloading.
The attack motivation is suppressed if the penalty of being
detected is high, possibly due to an accurate attack detection
VOLUME 4, 2016 2287

FIGURE 4. SEs of the secure offloading game G if Eqs. (8b), (16b)
and (46b) hold, in which the mobile device applies a full offloading rate
(full rate), the smart attacker chooses spoofing, jamming or no attack,
and the security agent enters either the fast mode or safe mode.
by the security agent (i.e., Theorem 6). The security agent
applies the safe mode, if the mobile device suffers from heavy
attack loss (i.e., Theorem 8 and Lemma 1). Otherwise, the
security agent chooses the fast mode (i.e., Theorems 6 and 7).
VI. DYNAMIC MOBILE OFFLOADING GAME
To model simulations in which a mobile device repeats
offloading of its applications and data in dynamic radio envi-
ronments, we formulate a dynamic mobile offloading game
consisting of a mobile device, smart attacker, and security
agent that are unaware of the system parameters such as the
attack cost (C), the offloading gain and the current channel
condition (hn
T ). Based on Q-learning, the mobile device deter-
mines its offloading rate based on the actions of its opponents
and the channel condition in the previous time slot. To this
end, the mobile device observes the system state denoted by
s at time n given by sn = [yn−1, zn−1, hn−1
T ]. In this game,
the offloading rate of the mobile device is quantified into L
levels, i.e., xn ∈ {i/(L − 1)}0≤i≤L−1 for simplicity.
Let Q(s, x) denote the quality function of the mobile
device for offloading rate x and state s. The value func-
tion denoted by V(s) represents the maximum value of the
quality function at state s. The mobile device updates its
Q-function based on its utility u and the value function as
follows:
Q sn
, xn
← (1 − α)Q sn
, xn
+ α u sn
, xn
+ δV sn+1
(47)
V sn
= max
x
Q sn
, x , (48)
where α ∈ (0, 1] is a learning factor indicating the weight
of the current estimate of the function Q in the update
of the quality function, and the discount factor δ repre-
sents the uncertainty of the mobile device about the future
rewards.
By applying the -greedy policy [22], the mobile device
chooses its offloading rate xn to maximize its current
Q-function with a high probability 1 − , while the
other L − 1 rates are taken with equal probability, i.e.,
Pr(xn
) =



1 − , xn = arg maxx Q (sn, x)
L − 1
, o.w.
(49)
The secure offloading process of the mobile device is summa-
rized in Algorithm 1. This learning-based mobile offloading
strategy is proposed to provide insights into the dynamic
mobile offloading game among the mobile device, the smart
attacker and the security agent, and is compared with a bench-
mark offloading strategy via simulations in the next section.
Algorithm 1 Secure Offloading Strategy With Q-Learning
Initialize Q(s, x) = 0, V(s) = 0, y0, z0, h0
T
For n = 1, 2, 3, ...
Update the state sn = [yn−1, zn−1, hn−1
T ]
Choose the offloading rate xn via (49)
Offload to the cloud at rate xn
Observe yn, zn and hn
T
Obtain utility u
Update Q(sn, xn) via (47)
Update V(sn) via (48)
End for
VII. SIMULATION RESULTS
Simulations have been performed to evaluate the performance
of the dynamic secure offloading game with L = 11, C =
[0, 0; −0.1, −0.3; −0.5, −0.8], HT = HE = {0.8, 0.9, 1},
NT = NE = 3, PT = PE = 1, σ = 0.1, β = 0.2, α = 0.9,
δ = 0.7, and = 0.95. We initialize z0, h0
T and h0
E randomly
and uniformly, and set pm,k = qm,k with
pm,k
=
0.5, (m, k) ∈ (1, 2), (NT , NT − 1), (i, i)|1≤i≤NT
0.25, 2 ≤ m ≤ NT − 1, k = m ± 1.
(50)
Fig. 5 presents the performance of the proposed offload-
ing strategy over time, in which both the attacker and the
security agent make decisions based on Q-learning. As a
benchmark, we evaluated a random offloading strategy, in
which the mobile device chooses its offloading rate randomly
and uniformly with x ∈ [0, 1]. As shown in Fig. 5 (a), the
spoofing rate decreases rapidly since the start of the dynamic
game, e.g., the spoofing rate decreases by 77% to 7% after
1000 time slots, which is 43% lower than that of the ran-
dom offloading strategy. In addition, the proposed offloading
strategy reduces the jamming rate faster than the random
offloading strategy, e.g., the jamming rate of the proposed
offloading strategy converges to 6% after 500 time slots,
while it takes the random offloading strategy 700 time slots to
reach the same value. As shown in Fig. 5 (b), the utility of the
mobile device in the proposed offloading system converges
rapidly to a high value, e.g., the utility increases by 53%
after 2000 time slots, which is 2.9 times higher than that
2288 VOLUME 4, 2016

FIGURE 5. Performance of the dynamic offloading game, in which the
smart attacker chooses its strategies based on Q-learning, with
C = [0, 0; −0.1, −0.3; −0.5, −0.8], σ = 0.1 and β = 0.2. (a) Attack rate.
(b) Utility of the mobile device.
of the benchmark strategy, because the mobile device learns
the system parameters quickly and adjusts its offloading rate
accordingly.
In Fig. 6, we investigate the impact of the channel con-
ditions on the offloading game, showing that the average
offloading rate increases with the channel gain, and sharply
increases to 0.82 with hT = 0.2, which is 64% higher
than that of the benchmark strategy, because the mobile
device is motivated to offload more data to the cloud under
good channel conditions. Fig. 6 (b) indicates that the pro-
posed offloading strategy reduces the attack rates quickly.
For example, the average spoofing rate of the smart attacker
decreases by 47% to 9.4% and the average jamming rate
decreases by 8% to 7.1% with hT = 1 compared to the
benchmark strategy. Moreover, the performance advantage
of the proposed offloading strategy increases with hT , e.g.,
the gain of the proposed strategy regarding the spoofing rate
is 31% with hT = 0.4, and increases to 45% with hT = 0.8.
The security agent chooses its protection mode to maximize
its utility based on the offloading rate and the attack mode in
the last time slot. As shown in Fig. 6 (c), the average utility
of the mobile device increases with the channel gain, e.g.,
the average utility increases by 4.64 times if hT increases
from 0.2 to 1. In addition, compared with the random
FIGURE 6. Performance of the dynamic offloading game, in which the
smart attacker chooses its strategy based on Q-learning, with
C = [0, 0; −0.1, −0.3; −0.5, −0.8], σ = 0.1 and β = 0.2. (a) Average
offloading rate. (b) Average attack rate. (c) Average utility of the mobile
device.
offloading strategy, the average utility of the proposed
scheme improves by 93% with hT = 1, because the mobile
device can choose an offloading rate to reach a balance
between the transmission cost, security risks and cloud per-
formance gain experimentally.
VIII. CONCLUSIONS
In this paper, we have investigated a mobile offloading game
against smart attacks, in which a security agent protects a
serving AP with two defense modes. We have derived the
VOLUME 4, 2016 2289

NEs and SEs of the secure offloading game and provided
conditions for their existence under various radio channel
scenarios. We have further proposed a Q-learning based
mobile offloading strategy for dynamic radio environments,
in which mobile devices derive the optimal offloading rates
experimentally. Simulation results show that both the util-
ity of the mobile device and the security performance are
improved compared with the benchmark strategy. If the chan-
nel gain is high, both the mobile offloading rate and the
attack strength increase, and the security agent applies an
advanced defense mode with both higher-layer and physical-
layer security mechanisms to protect the offloading against
smart attacks. For instance, in this situation, the average
utility of the mobile device increases in one example by 290%
and the spoofing rate decreases by 50% compared with the
random strategy.
APPENDIX
Lemma 1: The static offloading game G has an SE
(1, 1, 1), if (8b) and one of Eqs. (51)-(52) hold, where
max log
(1 + PE hE )(1 + PT hT )
1 + PE hE + PT hT
− C1
1 + C0
2 ,
− C1
1 , C0
2 − C1
2 ≤ β < C0
1 − C1
1 (51)
−C1
1 < β < min{C0
y − C1
y }, ∀y = 1, 2
C1
1 ≥ log (1+PE hE )(1+PT hT )
1+PE hE +PT hT
+ C1
2 .
(52)
The game G has an SE (1, 2, 1), if (16b) and one of
Eqs. (53)-(54) hold, where



β ≥ max{C0
y − C1
y }, ∀y = 1, 2 (53a)
C0
2 ≥ max log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
,
log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
+ C0
1 (53b)



C0
2 ≥ log
1 + PE hE + PT hT
(1 + PE hE )(1 + PT hT )
(54a)
C0
2 − C1
2 ≤ β < min C0
1 − C1
1 ,
log
(1 + PE hE )(1 + PT hT )
1 + PE hE + PT hT
+ C0
2 − C1
1 . (54b)
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LIANG XIAO (M’09–SM’13) received the
B.S. degree in communication engineering from
the Nanjing University of Posts and Telecommuni-
cations, Nanjing, China, in 2000, the M.S. degree
in electrical engineering from Tsinghua Univer-
sity, Beijing, China, in 2003, and the Ph.D. degree
in electrical engineering from Rutgers University,
New Brunswick, NJ, USA, in 2009. She is cur-
rently a Professor with the Department of Commu-
nication Engineering, Xiamen University, Fujian,
China. Her current research interests include smart grids, network security,
and wireless communications.
2290 VOLUME 4, 2016

CAIXIA XIE received the B.S. degree in
communication engineering from Xiamen Uni-
versity, Xiamen, China, in 2015, where she
is currently pursuing the M.S. degree with
the Department of Communication Engineering.
Her research interests include network security
TIANHUA CHEN received the B.S. degree in
communication engineering from Xiamen Uni-
versity, Xiamen, China, in 2014, where she
is currently pursuing the M.S. degree with
the Department of Communication Engineering.
Her research interests include network security
HUAIYU DAI (M’03–SM’09) received the
B.E. and M.S. degrees from Tsinghua Univer-
sity, Beijing, China, in 1996 and 1998, respec-
tively, and the Ph.D. degree from Princeton
University, Princeton, NJ, in 2002, all in electrical
engineering.
He was with Bell Labs, Lucent Technolo-
gies, Holmdel, NJ, in summer 2000, and with
AT&T Labs-Research, Middletown, NJ, in sum-
mer 2001. He is currently a Professor of Electrical
and Computer Engineering with NC State University, Raleigh. His research
interests are in the general areas of communication systems and networks,
advanced signal processing for digital communications, and communication
theory and information theory. His current research focuses on networked
information processing and crosslayer design in wireless networks, cognitive
radio networks, wireless security, and associated information-theoretic and
computation-theoretic analysis.
He has served as an Editor of the IEEE TRANSACTIONS ON COMMUNICATIONS,
SIGNAL PROCESSING, and Wireless Communications. Currently he is an Area
Editor in charge of wireless communications for the IEEE TRANSACTIONS
ON COMMUNICATIONS. He co-edited two special issues of EURASIP journals
on distributed signal processing techniques for wireless sensor networks,
and on multiuser information theory and related applications, respectively.
He co-chaired the Signal Processing for Communications Symposium of
the IEEE Globecom 2013, the Communications Theory Symposium of the
IEEE ICC 2014, and the Wireless Communications Symposium of the IEEE
Globecom 2014.
H. VINCENT POOR (S’72–M’77–SM’82–F’87)
received the Ph.D. degree in EECS from Prince-
ton University, in 1977. From 1977 until 1990,
he was on the faculty of the University of Illi-
nois at Urbana–Champaign. Since 1990, he has
been on the faculty of Princeton University,
where he is the Michael Henry Strater University
Professor and the Dean of the School of Engineer-
ing and Applied Science. He has also held visit-
ing appointments at several universities, including
most recently at Stanford University and Imperial College. His research
interests are in the area of wireless networks and related ﬁelds. Among his
publications in these areas is the recent book Mechanisms and Games for
Dynamic Spectrum Allocation (Cambridge University Press, 2014).
Dr. Poor is a member of the National Academy of Engineering and
the National Academy of Sciences, and is a foreign member of the Royal
Society. He is also a fellow of the American Academy of Arts and Sciences,
the National Academy of Inventors, and other national and international
academies. He received the Marconi and Armstrong Awards of the IEEE
Communications Society in 2007 and 2009, respectively. Recent recognition
of his work includes the 2014 URSI Booker Gold Medal, the 2015 EURASIP
Athanasios Papoulis Award, the 2016 John Fritz Medal, and honorary doctor-
ates from Aalborg University, Aalto University, HKUST, and the University
of Edinburgh.
VOLUME 4, 2016 2291

A mobile offloading game against smart attacks

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