# Securing Cooperative Spectrum Sensing against DC-SSDF Attack Using Trust Fluctuation Clustering Analysis in Cognitive Radio Networks

Authors: Feng Zhao; Shaoping Li; Jingyu Feng
Journal: Wireless Communications and Mobile Computing
 (2019)

---

## Abstract

Cooperative spectrum sensing (CSS) has been recognized as a forceful approach to promote the utilization of spectrum bands. Nevertheless, all secondary users (SU) are assumed as honest in CSS, thus giving opportunities for attackers to launch the spectrum sensing data falsification (SSDF) attack. To defend against such attack, many efforts have been made to trust mechanism. In this paper, we argue that securing CSS with only trust mechanism is not enough and report the description of dynamic-collusive SSDF attack (DC-SSDF attack). To escape the detection of trust mechanism, DC-SSDF attackers can maintain high trust by submitting true sensing data dynamically and then fake sensing data in the collaborative manner to increase their attack strength. Noting that the resonance phenomenon may appear in the trust value curve of DC-SSDF attackers, a defense scheme called TFCA is proposed from the design idea of trust fluctuation clustering analysis to suppress DC-SSDF attack. In the TFCA scheme, the decreasing property of trust value in the resonance phenomenon is adopted to measure the similarity distance between two attackers. Based on the similarity distance computation, the binary clustering algorithm is designed by electing initial binary samples to identify DC-SSDF attackers. Finally, trust mechanism can be perfected by TFCA to correct DC-SSDF attackers’ trust value. Simulation results show that our TFCA scheme can improve the accuracy of trust value calculation, thus reducing the strength of DC-SSDF attack successfully.


---

## Body

## 1. Introduction

Currently, spectrum bands are becoming more and more scarce with the rapid development of wireless communication and the huge access demand of IOT devices. However, a large number of the assigned spectra are not utilized efficiently by licensed primary users (PU). According to the Federal Communications Commission (FCC) [1], temporal and geographical variations in the utilization of the assigned spectrum range from 15% to 85%. To solve the contradiction between the spectrum scarcity and low spectrum utilization, it is possible that opportunistic access of the valid spectrum bands should be given to unlicensed secondary users [2]. Without any interference to PUs, cognitive radio (CR) has been considered as an emerging technology that can allow a secondary user (SU) to sense and make efficient use of any available valid PU spectrum bands.To enhance the detection performance, cooperative spectrum sensing (CSS) [3] has recently received significant attention as a valuable method in CR technology to avoid the case of deep shadowing and multipath fading by exploiting spatial diversity via the sensing results of different SUs. Nevertheless, all secondary users are assumed as honest in CSS, thus giving opportunities for attackers to fake sensing data by SSDF attack [4]. At first, attackers submit false sensing data by the static and individual way. This common SSDF attack can be easily suppressed by trust mechanism. Such attackers will hold a lower trust value when they always submit false sensing data individually. Various trust mechanism studies have been proposed [5–8]. They can estimate whether cooperating SUs are honest or not by their sensing behaviors in the past and then give low weights to malicious SUs or even delete their sensing data when making a final decision.To escape the detection of trust mechanism, attackers have to change their attack strategies. They can launch SSDF attack with a dynamic manner to maintain high trust value [9] (hereinafter “DSSDF"). In addition, some attackers conspire with each other to submit false sensing data intentionally [10] (hereinafter “CSSDF”). If there are a sufficient number of CSSDF attackers, conspirators can increase the strength of attack and mislead FC make a wrong final decision. Fortunately, it is easy to crush DSSDF attackers one by one, if they launch DSSDF attack individually. CSSDF attackers can be easily detected with an abnormality detection algorithm by analyzing their highest similarities, if they launch SSDF in the static manner.In this paper, we report the description of dynamic-collusive SSDF attack (hereinafter “DC-SSDF”), in which the attackers with the dynamic and collaborative manner can not only escape the detection of trust mechanism but also increase the attack strength. From the design idea of trust fluctuation clustering analysis, we propose a defense scheme called TFCA to suppress DC-SSDF attack. The main contributions of this paper are as follows:(i)
Conduct an in-depth investigation on DC-SSDF attack, which is conducted by three attack procedures in a round mode: “Dynamically prompting”, “Collaborative attack”, and “Self-check”. The harmfulness of such attack is great. With high trust value, DC-SSDF attackers can damage the fairness and usability of CSS more easily. A high trust value means that an SU’s sensing data can be accepted by CSS. By faking sensing data with together, DC-SSDF attackers with high trust value can deceive honest SUs to interfere with PUs or monopolize primary spectrum bands via CSS.
(ii)
Estimate the sensing similarity among SUs from the decreasing property of trust value in the resonance phenomenon. DC-SSDF attackers cooperate together in the “Collaborative attack” phase while prompting their trust value, respectively, in the “Dynamically prompting” phase. So, we can find that the resonance phenomenon may appear in the trust value curve of them. It specially is obvious that DC-SSDF attackers may behave as the sensing similarity related on decreasing trust value in the “Collaborative attack” phase. In the TFCA scheme, we utilize the decreasing property of trust value in the resonance phenomenon to estimate the sensing similarity by measuring the distance between any two SUs, which can avoid mass mathematical analysis and computation.
(iii)
Design a binary clustering algorithm to differentiate DC-SSDF attackers and honest SUs. The resonance frequency of the two SUs is recorded in line with their trust value’s decreasing property in the resonance phenomenon. Then, DC-SSDF attackers can get the higher resonance frequency among themselves while honest SUs can get the lower resonance frequency among themselves. Based on this, we can use the analysis of the maximum and minimum for the resonance frequency to elect DC-SSDF samples and honest samples rapidly, thus avoiding more iterations of the algorithm.The rest of this paper is as follows. In Section2, preliminaries related to CSS and trust mechanism are described. DC-SSDF attack is analyzed in Section 3 and the TFCA scheme is designed to defend against it in Section 4. Simulation analysis of DC-SSDF attack and the TFCA scheme is performed in Section 5. Finally, we give the conclusions of this paper in Section 6. In addition, the abbreviations and key variables used in this paper are listed in Tables 1 and 2, respectively.Table 1
Abbreviations used in this paper.
Abbreviations
Explanation
CSS
Cooperative spectrum sensing
SU
Secondary user
C
Set of Cooperating SUs
S
U
i
Thei-th SU
PU
Primary user
SSDF
Spectrum sensing data falsification
DC-SSDF
Dynamic-collusive SSDF
TFCA
Trust fluctuation clustering analysis
FC
Fusion center
Φ
1
DC-SSDF samples
Φ
2
Honest samples
Ψ
1
Set of DC-SSDF attackers
Ψ
2
Set of honest SUsTable 2
Key variables used in this paper.
Variables
Explanation
d
Final decision of FC
d
i
Final decision ofS
U
i
h
i
Number of true sensing ofS
U
i
f
i
Number of false sensing ofS
U
i
t
i
k
Trust value ofS
U
i at sensing time k
T
i
Trust vector ofS
U
i
r
i
j
Resonance frequency betweenS
U
i and S
U
j
d
i
s
i
j
Similar distance betweenS
U
i and S
U
j
R
n
×
n
Resonance frequency among cooperating SUs
R
i
Resonance frequency ofS
U
i corresponding to the other cooperating SUs
ρ
i
Attenuation penalty factor ofS
U
i at sensing time k


## 2. Preliminaries

### 2.1. Cooperative Spectrum Sensing

A CSS action can be modeled as a parallel fusion network, in which the fusion center (FC) controls the action of CSS, including the process of individual sensing, data reporting, and decision-making, as shown in Figure1 [3]. Firstly, the method of energy detection is exploited by each SU to individually sense the PU signal through the sensing channel, which is the preselected licensed frequency band for observing the primary spectrum between the PU transmitter and each cooperating SU. Secondly, all individual sensing data are submitted to FC through the reporting channel, which is a control channel for sending individual sensing information between each cooperating SU and the initiator SU. With the two types of given channels, it can be seen that the CSS process between SUs seems to not waste any more spectrums. Finally, the received individual sensing data are fused by FC to determine the presence of PU. With the “AND”, “OR”, or “Majority” rule, FC can make the final decision [11].Figure 1
Modeling CSS as a parallel fusion network.Specially, individual sensing for PU signal with the energy detection can be abstracted as the “0-1” hypothesis problem [12]:(1)
y
t
=
w
t
,
H
0
g
t
·
p
t
+
w
t
,
H
1where y
(
t
) represents the detected PU signal by each SU, p
(
t
) is the transferred PU signal, g
(
t
) is the sensing channel gain, w
(
t
) is the zero-mean additive white Gaussian noise, andt is the sample parameter. H
0 and H
1 denote the hypothesis of absent and present PU signals, respectively. When the estimated y
(
t
) is greater than the energy threshold, the PU signal can be determined as present. Otherwise, no PU signal is detected.In the process of individual sensing, the sensing data at each SU can be expressed as a binary variable as. For example,d
i indicates the sensing data of S
U
i, which is expressed as(2)
d
i
=
0
,
H
0
1
,
H
1where “0” and “1” represent the hypothesis of the inexistence and the existence of PU signal, respectively. Correspondingly, FC also make the final decision binary with the “AND”, “OR”, and “Majority” rule. Under the “AND” rule, the final decisiond=1 if all d
i=1. On the contrary,d=1 if one d
i=1 under “OR" rule. The “Majority” rule requires at least a half of SUs to report “1”. The “AND" rule works well when the number of cooperating SUs is small, whereas the “OR" rule works best when the number of SUs is large, and the “Majority” rule can be obtained from the k out of N rule under the condition when k
≥
N
/
2 [3]. Generally, the “Majority” rule is the best choice to make the final decision, whereas one false sensing data can disturb the decision result of the “AND” and “OR” rule. In Section 5, the simulation of suppressing DC-SSDF attack success ratio is performed to analyze the three fusion rules more clearly.


### 2.2. Trust Mechanism

Trust mechanism has become more and more significant in many application scenarios, including e-commerce [13], P2P networks [14], internet of things [15], and online social networks [16].In CSS area, trust mechanism also plays important roles. Typical CSS trust mechanism schemes are as follows. In [5], the authors proposed a trust-aware hybrid spectrum sensing scheme, in which the Beta reputation is employed to calculate trust value. In [6], the authors proposed a reliable CSS scheme with the assistance of trusted SUs to mitigate SSDF attack. In [7], the authors considered the construction of trust mechanism from the perspective of the access competition related to vacant PU spectrum bands. In [8], the authors proposed a trust management scheme by considering multiple decision factors (hereinafter “MFTM"), including (a) history-based trust factor, the trust level of an SU during the period of spectrum sensing, (b) active factor, the level of activity of an SU in the process of spectrum sensing, (c) incentive factor, a reward or incentive for the honest SUs, also serving as a punishment with decrease in trust level for the attackers, and (d) consistency factor, the constancy of maintaining a good trust level. The commonality of these existing typical trust schemes is that the trust value of an SU can be calculated by his previous sensing behaviors and the sensing data of malicious SUs should be deleted when making a final decision.With this commonality, a basic trust mechanism called BTM is abstracted to depict the existing typical trust schemes. Since the sensing data of each SU can be regarded as the “0-1” variable in CSS, it is possible for each SU to conduct two types of sensing behaviors: true and false. In this case, we can calculate the trust value of each SU with two indexes: the number of true sensing behaviors (tru) and the number of false sensing behaviors (fal). Currently, the beta function is considered as one of the most popular modes using binary input to calculate trust value. It first counts the number of true and false behaviors that a user has conducted and then calculates the trust value with the beta probability density function-B
e
t
a
(
α
,
β
) [17].(3)
B
e
t
a
α
,
β
=
Γ
α
+
β
Γ
α
Γ
β
ω
α
-
1
1
-
ω
β
-
1 where ω is the probability of sensing behaviors, 0
≤
ω
≤
1, α
>
0, β
>
0.For instance,h
i and f
i represent the number of true and false sensing behaviors conducted by S
U
i. Then, the trust value of S
U
i can be calculated as(4)
t
i
=
B
e
t
a
h
i
+
1
,
f
i
+
1Note that the caseΓ
(
n
)
=
(
n
-
1
)
! whenn is an integer [18]. The expectation value of (4) can be deduced as E
[
B
e
t
a
(
α
,
β
)
]
=
α
/
(
α
+
β
). Therefore, t
i can be further calculated as(5)
t
i
=
1
+
h
i
2
+
h
i
+
f
i


## 2.1. Cooperative Spectrum Sensing

A CSS action can be modeled as a parallel fusion network, in which the fusion center (FC) controls the action of CSS, including the process of individual sensing, data reporting, and decision-making, as shown in Figure1 [3]. Firstly, the method of energy detection is exploited by each SU to individually sense the PU signal through the sensing channel, which is the preselected licensed frequency band for observing the primary spectrum between the PU transmitter and each cooperating SU. Secondly, all individual sensing data are submitted to FC through the reporting channel, which is a control channel for sending individual sensing information between each cooperating SU and the initiator SU. With the two types of given channels, it can be seen that the CSS process between SUs seems to not waste any more spectrums. Finally, the received individual sensing data are fused by FC to determine the presence of PU. With the “AND”, “OR”, or “Majority” rule, FC can make the final decision [11].Figure 1
Modeling CSS as a parallel fusion network.Specially, individual sensing for PU signal with the energy detection can be abstracted as the “0-1” hypothesis problem [12]:(1)
y
t
=
w
t
,
H
0
g
t
·
p
t
+
w
t
,
H
1where y
(
t
) represents the detected PU signal by each SU, p
(
t
) is the transferred PU signal, g
(
t
) is the sensing channel gain, w
(
t
) is the zero-mean additive white Gaussian noise, andt is the sample parameter. H
0 and H
1 denote the hypothesis of absent and present PU signals, respectively. When the estimated y
(
t
) is greater than the energy threshold, the PU signal can be determined as present. Otherwise, no PU signal is detected.In the process of individual sensing, the sensing data at each SU can be expressed as a binary variable as. For example,d
i indicates the sensing data of S
U
i, which is expressed as(2)
d
i
=
0
,
H
0
1
,
H
1where “0” and “1” represent the hypothesis of the inexistence and the existence of PU signal, respectively. Correspondingly, FC also make the final decision binary with the “AND”, “OR”, and “Majority” rule. Under the “AND” rule, the final decisiond=1 if all d
i=1. On the contrary,d=1 if one d
i=1 under “OR" rule. The “Majority” rule requires at least a half of SUs to report “1”. The “AND" rule works well when the number of cooperating SUs is small, whereas the “OR" rule works best when the number of SUs is large, and the “Majority” rule can be obtained from the k out of N rule under the condition when k
≥
N
/
2 [3]. Generally, the “Majority” rule is the best choice to make the final decision, whereas one false sensing data can disturb the decision result of the “AND” and “OR” rule. In Section 5, the simulation of suppressing DC-SSDF attack success ratio is performed to analyze the three fusion rules more clearly.


## 2.2. Trust Mechanism

Trust mechanism has become more and more significant in many application scenarios, including e-commerce [13], P2P networks [14], internet of things [15], and online social networks [16].In CSS area, trust mechanism also plays important roles. Typical CSS trust mechanism schemes are as follows. In [5], the authors proposed a trust-aware hybrid spectrum sensing scheme, in which the Beta reputation is employed to calculate trust value. In [6], the authors proposed a reliable CSS scheme with the assistance of trusted SUs to mitigate SSDF attack. In [7], the authors considered the construction of trust mechanism from the perspective of the access competition related to vacant PU spectrum bands. In [8], the authors proposed a trust management scheme by considering multiple decision factors (hereinafter “MFTM"), including (a) history-based trust factor, the trust level of an SU during the period of spectrum sensing, (b) active factor, the level of activity of an SU in the process of spectrum sensing, (c) incentive factor, a reward or incentive for the honest SUs, also serving as a punishment with decrease in trust level for the attackers, and (d) consistency factor, the constancy of maintaining a good trust level. The commonality of these existing typical trust schemes is that the trust value of an SU can be calculated by his previous sensing behaviors and the sensing data of malicious SUs should be deleted when making a final decision.With this commonality, a basic trust mechanism called BTM is abstracted to depict the existing typical trust schemes. Since the sensing data of each SU can be regarded as the “0-1” variable in CSS, it is possible for each SU to conduct two types of sensing behaviors: true and false. In this case, we can calculate the trust value of each SU with two indexes: the number of true sensing behaviors (tru) and the number of false sensing behaviors (fal). Currently, the beta function is considered as one of the most popular modes using binary input to calculate trust value. It first counts the number of true and false behaviors that a user has conducted and then calculates the trust value with the beta probability density function-B
e
t
a
(
α
,
β
) [17].(3)
B
e
t
a
α
,
β
=
Γ
α
+
β
Γ
α
Γ
β
ω
α
-
1
1
-
ω
β
-
1 where ω is the probability of sensing behaviors, 0
≤
ω
≤
1, α
>
0, β
>
0.For instance,h
i and f
i represent the number of true and false sensing behaviors conducted by S
U
i. Then, the trust value of S
U
i can be calculated as(4)
t
i
=
B
e
t
a
h
i
+
1
,
f
i
+
1Note that the caseΓ
(
n
)
=
(
n
-
1
)
! whenn is an integer [18]. The expectation value of (4) can be deduced as E
[
B
e
t
a
(
α
,
β
)
]
=
α
/
(
α
+
β
). Therefore, t
i can be further calculated as(5)
t
i
=
1
+
h
i
2
+
h
i
+
f
i


## 3. DC-SSDF Attack Overview

Since the sensing data are usually viewed as the “0-1” variable, it is possible for attackers to disturb CSS and launch SSDF attack by submitting false sensing data.Actually, the basic goal of SSDF attack is to illegally occupy or disturb the PU spectrum bands by manipulating the final decision of FC with using the two patterns [9].(i)
Always-absent: some attackers submit false “0” sensing data to show the PU signal is absent, even though some PUs are using their spectrums. As a result, a wrong final decision is made by FC to show that the PU spectrum bands are absent. The intention of such attackers is to give interference to some PUs.
(ii)
Always-present: some attackers submit false “1” sensing data to declare that the PU signal is present, even though no PU signals are detected. As a result, a wrong final decision is made by FC to show that the PU spectrum bands are present. The intention of such attackers is to monopolize the PU spectrum bands via CSS.At first, attackers always submit false sensing data individually. That is, such two kinds of SSDF attack patterns are launched in the static and individual way. This original SSDF attack patterns [4] can be easily detected by current trust mechanism such as [5–8], since the original SSDF attackers will get a lower trust value when they always submit false sensing data individually.In this case, attackers have to change their strategies, thus finding two types of attack modes: DSSDF and CSSDF. For the first attack mode, attackers launch SSDF in a dynamic manner to escape the detection of trust mechanism. They can utilize dynamic behaviors that allow them to maintain high trust value in an alternant process of submitting true and false sensing data [19]. But, it is easy to crush DSSDF attackers one by one, if they launch DSSDF attack individually. To increase the strength of SSDF attack, some attackers form collusion with each other to fake sensing data. They can fake honest SUs’ statistical characteristics by collusion when they launch SSDF attack [20]. But, CSSDF attackers may be easily detected with an abnormality detection algorithm by analyzing their highest similarities, if they launch SSDF in the static manner. Except for DSSDF and CSSDF attack, CFF attack is also found in our previous publication [21]. Since the feedback data from initiator SUs are generally unchecked, one of CFF attackers can disguise as an initiator SU who sends the feedback in accordance with the sensing data of their conspirators who play the role of cooperating SUs, resulting in promoting their conspirators’ trust value quickly. A two-level defense scheme called FeedGuard from the design ideas of feedback trust and I-C frequency correlation analysis is proposed in [21] to defend against CFF attack.In this paper, we find that the attackers with the dynamic and collaborative manner can not only escape the detection of trust mechanism but also increase the attack strength. This new SSDF attack mode is named as DC-SSDF in this paper. Obviously, DC-SSDF attack is the latest evolution of SSDF attack, as shown in Figure2.Figure 2
Evolution of SSDF attack.Similar to DSSDF attackers, DC-SSDF attackers are extremely sensitive to trust value before launching attack. AssumingS
U
i is one of DC-SSDF attackers, he launches DC-SSDF attack under the constraint(6)
δ
≤
t
i
≤
δ
+
λwhere δ is the threshold of trust value and λ (0
≤
λ
≤
1
-
δ) is the trust warning line of DC-SSDF attackers.In (5), t
i
=
0.5 when h
i
=
f
i
=
0. For t
i
∈
[
0,1
], δ can be set to the moderate value 0.5. For t
i
≥
δ, S
U
i will not be identified by trust mechanism since he is marked as honest. This inspires DC-SSDF attackers to maintain high trust value for themselves. That is, S
U
i should maintain his trust value within [
δ
,
δ
+
λ
]. It is late for prompting trust value when t
i
≤
δ. In this case, S
U
i is marked as malicious by trust schemes and anyone will not trust him again. Under the constraint δ
≤
t
i
≤
δ
+
λ, the DC-SSDF attack procedure can be conducted in a round mode including “Collaborative attack”→“Self-check”→“Dynamically prompting” phases, as shown in Figure 3.(i)
Dynamically prompting: DC-SSDF attackers submit true sensing data dynamically to prompt their trust value all by themselves until t
i
≥
δ
+
λ.
(ii)
Collaborative attack: DC-SSDF attackers fake sensing data in the collaborative manner until the half of them cannot maintain δ
≤
t
i
≤
δ
+
λ.
(iii)
Self-check: Each S
U
i self-checks whether t
i
≤
δ at the end of each collaborative attack. Yes means continue to the “Collaborative attack" phase. No means go to the “Dynamically prompting" phase.Figure 3
A round of DC-SSDF attack procedure.


## 4. Defending against DC-SSDF Attack Using Trust Fluctuation Clustering Analysis

We capture the core phases, “Dynamically prompting" and “Collaborative attack" of DC-SSDF attack, and then introduce the design idea of Trust Fluctuation Clustering Analysis including trust fluctuation analysis for distance measure and binary clustering analysis to detect DC-SSDF attackers. Meanwhile, the implementation strategies of TFCA are designed to perfect trust mechanism.


### 4.1. Trust Fluctuation Analysis for Similarity Distance Measure

We have known that the attackers who conduct true or false sensing behaviors alternately would maintain high trust value. Accordingly, the trust value should be calculated at each sensing time. ForS
U
i, his trust value at sensing timek can be described as t
i
k, and then (7) can be further modified as(7)
t
i
k
=
1
+
h
i
k
2
+
h
i
k
+
f
i
kwhere h
i
k and f
i
k represent the true of honest and false sensing behaviors of S
U
i at sensing timek. For S
U
i, his trust value from the initial sensing time to the current sensing time can form the trust vector T
i
=
{
t
i
1
,
…
,
t
i
k
,
…
,
t
i
h
}. Without loss of generality, if no CSS action has been involved by S
U
i at sensing timek, we can set t
i
k
=
t
i
k
-
1.When launching DC-SSDF attack,S
U
i’s trust value will increase in the “Dynamically prompting” phase but decrease in the “Collaborative attack” phase. To further analyze the fluctuation of trust value for any two of DC-SSDF attackers (such as S
U
i and S
U
j), we perform a simple simulation scenario with a higher value in λ such as 0.4, as shown in Figure 4. It can be found that the two DC-SSDF attackers’ trust value fluctuates between δ and δ
+
λ. With the increase of sensing time, the more efforts of “Dynamically prompting” they make, the more opportunities to “Collaborative attack” they will get. Specially, we can find that the resonance phenomenon appears in the trust value curve of them. To depict the similarity of any two DC-SSDF attackers in the process of fluctuation, we can record the resonance frequency (r
i
j) between the two SUs by Procedure 1. Considering that DC-SSDF attackers cooperate together in the “Collaborative attack” phase while prompting their trust value all by themselves in the “Dynamically prompting” phase, r
i
j should be recorded when the trust value of S
U
i and S
U
j decreases at the same time after coming into the “Collaborative attack” phase.Procedure 1:Record r
i
j value.
Input:  T
i, T
j;
Output:  r
i
j;
(1) Initialize r
i
j
=
0;
(2) for  k
=
1
,
k
≤
m
a
x
T
i
,
T
j
,
k
+
+  do
(3)
if  t
i
k
-
1
>
t
i
k
&
&
t
j
k
-
1
>
t
j
k  then
(4)
r
i
j
+
+;
(5)
end if
(6) end forFigure 4
Fluctuation analysis of trust value for any two of DC-SSDF attackers.The distance metric is generally useful to measure the similarity among the vectors (such asT
i and T
j). When S
U
j is one of DC-SSDF companions of S
U
i, they may behave similar to trust fluctuation after several rounds of “Collaborative attack” phase. In the clustering analysis, such similar trust fluctuation can make S
U
i and S
U
j get a shorter distance. In our TFCA scheme, we should improve the calculation of the distance in line with the characteristic of trust fluctuation between T
i and T
j before designing the binary clustering algorithm. For S
U
i and S
U
j, their distance can be measured as(8)
s
d
i
j
=
r
i
j
m
a
x
T
i
,
T
j
∑
k
=
1
r
i
j
t
i
k
-
t
j
k
2
+
m
a
x
T
i
,
T
j
-
r
i
j
m
a
x
T
i
,
T
junder the constraint(9)
t
i
k
-
1
>
t
i
k
&
&
t
j
k
-
1
>
t
j
kwhere T
i and T
j are the number of elements in T
i and T
j, respectively. Obviously, if S
U
i and S
U
j often launch the “Collaborative attack” phase together, they will get a shorter distance. If not, d
i
j will be stretched by the second part of (11).


### 4.2. Binary Clustering Algorithm Design

The ultimate purpose of our TFCA scheme is to detect DC-SSDF attackers. To achieve this goal, the K-means algorithm is a good choice since DC-SSDF attackers show some clustering features in the light of their collaborative behaviours. However, the K-means algorithm [22] cannot be applied directly in detecting DC-SSDF attackers due to the two problems. The one is that the selected sample should be definitely differentiated as a DC-SSDF attacker or an honest SU. So, it is unsuitable to select K samples as the initial mean vectors. Another one is that we utilize the decreasing property of trust value in the resonance phenomenon to measure the distance between two SUs. In this case, if we use the mean of all vectors in a cluster to measure the distance, the decreasing property would be cleared.In our TFCA scheme, we design a binary clustering algorithm to differentiate DC-SSDF attackers and honest SUs. Firstly, we select two samples as the initial mean vectors by analyzing the resonance frequency of cooperating SUs set (denoted asC) at the current sensing time. For all SUs inC, their r
i
j value can compose a matrix R
n
×
n in whichn is the number of elements inC.(10)
R
n
×
n
=
r
11
⋯
r
1
j
⋯
r
1
n
⋮
⋯
⋮
⋯
⋮
r
i
1
⋯
r
i
j
⋯
r
i
n
⋮
⋯
⋮
⋯
⋮
r
n
1
⋯
r
n
j
⋯
r
n
nIn the matrix, the resonance frequency vector ofS
U
i corresponding to the other cooperating SUs can be denoted as R
i
=
(
r
i
1
,
…
,
r
i
j
,
…
,
r
i
n
). It is worth noting that DC-SSDF attackers can get the higher resonance frequency among themselves while honest SUs can get the lower resonance frequency among themselves. We can elect the SUs who hold the maximum from each R
i (i
∈
1,2
,
…
,
n) to compose the DC-SSDF samples (Φ
1). Meanwhile, we can elect the SUs who hold the minimum from each R
i (i
∈
1,2
,
…
,
n) to compose the honest samples (Φ
2). This election can be performed by Procedure 2.Procedure 2:Elect binary clustering samples.
Input:  R
n
×
n;
Output:  Φ
1 and Φ
2;
(1) Initialize Φ
1
=
Φ
2
=
∅;
(2) for  i
=
1
,
i
≤
n
,
i
+
+  do
(3)
Φ
1
=
{
a
r
g
m
a
x
(
R
i
)
}
∪
Φ
1;
(4)
Φ
2
=
{
a
r
g
m
i
n
(
R
i
)
}
∪
Φ
2;
(5) end forSecondly, to avoid clearing the decreasing property of trust value in the resonance phenomenon, we employ the elements of the generated cluster belonging toΦ
1 to calculate the new mean vector at each clustering iteration, rather than using all the elements of the generated cluster.Finally, the binary clustering algorithm can be designed by Procedure3 to detect DC-SSDF attackers.Procedure 3:Binary clustering algorithm.
Intput:  C, Φ
1, Φ
2 and R
n
×
n;
Output:  the set of DC-SSDF attackers (Ψ
1) and honest SUs (Ψ
2);
(1) Randomly select an element from Φ
1 and Φ
2 respectively and use their trust vector as the initial mean vector {
μ
1
,
μ
2
};
(2) repeat
(3) Initialize Ψ
1
=
Ψ
2
=
∅;
(4) for  i
=
1
,
i
≤
C
,
i
+
+  do
(5)Measure the distance d
i
j between S
U
i and μ
j (1
≤
j
≤
2) with equation (11);
(6)
if  d
i
1
<
d
i
2  then
(7)
Ψ
1
=
{
S
U
i
}
∪
Ψ
1;
(8)
else
(9)
Ψ
2
=
{
S
U
i
}
∪
Ψ
2;
(10)
end if
(11) end for
(12) for  j
=
1
,
j
≤
2
,
j
+
+  do
(13)Calculate the new mean vector  μ
~
j
=
1
/
|
Φ
j
∩
Ψ
j
|
∑
S
U
k
∈
(
Φ
j
∩
Ψ
j
)
T
k;
(14)
if  μ
~
j
≠
μ  then
(15)Update μ
=
μ
~
j;
(16)
else
(17)Keep the current mean vector unchanged;
(18)
end if
(19) end for
(20) until the current mean vector is not updated again


### 4.3. Perfect Trust Mechanism

When DC-SSDF attackers are detected, typical issues in perfecting trust mechanism focus on(
1
) reducing theirhon data with the attenuation penalty factor (ρ) and (
2
) deleting their sensing data.For the first issue, it will be difficult for DC-SSDF attackers to maintain high trust value, thus ensuring the accuracy of trust calculation. IfS
U
i is detected as a DC-SSDF attacker, his penalty factor at sensing timek can be calculated as(11)
ρ
i
k
=
v
a
r
R
i
v
a
r
R
i
+
m
a
x
R
iwhere v
a
r
(
R
i
) and m
a
x
(
R
i
) denote the variance and maximum of R
i, respectively. The smaller value of v
a
r
(
R
i
) means that the resonance frequency of S
U
i corresponding to the other cooperating SUs is more consistent. Thus, h
i
k would be punished by more attenuation, and vice verse. The more m
a
x
(
R
i
) also makes more attenuation to h
i
k.For the second issue, it would be hard for DC-SSDF attackers to manipulate the final decision again.Procedure4 is performed to perfect trust mechanism, in which d
i is the sensing data of S
U
i andd is the final decision made by FC.Procedure 4:Perfect trust mechanism.
Input:  C, h
i
k
-
1, f
i
k
-
1
Ψ
1, Ψ
2 and R
n
×
n;
Output:  h
i
k, f
i
k
(1) for  each S
U
i
∈
C  do
(2)
if  S
U
i
∈
Ψ
1  then
(3)
h
i
k
=
h
i
k
-
1
∗
v
a
r
(
R
i
)
v
a
r
(
R
i
)
+
m
a
x
(
R
i
)
(4)
f
i
k
=
f
i
k
-
1
+
1
(5)deleted S
U
i’s sensing data
(6)
else
(7)
if  d
i
=
=
d  then
(8)
h
i
k
=
h
i
k
-
1
+
1
(9)
else
(10)
f
i
k
=
f
i
k
-
1
+
1
(11)
end if
(12)
end if
(13) end for


## 4.1. Trust Fluctuation Analysis for Similarity Distance Measure

We have known that the attackers who conduct true or false sensing behaviors alternately would maintain high trust value. Accordingly, the trust value should be calculated at each sensing time. ForS
U
i, his trust value at sensing timek can be described as t
i
k, and then (7) can be further modified as(7)
t
i
k
=
1
+
h
i
k
2
+
h
i
k
+
f
i
kwhere h
i
k and f
i
k represent the true of honest and false sensing behaviors of S
U
i at sensing timek. For S
U
i, his trust value from the initial sensing time to the current sensing time can form the trust vector T
i
=
{
t
i
1
,
…
,
t
i
k
,
…
,
t
i
h
}. Without loss of generality, if no CSS action has been involved by S
U
i at sensing timek, we can set t
i
k
=
t
i
k
-
1.When launching DC-SSDF attack,S
U
i’s trust value will increase in the “Dynamically prompting” phase but decrease in the “Collaborative attack” phase. To further analyze the fluctuation of trust value for any two of DC-SSDF attackers (such as S
U
i and S
U
j), we perform a simple simulation scenario with a higher value in λ such as 0.4, as shown in Figure 4. It can be found that the two DC-SSDF attackers’ trust value fluctuates between δ and δ
+
λ. With the increase of sensing time, the more efforts of “Dynamically prompting” they make, the more opportunities to “Collaborative attack” they will get. Specially, we can find that the resonance phenomenon appears in the trust value curve of them. To depict the similarity of any two DC-SSDF attackers in the process of fluctuation, we can record the resonance frequency (r
i
j) between the two SUs by Procedure 1. Considering that DC-SSDF attackers cooperate together in the “Collaborative attack” phase while prompting their trust value all by themselves in the “Dynamically prompting” phase, r
i
j should be recorded when the trust value of S
U
i and S
U
j decreases at the same time after coming into the “Collaborative attack” phase.Procedure 1:Record r
i
j value.
Input:  T
i, T
j;
Output:  r
i
j;
(1) Initialize r
i
j
=
0;
(2) for  k
=
1
,
k
≤
m
a
x
T
i
,
T
j
,
k
+
+  do
(3)
if  t
i
k
-
1
>
t
i
k
&
&
t
j
k
-
1
>
t
j
k  then
(4)
r
i
j
+
+;
(5)
end if
(6) end forFigure 4
Fluctuation analysis of trust value for any two of DC-SSDF attackers.The distance metric is generally useful to measure the similarity among the vectors (such asT
i and T
j). When S
U
j is one of DC-SSDF companions of S
U
i, they may behave similar to trust fluctuation after several rounds of “Collaborative attack” phase. In the clustering analysis, such similar trust fluctuation can make S
U
i and S
U
j get a shorter distance. In our TFCA scheme, we should improve the calculation of the distance in line with the characteristic of trust fluctuation between T
i and T
j before designing the binary clustering algorithm. For S
U
i and S
U
j, their distance can be measured as(8)
s
d
i
j
=
r
i
j
m
a
x
T
i
,
T
j
∑
k
=
1
r
i
j
t
i
k
-
t
j
k
2
+
m
a
x
T
i
,
T
j
-
r
i
j
m
a
x
T
i
,
T
junder the constraint(9)
t
i
k
-
1
>
t
i
k
&
&
t
j
k
-
1
>
t
j
kwhere T
i and T
j are the number of elements in T
i and T
j, respectively. Obviously, if S
U
i and S
U
j often launch the “Collaborative attack” phase together, they will get a shorter distance. If not, d
i
j will be stretched by the second part of (11).


## 4.2. Binary Clustering Algorithm Design

The ultimate purpose of our TFCA scheme is to detect DC-SSDF attackers. To achieve this goal, the K-means algorithm is a good choice since DC-SSDF attackers show some clustering features in the light of their collaborative behaviours. However, the K-means algorithm [22] cannot be applied directly in detecting DC-SSDF attackers due to the two problems. The one is that the selected sample should be definitely differentiated as a DC-SSDF attacker or an honest SU. So, it is unsuitable to select K samples as the initial mean vectors. Another one is that we utilize the decreasing property of trust value in the resonance phenomenon to measure the distance between two SUs. In this case, if we use the mean of all vectors in a cluster to measure the distance, the decreasing property would be cleared.In our TFCA scheme, we design a binary clustering algorithm to differentiate DC-SSDF attackers and honest SUs. Firstly, we select two samples as the initial mean vectors by analyzing the resonance frequency of cooperating SUs set (denoted asC) at the current sensing time. For all SUs inC, their r
i
j value can compose a matrix R
n
×
n in whichn is the number of elements inC.(10)
R
n
×
n
=
r
11
⋯
r
1
j
⋯
r
1
n
⋮
⋯
⋮
⋯
⋮
r
i
1
⋯
r
i
j
⋯
r
i
n
⋮
⋯
⋮
⋯
⋮
r
n
1
⋯
r
n
j
⋯
r
n
nIn the matrix, the resonance frequency vector ofS
U
i corresponding to the other cooperating SUs can be denoted as R
i
=
(
r
i
1
,
…
,
r
i
j
,
…
,
r
i
n
). It is worth noting that DC-SSDF attackers can get the higher resonance frequency among themselves while honest SUs can get the lower resonance frequency among themselves. We can elect the SUs who hold the maximum from each R
i (i
∈
1,2
,
…
,
n) to compose the DC-SSDF samples (Φ
1). Meanwhile, we can elect the SUs who hold the minimum from each R
i (i
∈
1,2
,
…
,
n) to compose the honest samples (Φ
2). This election can be performed by Procedure 2.Procedure 2:Elect binary clustering samples.
Input:  R
n
×
n;
Output:  Φ
1 and Φ
2;
(1) Initialize Φ
1
=
Φ
2
=
∅;
(2) for  i
=
1
,
i
≤
n
,
i
+
+  do
(3)
Φ
1
=
{
a
r
g
m
a
x
(
R
i
)
}
∪
Φ
1;
(4)
Φ
2
=
{
a
r
g
m
i
n
(
R
i
)
}
∪
Φ
2;
(5) end forSecondly, to avoid clearing the decreasing property of trust value in the resonance phenomenon, we employ the elements of the generated cluster belonging toΦ
1 to calculate the new mean vector at each clustering iteration, rather than using all the elements of the generated cluster.Finally, the binary clustering algorithm can be designed by Procedure3 to detect DC-SSDF attackers.Procedure 3:Binary clustering algorithm.
Intput:  C, Φ
1, Φ
2 and R
n
×
n;
Output:  the set of DC-SSDF attackers (Ψ
1) and honest SUs (Ψ
2);
(1) Randomly select an element from Φ
1 and Φ
2 respectively and use their trust vector as the initial mean vector {
μ
1
,
μ
2
};
(2) repeat
(3) Initialize Ψ
1
=
Ψ
2
=
∅;
(4) for  i
=
1
,
i
≤
C
,
i
+
+  do
(5)Measure the distance d
i
j between S
U
i and μ
j (1
≤
j
≤
2) with equation (11);
(6)
if  d
i
1
<
d
i
2  then
(7)
Ψ
1
=
{
S
U
i
}
∪
Ψ
1;
(8)
else
(9)
Ψ
2
=
{
S
U
i
}
∪
Ψ
2;
(10)
end if
(11) end for
(12) for  j
=
1
,
j
≤
2
,
j
+
+  do
(13)Calculate the new mean vector  μ
~
j
=
1
/
|
Φ
j
∩
Ψ
j
|
∑
S
U
k
∈
(
Φ
j
∩
Ψ
j
)
T
k;
(14)
if  μ
~
j
≠
μ  then
(15)Update μ
=
μ
~
j;
(16)
else
(17)Keep the current mean vector unchanged;
(18)
end if
(19) end for
(20) until the current mean vector is not updated again


## 4.3. Perfect Trust Mechanism

When DC-SSDF attackers are detected, typical issues in perfecting trust mechanism focus on(
1
) reducing theirhon data with the attenuation penalty factor (ρ) and (
2
) deleting their sensing data.For the first issue, it will be difficult for DC-SSDF attackers to maintain high trust value, thus ensuring the accuracy of trust calculation. IfS
U
i is detected as a DC-SSDF attacker, his penalty factor at sensing timek can be calculated as(11)
ρ
i
k
=
v
a
r
R
i
v
a
r
R
i
+
m
a
x
R
iwhere v
a
r
(
R
i
) and m
a
x
(
R
i
) denote the variance and maximum of R
i, respectively. The smaller value of v
a
r
(
R
i
) means that the resonance frequency of S
U
i corresponding to the other cooperating SUs is more consistent. Thus, h
i
k would be punished by more attenuation, and vice verse. The more m
a
x
(
R
i
) also makes more attenuation to h
i
k.For the second issue, it would be hard for DC-SSDF attackers to manipulate the final decision again.Procedure4 is performed to perfect trust mechanism, in which d
i is the sensing data of S
U
i andd is the final decision made by FC.Procedure 4:Perfect trust mechanism.
Input:  C, h
i
k
-
1, f
i
k
-
1
Ψ
1, Ψ
2 and R
n
×
n;
Output:  h
i
k, f
i
k
(1) for  each S
U
i
∈
C  do
(2)
if  S
U
i
∈
Ψ
1  then
(3)
h
i
k
=
h
i
k
-
1
∗
v
a
r
(
R
i
)
v
a
r
(
R
i
)
+
m
a
x
(
R
i
)
(4)
f
i
k
=
f
i
k
-
1
+
1
(5)deleted S
U
i’s sensing data
(6)
else
(7)
if  d
i
=
=
d  then
(8)
h
i
k
=
h
i
k
-
1
+
1
(9)
else
(10)
f
i
k
=
f
i
k
-
1
+
1
(11)
end if
(12)
end if
(13) end for


## 5. Simulation Results and Discussion

### 5.1. Simulation Setup

We perform computer simulations with Matlab to validate the performance of the TFCA scheme. The simulation elements are shown in Table3.Table 3
Description of simulation elements.
Parameters
Description
Default
N
s
Number of SUs
60
N
p
Number of PUs
5
cycle
Number of cycle simulation
100
round
Rounds of attack
50
p
a
Percentage of attackers
0~50%
λ
Trust warning line
0.4
δ
Threshold of trust value
0.5The cycle-based fashion is used to perform simulations. At each cycle, some SUs are selected randomly to execute a number of CSS actions by cooperation. Trust mechanism is employed to execute all CSS actions and update the trust value on the corresponding SUs. By several cycles, a trusted CSS network will be gradually formed with trust mechanism.


### 5.2. Simulation Results

To analyze the simulation result of our TFCA scheme better, we compare it with BTM and MFTM [9].As we know, an attacker such asS
U
i can be detected when t
i
k
<
δ at sensing timek. So, the main goal of DC-SSDF attackers is to prompt trust value. To increase the attack strength, S
U
i must become a high-trust attacker; i.e., s
t
i
≥
δ. Due to the “Dynamically prompting" phases, DC-SSDF attack can make attackers deviate the actual trust value and cause some network trust errors (nte) by forming high-trust attackers. Higher errors mean the lower accuracy in the trust value calculation.nte can be specified by(12)
n
t
e
=
1
N
s
∑
i
=
1
N
s
1
t
′
i
k
t
′
i
k
-
t
i
k
2where t
′
i
k and t
i
k are the actual and measured trust value of S
U
i at sensing timek, respectively.Innte simulation, the actual trust value for an attacker is randomly assigned in the interval (
0
,
δ
]. As shown in Figure 5, the TFCA scheme is better than BTM and MFTM in reducingnte. Without any guard measures, thente curve increases rapidly in the BTM scheme. Although four decision factors are involved in the MFTM scheme to perfect the trust value calculation, it ignores the factor that attackers may prompt trust value by collusion. Consequently, the MFTM scheme also fails to reducente. By reducing DC-SSDF attackers’hon data with the attenuation penalty factor (a
p), it can be found thatnte curve with TFCA increases smoothly. Even when the number of DC-SSDF attackers is 30,nte of TFCA achieves 0.0475.Figure 5
nte with the guard of TFCA.Generally, high-trust DC-SSDF attackers submit false sensing data, which would cause a mass of malicious responses at each cycle. The effectiveness of the TFCA scheme can be also validated in terms of reducing malicious responses, as shown in Figure6. Without any guard measures, DC-SSDF attackers’ trust value decreases slowly in the BTM scheme, which can make them get more opportunities to submit false sensing data, resulting in the increase of malicious responses. Since the punishment to trust level for the attackers is considered in the MFTM scheme, they get less attack chances. So, the MFTM scheme is better than BTM. In the TFCA scheme, the identified DC-SSDF attackers have no right to request CSS since their trust value can be attenuated to below δ. Then, it is difficult to prompt their conspirators’ trust value again, thus suppressing malicious responses more effectively.Figure 6
Suppressing malicious responses.We also analyze the performance of our TFCA scheme in terms of attack success ratio. This simulation is performed at the always-absent and always-present attack patterns.It can be found that the TFCA scheme is also better in suppressing attack success ratio than BTM and MFTM under the “OR” rule at the always-absent attack pattern and the “AND” rule at always-present attack pattern, as shown in Figure7. At always-present attack pattern, the damage of attacks is the biggest under the “OR” rule only when one false “1” data can make the final decision as “1”. At always-absent attack pattern, the damage of attacks is the biggest under the “AND" rule only when one false “0” data can make the final decision as “0". Under the “Majority" rule, the TFCA scheme can reduce attack success ratio to some extent with using the binary clustering algorithm. Although the damage of attacks against the “Majority” rule amplifies with the number of attackers, the TFCA scheme is better in suppressing attack success ratio better than BTM and MFTM at the always-absent and always-present attack patterns. The reason is that the majority of sensing data are “1” or “0” under the “Majority” rule; the final decision will be “1” or “0”. According to this simulation analysis, we can validate that the “Majority" rule is the best choice to make the final decision in CSS.Figure 7
Suppressing DC-SSDF attack success ratio.
(a)
Always-absent
(b)
Always-present
(c)
Always-absent
(d)
Always-present
(e)
Always-absent
(f)
Always-presentWe have known that the binary clustering algorithm can make our TFCA scheme suppress DC-SSDF attack. Another question is how about the convergence of the binary clustering algorithm. To validate the binary clustering algorithm better, we compare it with the K-means algorithm by observing the convergence of the number of DC-SSDF attackers. As shown in Figure8, the binary clustering algorithm begins to converge after 9 iterations when the ratio of attackers is 20%, whereas the K-means algorithm begins to converge after 15 iterations. In the binary clustering algorithm, we can analyze the maximum and minimum of the resonance frequency to definitely differentiate the selected samples as DC-SSDF samples and honest samples. Then, we can employ the elements of the generated cluster who also belong to the DC-SSDF samples to calculate the new mean vector at each clustering iteration. In the K-means algorithm, samples are selected randomly, and then all the elements of the generated cluster to calculate the new mean vector at each clustering iteration. Therefore, the binary clustering algorithm also converges faster than the K-means algorithm, even though the ratio of attackers becomes 40%.Figure 8
Convergence of the binary clustering algorithm.


## 5.1. Simulation Setup

We perform computer simulations with Matlab to validate the performance of the TFCA scheme. The simulation elements are shown in Table3.Table 3
Description of simulation elements.
Parameters
Description
Default
N
s
Number of SUs
60
N
p
Number of PUs
5
cycle
Number of cycle simulation
100
round
Rounds of attack
50
p
a
Percentage of attackers
0~50%
λ
Trust warning line
0.4
δ
Threshold of trust value
0.5The cycle-based fashion is used to perform simulations. At each cycle, some SUs are selected randomly to execute a number of CSS actions by cooperation. Trust mechanism is employed to execute all CSS actions and update the trust value on the corresponding SUs. By several cycles, a trusted CSS network will be gradually formed with trust mechanism.


## 5.2. Simulation Results

To analyze the simulation result of our TFCA scheme better, we compare it with BTM and MFTM [9].As we know, an attacker such asS
U
i can be detected when t
i
k
<
δ at sensing timek. So, the main goal of DC-SSDF attackers is to prompt trust value. To increase the attack strength, S
U
i must become a high-trust attacker; i.e., s
t
i
≥
δ. Due to the “Dynamically prompting" phases, DC-SSDF attack can make attackers deviate the actual trust value and cause some network trust errors (nte) by forming high-trust attackers. Higher errors mean the lower accuracy in the trust value calculation.nte can be specified by(12)
n
t
e
=
1
N
s
∑
i
=
1
N
s
1
t
′
i
k
t
′
i
k
-
t
i
k
2where t
′
i
k and t
i
k are the actual and measured trust value of S
U
i at sensing timek, respectively.Innte simulation, the actual trust value for an attacker is randomly assigned in the interval (
0
,
δ
]. As shown in Figure 5, the TFCA scheme is better than BTM and MFTM in reducingnte. Without any guard measures, thente curve increases rapidly in the BTM scheme. Although four decision factors are involved in the MFTM scheme to perfect the trust value calculation, it ignores the factor that attackers may prompt trust value by collusion. Consequently, the MFTM scheme also fails to reducente. By reducing DC-SSDF attackers’hon data with the attenuation penalty factor (a
p), it can be found thatnte curve with TFCA increases smoothly. Even when the number of DC-SSDF attackers is 30,nte of TFCA achieves 0.0475.Figure 5
nte with the guard of TFCA.Generally, high-trust DC-SSDF attackers submit false sensing data, which would cause a mass of malicious responses at each cycle. The effectiveness of the TFCA scheme can be also validated in terms of reducing malicious responses, as shown in Figure6. Without any guard measures, DC-SSDF attackers’ trust value decreases slowly in the BTM scheme, which can make them get more opportunities to submit false sensing data, resulting in the increase of malicious responses. Since the punishment to trust level for the attackers is considered in the MFTM scheme, they get less attack chances. So, the MFTM scheme is better than BTM. In the TFCA scheme, the identified DC-SSDF attackers have no right to request CSS since their trust value can be attenuated to below δ. Then, it is difficult to prompt their conspirators’ trust value again, thus suppressing malicious responses more effectively.Figure 6
Suppressing malicious responses.We also analyze the performance of our TFCA scheme in terms of attack success ratio. This simulation is performed at the always-absent and always-present attack patterns.It can be found that the TFCA scheme is also better in suppressing attack success ratio than BTM and MFTM under the “OR” rule at the always-absent attack pattern and the “AND” rule at always-present attack pattern, as shown in Figure7. At always-present attack pattern, the damage of attacks is the biggest under the “OR” rule only when one false “1” data can make the final decision as “1”. At always-absent attack pattern, the damage of attacks is the biggest under the “AND" rule only when one false “0” data can make the final decision as “0". Under the “Majority" rule, the TFCA scheme can reduce attack success ratio to some extent with using the binary clustering algorithm. Although the damage of attacks against the “Majority” rule amplifies with the number of attackers, the TFCA scheme is better in suppressing attack success ratio better than BTM and MFTM at the always-absent and always-present attack patterns. The reason is that the majority of sensing data are “1” or “0” under the “Majority” rule; the final decision will be “1” or “0”. According to this simulation analysis, we can validate that the “Majority" rule is the best choice to make the final decision in CSS.Figure 7
Suppressing DC-SSDF attack success ratio.
(a)
Always-absent
(b)
Always-present
(c)
Always-absent
(d)
Always-present
(e)
Always-absent
(f)
Always-presentWe have known that the binary clustering algorithm can make our TFCA scheme suppress DC-SSDF attack. Another question is how about the convergence of the binary clustering algorithm. To validate the binary clustering algorithm better, we compare it with the K-means algorithm by observing the convergence of the number of DC-SSDF attackers. As shown in Figure8, the binary clustering algorithm begins to converge after 9 iterations when the ratio of attackers is 20%, whereas the K-means algorithm begins to converge after 15 iterations. In the binary clustering algorithm, we can analyze the maximum and minimum of the resonance frequency to definitely differentiate the selected samples as DC-SSDF samples and honest samples. Then, we can employ the elements of the generated cluster who also belong to the DC-SSDF samples to calculate the new mean vector at each clustering iteration. In the K-means algorithm, samples are selected randomly, and then all the elements of the generated cluster to calculate the new mean vector at each clustering iteration. Therefore, the binary clustering algorithm also converges faster than the K-means algorithm, even though the ratio of attackers becomes 40%.Figure 8
Convergence of the binary clustering algorithm.


## 6. Conclusions

We report the description of DC-SSDF attack and present the TFCA scheme to defend against this attack in this paper. The TFCA scheme is designed in three successive stages: trust fluctuation analysis, binary clustering algorithm design, and perfect trust mechanism, in which trust fluctuation clustering analysis is introduced to construct the TFCA scheme since the resonance phenomenon may appear in the trust value curve of DC-SSDF attackers. Simulation results show that our TFCA scheme can ensure the accuracy of trust value calculation and suppress DC-SSDF attack success ratio to some extent.



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*Source: 3174304-2019-03-03.xml*