Milcom 2015 Track 3 - Cyber Security and Trusted Computing

Multinomial Trust in Presence of Uncertainty andAdversaries in DSA networks
Shameek Bhattacharjee, Mainak Chatterjee, Kevin Kwiat and Charles Kamhoua
Abstract—Dynamic spectrum access (DSA) networks allow
opportunistic spectrum access to license exempt secondary nodes.
Usually secondary nodes employ a cooperative sensing mechanism to correctly infer spectrum occupancy. However, thepossibility of falsification of locally sensed occupancy report,
also known as secondary spectrum data falsification (SSDF) can
cripple the operation of secondary networks.
In this paper, we propose a multivariate Bayesian trustmodel for secondary nodes in a distributed DSA network. The
proposed model accurately incorporates anomalous behavior aswell as monitoring uncertainty that might arise from an anomaly
detection scheme. We also propose possible extensions to the
SSDF attack techniques. Subsequently, we use a machine learning
approach to learn the thresholds for classifying nodes as honest
or malicious based on their trust values. The threshold basedclassification is shown to perform well under different pathloss environments and with varying degrees of attacks by themalicious nodes. We also show the trust based fusion model
can be used by nodes to disregard a node’s information whilefusing the individual reports. Using the fusion scheme, we report
the improvements of cooperative spectrum decisions for various
multi-channel SSDF techniques.1

I. I NTRODUCTION
Dynamic Spectrum Access (DSA) allows non-licensed users(secondary users) to opportunistically sense-and-use fallow
licensed bands when the licensed users (primary users) are
not using their bands. In order for the secondary users not tointerfere with the primary users, they must continuously sense
the bands to evaluate if the bands are vacant. Such sensing
done through stand-alone secondary users are subject to thetypical wireless channel induced noise; hence they might notcorrectly infer the true occupancy of a band. Hence a networkof secondary users participate in cooperative spectrum sensing
where each share his local sensing results with others. The
final inference on the occupancy of various bands is obtainedusing some fusion rule that fuses multiple local sensing
results as shared by various secondary users. However, suchdependence on multiple sensing results from various sources
has opened avenues of attacks and made channel accessdecisions in DSA networks susceptible to various unforeseen
vulnerabilities [1].
One of the most common forms of attack is the Secondary Spectrum Data Falsification (SSDF) attack, wheresome malicious users share false local sensing opinions that
1 Bhattacharjee, and Chatterjee are with EECS department at the Universityof Central Florida, Orlando. Emails: {shameek, mainak}@eecs.ucf.edu. Kwiat
and Kamhoua are with Information Directorate at the Air Force ResearchLaboratory, Rome, NY. Email: {kevin.kwiat,charles.kamhoua.1}@us.af.mil.
Approved for Public Release; Distribution Unlimited:88ABW-2015-1368,
Dated 24 Mar 15. This research was partially funded by the Florida Centerfor Cybersecurity under Subagreement: 2108-1072-00-A.

978-1-5090-0073-9/15/$31.00 ©2015 IEEEmight compromise the accuracy of fused spectrum occupancy
inference [1], [4]. In SSDF attacks, the malicious user may advertise ‘empty’ as ‘occupied’ resulting in denial of spectrum oradvertise ‘occupied’ as ‘empty’ to induce a punishable breachof regulations. Either way, this would severely cripple theoperation of secondary nodes. There has been some researchthat focused on defense against SSDF attacks via isolationof malicious nodes [4], [8], [9] or disregarding informationfrom nodes whose reputation is lesser than acceptable [2], [3],[4]. Also, most works classify users as either trustworthy ornot. Due to unavailability of complete information, such strictbinary classification of evidence may be impractical. Someof the earlier works [4], [8] analyzed defense strategies for
single channel networks, although multi-channel spectrum data
is usually shared during cooperative sensing.
In this paper, we propose a framework to cope with smart
malicious users in a distributed multi-channel DSA network
who employ various extensions of SSDF attack techniques. We
introduce a multinomial Bayesian trust model that considers
any uncertainty that might arise from an imperfect anomaly
monitoring mechanism. First, we identify the strategies that amalicious secondary user might adopt to inflict the maximum
damage while remaining undetected as long as possible. In thatregard, we propose three variations of multi-channel SSDF
attacks and provide the defense mechanisms by evaluating
the trustworthiness of the users that share spectrum usage
information. Instead of the commonly used binomial models(Beta distribution), we use a multinomial Dirichlet distribution [6] and subjective logic [7] (Josang’s Belief model) forcomputing the trust of the users addressing the shortcomingsof binary classification and uncertainties that arise due to lackof complete evidence. We argue that anomaly detection basedon signal strength prediction is highly dependent on path loss
and hence incorporate it in the proposed trust model. We also
validate our model for different path loss environments anddifferent SSDF strategies.
II. S YSTEM M ODEL AND A SSUMPTIONS
We assume an ad-hoc secondary network with n secondary
nodes of which some fraction are malicious. Secondary node i
continuously scans N channels to determine whether a channel
is occupied or not and constructs its observed local binary
occupancy vector as: 1 for ‘occupied’ and 0 for ‘unoccupied’.
This decision is arrived upon by comparing the energy sensed
on a channel with a common normalization threshold. Oncea binary vector is created, secondary node i broadcasts it to
its neighbors. Any node j within a sharing radius R from611

Milcom 2015 Track 3 - Cyber Security and Trusted Computing

node i is considered to be i’s neighbor and would hear
the broadcast messages (binary occupancy vectors) from its
neighbors. An honest node would broadcast the same vector as
it observed while malicious node would broadcast a modified
one i.e., falsify the occupancy of some channels. Based on thereceived vectors, all nodes will employ some majority voting
fusion technique to obtain a better estimate about the spectrum
occupancy of all N channels [4], [5]. We assume the presenceof a trust enforcement entity to which all nodes periodicallyreport the calculated trust values of its neighbors. This entity
maintains long term history or average reputation of each node
as observed/experienced by their neighbors. Given that, we do
not consider bad-mouthing attacks where nodes lie about thetrust of other nodes to the enforcement entity. Such a feature
has been already discussed in [10] and can be incorporated in
our model without loss of generality.
A. Anomaly Detection and Evidence Gathering
In this paper, instead of proposing an anomaly detection
scheme, we assume that the anomaly detection mechanism
as discussed in [2] is already in place. For each channel,
the anomaly detection mechanism provides one of the threepossible observations: (i) matches indicating positive behavior(denoted by ϕ), (ii) mismatches indicating negative/anomalous
behavior (denoted by β), and (iii) undecided (denoted by µ )indicating inability to classify a channel as either positive or
negative. For each neighbor j, node i constructs an evidence
vector of length N , which corresponds to the predicted inference on each channel as ϕ, β or µ. The total number ofmatches, mismatches and undecided accumulated against node
j by node i at any time slot t given its advertised vector is ηϕt ,ηβt and ηµt respectively. Of course ηϕt + ηβt + ηµt = N . Eachchannel wise observation is independent of each other. The
advantage of the anomaly detection scheme in [2] is that it
works even for densities greater than 50% of malicious nodes.
Other schemes that produce binary evidence based on majority
voting are not robust to high local densities of malicious nodes
in distributed networks.
B. SSDF Attack Models
Traditionally, SSDF attacks have been viewed as ‘denial’(changing 0’s to 1’s ) or ‘induced’ (changing 0’s to 1’s).
Hence given a channel, an SSDF attacker would have two
strategies: ‘always denial’ or ‘always induced’. However, we
argue that falsifying every bit of its occupancy vector all thetime may facilitate easy and quick detection of malicious users.
Also, changing every bit at all times can increase the cost ofresource limited attackers. Hence a smart malicious attacker
would refrain from such a simplistic strategy and employ
some probabilistic or randomized attack strategies where somechannels are attacked and some are reported correctly. We
propose and analyzed three extensions to SSDF attacks.
1. Deterministic magnitude SSDF attack: A malicious nodefalsifies on a fixed number of channels every time slot. The
fraction of channels falsified on every time slot is denoted
as Dattack . Dattack = 0.50 means half of the total number ofchannels are falsified on each time slot. However, the channels
falsified on are randomized every time slot.
2. Probabilistic magnitude SSDF attack: A malicious nodefalsifies opinions on a random number of channels every timeslot, and the channels falsified are also random. However, suchnodes follow a long term average, Pattack , which represents
how aggressive a malicious node is. Pattack = 0.60 meansthat the probability of a channel’s report being changed is
60%. Thus, any number of channels (from 0 to N ) can bechanged in a time slot.
3. Collaborative deterministic magnitude SSDF attack: The
malicious nodes collaborate to agree upon the channels
they falsify. If the channel set remains same, it is calledstatic collaborative attack (channel preference); otherwise itis called dynamic collaborative attack. We denote this attackcolby Dattack. Collaborative attacks are harder to defend against
as the probability of blinding the majority voting fusion ruleincreases. Here, the channels attacked over time may berandom.
col
The values of Dattack , Pattack , Dattack
may be dictated by
the attack budget a malicious user can afford or how conservative (to avoid easy detection) or aggressive a malicious user
wants to be. It may be noted that very high values facilitate
easy detection while very low values cannot significantly affectthe majority voting rule.
III. M OTIVATION FOR A M ULTINOMIAL T RUST M ODEL
Existing binary trust models like [3], [4], [8] do not accountfor evidence with three or more possible outcomes. In suchanomaly detection models, the central fusing entity gathers
all opinions and performs a majority voting to find the fusedresult for every channel. If advertised opinion of a participating
node does not agree with the fused result, it is considered as
negative rating; else the node’s behavior is considered positive.
This only works well in centralized architectures where thenumber of malicious nodes compared to the total nodes is lessthan 50% [9]. As a remedy, a signal bound prediction based
anomaly detection scheme has been proposed in [2], which
produces multinomial evidence namely match, mismatch andundecided as discussed before. While calculating trust, theundecided ones are accounted for by splitting them into either
positive or negative ratings. Given ηϕ ηβ and ηµ as definedin Section II-A, trust computed by node i for neighbor j is
η jη jgiven as:
η j+ µ ϕ
E j,i =ϕηϕj +ηβ jη ϕj + η β j + η µ j(1)where 0 ≤ E j,i ≤ 1.
Partial splitting of the undecided ones in the ratio ofobserved matches and mismatches is justified only when thechannels attacked are uniformly random. However, when thechannels are attacked with some pseudo-random preference on
certain channels, such splitting is not justified. An intelligent
adversary might employ a variety of statistical techniques andhave some preference on a subset of channels to be attacked
violating the assumption that ηµ can split in the ratio ofmatches and mismatches.

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Milcom 2015 Track 3 - Cyber Security and Trusted Computing

TABLE IT RUST-O PINION TUPLE ; N=40
Scenario
1
2
3
4
5
6

ϕ
14
19
22
10
31
22

β
13
18
0
0
0
14

µ
13
3
18
30
9
4

E j,i
0.51
0.51
1.00
1.00
1.00
0.61

Binary models only work in environments where numberof uncertain ratings are not high. However, if the number of
uncertain ratings is very high, such models cannot distinguishbetween large and small proportions of uncertain ratings.
Consider the 6 scenarios as shown in Table I. Scenarios 1, 2,
and 6 have sufficient number of mismatches to given a lower
values than scenarios 3, 4, and 5 with no mismatches. Note,though there are a varying number of undecided in scenarios
3, 4, and 5, they have the same trust value. Consider scenarios
4 and 5, where both produce a high trust value 1.00 although
the number of positive ratings in scenario 4 is three times lessthan scenario 5, while the undecided in scenario 4 is much
more than compared to scenario 5. This trust model assumes
that having no mismatches is an index of being an honest
node although in reality many opinions may be undecided. In
data mining, this is popularly known as not being robust tonull invariance where evidence supports conclusions that areneither True nor False. Hence even if statistical preference
is not employed, there is a small non-zero probability that
all channels which were attacked were inferred as undecided.
Such a possibility is high when there are a large number ofundecided opinions in the trust evidence. Hence a better trustmodel is one which would give more trust value to scenario 5
and a less trust value to scenario 4. This calls for the use ofmultinomial trust modeling such as the Dirichlet distribution,
which is the multivariate generalization of the corresponding
binomial models (Beta distribution).
IV. D IRICHLET E XPECTATION BASED T RUST M ODEL
Multinomial distribution is the multi-variate generalizationof the binomial distribution with k > 2 possible outcomes
where each trial results in exactly one out of k possible outcomes in a total of N trials. Given this, number of occurrences
di of each outcome i;(1 ≤ i ≤ k), the observations data can bedenoted with observation vector D = {di |1 ≤ i ≤ k}. Similarly let xi be the unknown probability of occurrence of eachoutcome denoted by probability vector X = {xi |1 ≤ i ≤ k}.
Given this D is said to have a multinomial distribution withparameters N and X. However initially X is unknown andhence the problem is Bayes estimation of parameters in X
given data D.
In our problem we can model the observation counts match,mismatch and undecided as the possible outcomes on theinference over each channel; hence k = 3 and the total
number of channels being N . Thus observation counts fromthe trust evidence fit very well with the concept of multinomial
distribution. Hence the problem of trustworthiness can be
answered once we know posterior probabilities of occurrences~ from a node jof seeing a match, mismatch or undecided X~
based the evidence D. In Bayesian systems X is updated overtime with incrementally acquired evidence D.
Dirichlet distribution is often used as a conjugate prior fora multinomial distribution because both prior and posterior
retain the same form. Hence the unknown degree of belief
associated with the three outcomes can be calculated assuming
conjugate priors. In Bayesian systems, a prior probability
distribution p(x) is said to be conjugate to the class of distributions p(D|x) if the resulting posterior p(x|D) is in the samefamily as p(x). In such a case, the resultant posterior p(x|D)
can be used as prior (if required) for further belief updates
as incrementally new evidence D over time is received. The
observation counts constitiute evidence parameter D; X forms
the probability parameter. In short, X is said to have a
Dirichlet distribution with parameter D and is denoted asX ∼ Dir(D). Such degrees of beliefs can be used to model
trust and reputation [6].
In terms of Bayesian systems, if x1 , · · · , xk are the unknown probabilities associated with k events, and the evidence
is di , then the posterior degree of belief on each xi having
accounted for evidence parameter di is given by Eqn .2. The
evidence parameter di , is defined as di = ri + Cai , where ri
represents the most recent count for event i and ai represents
a prior base rate and C represents an a-priori constant which
dictates whether an informative or non informative prior is
initially assumed [6]. The posterior p(xi |di ) can be calculatedusing the posterior Dirichlet multinomial distribution function
Pkgiven by:kY
i=1 di )~ = Γ(
xdi i −1 ,(2)
f (~x|d)Qk
i=1 Γ(di ) i=1
Pk
where x1 , x2 , · · · , xk ≥ 0,i=1 xi = 1, d1 , · · · , dn > 0,with restriction that xi 6= 0. The relation between observation
parameter di and actuallyobserved outcomes ri is that ri +PkC.ai = di , where i=1 ai = 1 and C > 0, ai > 0 such thatzero occurrence of an outcome preserves the condition thatdi > 0.
Since trust is an expectation of a node’s behavior, the node’s
trust is given by the mean vector for Eqn. (2) and is given as~ = P diE(xi |d)ki=1 di(3)where di is a known as the total evidence mass for event i. The
degrees of belief associated with the outcomes are expressedas the mean of each outcome.
A. Applying Dirichlet model to trust evidence
The most recent observation vector is the multinomial trust
evidence r = {ηϕ , ηβ , ηµ }. Thus,
d1 = ηϕ + Cai ; d2 = ηβ + Cai and d3 = ηµ + Cai .
Since there is no reason to believe a node has a particularpre-disposition to behave in a positive, negative or uncertain
way, we assume a uniformly distributed non-informative prior.
Since there are 3 outcomes, the prior initial base rate ai = 13
and C = 3. Given this d1 = ηϕ + 1; d2 = ηβ + 1; d3 = ηµ + 1.

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Milcom 2015 Track 3 - Cyber Security and Trusted Computing

Now that we have the parameters of the Dirichlet distribution
we can express the expected degrees of belief associated withthe events of match, mismatch and undecided in terms of theobserved trust evidence using Eqn. (3) as
Eϕ =ηϕ + 1
ηϕ + 1 + ηβ + 1 + ηµ + 1
η +1

(4)

η +1

Similarly, Eβ = ηϕ +ηββ +ηµ +3 and Eµ = ηϕ +ηµβ +ηµ +3 .
bHence for each node j, we have Eϕ = Ejirepresentingddegree of belief, Eβ = Eji representing degree of disbeliefuand Eµ = Ejireflecting degree of uncertainty of node jbased on gathered trust evidence of node i from the anomaly
monitoring phase.
B. Interpreting belief as subjective logic for trust modeling
The proposition that a node will cooperate is either trueor false and hence is a binary proposition. However, due
to inherent uncertainty and imperfect knowledge caused bylack of evidence it is not possible to infer with certainty
that the proposition is true or false. Hence we only havean opinion about this proposition and trust is often reported
as the expected opinion [7]. This translates the problem into
degrees of belief, disbelief and uncertainty represented by
b
d
u
b
d
u
Eji
, Eji
, Eji
where Eji
+ Eji
+ Eji
= 1. Josang’s belief
model is typically used to deal with such uncertainty in a
proposition of binary state space (honest or not), but the
beliefs are multinomial [7] where one of the features express
uncertainty. Josang’s definition of opinion ω = {b, d, u, a} isa quadruple where the components respectively correspond tothe belief, disbelief, uncertainty, and relative atomicity suchthat a, b, d, u ∈ [0, 1] and b + d + u = 1. The expected opinion
pertinent to the positive interaction or belief is given asE(ω) = b + au

(5)

where a is known as the relative atomicity which determines
how uncertainty contributes to the final expected opinion.
Since the proposition that a node will cooperate or not isbinary, we treat a as 0.5 which is the value of relativebdu
atomicity in our model and Ebi= b, Ebi= d, Ebi= u.
Hence the expected opinion on the proposition that the node
is cooperative or not is given by
ω
b
u
Eji
= Ebi
+ (a)Ebi

The normalized conservative trust weight is given by−|rE ω |ji
if rEji ω > 0;
 1−e−|rE ω |wji =ji−(1 − e) if rEji ω < 0;0
if rEji ω = 0

where wji ∈ [−1, 1]. For performance and results, we mostly
use the absolute value of node j’s normalized trust weight
which is average of all trust ratings calculated by node j’sneighbors so that there is no bias for one particular pair andalso because we cannot plot all node pairs. Hence averagetrust rating of a particular node j can be represented as wj .
D. An illustrative example of Dirichlet Trust Computation
The scenarios in Table II represent trust evidence on a particular time slot for 40 channels for different nodes. Scenarios
1, 2, and 6 have both occurrences of mismatches while 3,
4 and 5 do not. Intuitively, we would expect 3, 4 and 5 tohave higher trust than 1, 2 and 7. However, scenario 4 hashigh number of uncertain ratings as opposed to 5. The binarymodels cannot capture relative uncertainty with just one value.
Hence E j,i gives the same answer for scenarios 4 and 5. This
ambiguity is resolved by the Dirichlet expectation model.
If we observed the corresponding values for the same in ourmodel given by E(ω), we observe that our model captures thepresence of a high number of uncertain ratings by generating
a trust value of 0.61 for scenario 4, whereas giving a higher
value of 0.86 to scenario 5, differentiates between scenarios 4
and 5. We can also see that scenario 3 which has less uncertain
ratings than 4 but more uncertain ratings than 5, has a trust
value intermediate to the scenarios 4 and 5. This demonstrates
that given no evidence of mismatch, lower uncertainty should
be awarded with higher trust.
Among the scenarios with non-zero evidence of mismatches, scenario 6 has least number of undecided and mostnumber of matches. Hence scenario 6 achieves higher trust
value than scenarios 1, 2, and 7 but lower than scenarios 3, 4,
and 5.
TABLE IIT RUST-O PINION TUPLE ; N=40
Scenario
1
2
3
4
5
6
7

(6)

C. A Conservative Weighted Trust MetricωEji
is a number between 0 and 1 making the separation
between non trustworthy and the trustworthiness nodes difficult to depict or visualize. Hence we use a Shapley log valueωwith Eqn. 7 to transform Eji
to a generic value on the real line
where non-trustworthy nodes have a monotonically decreasing
values and trustworthy nodes have monotonically increasing
values. Subsequently, we report the normalized weight wji bygiving a value between [−1, 1] using Eqn. 8. The Shapley log
value is given as!
ωEjiω = log2(7)rEjiω
1 − Eji

(8)

ϕ
14
19
22
10
31
22
12

β
13
18
0
0
0
15
22

µ
13
3
18
30
9
3
6

E j,i
0.518
0.513
1.00
1.00
1.00
0.594
0.353

ω
Eji
0.5116
0.5166
0.755
0.616
0.860
0.581
0.383

wji
0.044
0.064
0.664
0.361
0.837
0.281
−0.476

V. S IMULATION M ODEL AND R ESULTS
To validate the trust model, we conduct extensive simulation
experiments where we consider a 100 × 100 grid with 30
randomly scattered nodes. Each node scans N = 40 channels
and has a sharing radius of 30 units. The nodes 1, 3, 4, 5, 6, 9,
20, 27, and 29 are programmed as malicious while the rest arehonest. We consider both cases when the malicious node attack
independently and collaboratively. For training set learning,
we consider an environment with path loss of 4. For testing614

Milcom 2015 Track 3 - Cyber Security and Trusted Computing

sets, we show that proposed model correctly classifies nodes
as malicious or honest for networks with different pathloss
factors and magnitudes of attack. We vary the path loss factor
from 3 to 5. Both Dattack and Pattack are varied from 0.30
to 0.90.
A. Instantaneous and Average Trust: Node pair perspective
Figure 1 shows the comparison of both instantaneous andaverage trust values between honest node 16 and malicious
node 20, as calculated by one of their respective neighbors
3 and 28. Regardless of the temporal uncertainty of evidenceof certain time slots, we observe that honest node 16 clearly
has a higher trust value than 20. This is true for both the
instantaneous values and the long term moving average. The
honest node’s trust value is more stable as it does not attack at
all while malicious node employs Pattack = 0.50 over time.
Hence, there is a large difference between a malicious andhonest node.
0.6
Moving Avg Trust (Mal)Instantaneous Trust (Mal)Instantaneous Avg Trust (Honest)
Moving Avg Trust (Honest)

Average Weighted Trust

0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0

50

Fig. 1.

100

150
Time

200

250

300

Comparison of trust of malicious and honest nodes

18

Percentage of DecisionError

16
14

Deterministic Magnitude SSDF
Probabilistic Magnitude SSDF
Collaborative Deterministic SSDF

12
10
8

damage than most values of Pattack and Dattack , except when
Pattack > 0.80. This validates intuition because collaboratively modifying opinions increases the probability of compromising the fused decision. However, when independent nodes
attack with a high magnitude (> 0.80), they automaticallywill have common channels between them. Hence explicit
deterministic collaboration does not yield similar benefits forexcessively high attack magnitudes as it loses to additional
diversity provided by Pattack .
C. Classification ThresholdTo identify malicious nodes, there must be an observation orlearning phase to make sure that the model is generic enoughto correctly classify under a wide range of scenarios. In thatregard, we propose a machine learning based approach thatconsiders relevant network, radio, and topological parameters.
We generate training data sets for different path loss environments and varying Pattack seeking to find an optimal thresholdwclassif y to decide whether a node is malicious or not. We
have identified the following:
Effects of pathloss: Given the anomaly detection model, we
have found that the variation of pathloss effects the degreeof uncertainty in evidence as shown in Table III. In general,
we found if the path loss factors are too high or too low theaverage uncertainty is less evident; whereas an intermediate
value increases uncertainty. A network with pathloss factor 4
induces maximum uncertainty while pathloss lower or higher
reduce uncertainty. Hence we choose pathloss 4 as a parameterof our training since it induces maximum uncertainty.
Effects of magnitude of attack: In general, if we can detect
for lower magnitudes of attack, then we can detect for higher
magnitudes of attack as well. Hence, we use training data sets
mostly considering lower magnitudes of attack. However, too
low of a magnitude defeats the purpose of an attack when amajority voting is used for decision making. Hence, to strike abalance between attacking and avoiding detection we choose
an intermediate attack magnitude of 0.5 for training set.

6

TABLE IIIE FFECT OF PATHLOSS ON UNCERTAINTY; W ORST CASE Pattack = 0.50

4
2
0.2

Fig. 2.

0.3

0.4

0.5
0.6
0.7
Magnitude of Attack

0.8

0.9

Pathloss
3
4
5
5.5

1

Errors for different and varying SSDF attack magnitudes

B. Comparison between SSDF attack strategies
Fig. 2 shows how the different SSDF strategies affectthe average utility of cooperative sensing with increasing
magnitude of attack in the absence of a defense mechanism.
In general, we see the obvious trend that the fraction ofdecision errors increases as the malicious nodes increase theirmagnitude of attack. We observe that for higher magnitudes ofattack (above 0.50), Pattack produces more mismatches than
Dattack . This is because, for Pattack = m, the fraction ofchannels attacked could be more than m. This, coupled withthe fact that different channels are being attacked, increases
the chances of circumventing the majority voting rule. We
also observe that a collaborative attack is able to do more

Average Eµ0.166065
0.426087
0.305750
0.200618

1) Training data sets: We run a support vector machine(SVM) over training examples to map trust values into support
vectors and find the optimal hyper- plane (which in our caseis a single line due to the linear nature of the data with
only one feature i.e., the trust value). This optimal hyperplane that divides the feature space into two regions (upperand lower), can act as a robust classification threshold todistinguish between malicious or honest nodes. The lower
and upper regions of SVM contains labels corresponding tomalicious nodes and honest nodes respectively. In Figure. 3(a),‘+’ represents the labels corresponding honest nodes and ‘*’
represents labels corresponding to the malicious node, along615

Milcom 2015 Track 3 - Cyber Security and Trusted Computing

with the optimal hyper-plane. The choice of the threshold
is a tunable parameter. Our objective is to mimic the worst
case scenario for classification; thus we place emphasis on
the lower probabilities of attack when classification is hard.
From Figs. 3(a) and 3(b), we choose 0.29 as it is the valueof the optimal hyper-plane for the training set T1 = T (4, 0.5)
with the worst case parameters.
01
Support Vectors

0.6
0.5
0.4
0.3
0.2

0.8
Conservative Weighted Trust

0.6

0.6

Average Weighted Trust

Average Weighted Trust

Honest Nodes
Malicious Nodes

Classification threshold=0.29

0.4
0.2
0

0
1
Support Vectors

Fig. 4.

0.4

5

10

15
Node ID

20

25

Malicious Nodes

0.2

−0.2
0

30

5

10

15
Node ID

20

25

30

(a)
(b)
(a) Pathloss=3, Pattack = 0.50 (b) Pathloss=5, Pattack = 0.50

1.2

0

1
1

0.8classification threshold=0.29
Average Weighted Trust

0.8
0.6
classification threshold=0.29
0.4

−0.6

0.2

Fig. 3.

Honest Nodes

0.4

0.2

−0.4

0
−0.1

Classification threshold=0.29

0.6

0

−0.4
0

−0.2

0.1

0.8

−0.2

Average Weighted Trust

Conservative Weighted Trust

0.7

1
0.8

1

0.9
0.8

1.2
1

(a)
(b)
(a) Pathloss=4, Pattack = 0.50 (b) Pathloss=3, Pattack = 0.80

Honest Nodes0

Malicious Nodes

−0.2
−0.4

0.6
0.4

Honest Nodes
Malicious Nodes
Classification Line

0.2
0
−0.2
−0.4
−0.6
−0.8

−0.6
−0.8
0

5

10

15
Node ID

20

25

−1
0

30

5

10

15
Node ID

20

25

30

D. Performance of Trust Model

VI. C ONCLUSIONSIn this paper, we argue that binary trust models are notappropriate when SSDF attacks are launched in a distributed
DSA network. In that regard, we propose a multinomial
Bayesian trust framework based on a Dirichlet distribution andsubjective logic for assigning a trust value that better models
the evidence gathered from an anomaly monitoring scheme.
We present a machine learning based approach for calculatinga classification threshold to decide whether nodes are honest
or malicious. We also provide an instantaneous Dirichlet trust
based fusion model, whereby we disregard information sent bypotentially misbehaving nodes which increases the accuracy ofcooperative sensing.

Fig. 5.

(a)(b)(a) Pathloss=3, Pattack = 0.80 (b) Pathloss=3, Pattack = 0.80

18

16

16

12
10
8
6

12

10

8

6

4

4
2
0.2

Blind Fusion
Conservative Trust Based Fusion

14

Blind Fusion
Conservative Trust Based Fusion

Percentage of Mismatches

14
Percentage of Mismatches

The performance of our trust model has two aspects. First,
malicious node detection using steady state values of eachnode as calculated by its neighbors and then robust fusion
using instantaneous trust values.
1) Malicious Node Identification: We use wclassif y = 0.29
as the threshold below which we treat them as malicious. We
see from Figs. 4(a), 4(b), 5(a), and 5(b), that for a variety ofpathloss environments and for both higher and lower attack
magnitudes of 0.8 and 0.5, we are able to distinguish between
malicious and honest nodes with a high degree of certainty.
Even among honest nodes, trustworthiness varies with theamount of uncertainty in their evidence.
2) Robust Fusion Spectrum: In Fig. 6(a), we see theperformance benefit under Pattack from blind fusion, andobserve much lower percentage of mismatches from ideal.
Similarly, Fig. 6(b) also shows similar results for collaborative
SSDF although it does not perform very effectively very low
magnitudes, (because our training examples did not train forvery low values as impractical). However, for most values,
the performance benefit derived from a correct decision for
all nodes in the network is high.

0.3

0.4

0.5
0.6
0.7
Probability of Attack

0.8

0.9

2
0.2

0.3

(a)
Fig. 6.

0.4

0.5
0.6
0.7
Probability of Attack

0.8

0.9

(b)

col
Performance of Trust based Fusion with (a) Pattack (b) Dattack

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