Research Article An Analytical Study on Eavesdropping...

Research ArticleAn Analytical Study on Eavesdropping Attacks inWireless Nets of Things

Xuran Li1 Hao Wang2 Hong-Ning Dai1 Yuanyuan Wang1 and Qinglin Zhao1

1Faculty of Information Technology Macau University of Science and Technology Avenida Wai Long Room A208 Taipa Macau2Big Data Lab Faculty of Engineering and Natural Sciences Norwegian University of Science amp Technology Postboks 15176025 Alesund Norway

Correspondence should be addressed to Hong-Ning Dai hndaiieeeorg

Received 28 July 2015 Accepted 7 December 2015

Academic Editor Jong-Hyouk Lee

Copyright copy 2016 Xuran Li et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The security of Internet of Things (IoT) has received extensive attention recently This paper presents a novel analytical modelto investigate the eavesdropping attacks in Wireless Net of Things (WNoT) Our model considers various channel conditionsincluding the path loss the shadow fading effect and Rayleigh fading effect Besides we also consider the eavesdroppers in WNoTequippedwith either omnidirectional antennas or directional antennas Extensive simulation results show that ourmodel is accurateand effective to model the eavesdropping attacks in WNoT Besides our results also indicate that the probability of eavesdroppingattacks heavily depends on the shadow fading effect the path loss effect Rayleigh fading effect and the antenna models Inparticular we find that the shadow fading effect is beneficial to the eavesdropping attacks while both the path loss effect andRayleigh fading effect are detrimental Besides using directional antennas at eavesdroppers can also increase the eavesdroppingprobability Our results offer some useful implications on designing antieavesdropping schemes in WNoT

1 Introduction

As one of the most promising information and communica-tion technologies (ICT) IoT has received extensive attentionsfrom both academia and industry recently The basic idea ofIoT is to integrate ldquosmartrdquo objects the things into the Internetwith provision of various services to users [1 2] The typicalkiller applications of IoT include the logistic managementwith RFID technology [3] environmental monitoring withwireless sensor networks [4] smart homes [5] e-health[6] smart grids [7] Maritime Industry [8] and so forthThere are a number of diverse smart objects ranging fromsmall Radiofrequency Identification (RFID) tags to sensorsactuators mobile phones smart appliances smart metersand so forth Due to the device heterogeneity variouswirelesscommunication technologies (such as ISOIEC 18000 [3]IEEE 802154 [9] and Bluetooth [10]) are also exploited tointerconnect the smart devices to form a Wireless Net ofThings (WNoT) Note that the conventional wired commu-nication technologies (Ethernets fiber-optic communication

etc) are also mandatory to connect the WNoT with the restof the Internet

Security is one of the fundamental issues in IoT since itis the prerequisite for most IoT applications [11ndash14] Thereraise a number of security threats in IoT especially inWNoTwhere the conventional security countermeasures used inwired networks may not work well in WNoT due to thefollowing inherent constraints of WNoT (i) the wirelessmedium is open for any nodes [15] (ii) it is extremely difficultto deploy centralized control mechanisms in such distributedWNoT [2 16 17] Eavesdropping attack as one of typicalsecurity threats in wireless communication systems hasattracted considerable attention recently [18ndash24] since manyadversary attacks often follow the eavesdropping activity forexample the man-in-the-middle attack [25] and the hear-and-fire attack [19]

Figure 1 shows a typical example of eavesdropping attacksin a warehouse environment where each product is attachedwith an RFID tag which can passively communicate with

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 4313475 10 pageshttpdxdoiorg10115520164313475

2 Mobile Information Systems

RFID-reader

Eavesdropper

Eavesdropper

RFIDRFID

RFID-reader

Figure 1 An example of eavesdropping activities in WNoT where there are several eavesdroppers who are wiretapping the confidentialongoing communications between RFID tags and RFID-readers

RFID-readers In this environment the confidential com-munications between RFID-readers and RFID tags can beeasily wiretapped by eavesdroppers since it is difficult toapply antieavesdropping countermeasures (eg encryptions)in this scenario due to the limited computational capabilityand the energy-constraint of RFID tagsNote thatwe considerthe far-field wireless communications in this scenario [26]

11 Related Works Most of current studies have been con-centrated on protecting the confidential communications ofsmart objects in WNoT which are also named as good nodesin this paper Encryption is one of the most commonly usedtechniques to protect the confidential communications inwireless personal area networks [11] wireless local area net-works (eg WEP [27] WPA and WPA2 [28]) wireless cel-lular networks (eg Cellular Message Encryption Algorithm[29]) and encryption algorithms forwireless sensor networks[30] However it is infeasible to apply cryptography-basedtechniques in WNoT due to the following reasons (a) theinferior computational capability of smart objects [2] (b) thelimited battery power of smart objects (eg the passive RFIDscan only harvest the energy from the readers) [1 31] and(c) the difficulty of managing the widely distributed smartobjects in centralized manner which is the necessity for theencryption algorithms [11 32 33]

An alternate approach is either to design light-weightedencryption schemes [34] or to generate noise to limit theamount of information that can be extracted by an eavesdrop-per [35 36] However one of the most important premises ofthe above schemes is that we shall have enough knowledge ofthe channel condition of eavesdroppers as indicated in [37ndash42] which nevertheless has received little attention Besidesthe wireless channel in WNoT fluctuates from time to timeand is affected by various fading effects including the path

loss the shadowing effect and the multipath effect [43]Furthermoremost of current studies inWNoT only considerthe nodes equipped with omnidirectional antennas whichradiatereceive RF signals in all directions (ie a less efficientway to propagate RF signals) As shown in some of themost recent studies [44 45] directional antennas can beused at readers Compared with omnidirectional antennasdirectional antennas can concentrate the transmissions tosome desired directions so that the performance can befurther improved

However little attention has been paid to investigatingthe eavesdropping behaviors conducted by the eavesdroppersin WNoT which is nevertheless important for us to offerbetter protection on the confidential communications sincewe can design antieavesdropping schemeswith clearer targetsif we have a better knowledge on the eavesdroppers althoughwe conducted a preliminary study on the eavesdroppingprobability of wireless ad hoc networks in [46] But thispaper is significantly different from our previous work [46]in the following aspects (1) we are concerned with theeavesdropping activities in WNoT in this paper while theprevious paper investigated the eavesdropping attacks inwireless ad hoc networks (2) we propose a novel analyticalmodel on the eavesdropping probability in this paper wherethe channel randomness (including Rayleigh fading effectand the shadowing effects) is considered while the previouspaper only considered a simplified geometric model (3) weconduct extensive simulations to verify the accuracy of ourproposed model in this paper while the previous paper onlypresented the numerical results

12 Contributions The aforementioned issues motivate usto conduct an investigation on the eavesdropping attacks inWNoT In this paper we analyze the eavesdropping activities

Mobile Information Systems 3

Table 1 Summary of effects on eavesdropping attacks

Factors Effects on eavesdropping attacksDirectional antenna PositiveShadow fading PositivePath loss NegativeRayleigh fading Negative

conducted by eavesdroppers with consideration of variouschannel conditions and different types of antennas To thebest of our knowledge this is the first study on analyzingthe eavesdropping attacks in WNoT from the viewpoints ofeavesdroppers Ourmajor research contributions in this papercan be summarized as follows

(i) We formally establish an analytical framework toinvestigate the probability of eavesdropping attacksinWNoTwith consideration of channel randomnessIn particular we consider the path loss effect theshadow fading effect andRayleigh fading effect in ourmodel Besides we also take both omnidirectionalantennas and directional antennas into account of ouranalytical framework

(ii) Extensive simulations show that the simulationresultsmatch the analytical results indicating that ouranalytical model is accurate and effective Our resultsalso show that both the path loss effect and Rayleighfading effect are detrimental to the probability ofeavesdropping attacks while the shadow fading effectis beneficial to the eavesdropping attacks in WNoTBesides our results also indicate that using directionalantennas at eavesdroppers can significantly improvethe probability of eavesdropping attacks We summa-rize our major findings in Table 1

(iii) Our results can provide many useful implications ondesigning antieavesdropping schemes in WNoTThisis because we can provide the better protection onthe confidential communications if we have the betterknowledge about the eavesdroppers as implied in theprevious studies [37ndash42] For example we can designlight-weight encryption algorithms by exploiting theknown channel features [47 48] Besides we onlyneed to encrypt the communications in the area or thedirection that is vulnerable to eavesdropping attacksso that the security cost due to the computationalcomplexity can be greatly saved

The rest of this paper is organized as follows Section 2presents the models used in this paper We then give theanalysis on the eavesdropping attacks in Section 3 Theimpacts of channel randomness with consideration of theshadow fading effect and Rayleigh fading effect are discussedin Section 4 Finally we conclude the paper in Section 5

2 Models

In this section we present the models used in this paper (SeeNotations and Symbols section)

21 Node Distribution In this paper we assume that all thesmart objects (or nodes) are randomly distributed in a 2Darea A according to a homogeneous Poisson point processwith density 120588 We denote the number of nodes in an areaAby a random variable119873 Then the probability mass functionof119873 is given as follows

119891119873 (119899) =

(120588A)119899

119899119890minus120588A

(1)

where 120588A is the expected number of nodes in areaA

22 Channel Model We assume that all nodes use the com-mon transmission powerP

119905similar to [49]The channel gain

from a node 119894 to an eavesdropper 119895 at a distance 119903 is denotedby 120574

119894119895(119903) Thus the received power at the eavesdropper is

P119905sdot 120574119894119895(119903) The signal-to-interference-plus-noise ratio (SINR)

at the eavesdropper denoted by Λ is defined to be

Λ =P

119905sdot 120574

119894119895 (119903)

120578 + sum119873

119896 =119894P

119905sdot 120574

119896119895 (119903) (2)

where 120578 is the power of the white noise and 119873 denoted thenumber of good nodes

The transmission from node 119894 can be successfully eaves-dropped by an eavesdropper if and only if

Λ ge 120573 (3)

where120573 is theminimumsignal to interference andnoise ratioIn our analysis of eavesdropping activities we ignore the

impact of interference due to the following reasons Firstthe passive eavesdroppers in WNoT do not transmit activelyand therefore contribute nothing to the interference Secondthe interference is proved to converge when efficient MACschemes are exploited and the traffic is low in a large-scalenetwork [50 51] Thus our analytical results in this papercan be regarded as the upper bound of the eavesdroppingprobability We then have

Λ =P

119905sdot 120574

119894119895 (119903)

120578ge 120573 (4)

23 Antennas There are different types of antennas used inwireless communication systems omnidirectional antennas(named Omni in short) and directional antennas (namedDir in short) Most of conventional smart objects aretypically equipped with omnidirectional antennas whichradiatecollect radio signals intofrom all directions equallyDifferent from an omnidirectional antenna a directionalantenna can concentrate transmitting or receiving capabilityon some desired directions consequently leading to theimproved network performance To model the transmittingor receiving capability of an antenna we denote the antennagain by 119866 It is obvious that an omnidirectional antenna hasa constant antenna gain that is 119866

119900= 1 in all directions

We next give the antenna gain of a directional antennaSince it is difficult to model a realistic directional antennawith precise values of antenna gain in each direction [52] we


Directionalantenna

Main lobe120579m

Side-lobesback-lobes

Figure 2 Directional antenna model

use an approximate antenna model which was first proposedin [53] This model is also named as Keyhole due to thegeometrical analogy to the archaic keyhole in 2D planeas shown in Figure 2 In this model the sector with angle120579119898represents the main lobe of the antenna which has the

maximum gain denoted by 119866119898(where 120579

119898is also called the

antenna beamwidth) and the circular part represents theside-lobes and back-lobes with lower antenna gain denotedby 119866

119904 In particular when 119866

119898and 120579

119898are given [53 54] we

can calculate 119866119904as follows

119866119904=

2 minus 119866119898(1 minus cos (120579

1198982))

1 + cos (1205791198982)

(5)

3 Analysis on Eavesdropping Attacks

This section presents our analytical framework to modelthe eavesdropping activities in WNoT In particular we firstanalyze effective eavesdropping area in Section 31 which isthen used to derive the probability of eavesdropping attacks inSection 32 Section 33 presents the empirical results

31 Deterministic Path Loss Model We first consider that thechannel gain ismainly determined by the large-scale path losseffect [43] Thus the channel gain is given by

120574119894119895 (119903) = 119862 sdot 119866

119892sdot 119866

119890sdot1

119903120572 (6)

where119862 is a constant 119903 is the distance between the good nodeand the eavesdropper119866

119892and119866

119890are the antenna gains for the

good node and the eavesdropper respectively and 120572 is thepath loss exponent ranging from 2 to 4 [43]

As shown in Section 22 an eavesdropper can successfullywiretap a transmission if and only if itsΛ ge 120573 In other wordsthe probability of no transmission eavesdropped is given by119875(Λ lt 120573) Substituting (6) into inequality (4) and rearranging119875(Λ lt 120573) we have

119875 (Λ lt 120573) = 119875(P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 119903120572lt 120573)

= 119875(119903 gt (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

)

(7)

We then define a random variable 119877 as

119877 = (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

(8)

which is referred to the eavesdropping range of an eaves-dropper After substituting (8) into inequality (7) we have119875(Λ lt 120573) = 119875(119903 gt 119877) which implies that a transmissioncannot be eavesdropped by an eavesdropper if and only ifthe transmitter falls outside the eavesdropping range 119877 of theeavesdropper

We then analyze the effective eavesdropping area of aneavesdropper which is defined as 119864[120587119877

2] = 120587119864[1198772] where119864[1198772] is the second moment of the eavesdropping range 119877The effective eavesdropping area is a critical region that onlywhen the good node falls in this region its transmission canbe eavesdropped by eavesdroppers We then have

119864 [1205871198772] = 120587119864[(

119862 sdotP119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

] (9)

32 Probability of Eavesdropping Attacks We model thesuccessful chance of eavesdropping attacks by the probabilityof eavesdropping attacks denoted by 119875(119864) To derive 119875(119864) weneed to analyze the probability of no good node being eaves-dropped first We denote the number of good nodes falling inthe eavesdropping area by a random variable 119884 Since goodnodes are randomly distributed according to a homogeneousPoisson point process (as shown in Section 21) we then havethe probability of no good node falling in the eavesdroppingarea which is given by the following equation

119875 (119884 = 0) = 119890minus120588sdot119864[120587119877

2] (10)

We then can calculate 119875(119864) as follows

119875 (119864) = 1 minus 119875 (119884 = 0) = 1 minus 119890minus120588sdot119864[120587119877

2] (11)

After substituting 119864[1205871198772] in (11) by Right-Hand Side

(RHS) of (9) we have

119875 (119864) = 1

minus exp(minus120588 sdot 120587119864[(119862 sdotP

119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

]) (12)

The physical meaning of 119875(119864) is the probability that aneavesdropper can successfully eavesdrop at least one trans-mission in WNoT Besides as shown in (12) the probabilityof eavesdropping attacks heavily depends on the path losseffect Note that thismodel can be extended to amore generalcase with consideration of the shadow fading effect and theRayleigh fading effect which will be analyzed in Section 4

33 Empirical Results We conduct extensive simulations toverify the effectiveness and the accuracy of our proposedmodel In our simulations the probability of eavesdroppingattacks in a WNoT is calculated by

1198751015840(119864) =

Ψ

Ω (13)


0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Figure 3 Probability of eavesdropping attacks 119875(119864) with path losseffect only when 120572 = 25 35 and SINR threshold 120573 = 10 dB

where Ω and Ψ denote the number of total WNoT topolo-gies and the number of WNoT topologies that have beeneavesdropped respectively We say that a WNoT topology iseavesdropped when any smart object (node) in this topologyis eavesdropped Note that we denote the simulation resultsby 119875

1015840(119864) in order to differentiate it from the analyticalvalue 119875(119864) To minimize the impacts of the border effectswe conduct the simulations within an 119897 times 119897 area with theexclusion of the nodes falling in the outer box 1198971015840 times 1198971015840 where1198971015840 shall be significantly larger than 119897 [55] Note that 119897 ischosen as 3000m in our simulations We fix the numberof eavesdroppers and choose the node density 120588 for thegood nodes ranging from 10minus5 to 10minus1 The other systemparameters are selected as follows 119862 = 10 P

119905= 1mWatt

120578 = 001mWatt and 120573 = 10 dB We consider eavesdroppersequipped with either omnidirectional antenna (Omni) ordirectional antenna (Dir) while the good nodes are equippedwith omnidirectional antennas only

Figure 3 shows both the analytical results and the simu-lation results of the probability of eavesdropping attacks withthe path loss effect onlyThe curves and themarkers representthe analytical results and simulation results respectivelyIt is shown in Figure 3 that the simulation results have agood agreement with the analytical results implying that ourmodel is quite accurate

As shown in Figure 3 we also find that the probability ofeavesdropping attacks decreases with the increased path lossexponent 120572 implying that the path loss effect has the negativeimpact on eavesdropping attacks Besides we also find thatusing directional antennas at eavesdroppers can increase theprobability of eavesdropping attacks although this effect is notthat significant when the path loss effect is increased (eg 120572 =

35)

4 Impacts of Channel Randomness onEavesdropping Attacks

In this section we extend our analytical model in Section 3to more general cases in consideration of two different effectsof channel randomness (1) shadow fading effect and (2)

Rayleigh fading effect which will be presented in Sections41 and 42 respectively We then give the empirical resultsin Section 43

In order to model the two random effects we introducethe packet eavesdropping probability denoted by 119875

119864|Λ(119910)

which is defined as the probability that a packet is successfullyeavesdropped by an eavesdropper when the average signal-to-interference-noise ratio Λ = 119910

We then extend the analysis of eavesdropping range inSection 31 with consideration of the packet eavesdroppingprobability 119875

119864|Λ(119910) We first consider the case that the packet

eavesdropping probability 119875119864|Λ

(119910) tends to approach a stepfunction if good long code is used [56] In particular we havethe cumulative distribution function (CDF) of eavesdroppingrange 119877 which is defined as follows

119865119877 (119903) = 119875 [Λ (119903) lt 120573] = 119865

119877(

120578 sdot 120573

P119905sdot 119866

119892sdot 119866

119890

) (14)

In amore general casewhen119875119864|Λ

(119910) is not a step functionthe cumulative distribution function is

119865119877 (119903) = 1 minus int

+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)119875119864|Λ (119909) d119909 (15)

where 119891119877is the probability density function (PDF) of 119877

41 Shadow Fading Effect Following the similar approach[51] we can derive the probability density function of 119877 withconsideration of the shadow fading effect as follows

119891119877 (119909) =

1

radic2120587120590119909

sdot exp(minus1

2(ln119909 minus ln (119862 sdot 119903

minus120572)

120590)

2

)

(16)

where 119903 is the distance between a good node and aneavesdropper and 120590 is the standard deviation of the Gaussiandistribution describing the shadow fading effect

We then have the second moment of random variable 119877

given as follows

119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903 (17)

After substituting [1 minus 119865119897(120578120573P

119905119860119866)] in (17) with RHS of

(15) and RHS of (16) (note that 119875119864|Λ

(119886) = 1) we finally have

119864 [1198772] = int

+infin

0

2119903int+infin

120578120573P119905119860119866

1

radic2120587120590119886

sdot 119890minus(12)((ln 119886minusln(119862sdot119903minus120572))120590)2d119886 d119903

(18)


where 119860119866

= 119864[(119866119892119866119890)2120572

] which is defined as the effectiveantenna gain factor It is obvious that the effective antennagain factor depends on both the antenna gains and the pathloss effect

Let 119909 = (ln 119886 minus ln119862119903minus120572)120590 = ln(119886119903120572119862)120590 we then have

119864 [1198772] = int

+infin

0

2119903int+infin

ln(120578120573119903minus120572P119905119860119866119862)120590

1

radic2120587119890minus11990922d119909 d119903 (19)

Since the integrals converge absolutely applying Fubinirsquostheorem [57] we next get

119864 [1198772] = (

P119905119860119866119862

120578120573)

2120572

exp((radic2120590

120572)

2

) (20)

Finally we have the probability of eavesdropping attackswhich is given as the following equation

119875 (119864) = 1

minus exp(minus120588120587(P

119905119860119866119862

120578120573)

2120572

exp(radic2120590

120572)

2

) (21)

The probability of eavesdropping attacks in (21) is moregeneral than that in (12) This is because (21) becomes (12)when 120590 becomes 0 implying that there is no shadow fadingeffect and SINR is completely determined by the path losseffect

42 Rayleigh Fading Effect Rayleigh fading effect is a stochas-tic model for wireless propagation when there are a largenumber of statistically independent reflected and scatteredpaths from the transmitters to the receivers (or the eavesdrop-pers)

In the following procedure we consider the channelcondition with superimposed shadow fading and Rayleighfading effects We then derive the secondmoment of randomvariable 119877 Since (17) still holds we have

119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903

= int+infin

0

2119903int+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)

sdot 119875119864|Λ (119909) d119909 d119903

(22)

where 119891119877((120578119909P

119905119866119892119866119890) | 119903) which can be calculated by (16)

We next derive 119875119864|Λ

(119909) Since the instantaneous SINR isexponentially distributed with mean Λ = 119910 [51] with thegiven average SINR value Λ and the given SINR threshold120573 the packet eavesdropping probability 119875

119864|Λ(119910) can be

calculated by

119875119864|Λ

(119910) = int+infin

120573

119891Λ(119910) d119909 = int

+infin

120573

1

119910sdot 119890

minus119909119910d119909

= 119890minus120573119910

(23)

After substituting the corresponding parts in (22) by (16)and (23) we finally have the effective eavesdropping range asfollows

119864 [1198772] = int

+infin

0

int+infin

0

119890minus(120578sdot120573)(119909sdotP

119905sdot119860119866)sdot 2119903

1

radic2120587120590119909

sdot 119890minus(12)((ln119909minusln(119862sdot119903minus120572))120590)2d119903 d119909

= int+infin

minusinfin

int+infin

0

1

radic2120587119890minus11990922

sdot 2119903

sdot 119890minus(120578sdot120573sdot119903

120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903 d119909

(24)

where119860119866= 119864[(119866

119892119866119890)2120572

] is the effective antenna gain factorThe integral in (24) can be calculated by the following

equation [58]

int+infin

0

2119903 sdot 119890minus(120578sdot120573sdot119903

120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903

=2

120572Γ (

2

120572) sdot (

120578 sdot 120573 sdot 119890minus120590119909

119862 sdotP119905sdot 119860

119866

)

minus2120572

(25)

where Γ(sdot) represents the general Gamma functionSubstituting (25) into (24) and applying it to (11) we

finally have

119875 (119864) = 1 minus 119890minus120588120587(2120572)Γ(2120572)sdot((120578sdot120573)(119862sdotP

119905sdot119860119866))minus2120572

sdot119890(radic2120590120572)

2

(26)

43 Empirical Results We have conducted extensive sim-ulations to evaluate the accuracy of our extended modelIn order to compare the new results with those under thecase without shadowing effects in Section 33 we choose thesame system parameters as those in Section 33 Note thatin order to eliminate the impacts of the border effect theborder area of the simulation area shall be slightly increasedSimilarly we also consider eavesdroppers equipped witheither omnidirectional antennas or directional antennas

Figure 4 shows the empirical results of the probabilityof eavesdropping attacks with shadow fading effects wherethe shadow fading deviation 120590 = 3 Note that the curvesand the markers represent the analytical results and simu-lation results respectively Figure 3 also indicates that thesimulation results match the analytical results implying theaccuracy of our model

As shown in Figure 4 we find that the probability ofeavesdropping attacks is affected by both the path loss effectand the shadow fading effect In particular 119875(119864) decreaseswith the increased path loss exponent 120572 implying that thepath loss effect is detrimental In other words the path losseffect will decrease the probability of eavesdropping attackswhich agrees with the previous results without the shadowingeffect (see Figure 3) On the contrary the shadow fading effectis beneficial More specifically if we compare Figure 4 withFigure 3 we can find that 119875(119864) increases with the increasedvalues of the shadow fading deviation 120590 (eg 120590 is increasedfrom0 to 3)This effect is remarkablewhen the path loss effectis less notable (eg 120572 = 25) However119875(119864) does not increase


Table 2 Comparison between the results under the channel with shadow fading effect only and the results under the channel withsuperimposed shadowing and Rayleigh fading effects when 120572 = 3 120590 = 3 and SINR threshold 120573 = 10 dB

Node density Shadow fading effect only (Figure 4) Superimposed shadow fading andRayleigh fading effects (Figure 5)

120588 Omni Dir Omni Dir1 times 10

minus5 00050 00059 00045 (minus1000) 00053 (minus1017)1 times 10

minus4 00489 00572 00443 (minus941) 00518 (minus944)1 times 10minus3 03945 04453 03642 (minus768) 04126 (minus734)1 times 10minus2 09934 09972 09892 (minus420) 09951 (minus210)

0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus5

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Dir_anaOmni_ana

Dir_simOmni_sim

Figure 4 Probability of eavesdropping attacks119875(119864)with shadowingeffect (120590 = 3) only when 120572 = 25 35 and SINR threshold 120573 = 10 dB

significantly with the increased values of 120590 when 120572 = 35Furthermore we also find that using directional antennas ateavesdroppers can increase the probability of eavesdroppingattacks with consideration of the shadowing effect

We then investigate the probability of eavesdroppingattacks under the channel with the superimposed shadowfading and Rayleigh fading effects Figure 5 shows the resultswith the presence of both shadow fading and Rayleigh fadingeffects where the shadow fading deviation 120590 = 3 As shownin Figure 5 we find that the probability of eavesdroppingattacks is affected by both the shadow fading effect and theRayleigh fading effect Moreover Figure 5 also indicates thatRayleigh fading effect has a negative impact on the probabilityof eavesdropping attacks even though it is not that noticeablecompared with the path loss effect

To illustrate the detrimental effect of Rayleigh fadingeffect we conduct comparative study on the numerical resultsof the probability of eavesdropping attacks119875(119864) In particularTable 2 illustrates the comparison between the results of 119875(119864)

under the channel with shadow fading effect only and theresults under the channel with the superimposed shadowfading effect and Rayleigh fading effect when 120572 = 3 and120590 = 3 corresponding to Figures 4 and 5 respectively

0

01

02

03

04

05

06

07

08

09

10

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus3

10minus2

10minus1

Node density

Dir_anaOmni_ana

Dir_simOmni_sim

120572 = 25 120572 = 35

Figure 5 Probability of eavesdropping attacks 119875(119864) with superim-posed shadowing effect and Rayleigh fading effect when 120590 = 3 andSINR threshold 120573 = 10 dB

To make it clearer we italicize the results with directionalantennas in Table 2 It is shown in Table 2 that Rayleighfading effect will decrease the probability of eavesdroppingattacks compared with the results under the channel withthe shadow fading effect only For example Rayleigh fadingeffect leads to the decrement of nearly 10 in terms of theprobability of eavesdropping attacks when the node density120588 = 10

minus5 Besides Table 2 also indicates that using directionalantennas at eavesdroppers can increase the probability ofeavesdropping attacks which is similar to the previousfindings

We also give the results under the scenario of eavesdrop-ping attacks with Rayleigh fading effect only Figure 6 showsthe empirical results of the probability of eavesdroppingattacks under the channel with Rayleigh fading effect onlywhere120590 = 0 indicating no shadow fading effect Similar to theprevious results we also denote the analytical results by thecurves and the simulation results by the markers as shownin Figure 6 It is shown in Figure 6 that the simulation resultshave a good agreement with the analytical results implyingthat our analytical model is quite accurate


0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Figure 6 Probability of eavesdropping attacks 119875(119864) with Rayleighfading effect only (without shadowing effect) where SINR threshold120573 = 10 dB and 120590 = 0

As shown in Figure 6 we can see that the probabilityof eavesdropping attacks also depends on both the pathloss effect and Rayleigh fading effect In particular 119875(119864)

drops significantly when the path loss effect becomes morenotable (eg 120572 = 35) as shown in Figure 6 Besides underthe wireless channel with Rayleigh fading effect 119875(119864) inFigure 6 is even lower than that without Rayleigh fadingeffect in Figure 3 implying that Rayleigh fading effect is alsodetrimental to the eavesdropping attacks The reason mayowe to the counteracting effect of the multipath scatteringsignals under the channel with Rayleigh fading effect [43]

44 Discussions and Implications of Our Results Our simu-lation results imply that using directional antennas at eaves-droppers in WNoT can significantly increase the probabilityof eavesdroppingThus directional antennas are beneficial toeavesdroppers The improvement mainly owes to the effectthat a directional antenna can accumulate the receivingcapability of desired directions However we can not ignoreanother effect that a directional antenna can also narrowthe angle of the receiving directions More specifically withthe increased path loss (ie the larger 120572) the second effectcan even counteract the first effect Take Figure 6 as anexample The gap between the results of omnidirectionaleavesdroppers and the results of directional eavesdropperswith 120572 = 25 is significantly bigger than that with 120572 = 35

Secondly as shown in our results both the path losseffect andRayleigh fading are always detrimental to the eaves-dropping probability while shadowing effect and directionalantennas are beneficial to the eavesdropping probabilityOur findings are useful to help to design more effectiveantieavesdropping schemes in WNoT This is because weneed the knowledge of eavesdroppers (such as the channel

characteristics) so thatwe can design the light-weight encryp-tion algorithms as indicated in the previous studies [37ndash42]Besides we only need to take antieavesdropping measures inthe area or the direction that is vulnerable to eavesdroppingattacks so that the security cost due to the computationalcomplexity can be greatly saved For example we can generatethe noise only in the direction of eavesdroppers when theeavesdroppers are equipped with directional antennas whilethere is no noise in other directions This new scheme mayhave a better performance than the existing one [35]

5 Conclusion

In this paper we propose an analytical model to investigatethe eavesdropping probability in Wireless Net of Things(WNoT) with consideration of channel randomness includ-ing the path loss effect the shadow fading effect and Rayleighfading effect After conducting extensive simulations weshow that our model is quite accurate Besides we have alsoshown that the eavesdropping probability heavily dependson the path loss effect the shadow fading effect andRayleigh fading effect More specifically we find that theeavesdropping probability increases when the shadow fadingfactor 120590 increases and decreases when the path loss effectincreases implying that the path loss effect is detrimentalto the eavesdropping attacks while the shadow fading isbeneficial to the eavesdropping attacks Moreover similarto the path loss effect Rayleigh fading is also destructiveto the eavesdropping attacks Furthermore our results alsoindicate that using directional antennas at eavesdropperscan significantly improve the probability of eavesdroppingattacks

Notation and Symbols

A 2D area that nodes are randomlydistributed

120588 Density of the homogeneous Poissonpoint process

P119905 Transmission power of nodes

119903 Distance between the good node and theeavesdropper

120574119894119895(119903) Channel gain from a good node 119894 to an

eavesdropper 119895 at a distance 119903

Λ SINR at an eavesdropper120573 Threshold value of SINR for

eavesdropping a node successfully120578 Power of the white noise119873 Number of good nodes120572 Path loss exponent119866119898 119866

119904 Antenna gain of main lobe antenna gainof side-lobe

120579119898 Main lobe beam-width of the keyhole

antenna119866119892 119866

119890 Antenna gain of good node antenna gainof eavesdropper

119875(119864) Probability of eavesdropping attacks119897 Side length of topology area119877 Eavesdropping range of an eavesdropper


Ω Number of total WNoT topologiesΨ Number of WNoT topologies that have

been eavesdroppedΛ Average SINR value119875119864|Λ

(119910) Packet eavesdropping probability when theaverage SINR is 119910

120590 Standard deviation of the Gaussian distri-bution describing the shadow fading effect

119860119866 Effective antenna gain factor

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The work described in this paper was partially supported byMacao Science and Technology Development Fund underGrant no 0962013A3 and Grant no 1042014A3 andsupported by Innovation Norway through the project ldquoGCEBLUE Maritime Big Datardquo The authors would like to thankGordon K-T Hon for his helpful comments that greatlyimprove the quality of this paper

References

[1] L Atzori A Iera and G Morabito ldquoThe internet of things asurveyrdquoComputer Networks vol 54 no 15 pp 2787ndash2805 2010

[2] D Miorandi S Sicari F De Pellegrini and I Chlamtac ldquoInter-net of things vision applications and research challengesrdquo AdHoc Networks vol 10 no 7 pp 1497ndash1516 2012

[3] ISOIEC 18000 2013 httpenwikipediaorgwikiISOIEC18000

[4] J Yick B Mukherjee and D Ghosal ldquoWireless sensor networksurveyrdquoComputerNetworks vol 52 no 12 pp 2292ndash2330 2008

[5] C Dixon R Mahajan S Agarwal et al ldquoAn operating systemfor the homerdquo in Proceedings of the 9th USENIX Conference onNetworked SystemsDesign and Implementation (NSDI rsquo12) p 25USENIX Association San Jose Calif USA April 2012

[6] K Habib A Torjusen and W Leister ldquoSecurity analysis ofa patient monitoring system for the Internet of Things ineHealthrdquo in Proceedings of the International Conference oneHealth Telemedicine and Social Medicine (eTELEMED rsquo15)Lisbon Portugal February 2015

[7] Z Fan P Kulkarni S Gormus et al ldquoSmart grid com-munications overview of research challenges solutions andstandardization activitiesrdquo IEEE Communications Surveys andTutorials vol 15 no 1 pp 21ndash38 2013

[8] H Wang O Osen G Li W Li H-N Dai and W Zeng ldquoBigdata and industrial internet of things for the maritime industryin Northwestern Norwayrdquo in Proceedings of the IEEE Region 10Conference (TENCON rsquo15) Macau China November 2015

[9] IEEE 802154 2011 httpstandardsieeeorggetieee802down-load802154-2011pdf

[10] Bluetooth Core Specification 42 2014 httpwwwbluetoothorg

[11] J Granjal E Monteiro and J Sa Silva ldquoSecurity for the internetof things a survey of existing protocols and open research

issuesrdquo IEEE Communications Surveys amp Tutorials vol 17 no3 pp 1294ndash1312 2015

[12] A GrauHow to Build a Safer Internet ofThings IEEE Spectrum2015

[13] S Sicari A Rizzardi L A Grieco and A Coen-PorisinildquoSecurity privacy and trust in Internet of Things the roadaheadrdquo Computer Networks vol 76 pp 146ndash164 2015

[14] G Strazdins and H Wang ldquoOpen security and privacy chal-lenges for the internet of thingsrdquo in Proceedings of the 10thInternational Conference on Information Communications andSignal Processing (ICICS rsquo15) 2015

[15] C Cai Y Cai X Zhou W Yang and W Yang ldquoWhen doesrelay transmission give a more secure connection in wireless adhoc networksrdquo IEEE Transactions on Information Forensics andSecurity vol 9 no 4 pp 624ndash632 2014

[16] N A Alrajeh S Khan and B Shams ldquoIntrusion detectionsystems in wireless sensor networks a reviewrdquo InternationalJournal of Distributed Sensor Networks vol 2013 Article ID167575 7 pages 2013

[17] N Meghanathan ldquoA survey on the communication protocolsand security in cognitive radio networksrdquo International Journalof CommunicationNetworks and Information Security vol 5 no1 pp 19ndash38 2013

[18] M Anand Z G Ives and I Lee ldquoQuantifying eavesdroppingvulnerability in sensor networksrdquo inProceedings of the 2nd Inter-national Workshop on Data Management for Sensor Networks(DMSN rsquo05) pp 3ndash9 August 2005

[19] J-C Kao and R Marculescu ldquoEavesdropping minimization viatransmission power control in ad-hoc wireless networksrdquo inProceedings of the 3rd Annual IEEE Communications Societyon Sensor and Ad Hoc Communications and Networks (SECONrsquo06) vol 2 pp 707ndash714 IEEE Reston Va USA September2006

[20] H-N Dai D Li and R C-W Wong ldquoExploring securityimprovement of wireless networks with directional antennasrdquoin Proceedings of the IEEE 36th Conference on Local ComputerNetworks (LCN rsquo11) pp 191ndash194 Bonn Germany October 2011

[21] X Lu F Wicker P Lio and D Towsley ldquoSecurity estimationmodel with directional antennasrdquo in Proceedings of the IEEEMilitary Communications Conference (MILCOM rsquo08) pp 1ndash6IEEE San Diego Calif USA November 2008

[22] Q Wang H-N Dai and Q Zhao ldquoEavesdropping securityin wireless Ad Hoc networks with directional antennasrdquo inProceedings of the 22nd Wireless and Optical CommunicationsConference (WOCC rsquo13) pp 687ndash692 May 2013

[23] H-N Dai Q Wang D Li and R C-W Wong ldquoOn eaves-dropping attacks in wireless sensor networks with directionalantennasrdquo International Journal of Distributed Sensor Networksvol 2013 Article ID 760834 13 pages 2013

[24] E Alsaadi and A Tubaishat ldquoInternet of things features chal-lenges and vulnerabilitiesrdquo International Journal of AdvancedComputer Science and Information Technology vol 4 no 1 pp1ndash13 2015

[25] F Anjum and P Mouchtaris Security for Wireless Ad HocNetworks Wiley-Interscience 1st edition 2007

[26] R Want ldquoAn introduction to RFID technologyrdquo IEEE PervasiveComputing vol 5 no 1 pp 25ndash33 2006

[27] IEEE 80211a-1999 httpstandardsieeeorggetieee802down-load80211a-1999pdf

[28] IEEE 80211i-2004 httpstandardsieeeorggetieee802down-load80211i-2004pdf


[29] D Wagner B Schneier and J Kelsey ldquoCryptanalysis ofthe cellular message encryption algorithmrdquo in Advances inCryptologymdashCRYPTO rsquo97 vol 1294 of Lecture Notes in Com-puter Science pp 526ndash537 Springer Berlin Germany 1997

[30] M Turkanovic B Brumen and M Holbl ldquoA novel userauthentication and key agreement scheme for heterogeneous adhoc wireless sensor networks based on the Internet of Thingsnotionrdquo Ad Hoc Networks vol 20 pp 96ndash112 2014

[31] A-R Sadeghi C Wachsmann and M Waidner ldquoSecurityand privacy challenges in industrial internet of thingsrdquo inProceedings of the 52nd Annual Design Automation Conference(DAC rsquo15) San Francisco Calif USA June 2015

[32] S L Keoh S S Kumar and H Tschofenig ldquoSecuring theinternet of things a standardization perspectiverdquo IEEE Internetof Things Journal vol 1 no 3 pp 265ndash275 2014

[33] Z Yan P Zhang and A V Vasilakos ldquoA survey on trustmanagement for internet of thingsrdquo Journal of Network andComputer Applications vol 42 pp 120ndash134 2014

[34] B Azimi-Sadjadi A Kiayias AMercado and B Yener ldquoRobustkey generation from signal envelopes in wireless networksrdquoin Proceedings of the 14th ACM Conference on Computer andCommunications Security (CCS rsquo07) pp 401ndash410 Denver ColoUSA November 2007

[35] O Savry F Pebay-Peyroula F Dehmas G Robert and JReverdy ldquoRFID noisy reader how to prevent from eavesdrop-ping on the communicationrdquo in Cryptographic Hardware andEmbedded SystemsmdashCHES 2007 vol 4727 of Lecture Notesin Computer Science pp 334ndash345 Springer Berlin Germany2007

[36] A Mukherjee S A A Fakoorian J Huang and A LSwindlehurst ldquoPrinciples of physical layer security in multiuserwireless networks a surveyrdquo IEEE Communications Surveys andTutorials vol 16 no 3 pp 1550ndash1573 2014

[37] G P Hancke ldquoPractical eavesdropping and skimming attackson high-frequency RFID tokensrdquo Journal of Computer Securityvol 19 no 2 pp 259ndash288 2011

[38] F Oggier and B Hassibi ldquoThe secrecy capacity of the MIMOwiretap channelrdquo IEEE Transactions on InformationTheory vol57 no 8 pp 4961ndash4972 2011

[39] R Liu T Liu H V Poor and S Shamai ldquoMultiple-inputmultiple-output gaussian broadcast channels with confidentialmessagesrdquo IEEETransactions on InformationTheory vol 56 no9 pp 4215ndash4227 2010

[40] X He A Khisti and A Yener ldquoMIMOmultiple access channelwith an arbitrarily varying eavesdropper secrecy degrees offreedomrdquo IEEE Transactions on InformationTheory vol 59 no8 pp 4733ndash4745 2013

[41] I Hero ldquoSecure space-time communicationrdquo IEEETransactionson Information Theory vol 49 no 12 pp 3235ndash3249 2003

[42] Y Zou B Champagne W-P Zhu and L Hanzo ldquoRelay-selection improves the security-reliability trade-off in cognitiveradio systemsrdquo IEEE Transactions on Communications vol 63no 1 pp 215ndash228 2015

[43] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall Upper Saddle River NJ USA 2nd edition2002

[44] A Sawadi An RFID directional antenna for location positioning[PhD dissertation] University of Windsor 2012

[45] D M Dobkin The RF in RFID Passive UHF RFID in PracticeNewnes 2nd edition 2012

[46] X Li H-N Dai and Q Zhao ldquoAn analytical model oneavesdropping attacks in wireless networksrdquo in Proceedings ofthe IEEE International Conference on Communication Systems(ICCS rsquo14) pp 538ndash542 IEEE Macau China November 2014

[47] S Mathur W Trappe N Mandayam C Ye and A ReznikldquoRadio-telepathy extracting a secret key from an unauthenti-cated wireless channelrdquo in Proceedings of the ACM 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 128ndash139 ACM San Francisco Calif USASeptember 2008

[48] F Huo and G Gong ldquoA new efficient physical layer OFDMencryption schemerdquo in Proceedings of the 33rd IEEE Conferenceon Computer Communications (INFOCOM rsquo14) pp 1024ndash1032Toronto Canada May 2014

[49] P Gupta and P R Kumar ldquoThe capacity of wireless networksrdquoIEEETransactions on InformationTheory vol 46 no 2 pp 388ndash404 2000

[50] M Franceschetti O Dousse D N Tse and P Thiran ldquoClosingthe gap in the capacity of wireless networks via percolationtheoryrdquo IEEE Transactions on Information Theory vol 53 no3 pp 1009ndash1018 2007

[51] D Miorandi E Altman and G Alfano ldquoThe impact of channelrandomness on coverage and connectivity of ad hoc and sensornetworksrdquo IEEE Transactions on Wireless Communications vol7 no 3 pp 1062ndash1072 2008

[52] C A Balanis AntennaTheory Analysis and Design JohnWileyamp Sons New York NY USA 2nd edition 1997

[53] R Ramanathan ldquoOn the performance of ad hoc networkswith beamforming antennasrdquo in Proceedings of the 2nd ACMInternational Symposium on Mobile Ad Hoc Networking ampComputing (MobiHoc rsquo01) pp 95ndash105 ACM Long Beach CalifUSA October 2001

[54] Q Wang H-N Dai and Q Zhao ldquoConnectivity of wirelessAd Hoc networks impacts of antenna modelsrdquo in Proceedingsof the 14th International Conference on Parallel and DistributedComputing Applications and Technologies (PDCAT rsquo13) pp298ndash303 Taipei Taiwan December 2013

[55] C Bettstetter ldquoOn the connectivity of ad hoc networksrdquo TheComputer Journal vol 47 no 4 pp 432ndash447 2004

[56] M Zorzi and S Pupolin ldquoOutage probability in multipleaccess packet radio networks in the presence of fadingrdquo IEEETransactions on Vehicular Technology vol 43 no 3 pp 604ndash610 2002

[57] J Borwein D Bailey and R Girgensohn Experimentationin Mathematics Computational Paths to Discovery Wellesley2004

[58] I S Gradshteyn and I M Ryzhik Table of Integrals Series andProducts Academic Press New York NY USA 7th edition2007

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



RFID-reader

Eavesdropper

Eavesdropper

RFIDRFID

RFID-reader

Figure 1 An example of eavesdropping activities in WNoT where there are several eavesdroppers who are wiretapping the confidentialongoing communications between RFID tags and RFID-readers

RFID-readers In this environment the confidential com-munications between RFID-readers and RFID tags can beeasily wiretapped by eavesdroppers since it is difficult toapply antieavesdropping countermeasures (eg encryptions)in this scenario due to the limited computational capabilityand the energy-constraint of RFID tagsNote thatwe considerthe far-field wireless communications in this scenario [26]

11 Related Works Most of current studies have been con-centrated on protecting the confidential communications ofsmart objects in WNoT which are also named as good nodesin this paper Encryption is one of the most commonly usedtechniques to protect the confidential communications inwireless personal area networks [11] wireless local area net-works (eg WEP [27] WPA and WPA2 [28]) wireless cel-lular networks (eg Cellular Message Encryption Algorithm[29]) and encryption algorithms forwireless sensor networks[30] However it is infeasible to apply cryptography-basedtechniques in WNoT due to the following reasons (a) theinferior computational capability of smart objects [2] (b) thelimited battery power of smart objects (eg the passive RFIDscan only harvest the energy from the readers) [1 31] and(c) the difficulty of managing the widely distributed smartobjects in centralized manner which is the necessity for theencryption algorithms [11 32 33]

An alternate approach is either to design light-weightedencryption schemes [34] or to generate noise to limit theamount of information that can be extracted by an eavesdrop-per [35 36] However one of the most important premises ofthe above schemes is that we shall have enough knowledge ofthe channel condition of eavesdroppers as indicated in [37ndash42] which nevertheless has received little attention Besidesthe wireless channel in WNoT fluctuates from time to timeand is affected by various fading effects including the path

loss the shadowing effect and the multipath effect [43]Furthermoremost of current studies inWNoT only considerthe nodes equipped with omnidirectional antennas whichradiatereceive RF signals in all directions (ie a less efficientway to propagate RF signals) As shown in some of themost recent studies [44 45] directional antennas can beused at readers Compared with omnidirectional antennasdirectional antennas can concentrate the transmissions tosome desired directions so that the performance can befurther improved

However little attention has been paid to investigatingthe eavesdropping behaviors conducted by the eavesdroppersin WNoT which is nevertheless important for us to offerbetter protection on the confidential communications sincewe can design antieavesdropping schemeswith clearer targetsif we have a better knowledge on the eavesdroppers althoughwe conducted a preliminary study on the eavesdroppingprobability of wireless ad hoc networks in [46] But thispaper is significantly different from our previous work [46]in the following aspects (1) we are concerned with theeavesdropping activities in WNoT in this paper while theprevious paper investigated the eavesdropping attacks inwireless ad hoc networks (2) we propose a novel analyticalmodel on the eavesdropping probability in this paper wherethe channel randomness (including Rayleigh fading effectand the shadowing effects) is considered while the previouspaper only considered a simplified geometric model (3) weconduct extensive simulations to verify the accuracy of ourproposed model in this paper while the previous paper onlypresented the numerical results

12 Contributions The aforementioned issues motivate usto conduct an investigation on the eavesdropping attacks inWNoT In this paper we analyze the eavesdropping activities









2 Models



119891119873 (119899) =

(120588A)119899

119899119890minus120588A

(1)








Λ =P

119905sdot 120574

119894119895 (119903)

120578 + sum119873

119896 =119894P

119905sdot 120574

119896119895 (119903) (2)



Λ ge 120573 (3)



Λ =P

119905sdot 120574

119894119895 (119903)

120578ge 120573 (4)





Directionalantenna

Main lobe120579m








119898and 120579

119898are given [53 54] we


119866119904=

2 minus 119866119898(1 minus cos (120579

1198982))

1 + cos (1205791198982)

(5)




120574119894119895 (119903) = 119862 sdot 119866

119892sdot 119866

119890sdot1

119903120572 (6)


119892and119866




119875 (Λ lt 120573) = 119875(P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 119903120572lt 120573)

= 119875(119903 gt (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

)

(7)


119877 = (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

(8)




119864 [1205871198772] = 120587119864[(

119862 sdotP119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

] (9)


119875 (119884 = 0) = 119890minus120588sdot119864[120587119877

2] (10)



2] (11)



119875 (119864) = 1


119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

]) (12)



1198751015840(119864) =

Ψ

Ω (13)


0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35




119905= 1mWatt




35)





119864|Λ(119910)






119865119877 (119903) = 119875 [Λ (119903) lt 120573] = 119865

119877(

120578 sdot 120573

P119905sdot 119866

119892sdot 119866

119890

) (14)



119865119877 (119903) = 1 minus int

+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)119875119864|Λ (119909) d119909 (15)



119891119877 (119909) =

1

radic2120587120590119909

sdot exp(minus1

2(ln119909 minus ln (119862 sdot 119903

minus120572)

120590)

2

)

(16)



given as follows

119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903 (17)


119905119860119866)] in (17) with RHS of



119864 [1198772] = int

+infin

0

2119903int+infin

120578120573P119905119860119866

1

radic2120587120590119886


(18)


where 119860119866

= 119864[(119866119892119866119890)2120572



119864 [1198772] = int

+infin

0

2119903int+infin

ln(120578120573119903minus120572P119905119860119866119862)120590

1

radic2120587119890minus11990922d119909 d119903 (19)


119864 [1198772] = (

P119905119860119866119862

120578120573)

2120572

exp((radic2120590

120572)

2

) (20)


119875 (119864) = 1


119905119860119866119862

120578120573)

2120572

exp(radic2120590

120572)

2

) (21)




119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903

= int+infin

0

2119903int+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)

sdot 119875119864|Λ (119909) d119909 d119903

(22)

where 119891119877((120578119909P




119864|Λ(119910) can be

calculated by

119875119864|Λ


120573

119891Λ(119910) d119909 = int

+infin

120573

1

119910sdot 119890

minus119909119910d119909

= 119890minus120573119910

(23)


119864 [1198772] = int

+infin

0

int+infin

0

119890minus(120578sdot120573)(119909sdotP

119905sdot119860119866)sdot 2119903

1

radic2120587120590119909


= int+infin

minusinfin

int+infin

0

1

radic2120587119890minus11990922

sdot 2119903


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903 d119909

(24)

where119860119866= 119864[(119866

119892119866119890)2120572


equation [58]

int+infin

0


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903

=2

120572Γ (

2

120572) sdot (

120578 sdot 120573 sdot 119890minus120590119909

119862 sdotP119905sdot 119860

119866

)

minus2120572

(25)


finally have


119905sdot119860119866))minus2120572

sdot119890(radic2120590120572)

2

(26)










0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus5

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Dir_anaOmni_ana

Dir_simOmni_sim






0

01

02

03

04

05

06

07

08

09

10

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus3

10minus2

10minus1

Node density

Dir_anaOmni_ana

Dir_simOmni_sim

120572 = 25 120572 = 35






0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35







5 Conclusion













antenna119866119892 119866











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











2 Models



119891119873 (119899) =

(120588A)119899

119899119890minus120588A

(1)








Λ =P

119905sdot 120574

119894119895 (119903)

120578 + sum119873

119896 =119894P

119905sdot 120574

119896119895 (119903) (2)



Λ ge 120573 (3)



Λ =P

119905sdot 120574

119894119895 (119903)

120578ge 120573 (4)





Directionalantenna

Main lobe120579m








119898and 120579

119898are given [53 54] we


119866119904=

2 minus 119866119898(1 minus cos (120579

1198982))

1 + cos (1205791198982)

(5)




120574119894119895 (119903) = 119862 sdot 119866

119892sdot 119866

119890sdot1

119903120572 (6)


119892and119866




119875 (Λ lt 120573) = 119875(P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 119903120572lt 120573)

= 119875(119903 gt (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

)

(7)


119877 = (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

(8)




119864 [1205871198772] = 120587119864[(

119862 sdotP119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

] (9)


119875 (119884 = 0) = 119890minus120588sdot119864[120587119877

2] (10)



2] (11)



119875 (119864) = 1


119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

]) (12)



1198751015840(119864) =

Ψ

Ω (13)


0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35




119905= 1mWatt




35)





119864|Λ(119910)






119865119877 (119903) = 119875 [Λ (119903) lt 120573] = 119865

119877(

120578 sdot 120573

P119905sdot 119866

119892sdot 119866

119890

) (14)



119865119877 (119903) = 1 minus int

+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)119875119864|Λ (119909) d119909 (15)



119891119877 (119909) =

1

radic2120587120590119909

sdot exp(minus1

2(ln119909 minus ln (119862 sdot 119903

minus120572)

120590)

2

)

(16)



given as follows

119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903 (17)


119905119860119866)] in (17) with RHS of



119864 [1198772] = int

+infin

0

2119903int+infin

120578120573P119905119860119866

1

radic2120587120590119886


(18)


where 119860119866

= 119864[(119866119892119866119890)2120572



119864 [1198772] = int

+infin

0

2119903int+infin

ln(120578120573119903minus120572P119905119860119866119862)120590

1

radic2120587119890minus11990922d119909 d119903 (19)


119864 [1198772] = (

P119905119860119866119862

120578120573)

2120572

exp((radic2120590

120572)

2

) (20)


119875 (119864) = 1


119905119860119866119862

120578120573)

2120572

exp(radic2120590

120572)

2

) (21)




119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903

= int+infin

0

2119903int+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)

sdot 119875119864|Λ (119909) d119909 d119903

(22)

where 119891119877((120578119909P




119864|Λ(119910) can be

calculated by

119875119864|Λ


120573

119891Λ(119910) d119909 = int

+infin

120573

1

119910sdot 119890

minus119909119910d119909

= 119890minus120573119910

(23)


119864 [1198772] = int

+infin

0

int+infin

0

119890minus(120578sdot120573)(119909sdotP

119905sdot119860119866)sdot 2119903

1

radic2120587120590119909


= int+infin

minusinfin

int+infin

0

1

radic2120587119890minus11990922

sdot 2119903


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903 d119909

(24)

where119860119866= 119864[(119866

119892119866119890)2120572


equation [58]

int+infin

0


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903

=2

120572Γ (

2

120572) sdot (

120578 sdot 120573 sdot 119890minus120590119909

119862 sdotP119905sdot 119860

119866

)

minus2120572

(25)


finally have


119905sdot119860119866))minus2120572

sdot119890(radic2120590120572)

2

(26)










0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus5

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Dir_anaOmni_ana

Dir_simOmni_sim






0

01

02

03

04

05

06

07

08

09

10

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus3

10minus2

10minus1

Node density

Dir_anaOmni_ana

Dir_simOmni_sim

120572 = 25 120572 = 35






0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35







5 Conclusion













antenna119866119892 119866











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Directionalantenna

Main lobe120579m








119898and 120579

119898are given [53 54] we


119866119904=

2 minus 119866119898(1 minus cos (120579

1198982))

1 + cos (1205791198982)

(5)




120574119894119895 (119903) = 119862 sdot 119866

119892sdot 119866

119890sdot1

119903120572 (6)


119892and119866




119875 (Λ lt 120573) = 119875(P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 119903120572lt 120573)

= 119875(119903 gt (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

)

(7)


119877 = (P

119905sdot 119862 sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

1120572

(8)




119864 [1205871198772] = 120587119864[(

119862 sdotP119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

] (9)


119875 (119884 = 0) = 119890minus120588sdot119864[120587119877

2] (10)



2] (11)



119875 (119864) = 1


119905sdot 119866

119892sdot 119866

119890

120578 sdot 120573)

2120572

]) (12)



1198751015840(119864) =

Ψ

Ω (13)


0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35




119905= 1mWatt




35)





119864|Λ(119910)






119865119877 (119903) = 119875 [Λ (119903) lt 120573] = 119865

119877(

120578 sdot 120573

P119905sdot 119866

119892sdot 119866

119890

) (14)



119865119877 (119903) = 1 minus int

+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)119875119864|Λ (119909) d119909 (15)



119891119877 (119909) =

1

radic2120587120590119909

sdot exp(minus1

2(ln119909 minus ln (119862 sdot 119903

minus120572)

120590)

2

)

(16)



given as follows

119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903 (17)


119905119860119866)] in (17) with RHS of



119864 [1198772] = int

+infin

0

2119903int+infin

120578120573P119905119860119866

1

radic2120587120590119886


(18)


where 119860119866

= 119864[(119866119892119866119890)2120572



119864 [1198772] = int

+infin

0

2119903int+infin

ln(120578120573119903minus120572P119905119860119866119862)120590

1

radic2120587119890minus11990922d119909 d119903 (19)


119864 [1198772] = (

P119905119860119866119862

120578120573)

2120572

exp((radic2120590

120572)

2

) (20)


119875 (119864) = 1


119905119860119866119862

120578120573)

2120572

exp(radic2120590

120572)

2

) (21)




119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903

= int+infin

0

2119903int+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)

sdot 119875119864|Λ (119909) d119909 d119903

(22)

where 119891119877((120578119909P




119864|Λ(119910) can be

calculated by

119875119864|Λ


120573

119891Λ(119910) d119909 = int

+infin

120573

1

119910sdot 119890

minus119909119910d119909

= 119890minus120573119910

(23)


119864 [1198772] = int

+infin

0

int+infin

0

119890minus(120578sdot120573)(119909sdotP

119905sdot119860119866)sdot 2119903

1

radic2120587120590119909


= int+infin

minusinfin

int+infin

0

1

radic2120587119890minus11990922

sdot 2119903


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903 d119909

(24)

where119860119866= 119864[(119866

119892119866119890)2120572


equation [58]

int+infin

0


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903

=2

120572Γ (

2

120572) sdot (

120578 sdot 120573 sdot 119890minus120590119909

119862 sdotP119905sdot 119860

119866

)

minus2120572

(25)


finally have


119905sdot119860119866))minus2120572

sdot119890(radic2120590120572)

2

(26)










0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus5

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Dir_anaOmni_ana

Dir_simOmni_sim






0

01

02

03

04

05

06

07

08

09

10

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus3

10minus2

10minus1

Node density

Dir_anaOmni_ana

Dir_simOmni_sim

120572 = 25 120572 = 35






0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35







5 Conclusion













antenna119866119892 119866











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35




119905= 1mWatt




35)





119864|Λ(119910)






119865119877 (119903) = 119875 [Λ (119903) lt 120573] = 119865

119877(

120578 sdot 120573

P119905sdot 119866

119892sdot 119866

119890

) (14)



119865119877 (119903) = 1 minus int

+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)119875119864|Λ (119909) d119909 (15)



119891119877 (119909) =

1

radic2120587120590119909

sdot exp(minus1

2(ln119909 minus ln (119862 sdot 119903

minus120572)

120590)

2

)

(16)



given as follows

119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903 (17)


119905119860119866)] in (17) with RHS of



119864 [1198772] = int

+infin

0

2119903int+infin

120578120573P119905119860119866

1

radic2120587120590119886


(18)


where 119860119866

= 119864[(119866119892119866119890)2120572



119864 [1198772] = int

+infin

0

2119903int+infin

ln(120578120573119903minus120572P119905119860119866119862)120590

1

radic2120587119890minus11990922d119909 d119903 (19)


119864 [1198772] = (

P119905119860119866119862

120578120573)

2120572

exp((radic2120590

120572)

2

) (20)


119875 (119864) = 1


119905119860119866119862

120578120573)

2120572

exp(radic2120590

120572)

2

) (21)




119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903

= int+infin

0

2119903int+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)

sdot 119875119864|Λ (119909) d119909 d119903

(22)

where 119891119877((120578119909P




119864|Λ(119910) can be

calculated by

119875119864|Λ


120573

119891Λ(119910) d119909 = int

+infin

120573

1

119910sdot 119890

minus119909119910d119909

= 119890minus120573119910

(23)


119864 [1198772] = int

+infin

0

int+infin

0

119890minus(120578sdot120573)(119909sdotP

119905sdot119860119866)sdot 2119903

1

radic2120587120590119909


= int+infin

minusinfin

int+infin

0

1

radic2120587119890minus11990922

sdot 2119903


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903 d119909

(24)

where119860119866= 119864[(119866

119892119866119890)2120572


equation [58]

int+infin

0


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903

=2

120572Γ (

2

120572) sdot (

120578 sdot 120573 sdot 119890minus120590119909

119862 sdotP119905sdot 119860

119866

)

minus2120572

(25)


finally have


119905sdot119860119866))minus2120572

sdot119890(radic2120590120572)

2

(26)










0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus5

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Dir_anaOmni_ana

Dir_simOmni_sim






0

01

02

03

04

05

06

07

08

09

10

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus3

10minus2

10minus1

Node density

Dir_anaOmni_ana

Dir_simOmni_sim

120572 = 25 120572 = 35






0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35







5 Conclusion













antenna119866119892 119866











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




where 119860119866

= 119864[(119866119892119866119890)2120572



119864 [1198772] = int

+infin

0

2119903int+infin

ln(120578120573119903minus120572P119905119860119866119862)120590

1

radic2120587119890minus11990922d119909 d119903 (19)


119864 [1198772] = (

P119905119860119866119862

120578120573)

2120572

exp((radic2120590

120572)

2

) (20)


119875 (119864) = 1


119905119860119866119862

120578120573)

2120572

exp(radic2120590

120572)

2

) (21)




119864 [1198772] = int

+infin

0

2119903 [1 minus 119865119897(

120578 sdot 120573

P119905sdot 119860

119866

)] d119903

= int+infin

0

2119903int+infin

0

119891119877(

120578 sdot 119909

P119905sdot 119866

119892sdot 119866

119890

| 119903)

sdot 119875119864|Λ (119909) d119909 d119903

(22)

where 119891119877((120578119909P




119864|Λ(119910) can be

calculated by

119875119864|Λ


120573

119891Λ(119910) d119909 = int

+infin

120573

1

119910sdot 119890

minus119909119910d119909

= 119890minus120573119910

(23)


119864 [1198772] = int

+infin

0

int+infin

0

119890minus(120578sdot120573)(119909sdotP

119905sdot119860119866)sdot 2119903

1

radic2120587120590119909


= int+infin

minusinfin

int+infin

0

1

radic2120587119890minus11990922

sdot 2119903


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903 d119909

(24)

where119860119866= 119864[(119866

119892119866119890)2120572


equation [58]

int+infin

0


120572sdot119890minus120590119909

)(119862sdotP119905sdot119860119866)d119903

=2

120572Γ (

2

120572) sdot (

120578 sdot 120573 sdot 119890minus120590119909

119862 sdotP119905sdot 119860

119866

)

minus2120572

(25)


finally have


119905sdot119860119866))minus2120572

sdot119890(radic2120590120572)

2

(26)










0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus5

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Dir_anaOmni_ana

Dir_simOmni_sim






0

01

02

03

04

05

06

07

08

09

10

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus3

10minus2

10minus1

Node density

Dir_anaOmni_ana

Dir_simOmni_sim

120572 = 25 120572 = 35






0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35







5 Conclusion













antenna119866119892 119866











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus5

10minus3

10minus2

10minus1

120572 = 25 120572 = 35

Dir_anaOmni_ana

Dir_simOmni_sim






0

01

02

03

04

05

06

07

08

09

10

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

10minus4

10minus3

10minus2

10minus1

Node density

Dir_anaOmni_ana

Dir_simOmni_sim

120572 = 25 120572 = 35






0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35







5 Conclusion













antenna119866119892 119866











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

01

02

03

04

05

06

07

08

09

10

Node density

Prob

abili

ty o

f eav

esdr

oppi

ng at

tack

s P(E)

Dir_anaOmni_ana

Dir_simOmni_sim

10minus5

10minus4

10minus3

10minus2

10minus1

120572 = 25 120572 = 35







5 Conclusion













antenna119866119892 119866











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











Acknowledgments


References




































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article An Analytical Study on Eavesdropping...

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