an efficient top-query processing with result integrity verification

Research ArticleAn Efficient Top-119896 Query Processing with Result IntegrityVerification in Two-Tiered Wireless Sensor Networks

Ruiliang He1 Hua Dai1 Geng Yang1 Taochun Wang2 and Jingjing Bao3

1College of Computer Science amp Technology Nanjing University of Posts and Telecommunications Nanjing 210003 China2College of Mathematics and Computer Science Anhui Normal University Wuhu 241003 China3Tongda College of Nanjing University of Posts and Telecommunications Nanjing 210003 China

Correspondence should be addressed to Hua Dai daihuanjupteducn

Received 9 April 2015 Revised 13 July 2015 Accepted 27 July 2015

Academic Editor Mark Leeson

Copyright copy 2015 Ruiliang He et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In two-tiered wireless sensor networks storage nodes take charge of both storing the sensing data items and processing thequery request issued by the base station Due to their important role storage nodes are more attractive to adversaries in a hostileenvironment Once a storage node is compromised attackers may falsify or abandon the data when answering the query issued bythe base station which will make the base station get incorrect or incomplete result This paper proposes an efficient top-119896 queryprocessing scheme with result integrity verification named as ETQ-RIV in two-tiered sensor networks According to the basic ideathat sensor nodes submit some encoded message containing the sequence relationship as proof information for verification alongwith their collected sensing data items a data binding and collecting protocol and a verifiable query response protocol are proposedand described in detail Detailed quantitative analysis and evaluation experiments show that ETQ-RIV performs better than theexisting work in both communication cost and query result redundancy rate

1 Introduction

Since the traditional multihop architecture is not suitable forlarge-scale wireless sensor networks (WSNs) a novel two-tiered architecture has been proposed The two-tiered wire-less sensor networks (TWSNs) introduce storage nodes thatare abundant in energy memory and computing power totraditionalmultihopWSNs In such a two-tiered architecturethe storage node serves as an intermediate tier between thebase station and the sensor nodes which is shown in Figure 1The whole network is partitioned into several cells each ofwhich consists of a storage node and some sensor nodesnearby The sensing data are sent to and stored in the storagenode in the same cell after being collected by the sensornodes After receiving the queries issued by the base stationthe storage node processes the query over the data items thatare received from the sensor nodes and then returns the queryresult to the base station The two-tiered architecture is alsoknown to be indispensable for increasing network capacity

and scalability reducing system complexity and prolongingnetwork lifetime [1ndash3]

In TWSNs storage nodes not only store all the sensingdata of all the sensor nodes in the same cell but alsorespond to the query requests issued by the base stationwhichmakes the storage nodesmore attractive to adversariesOnce a storage node is compromised attackers may falsifyor abandon the data when the storage node is answering thequery issued by the base station which will make the basestation get incorrect or incomplete result In an applicationthat depends on the query result an incomplete result maylead to wrong decisions Therefore it is of great significanceto construct a verifiable query processing scheme by whichauthenticity and integrity of query results can be verified bythe base station

Top-119896 query is frequently used inWSNs aiming at gettingthe 119896 highest or lowest data in a specified region duringa specified time epoch For instance ldquoto get the 5 highesttemperature data of the second warehouse from 1200 to

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 538482 8 pageshttpdxdoiorg1011552015538482

2 Mathematical Problems in Engineering

Base station

Storage node

Sensornode

Cell

Figure 1 Network model of TWSN

1300rdquo is a typical top-119896 query that could be used as firedetection This paper proposes an efficient top-119896 query pro-cessing scheme with result integrity verification in TWSNsnamed as ETQ-RIV the basic idea of which is as followsThe sensor nodes submit some encoded message containingthe sequence relationship along with their collected sensingdata items to the storage nodes When the base station issuesqueries storage nodes send all the satisfied data items alongwith the encoded message as proof information to the basestation Then the base station can compute the result andverify the authenticity and integrity of it

ETQ-RIV is an improvement scheme of EVTQ proposedin our previous work [4] The improvements are as follows

(i) In the data collecting process each sensor node doesnot need to submit the out-bound HMAC whichfurther reduces the in-cell communication

(ii) With processing query the storage node needs tosend one HMAC for each unqualified sensor node inEVTQHowever in ETQ-RIV only oneHMAC for allnoncontributed sensor nodes is required which willgreatly reduce the query communication cost

The main contributions of this paper are as follows

(i) We propose a sequence relationship encoding basedmethod which makes storage nodes unable to falsifyor omit data items without being noticed

(ii) We give the two concrete protocols named as databinding and collecting protocol and verifiable queryresponse protocol to achieve ETQ-RIV which makethe base station capable of verifying the authenticityand integrity of the top-119896 query result

(iii) We present the quantitative analysis of communica-tion cost and redundancy rate of ETQ-RIV in detailand conduct experiments to evaluate the performanceof this work compared to present methods

The rest of this paper is organized as follows The relatedworks are presented in Section 2 Section 3 presents thepreliminaries including related models problem descriptionand performance evaluation index Section 4 presents thetwo protocols proposed in this paper Section 5 presentsthe theoretical analysis of the communication cost and

redundancy rate Section 6 presents the result and analysisof the simulation experiments In last section we make aconclusion for this paper

2 Related Works

The traditional multihop model is not suitable for large scalewireless sensor networks thus a novel two-tiered architecturewas proposed which is indispensable for increasing networkcapacity and scalability reducing system complexity andprolonging network lifetime [1ndash3]

In TWSNs the storage nodes play an important role andare more attractive to adversaries which may bring seriousdata security problems Therefore data privacy and securityhave been widely discussed in recent research work

Attentions have been paid to secure top-119896 query process-ing in two-tiered sensor networks recently A novel verifiablefine-grained top-119896 query processing scheme was proposedby Zhang et al [5] which is the first work of verifiable top-119896 query scheme in two-tiered sensor networks The basicidea of Zhangrsquos scheme is that each sensor node generateshashed message authentication code (HMAC) [6] for everythree consecutive data items to make query results verifiableHowever the long bits of HMACs result in high cost ofcommunications Liao and Li proposed a secure top-119896 queryscheme named PriSecTopk [7] based on order preservingencryption [8] and message authentication code (MAC) [9]which could not lower the communication cost either Maet al proposed a novel fine-grained verification schemefor top-k queries named VSFTQ [10] which uses symmet-ric encryption instead of message authentication VSFTQreduces the communication cost to a certain extent On thebasis of Zhangrsquos scheme andMarsquos scheme Dai et al proposedan efficient verifiable top-119896 query processing scheme inour previous work [4] which has a better performance incommunication cost Yu et al proposed a dummy reading-based anonymization framework [11 12] under which thequery results can be guaranteed by verifiable top-119896 query(VQ) schemes they proposed However the VQ schemerequires each sensor node to send the neighboring sensornode IDs and hashes corresponding to individual genuineencrypted readings which may lead to high communicationcost of sensor nodes Moreover to obtain the top-119896 queryresult the storage node is required to submit a top-(120578minus 1+119896)query result due to the dummy readings where 120578 is a systemparameter denoting the difference between the maximumand minimum encrypted readings within an epoch

There is a special kind of top-119896 query when 119896 equalsone which is also known as maxmin query For maxminquery processing Yao et al proposed a preliminary privacy-preserving scheme [13] based on prefix membership verifi-cation (PMV) mechanism [14 15] to compute the maximumor minimum value over encrypted data items Dai et alproposed an energy-efficient privacy-preserving MAXMINquery processing solution [16] based on 0-1 encoding tech-nique [17] which has a better performance compared to [13]

Besides top-119896 query secure range query has been widelydiscussed recently [18ndash23] The schemes proposed in [18ndash23]

Mathematical Problems in Engineering 3

ask for data items falling into specified ranges without dataprivacy disclosure and make query result verifiable

3 Models and Problem Statement

31 Models In this paper we consider the two-tiered networkmodel as shown in Figure 1Thewhole network is partitionedinto cells each of which consists of a storage node 119872 and 119899

homogeneous sensor nodes 1199041 1199042 119904

119899 119872 is abundant in

resources such as energy storage and computation whichis in charge of not only storing of all sensing data collectedby the sensor nodes in the same cell but processing andanswering of the query request issued by the base stationLimited in resource the sensor nodes just collect sensing dataand transmit them to the storage node in the cell As in [4] wetake the assumption that storage nodes know the topologicalinformation of the whole cell while a sensor node knowsthe locations of its neighboring nodes in one hop as well asthe storage nodersquos location of affiliated cells In addition thebase station knows the topological information of the wholenetwork

In TWSN a top-119896 query can be denoted as a three-element tuple 119876 = (119888 119905 119896) where 119888 represents the queryregion 119905 represents the time epoch of the query and 119896 is thequantity of required data items For simplicity of descriptionwe discuss the specific top-119896 query that covers only one cellin one time epoch It is easy to extend the proposed methodto achieve queries including multiple cells over multiple timeepochs

32 Problem Statement The threat model considered in thispaper is similar to [4] We assume that an arbitrary numberof storage nodes could be compromised and instructed torespond with falsified andor incomplete data as a top-119896query result to the base station In TWSN both sensor nodesand storage nodes could be compromised In general a sensornode only has very little information and the vast majority inthe whole network are uncompromised ones However thestorage node plays a more important role in the networkfor it stores all data items collected in the whole cell Oncea storage node is compromised the adversary may falsifyor abandon the data when the storage node answering thequery issued by the base station which will make the basestation get incorrect or incomplete result and mislead theuser into making wrong decisions Therefore storage nodestend to be more attractive and vulnerable to adversariesAlthough a compromised storage node may lead to leakageof data privacy it is not concerned in this paper In practicein some application of WSNs it is the data integrity insteadof data privacy that is more important For instance videosurveillance in a sensor network for building security isknown to adversaries thus requiring no privacyTherefore wefocus on the verifiable top-119896 query in this paper

Given a top-119896 query 119876 = (119888 119905 119896) we assume the storagenode 119872 returns a data set 119877 as query result The problemof interest is how the base station can verify whether 119877

satisfies both the authenticity and integrity requirementswhich means the following two rules must hold

(1) Authenticity Rule All data items in 119877 are surelycollected by sensor nodes in the query cell 119888 duringtime epoch 119905

(2) Integrity Rule There are exactly 119896 data items thatare indeed the 119896 highest data items among what arecollected by sensor nodes in the query cell 119888 duringtime epoch 119905 or equivalently

forall119903119894isin 119877119905andforall119889119895isin 119863119905 119877119905997888rarr 119903119894gt 119889119895 (1)

where119863119905represents the data set consisting of all data

items collected by sensor nodes in the query cell 119888during time epoch 119905

33 Evaluation Metrics In this paper the following twometrics are used to evaluate the performance of the proposedscheme

(1) Communication cost including in-cell communica-tion cost 119862

119868and query processing communication

cost 119862119876 119862119868represents the size in bits of data items

transmitted from all the sensor nodes to the storagein a cell in the data binding and collecting procedurewhile 119862

119876stands for the size of data items transmitted

from the storage node in the query cell to the base sta-tion during the verifiable query response procedure

(2) Redundancy rate of query result the proportion ofthe total size in bits of additional proof informationused to enable verifiable top-119896 queries to the totalsize in bits of response message in final query resultThis rate denoted as 120574 indicates the efficiency of thequery processing A lower redundancy ratemeans lessadditional communication cost required for verifica-tion The redundancy rate will be calculated by thefollowing equation

120574 =119897119904minus 119897119903

119897119904

times 100 (2)

where 119897119904is the size in bits of the total data items

returned by the storage node while 119897119903is the total data

size of final query result

4 Verifiable Top-119896 Query Processing

41 Assumptions and Definition Given a top-119896 query 119876119905=

(119888 119905 119896) we assume that the query covers just a cell 119888 in atime epoch 119905 which we have mentioned in previous sectionsThere are 119899 sensor nodes in the cell 119888 which can be denotedas Γ = 119904

1 1199042 119904

119899 Assume that an arbitrary sensor node

119904119894(1 le 119894 le 119899) collects 119873 data items denoted as 119863

119894=

1198891198941 1198891198942 119889119894119873 in each time epoch and sorts them into

descending order 119904119894shares a secret key 119870

119894with the base

station which is used to encode the proof information foreach data item by a HMAC function

42 Data Binding and Collecting Protocol In each timeepoch sensor node 119904

119894collects data and encodes them before

sending to the storage node 119872 in the same cell for storageThe detailed procedure is as follows


(1) 119904119894sorts the 119873 data items 119863

119894= 1198891198941 1198891198942 119889

119894119873 that

it collects in time epoch 119905 Without loss of generalitywe assume 119889

1198941gt 1198891198942

gt sdot sdot sdot gt 119889119894119873

after being sorted(2) According to the sequence of the sensing data items

119904119894computes the message verification code 119881(119889

119894119895) for

each data item 119881(119889119894119895) of the 119895th data item 119889

119894119895(1 le

119895 le 119873) can be computed as follows

119881(119889119894119895) = HMAC

119870119894(119905 119889

1198941 1198891198942 sdot sdot sdot 119889

119894119895) (3)

where HMAC119870119894(sdot) denotes encoding the correspond-

ing data using a HMAC function with key119870119894and is

the concatenation operator(3) 119904119894constructs a data collecting message MSG

119862accord-

ing to the following format and sends to the storagenode119872

MSG119862= ⟨id (119904

119894) 119905 1198891198941 119881 (119889

1198941) 1198891198942 119881 (1198891198942) 119889119894119873

119881 (119889119894119873

)⟩

(4)

(4) 119872 receives and stores the data collectingmessage of 119904119894

We denote the data set consisting of all the data itemsfrom all the sensor nodes in the cell as

DS119905= ⋃

119904119894isinΓ

1198891198941 119889119894119873 (5)

43 Verifiable Query Response Protocol Query processingand verification requires collaboration of the base station andthe storage node which works as follows According to thequery issued by the base station the storage node119872processesthis query and responds with the corresponding data itemsAt last the base station computes the query result and verifiesthe authenticity and integrity of the result The protocol isdescribed in detail as follows

Phase 1 (query request transmission) The base station sendsthe query 119876

119905= (119905 119896 119888) to119872 and waits for its feedback

Phase 2 (query message feedback) (1) After 119876119905has been

received 119872 computes the 119896 highest data items denotedas top119896(DS

119905) according to all the sensing data DS

119905which

was sent during the time epoch 119905 from the sensor nodes1199041 1199042 119904

119899 in cell 119862 top119896(DS

119905) satisfies the following

condition1003816100381610038161003816top119896 (DS

119905)1003816100381610038161003816 = 119896 and forall119889

119894

119889119895(119889119894isin top119896 (DS

119905) and 119889119895isin DS119905 top119896 (DS

119905)) 997888rarr 119889

119894gt 119889119895

(6)

Assuming that there are 120575119894data items sent by 119904

119894within

top119896(DS119905) that is to say 119889

1198941 1198891198942 119889119894120575119894 sube top119896(DS

119905) then

the following condition holds

120575119894=

1003816100381610038161003816119863119894 cap top119896 (DS119905)1003816100381610038161003816 0 le 120575

119894le min 119873 119896 (7)

(2)119872 constructs the following response message accord-ing to 120575

119894

(i) Given a sensor node 119904119894where 120575

119894gt 0 we call it the

contributed node the response message of which isnamed as msg1(119904119894) and it should be computed as

msg1 (119904119894)

=

⟨id (119904119894) 1198891198941 119889119894120575119894+1 119881 (119889

119894120575119894+1)⟩ 0 lt 120575119894le 119873 minus 1

⟨id (119904119894) 1198891198941 119889119894119873 119881 (119889

119894119873)⟩ 120575

119894= 119873

(8)

where 119889119894120575119894+1 is the maximum data item collected by 119904

119894

that is not in top119896(DS119905) and we call it the out-bound

of the 119904119894 If all the data items collected by 119904

119894are in

top119896(DS119905) its out-bound does not exist Otherwise

there will be one and only one out-bound as for 119904119894

(ii) We call the sensor node where 120575119894= 0 noncontributed

node There is only one response message msg0 for allnoncontributed nodes which should be computed as

msg0 = ⟨id (119904119894) 1198891198941 | 120575119894= 0and 119904

119894isin Γ

⨁

120575119894=0and119904119894isinΓ119881 (1198891198941)⟩

(9)

where⨁ is the exclusive or operator

(3) 119872 summarizes all the response message generated instep (2) constructs the query feedback message MSG

119876 and

sends it to the base station

MSG119876

= ⟨msg1 (119904119894) | 120575119894gt 0and 119904

119894isin Γ msg0⟩ (10)

Phase 3 (query result computation and verification) (1)Upon receiving the query feedbackmessage from119872 the basestation will do the preprocessing to confirm all the messagemsg1(119904119894) | 120575

119894gt 0 and 119904

119894isin Γ of each contributed node and the

message msg0 of all noncontributed nodes(2) The base station sorts all data items in the response

message and gets the 119896 highest data items which is the top-119896 query result We denote the top-119896 query result by 119877

119905 the

minimum data item of which is denoted as min(119877119905)

(3) The base station checks whether the following con-ditions hold in sequence If and only if all conditions aresatisfied the query result 119877

119905is an authentic and complete

result Otherwise the query result is abnormal

Condition 1 All sensor ID inmessage msg1(119904119894) | 120575119894gt 0and119904

119894isin

Γ and msg0 construct a set named Ω so that Ω = id(119904119894) |

119904119894isin Γ holds

Condition 2 Assume that 119904119894is an arbitrary sensor node

that contributes data items to message msg1(119904119894) | 120575119894

gt

0 and 119904119894

isin Γ and the response message of 119904119894is

⟨id(119904119894) 1198891198941 1198891198942 119889119894120583119894 119867119894⟩ where 119889

1198941gt 1198891198942 gt sdot sdot sdot gt 119889

119894120583119894

The base station then computes HMAC119870119894(119905 119889

1198941 sdot sdot sdot

119889119894120583119894

) where119870119894is a distinct key known only to 119904

119894and the base

station Then one of the following two conditions must hold

(1) 120583119894= 119873 and 119867

119894= 119867119896119894(119905 119889

1198941 sdot sdot sdot 119889

119894119873 Ψ) and 119889

119894119897119894ge

min(119877119905)


(2) 2 le 120583119894lt 119873 and 119867

119894= 119867119896119894(119905 1198891198941

sdot sdot sdot 119889119894119873

Ψ) and 119889119894119897119894

Condition 3 Let 1199041 1199042 119904

119901 be all the noncontributed

nodes and their response message msg0

is ⟨id(1199041) 1198891

id(1199042) 1198892 id(119904

119901) 119889119901 1198670⟩ in which all the data items

construct a set DS1015840 = 1198891 1198892 119889

119901 The base station

computes HMAC1198701

(119905 1198891) HMAC1198702

(119905 1198892) HMAC

119870119901(119905 119889

119901) using the key 119870

1 1198702 119870

119901shared with

1199041 1199042 119904

119901 respectively and the following condition holds

(1198670 = ⨁

119889119895isinDS1015840HMAC

119870119895(119905 119889

119895))

and (forall119889119895isinDS1015840 997888rarr119889

119895ltmin (119877

119905))

(11)

As described in previous two protocols the sensing dataitems collected by a sensor node are sorted in descendingorder and encoded with a HMAC function Each sensornode shares a secret key only with the base station andthe storage nodes know nothing about the keys In such acase it is computationally infeasible for the storage nodes tofalsify the message verification code as long as we choose aconsiderably complex HMAC algorithm such as SHA-1 [24]Thus it is impossible for storage nodes to falsify or concealdata items in the query result without being detected by thebase station Therefore the scheme proposed in this paperenables authenticity and integrity verification of the top-119896query result

5 Protocol Analysis

51 Communication Cost Analysis From data binding andcollecting protocol and verifiable query response protocol welearn that there are two kinds of communication costs in two-tiered sensor networks named as in-cell communication cost119862119868and query processing communication cost 119862

119876 Assume that

there are 119899 sensor nodes in a cell and each node ID has 119897id bitsEach sensor node collects 119873 data items in every time epocheach data item has 119897

119889bits and each HMAC code number

has 119897ℎbits In addition each time epoch number has 119897

119905bits

Assume that there are 119871 hops between each sensor node andthe storage node on average We assume that there are 120583

contributed nodes and n-120583 noncontributed nodes and 120582 ofthe 120583 contributed nodes contributes all the 119873 data items tothe query result Obviously we have 0 le 120582 le 119873 and 120582 le 119896

hold According to such two protocols we have

119862119868= 119899 sdot (119897id + 119897

119905+119873 sdot (119897

119889+ 119897ℎ)) sdot 119871

119862119876

= (120583 sdot 119897id + (119896 + 120583minus120582) sdot 119897119889+120583 sdot 119897ℎ)

+ ((119899 minus 120583) sdot 119897id + (119899 minus 120583) sdot 119897119889+ 119897ℎ)

= 119899 sdot 119897id + (119899 + 119896 minus 120582) sdot 119897119889+ (120583 + 1) sdot 119897

ℎ

(12)

52 Redundancy Rate Analysis We define the redundancyrate 120574 of query result as the proportion of the total size ofadditional proof information used for query result verifica-tion to the total size of response message in final query result

Table 1 Default evaluation parameters

Para n 119897id (bit) 119897119905(bit) 119897

119889(bit) 119897

ℎ(bit) 119873 119896

Val 250 32 32 32 128 20 10

We take the same assumption as Section 51 According to ourproposed protocols we have

120574 =119862119876minus (120583 sdot 119897id + 119896 sdot 119897

119889)

119862119876

times 100

=(119899 minus 120583) sdot 119897id + (119899 minus 120582) sdot 119897

119889+ (120583 + 1) sdot 119897

ℎ

119899 sdot 119897id + (119899 + 119896 minus 120582) sdot 119897119889+ (120583 + 1) sdot 119897

ℎ

times 100

(13)

6 Performance Evaluation

In this section we evaluate the performance of the schemeETQ-RIV proposed in this paper and compare it with theschemes VSFTQ EVTQ and AD-VQ which are proposedin [10] [4] and [11 12] respectively The four schemesVSFTQ EVTQ ETQ-RIV and AD-VQ are implemented onthe simulator of [25] with random sensor data items Wecompare the in-cell communication cost119862

119868 query processing

communication cost 119862119876 and the query result redundancy

rate 120574 of the four schemes respectively We also assume thatthe packet transmissions are both collision-free and error-free in our experiments

We take the assumption that we carry out the top-119896 queryjust in one cell with one storage node and 119899 sensor nodesThe 119899 sensor nodes are distributed uniformly over a two-dimensional region which covers an 80 lowast 80m2 area Eachsensor node collects 119873 data items during each time epochand its communication radius is 10 meters The bit lengths ofsensor node ID time epoch number sensing data item andHMAC code are represented by 119897id 119897119905 119897119889 and 119897

ℎ respectively

The default parameters are listed in Table 1 which are used inthe evaluations unless otherwise specified

In each measurement we generate 20 different networkswith different network IDs In each network the sensornodes are distributed randomly with different topology Themeasurement result is the average of 20 networks

61 In-Cell Communication Cost Evaluation With defaultparameters we evaluate the in-cell communication costs ofVSFTQ EVTQ ETQ-RIV and AD-VQ in different networksthe result of which is shown in Figure 2(a) Figure 2(a)indicates that our proposed scheme ETQ-RIV takes a littleless communication costs than VSFTQ and AD-VQ whileEVTQ takes the highest communication costs Comparedwith EVTQ AD-VQ and VSFTQ ETQ-RIV saves about377 286 and 097 of in-cell communication costson average respectively The reason is that in each schemesensor nodes are required to submit every data item alongwith some proof information EVTQ AD-VQ and ETQ-RIV use HMAC as proof information In EVTQ each sensornode submits onemore out-boundHMACbesides every dataitemrsquos proof information In AD-VQ each sensor requiressubmitting some information of neighboring nodes besides


Network ID1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

In-c

ell c

omm

unic

atio

n co

st (b

it)

46

48

5

52

54

56

58

6

62

64

66

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119868 versus network ID

In-c

ell c

omm

unic

atio

n co

st (b

it)n

200 250 300 350 400 450 5004

5

6

7

8

9

10

times106

ETQ-RIVEVTQ

VSFTQAD-VQ

(b) 119862119868 versus 119899

Figure 2 Evaluation results of in-cell communication costs

the HMAC information In ETQ-RIV the sensor nodes donot need the out-bound HMAC and neighboring nodesinformation so ETQ-RIV performs better than EVTQ andAD-VQ Different from the other three schemes VSFTQreplaces the HMACwith symmetric encryption of data itemrsquosorder score and the time epoch as proof information In ourevaluation the total bit length of proof information inVSFTQismore than ETQ-RIV As a result ETQ-RIV performs betterthan VSFTQ

Figure 2(b) indicates that the in-cell communicationcosts of the three schemes increase as the sensor nodenumber 119899 increases ETQ-RIV has the best performance asbefore and saves about 377 286 and 097 of in-cellcommunication costs on average compared with EVTQ AD-VQ and VSFTQ respectively The reason is same as thedescription in the previous section

62 Query Communication Cost Evaluation We evaluatetop-119896 query communication costs of VSFTQ EVTQ ETQ-RIV and AD-VQ as 119899 as well as 119896 increases Figure 3(a)indicates that the query communication costs of the fourschemes all increase as 119899 increases The reason is obviousthe larger 119899 the more noncontributed sensor nodes andthe more verification information for noncontributed nodesrequired to be submitted Figure 3(a) also shows that ETQ-RIV has the lowest query communication cost followedby VSFTQ EVTQ and then AD-VQ In detail the querycommunication cost of ETQ-RIV is about 9867 lowerthan AD-VQ 6430 lower than EVTQ and 4769 lowerthan VSFTQ In AD-VQ to obtain the top-119896 query result

the storage node is required to submit a top-(120578 minus 1 + 119896)

query result due to the dummy readings where 120578 is a systemparameter denoting the difference between the maximumand minimum encrypted readings within an epoch That iswhy AD-VQ has the highest query communication cost InEVTQ the storage node is required to send aHMAC as proofinformation for each unqualified sensor node that has no dataitem satisfying the query so its query communication cost ishigh In VSFTQ the storage node needs to send symmetricencryption of data itemrsquos order score and the time epochas proof information which takes more communication costthan ETQ-RIV However in ETQ-RIV only one HMAC isneeded for all noncontributed sensor nodes which greatlyreduces the query communication cost

Figure 3(b) shows that the query communication costs ofthe four schemes all increase as 119896 increases which is becausethe larger 119896 the more data items that need to be returned bythe storage node Similar to Figure 3(a) ETQ-RIV still hasthe lowest query communication cost which is about 9931lower than AD-VQ 5170 lower than EVTQ and 3844lower than VSFTQ The reason is as mentioned before onlyone HMAC is required for all noncontributed sensor nodesin ETQ-RIV

63 Redundancy Rate Evaluation We evaluate top-119896 queryresult redundancy rate of VSFTQ EVTQ ETQ-RIV and AD-VQ as 119896 increases Figure 4 indicates that the redundancyrates of the four schemes all decrease as 119896 increases Fur-thermore AD-VQ has the highest redundancy rate followedby EVQT VSFTQ and ETQ-RIV The redundancy rate of


n

200 250 300 350 400 450 5000

02

04

06

08

1

12

14

16

18

2

Que

ry co

mm

unic

atio

n co

st (b

it)

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119876 versus 119899

k

10 20 30 40 50 60 70 80 90 100

Que

ry co

mm

unic

atio

n co

st (b

it)ETQ-RIVEVTQ

VSFTQAD-VQ

107

106

105

104

(b) 119862119876 versus 119896

Figure 3 Evaluation results of query communication costs

k

10 20 30 40 50 60 70 80 90 100

Redu

ndan

cy ra

te (

)

80

82

84

86

88

90

92

94

96

98

100

ETQ-RIVEVTQ

VSFTQAD-VQ

120574 versus k

Figure 4 Evaluation results of query result redundancy rate

ETQ-RIV is about 1268 lower than AD-VQ 677 lowerthan EVTQ and 519 lower than VSFTQ The reason is asfollows A top-119896 query result can be divided into two parts

the satisfied data items of query result and the verificationinformation A larger 119896 implies more satisfied data items anda lower redundancy rate Compared with the other threeschemes only one HMAC is required for all noncontributedsensor nodes in ETQ-RIV which makes the ETQ-RIV lowestredundancy rate

According to the above evaluations and analysis wecan conclude that our proposed ETQ-RIV has better per-formance than the existing works [4 5 7 10ndash12] both incommunication costs and redundancy rate

7 Conclusions

In this paper we focus on the problem of verifiable top-119896query in two-tiered wireless sensor networks and propose anefficient top-119896 query processing scheme with result integrityverification which is denoted as ETQ-RIV To make thequery result verifiable each sensor node should submit someencoded message containing the sequence relationship asproof information for verification along with their collectedsensing data items Evaluation results show that ETQ-RIVcan decrease the redundancy rate of query result and thusdecrease both in-cell and query communication costs andperforms better than the existing works in communicationcosts

Conflict of Interests

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


Acknowledgments

This research was supported by the National NaturalScience Foundation of China under the Grants nos61300240 61402014 61472193 61373137 61373138 61272084and 61201163 the Natural Science Foundation of JiangsuProvince under the Grants nos BK20151511 and BK20141429the Project of Natural Science Research of Jiangsu Universityunder Grants nos 11KJA520002 and 14KJB520027 thePostdoctoral Science Foundation of China under Grant no2013M541703 and the Postdoctoral Science Foundation ofJiangsu Province under Grant no 1301042B

References

[1] O Gnawali K Y Jang J Paek et al ldquoThe tenet architecture fortiered sensor networksrdquo in Proceedings of the 4th ACM Con-ference on Embedded Networked Sensor Systems pp 153ndash166Boulder Colo USA 2006

[2] P Desnoyers D Ganesan and P Shenoy ldquoTSAR a two tiersensor storage architecture using interval skip graphsrdquo inProceedings of the 5th ACMConference on Embedded NetworkedSensor Systems pp 39ndash50 San Diego Calif USA November2005

[3] Y Diao D Ganesan G Mathur and P J Shenoy ldquoRethinkingdata management for storage-centric sensor networksrdquo inProceedings of the 3rd Biennial Conference on Innovative DataSystems Research (CIDR rsquo07) pp 22ndash31 Asilomar Calif USAJanuary 2007

[4] H Dai G Yang F Xiao and Q Zhou ldquoEVTQ an efficientverifiable top-k query processing in two-tiered wireless sensornetworksrdquo in Proceedings of the 9th International Conference onMobile Ad-Hoc and Sensor Networks (MSN rsquo13) pp 206ndash211IEEE Dalian China December 2013

[5] R Zhang J Shi Y Liu et al ldquoVerifiable fine-grained top-kqueries in tiered sensor networksrdquo in Proceedings of the 29thIEEE International Conference on Computer Communicationspp 1199ndash1207 San Diego Calif USA 2010

[6] H Krawczyk R Canetti and M Bellare ldquoHMAC keyed-hashing for message authenticationrdquo Tech Rep RFC 2104Internet Society Reston Va USA 1997

[7] X Liao and J Li ldquoPrivacy-preserving and secure top-k query intwo-tier wireless sensor networkrdquo in Proceedings of the GlobalCommunications Conference pp 335ndash341 Anaheim CalifUSA 2012

[8] R Agrawal J Kiernan R Srikant and Y Xu ldquoOrder-preservingencryption for numeric datardquo in Proceedings of the ACMSIGMOD International Conference on Management of Data pp563ndash574 Paris France June 2004

[9] R Rivest ldquoTheMD5message-digest algorithmrdquo Tech Rep RFC1321 Internet Society Reston Va USA 1992

[10] X Ma H Song J Wang J Gao and G Min ldquoA novelverification scheme for fine-grained top-k queries in two-tieredsensor networksrdquo Wireless Personal Communications vol 75no 3 pp 1809ndash1826 2014

[11] C M Yu N K Guo Y Chen et al ldquoTop-k query resultcompleteness verification in sensor networksrdquo in Proceeding ofthe IEEE Communications Workshops (ICC rsquo13) pp 1026ndash1030Budapest Hungary 2013

[12] C M Yu N K Guo Y Chen et al ldquoTop-k query resultcompleteness verification in tiered sensor networksrdquo IEEE

Transactions on Information Forensics and Security vol 9 no1 pp 109ndash124 2014

[13] Y Yao N Xiong J H Park L Ma and J Liu ldquoPrivacy-preserving maxmin query in two-tiered wireless sensor net-worksrdquoComputers ampMathematics with Applications vol 65 no9 pp 1318ndash1325 2013

[14] J Cheng H Yang S H Wong P Zerfos and S Lu ldquoDesignand implementation of cross-domain cooperative firewallrdquo inProceedings of the IEEE International Conference on NetworkProtocols (ICNP rsquo07) pp 284ndash293 Beijing ChinaOctober 2007

[15] A X Liu and F Chen ldquoCollaborative enforcement of firewallpolicies in virtual private networksrdquo in Proceedings of the 27thACM Symposium on Principles of Distributed Computing pp95ndash104 ACM August 2008

[16] H Dai G Yang and X Qin ldquoEMQP an energy-efficientprivacy-preservingMAXMIN query processing in tiered wire-less sensor networksrdquo International Journal of Distributed Sen-sor Networks vol 2013 11 pages 2013

[17] H Y Lin and W G Tzeng ldquoAn efficient solution to themillionairesrsquo problem based on homomorphic encryptionrdquo inProceedings of the 3rd International Conference on AppliedCryptography and Network Security pp 97ndash134 New York NYUSA 2005

[18] B Sheng and Q Li ldquoVerifiable privacy-preserving range queryin two-tiered sensor networksrdquo in Proceeding of the 27th IEEEInternational Conference onComputer Communications pp 46ndash50 IEEE Phoenix Ark USA April 2008

[19] B Sheng and Q Li ldquoVerifiable privacy-preserving sensornetwork storage for range queryrdquo IEEE Transactions on MobileComputing vol 10 no 9 pp 1312ndash1326 2011

[20] J Shi R Zhang and Y Zhang ldquoSecure range queries in tieredsensor networkrdquo in Proceedings of the 28th IEEE InternationalConference on Computer Communications pp 945ndash953 Rio deJaneiro Brazil 2009

[21] J Shi R Zhang and Y Zhang ldquoA spatiotemporal approach forsecure range queries in tiered sensor networksrdquo IEEE Transac-tions on Wireless Communications vol 10 no 1 pp 264ndash2732011

[22] F Chen and A X Liu ldquoSafeQ secure and efficient queryprocessing in sensor networksrdquo in Proceedings of the 29thIEEE International Conference on Computer Communications(INFOCOM rsquo10) pp 1ndash9 IEEE San Diego Calif USA March2010

[23] Y Yi R Li F Chen A X Liu and Y Lin ldquoA digital watermark-ing approach to secure and precise range query processing insensor networksrdquo in Proceedings of the International Conferenceon Computer Communications (IEEE INFOCOM rsquo13) pp 1950ndash1958 Turin Italy April 2013

[24] D Eastlake and P Jones ldquoUS secure hash algorithm 1 (SHA1)rdquoRFC 3174 Internet Society Reston Va USA 2001

[25] A Coman J Sander and M A Nascimento ldquoAdaptive pro-cessing of historical spatial range queries in peer-to-peer sensornetworksrdquo Distributed and Parallel Databases vol 22 no 2-3pp 133ndash163 2007

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Base station

Storage node

Sensornode

Cell

Figure 1 Network model of TWSN

1300rdquo is a typical top-119896 query that could be used as firedetection This paper proposes an efficient top-119896 query pro-cessing scheme with result integrity verification in TWSNsnamed as ETQ-RIV the basic idea of which is as followsThe sensor nodes submit some encoded message containingthe sequence relationship along with their collected sensingdata items to the storage nodes When the base station issuesqueries storage nodes send all the satisfied data items alongwith the encoded message as proof information to the basestation Then the base station can compute the result andverify the authenticity and integrity of it

ETQ-RIV is an improvement scheme of EVTQ proposedin our previous work [4] The improvements are as follows

(i) In the data collecting process each sensor node doesnot need to submit the out-bound HMAC whichfurther reduces the in-cell communication

(ii) With processing query the storage node needs tosend one HMAC for each unqualified sensor node inEVTQHowever in ETQ-RIV only oneHMAC for allnoncontributed sensor nodes is required which willgreatly reduce the query communication cost

The main contributions of this paper are as follows

(i) We propose a sequence relationship encoding basedmethod which makes storage nodes unable to falsifyor omit data items without being noticed

(ii) We give the two concrete protocols named as databinding and collecting protocol and verifiable queryresponse protocol to achieve ETQ-RIV which makethe base station capable of verifying the authenticityand integrity of the top-119896 query result

(iii) We present the quantitative analysis of communica-tion cost and redundancy rate of ETQ-RIV in detailand conduct experiments to evaluate the performanceof this work compared to present methods

The rest of this paper is organized as follows The relatedworks are presented in Section 2 Section 3 presents thepreliminaries including related models problem descriptionand performance evaluation index Section 4 presents thetwo protocols proposed in this paper Section 5 presentsthe theoretical analysis of the communication cost and

redundancy rate Section 6 presents the result and analysisof the simulation experiments In last section we make aconclusion for this paper

2 Related Works

The traditional multihop model is not suitable for large scalewireless sensor networks thus a novel two-tiered architecturewas proposed which is indispensable for increasing networkcapacity and scalability reducing system complexity andprolonging network lifetime [1ndash3]

In TWSNs the storage nodes play an important role andare more attractive to adversaries which may bring seriousdata security problems Therefore data privacy and securityhave been widely discussed in recent research work

Attentions have been paid to secure top-119896 query process-ing in two-tiered sensor networks recently A novel verifiablefine-grained top-119896 query processing scheme was proposedby Zhang et al [5] which is the first work of verifiable top-119896 query scheme in two-tiered sensor networks The basicidea of Zhangrsquos scheme is that each sensor node generateshashed message authentication code (HMAC) [6] for everythree consecutive data items to make query results verifiableHowever the long bits of HMACs result in high cost ofcommunications Liao and Li proposed a secure top-119896 queryscheme named PriSecTopk [7] based on order preservingencryption [8] and message authentication code (MAC) [9]which could not lower the communication cost either Maet al proposed a novel fine-grained verification schemefor top-k queries named VSFTQ [10] which uses symmet-ric encryption instead of message authentication VSFTQreduces the communication cost to a certain extent On thebasis of Zhangrsquos scheme andMarsquos scheme Dai et al proposedan efficient verifiable top-119896 query processing scheme inour previous work [4] which has a better performance incommunication cost Yu et al proposed a dummy reading-based anonymization framework [11 12] under which thequery results can be guaranteed by verifiable top-119896 query(VQ) schemes they proposed However the VQ schemerequires each sensor node to send the neighboring sensornode IDs and hashes corresponding to individual genuineencrypted readings which may lead to high communicationcost of sensor nodes Moreover to obtain the top-119896 queryresult the storage node is required to submit a top-(120578minus 1+119896)query result due to the dummy readings where 120578 is a systemparameter denoting the difference between the maximumand minimum encrypted readings within an epoch

There is a special kind of top-119896 query when 119896 equalsone which is also known as maxmin query For maxminquery processing Yao et al proposed a preliminary privacy-preserving scheme [13] based on prefix membership verifi-cation (PMV) mechanism [14 15] to compute the maximumor minimum value over encrypted data items Dai et alproposed an energy-efficient privacy-preserving MAXMINquery processing solution [16] based on 0-1 encoding tech-nique [17] which has a better performance compared to [13]

Besides top-119896 query secure range query has been widelydiscussed recently [18ndash23] The schemes proposed in [18ndash23]

























120574 =119897119904minus 119897119903

119897119904

times 100 (2)







1 1199042 119904



119894=



119894with the base







119894= 1198891198941 1198891198942 119889

119894119873 that


1198941gt 1198891198942




119894119895) for


119894119895(1 le


119881(119889119894119895) = HMAC

119870119894(119905 119889

1198941 1198891198942 sdot sdot sdot 119889

119894119895) (3)




119862accord-


MSG119862= ⟨id (119904

119894) 119905 1198891198941 119881 (119889

1198941) 1198891198942 119881 (1198891198942) 119889119894119873

119881 (119889119894119873

)⟩

(4)



DS119905= ⋃

119904119894isinΓ

1198891198941 119889119894119873 (5)







119905which


119899 in cell 119862 top119896(DS


condition1003816100381610038161003816top119896 (DS

119905)1003816100381610038161003816 = 119896 and forall119889

119894

119889119895(119889119894isin top119896 (DS

119905) and 119889119895isin DS119905 top119896 (DS

119905)) 997888rarr 119889

119894gt 119889119895

(6)


119894within


1198941 1198891198942 119889119894120575119894 sube top119896(DS

119905) then


120575119894=

1003816100381610038161003816119863119894 cap top119896 (DS119905)1003816100381610038161003816 0 le 120575

119894le min 119873 119896 (7)


119894




msg1 (119904119894)

=

⟨id (119904119894) 1198891198941 119889119894120575119894+1 119881 (119889

119894120575119894+1)⟩ 0 lt 120575119894le 119873 minus 1

⟨id (119904119894) 1198891198941 119889119894119873 119881 (119889

119894119873)⟩ 120575

119894= 119873

(8)


119894



119894are in





msg0 = ⟨id (119904119894) 1198891198941 | 120575119894= 0and 119904

119894isin Γ

⨁

120575119894=0and119904119894isinΓ119881 (1198891198941)⟩

(9)



119876 and


MSG119876

= ⟨msg1 (119904119894) | 120575119894gt 0and 119904

119894isin Γ msg0⟩ (10)


119894gt 0 and 119904




119905 the






119894isin





gt

0 and 119904119894


⟨id(119904119894) 1198891198941 1198891198942 119889119894120583119894 119867119894⟩ where 119889


119894120583119894



119889119894120583119894


119894and the base


(1) 120583119894= 119873 and 119867

119894= 119867119896119894(119905 119889


119894119873 Ψ) and 119889

119894119897119894ge

min(119877119905)


(2) 2 le 120583119894lt 119873 and 119867

119894= 119867119896119894(119905 1198891198941

sdot sdot sdot 119889119894119873

Ψ) and 119889119894119897119894

Condition 3 Let 1199041 1199042 119904



is ⟨id(1199041) 1198891

id(1199042) 1198892 id(119904





(119905 1198891) HMAC1198702

(119905 1198892) HMAC

119870119901(119905 119889

119901) using the key 119870

1 1198702 119870

119901shared with

1199041 1199042 119904


(1198670 = ⨁

119889119895isinDS1015840HMAC

119870119895(119905 119889

119895))


119895ltmin (119877

119905))

(11)


5 Protocol Analysis


119876 Assume that




119905bits




119862119868= 119899 sdot (119897id + 119897

119905+119873 sdot (119897

119889+ 119897ℎ)) sdot 119871

119862119876




ℎ

(12)



Para n 119897id (bit) 119897119905(bit) 119897

119889(bit) 119897

ℎ(bit) 119873 119896

Val 250 32 32 32 128 20 10



119889)

119862119876

times 100


119889+ (120583 + 1) sdot 119897

ℎ


ℎ

times 100

(13)







ℎ respectively





Network ID1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

In-c

ell c

omm

unic

atio

n co

st (b

it)

46

48

5

52

54

56

58

6

62

64

66

ETQ-RIVEVTQ

VSFTQAD-VQ

times106


In-c

ell c

omm

unic

atio

n co

st (b

it)n

200 250 300 350 400 450 5004

5

6

7

8

9

10

times106

ETQ-RIVEVTQ

VSFTQAD-VQ

(b) 119862119868 versus 119899










n

200 250 300 350 400 450 5000

02

04

06

08

1

12

14

16

18

2

Que

ry co

mm

unic

atio

n co

st (b

it)

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119876 versus 119899

k

10 20 30 40 50 60 70 80 90 100

Que

ry co

mm

unic

atio

n co

st (b

it)ETQ-RIVEVTQ

VSFTQAD-VQ

107

106

105

104

(b) 119862119876 versus 119896


k

10 20 30 40 50 60 70 80 90 100

Redu

ndan

cy ra

te (

)

80

82

84

86

88

90

92

94

96

98

100

ETQ-RIVEVTQ

VSFTQAD-VQ

120574 versus k





7 Conclusions





Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

































120574 =119897119904minus 119897119903

119897119904

times 100 (2)







1 1199042 119904



119894=



119894with the base







119894= 1198891198941 1198891198942 119889

119894119873 that


1198941gt 1198891198942




119894119895) for


119894119895(1 le


119881(119889119894119895) = HMAC

119870119894(119905 119889

1198941 1198891198942 sdot sdot sdot 119889

119894119895) (3)




119862accord-


MSG119862= ⟨id (119904

119894) 119905 1198891198941 119881 (119889

1198941) 1198891198942 119881 (1198891198942) 119889119894119873

119881 (119889119894119873

)⟩

(4)



DS119905= ⋃

119904119894isinΓ

1198891198941 119889119894119873 (5)







119905which


119899 in cell 119862 top119896(DS


condition1003816100381610038161003816top119896 (DS

119905)1003816100381610038161003816 = 119896 and forall119889

119894

119889119895(119889119894isin top119896 (DS

119905) and 119889119895isin DS119905 top119896 (DS

119905)) 997888rarr 119889

119894gt 119889119895

(6)


119894within


1198941 1198891198942 119889119894120575119894 sube top119896(DS

119905) then


120575119894=

1003816100381610038161003816119863119894 cap top119896 (DS119905)1003816100381610038161003816 0 le 120575

119894le min 119873 119896 (7)


119894




msg1 (119904119894)

=

⟨id (119904119894) 1198891198941 119889119894120575119894+1 119881 (119889

119894120575119894+1)⟩ 0 lt 120575119894le 119873 minus 1

⟨id (119904119894) 1198891198941 119889119894119873 119881 (119889

119894119873)⟩ 120575

119894= 119873

(8)


119894



119894are in





msg0 = ⟨id (119904119894) 1198891198941 | 120575119894= 0and 119904

119894isin Γ

⨁

120575119894=0and119904119894isinΓ119881 (1198891198941)⟩

(9)



119876 and


MSG119876

= ⟨msg1 (119904119894) | 120575119894gt 0and 119904

119894isin Γ msg0⟩ (10)


119894gt 0 and 119904




119905 the






119894isin





gt

0 and 119904119894


⟨id(119904119894) 1198891198941 1198891198942 119889119894120583119894 119867119894⟩ where 119889


119894120583119894



119889119894120583119894


119894and the base


(1) 120583119894= 119873 and 119867

119894= 119867119896119894(119905 119889


119894119873 Ψ) and 119889

119894119897119894ge

min(119877119905)


(2) 2 le 120583119894lt 119873 and 119867

119894= 119867119896119894(119905 1198891198941

sdot sdot sdot 119889119894119873

Ψ) and 119889119894119897119894

Condition 3 Let 1199041 1199042 119904



is ⟨id(1199041) 1198891

id(1199042) 1198892 id(119904





(119905 1198891) HMAC1198702

(119905 1198892) HMAC

119870119901(119905 119889

119901) using the key 119870

1 1198702 119870

119901shared with

1199041 1199042 119904


(1198670 = ⨁

119889119895isinDS1015840HMAC

119870119895(119905 119889

119895))


119895ltmin (119877

119905))

(11)


5 Protocol Analysis


119876 Assume that




119905bits




119862119868= 119899 sdot (119897id + 119897

119905+119873 sdot (119897

119889+ 119897ℎ)) sdot 119871

119862119876




ℎ

(12)



Para n 119897id (bit) 119897119905(bit) 119897

119889(bit) 119897

ℎ(bit) 119873 119896

Val 250 32 32 32 128 20 10



119889)

119862119876

times 100


119889+ (120583 + 1) sdot 119897

ℎ


ℎ

times 100

(13)







ℎ respectively





Network ID1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

In-c

ell c

omm

unic

atio

n co

st (b

it)

46

48

5

52

54

56

58

6

62

64

66

ETQ-RIVEVTQ

VSFTQAD-VQ

times106


In-c

ell c

omm

unic

atio

n co

st (b

it)n

200 250 300 350 400 450 5004

5

6

7

8

9

10

times106

ETQ-RIVEVTQ

VSFTQAD-VQ

(b) 119862119868 versus 119899










n

200 250 300 350 400 450 5000

02

04

06

08

1

12

14

16

18

2

Que

ry co

mm

unic

atio

n co

st (b

it)

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119876 versus 119899

k

10 20 30 40 50 60 70 80 90 100

Que

ry co

mm

unic

atio

n co

st (b

it)ETQ-RIVEVTQ

VSFTQAD-VQ

107

106

105

104

(b) 119862119876 versus 119896


k

10 20 30 40 50 60 70 80 90 100

Redu

ndan

cy ra

te (

)

80

82

84

86

88

90

92

94

96

98

100

ETQ-RIVEVTQ

VSFTQAD-VQ

120574 versus k





7 Conclusions





Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119894= 1198891198941 1198891198942 119889

119894119873 that


1198941gt 1198891198942




119894119895) for


119894119895(1 le


119881(119889119894119895) = HMAC

119870119894(119905 119889

1198941 1198891198942 sdot sdot sdot 119889

119894119895) (3)




119862accord-


MSG119862= ⟨id (119904

119894) 119905 1198891198941 119881 (119889

1198941) 1198891198942 119881 (1198891198942) 119889119894119873

119881 (119889119894119873

)⟩

(4)



DS119905= ⋃

119904119894isinΓ

1198891198941 119889119894119873 (5)







119905which


119899 in cell 119862 top119896(DS


condition1003816100381610038161003816top119896 (DS

119905)1003816100381610038161003816 = 119896 and forall119889

119894

119889119895(119889119894isin top119896 (DS

119905) and 119889119895isin DS119905 top119896 (DS

119905)) 997888rarr 119889

119894gt 119889119895

(6)


119894within


1198941 1198891198942 119889119894120575119894 sube top119896(DS

119905) then


120575119894=

1003816100381610038161003816119863119894 cap top119896 (DS119905)1003816100381610038161003816 0 le 120575

119894le min 119873 119896 (7)


119894




msg1 (119904119894)

=

⟨id (119904119894) 1198891198941 119889119894120575119894+1 119881 (119889

119894120575119894+1)⟩ 0 lt 120575119894le 119873 minus 1

⟨id (119904119894) 1198891198941 119889119894119873 119881 (119889

119894119873)⟩ 120575

119894= 119873

(8)


119894



119894are in





msg0 = ⟨id (119904119894) 1198891198941 | 120575119894= 0and 119904

119894isin Γ

⨁

120575119894=0and119904119894isinΓ119881 (1198891198941)⟩

(9)



119876 and


MSG119876

= ⟨msg1 (119904119894) | 120575119894gt 0and 119904

119894isin Γ msg0⟩ (10)


119894gt 0 and 119904




119905 the






119894isin





gt

0 and 119904119894


⟨id(119904119894) 1198891198941 1198891198942 119889119894120583119894 119867119894⟩ where 119889


119894120583119894



119889119894120583119894


119894and the base


(1) 120583119894= 119873 and 119867

119894= 119867119896119894(119905 119889


119894119873 Ψ) and 119889

119894119897119894ge

min(119877119905)


(2) 2 le 120583119894lt 119873 and 119867

119894= 119867119896119894(119905 1198891198941

sdot sdot sdot 119889119894119873

Ψ) and 119889119894119897119894

Condition 3 Let 1199041 1199042 119904



is ⟨id(1199041) 1198891

id(1199042) 1198892 id(119904





(119905 1198891) HMAC1198702

(119905 1198892) HMAC

119870119901(119905 119889

119901) using the key 119870

1 1198702 119870

119901shared with

1199041 1199042 119904


(1198670 = ⨁

119889119895isinDS1015840HMAC

119870119895(119905 119889

119895))


119895ltmin (119877

119905))

(11)


5 Protocol Analysis


119876 Assume that




119905bits




119862119868= 119899 sdot (119897id + 119897

119905+119873 sdot (119897

119889+ 119897ℎ)) sdot 119871

119862119876




ℎ

(12)



Para n 119897id (bit) 119897119905(bit) 119897

119889(bit) 119897

ℎ(bit) 119873 119896

Val 250 32 32 32 128 20 10



119889)

119862119876

times 100


119889+ (120583 + 1) sdot 119897

ℎ


ℎ

times 100

(13)







ℎ respectively





Network ID1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

In-c

ell c

omm

unic

atio

n co

st (b

it)

46

48

5

52

54

56

58

6

62

64

66

ETQ-RIVEVTQ

VSFTQAD-VQ

times106


In-c

ell c

omm

unic

atio

n co

st (b

it)n

200 250 300 350 400 450 5004

5

6

7

8

9

10

times106

ETQ-RIVEVTQ

VSFTQAD-VQ

(b) 119862119868 versus 119899










n

200 250 300 350 400 450 5000

02

04

06

08

1

12

14

16

18

2

Que

ry co

mm

unic

atio

n co

st (b

it)

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119876 versus 119899

k

10 20 30 40 50 60 70 80 90 100

Que

ry co

mm

unic

atio

n co

st (b

it)ETQ-RIVEVTQ

VSFTQAD-VQ

107

106

105

104

(b) 119862119876 versus 119896


k

10 20 30 40 50 60 70 80 90 100

Redu

ndan

cy ra

te (

)

80

82

84

86

88

90

92

94

96

98

100

ETQ-RIVEVTQ

VSFTQAD-VQ

120574 versus k





7 Conclusions





Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(2) 2 le 120583119894lt 119873 and 119867

119894= 119867119896119894(119905 1198891198941

sdot sdot sdot 119889119894119873

Ψ) and 119889119894119897119894

Condition 3 Let 1199041 1199042 119904



is ⟨id(1199041) 1198891

id(1199042) 1198892 id(119904





(119905 1198891) HMAC1198702

(119905 1198892) HMAC

119870119901(119905 119889

119901) using the key 119870

1 1198702 119870

119901shared with

1199041 1199042 119904


(1198670 = ⨁

119889119895isinDS1015840HMAC

119870119895(119905 119889

119895))


119895ltmin (119877

119905))

(11)


5 Protocol Analysis


119876 Assume that




119905bits




119862119868= 119899 sdot (119897id + 119897

119905+119873 sdot (119897

119889+ 119897ℎ)) sdot 119871

119862119876




ℎ

(12)



Para n 119897id (bit) 119897119905(bit) 119897

119889(bit) 119897

ℎ(bit) 119873 119896

Val 250 32 32 32 128 20 10



119889)

119862119876

times 100


119889+ (120583 + 1) sdot 119897

ℎ


ℎ

times 100

(13)







ℎ respectively





Network ID1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

In-c

ell c

omm

unic

atio

n co

st (b

it)

46

48

5

52

54

56

58

6

62

64

66

ETQ-RIVEVTQ

VSFTQAD-VQ

times106


In-c

ell c

omm

unic

atio

n co

st (b

it)n

200 250 300 350 400 450 5004

5

6

7

8

9

10

times106

ETQ-RIVEVTQ

VSFTQAD-VQ

(b) 119862119868 versus 119899










n

200 250 300 350 400 450 5000

02

04

06

08

1

12

14

16

18

2

Que

ry co

mm

unic

atio

n co

st (b

it)

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119876 versus 119899

k

10 20 30 40 50 60 70 80 90 100

Que

ry co

mm

unic

atio

n co

st (b

it)ETQ-RIVEVTQ

VSFTQAD-VQ

107

106

105

104

(b) 119862119876 versus 119896


k

10 20 30 40 50 60 70 80 90 100

Redu

ndan

cy ra

te (

)

80

82

84

86

88

90

92

94

96

98

100

ETQ-RIVEVTQ

VSFTQAD-VQ

120574 versus k





7 Conclusions





Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Network ID1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

In-c

ell c

omm

unic

atio

n co

st (b

it)

46

48

5

52

54

56

58

6

62

64

66

ETQ-RIVEVTQ

VSFTQAD-VQ

times106


In-c

ell c

omm

unic

atio

n co

st (b

it)n

200 250 300 350 400 450 5004

5

6

7

8

9

10

times106

ETQ-RIVEVTQ

VSFTQAD-VQ

(b) 119862119868 versus 119899










n

200 250 300 350 400 450 5000

02

04

06

08

1

12

14

16

18

2

Que

ry co

mm

unic

atio

n co

st (b

it)

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119876 versus 119899

k

10 20 30 40 50 60 70 80 90 100

Que

ry co

mm

unic

atio

n co

st (b

it)ETQ-RIVEVTQ

VSFTQAD-VQ

107

106

105

104

(b) 119862119876 versus 119896


k

10 20 30 40 50 60 70 80 90 100

Redu

ndan

cy ra

te (

)

80

82

84

86

88

90

92

94

96

98

100

ETQ-RIVEVTQ

VSFTQAD-VQ

120574 versus k





7 Conclusions





Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










n

200 250 300 350 400 450 5000

02

04

06

08

1

12

14

16

18

2

Que

ry co

mm

unic

atio

n co

st (b

it)

ETQ-RIVEVTQ

VSFTQAD-VQ

times106

(a) 119862119876 versus 119899

k

10 20 30 40 50 60 70 80 90 100

Que

ry co

mm

unic

atio

n co

st (b

it)ETQ-RIVEVTQ

VSFTQAD-VQ

107

106

105

104

(b) 119862119876 versus 119896


k

10 20 30 40 50 60 70 80 90 100

Redu

ndan

cy ra

te (

)

80

82

84

86

88

90

92

94

96

98

100

ETQ-RIVEVTQ

VSFTQAD-VQ

120574 versus k





7 Conclusions





Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









an efficient top-query processing with result integrity verification

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