Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 230140 8 pageshttpdxdoiorg1011552013230140

Research ArticlePerturbation-Based Schemes with Ultra-LightweightComputation to Protect User Privacy in Smart Grid

Wei Ren12 Liangli Ma3 and Yi Ren4

1 School of Computer Science China University of Geosciences Wuhan 430074 China2 Shandong Provincial Key Laboratory of Computer Network Jinan 250014 China3 School of Electronic Engineering Naval University of Engineering Wuhan 430033 China4Department of Computer Science National Chiao Tung University Hsinchu 30010 Taiwan

Correspondence should be addressed to Wei Ren weirencscugeducn

Received 22 August 2012 Revised 4 February 2013 Accepted 5 February 2013

Academic Editor Sunho Lim

Copyright copy 2013 Wei Ren 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

In smart grid smart meters are deployed to collect power consumption data periodically and the data are analyzed to improvethe efficiency of power transmission and distribution The collected consumption data may leak the usage patterns of domesticappliances so that it may damage the behavior privacy of customers Most related work to protect data privacy in smart gridrelies on cryptographic primitives for example encryption which induces a large amount of power consumption overhead In thispaper we make the first attempt to propose solutions without any cryptographic computation to protect user privacy The privacyin smart grid is formally defined in the paper Three schemes are proposed random perturbation scheme (RPS) random walkscheme (RWS) and distance-bounded random walk with perturbation scheme (DBS) Three algorithms are also proposed in eachscheme respectively All schemes are ultra-lightweight in terms of computation without relying any cryptographic primitive Theprivacy soundness and accuracy of proposed schemes are guaranteed and justified by strict analysis

1 Introduction

Smart grid is a typical application of Internet ofThingsM2Mor IP-based sensor networks It has been envisioned as akey method to reduce the emission of carbon dioxide andretard climate changes by improving the efficiency of powerdistribution and transmission

Smart grid relies on smart meters to collect power con-sumption data at user ends instantly Smart meters report thepower consumption data periodically to smart grid controlcenter (SGCC) SGCC thus can allocate necessary powerdistribution and schedule required power transmission Inaddition the SGCC can relocate the power requirements atuser ends by delivering power price to users Users thus canschedule the usage of their household appliances accordingto the forthcoming price

As smart meters report the power consumption dataperiodically the data may leak user privacy in daily life Forexample the data may be used for deducing user behavior

patterns such as when she gets up according to the dataof using microwave oven or toaster in the morning whenshe goes back home according to the data of using electricstove for cooking at afternoon or when she takes bath orgoes to bed at night according to the data of using waterheater or lamps Such privacy concerns have already beenacknowledged and reported by NIST [1] and significantlyaffect the deployment of smart meters

Although there exist several privacy protection or secu-rity improvement for smart grid currently [2ndash6] most ofthem rely on cryptographic primitives for example encrypt-ing the uploading data at smart meters Cryptographicoperations are usually not lightweight so that theywill induceextra power consumption at smart meters In addition thedata uploading may occur frequently and periodically sothe computation for data encryption occurs extensively Forexample data are uploaded to SGCC once in 10 minutesThe encryption for the data has to be 144 times a dayThus the energy consumption for encryption computation

2 International Journal of Distributed Sensor Networks

would be large for a month even at single smart meterMoreover the extra power consumption will be accumulatedto an unsatisfactory waste because the number of smartmeters in smart grid is huge Furthermore the decryptioncomputation at SGCC has to be conducted if the uploadingdata are encrypted at smart meters The energy consumptionof decryption at SGCC will thus extremely increase Lastbut not least the smart meters usually have resource andpower constraints like traditional sensors As the privacyprotection must be conducted at smart meters any com-putation for privacy protection should cost low energy totackle these constraints The frequent encryption operationsare undesirable Even though the encryption is lightweightin certain situations the key management for encryptionis also a difficult issue for deployment Therefore privacyprotection by encryption unfortunately contradicts the inten-tion of smart grid for saving energy an ultra-lightweightmethod without any cryptographic computation for privacyprotection is mandatory for a long run and a large scale

In this paper we propose perturbation-based schemeswith ultra-lightweight computation without any crypto-graphic computation Besides we strictly and formally defineand proof its privacy protection strengthWe adapt a rigorousmethod to state present and analyze the privacy protectionachievements All our presentations strictly follow the formalexpressions for better clarity and generality

The contributions of the paper are listed as follows(i) we propose ultra-lightweight privacy-protection schemesin terms of computation (and thus energy consumption)without any cryptographic computation (ii) we strictly definethe requirements on privacy soundness and accuracy insmart grid and proof the guarantee of those requirements

The rest of the paper is organized as follows In Section 2we discuss the basic assumption andmodels used throughoutthe paper Section 3 provides the detailed description of ourproposedmodels and analysis Section 4 gives an overview onrelevant prior work Finally Section 5 concludes the paper

2 Problem Formulation

21 Network Model Two major entities exist in smart gridsmart meter (denoted by SM hereafter) and SGCC

SM computes power consumption data and uploads themto SGCC periodically The period for computing powerconsumption data at SM is called sensing period The periodfor uploading power consumption data to SGCC is calleduploading period Without loss of generality suppose thesensing period and uploading period are both 119905minutes Thesensing times and uploading times in a day will thus be 119899 =[24 lowast 60119905] The total sensing data for a day are denoted asa set 119863119860119879119860

119904= 1198891199041 119889119904

119899 The total uploading data for a

day are denoted as a set119863119860119879119860119906= 119889119906

1 119889119906

119899 If SM does

not hide119863119860119879119860119904119863119860119879119860

119904will be the same as119863119860119879119860

119906

In smart grid utility price may vary in different timeslotsThe price information is delivered by SGCC in advanceUsers use such information to guide the power consumptionSM receives such information to calculate utility charge in amonth for users Suppose the prices for 119899 uploading periods

in a day are denoted as a set 119875119877119868119862119864 = 1199011 1199012 119901

119899 Thus

the total utility charge for a day issum119899119894=1119889119906119894lowast119901119894The total utility

charge for amonth is the summation of charges for all days inthismonth If the sensing data are changed into the uploadingdata for protecting privacy the total utility charge for a dayshould be remained correct

22 Attack Model and Trust Model Only adversaries whoattack user privacy are considered in this paper Adversariescan eavesdrop the channels between SM and SGCC those aredenoted asA

119888 Adversaries at SGCC can access all uploading

data by SM those are denoted asA119904 Both adversaries desire

to deduce the user behaviors in a day by analyzing theuploading data fromSM namely119863119860119879119860

119906 AsA

119888andA

119904have

the same viewon119863119860119879119860119906 we further do not distinguish those

two adversaries Both are denoted by the same notationASGCC is untrustworthy as we assume adversaries at

SGCC are interested in user privacy SM should be trustwor-thy It is a prerequisite for any further discussion sensing dataare at SM and all possible solutions are conducted at SMBesides if SM is untrustworthy users will not choose themSM can be easily evaluated and authorized by a TrustedThirdParty (TTP)

23 Security Definition and Design Goal Informally speak-ing the privacy is guaranteed if the adversaries (not only atSGCC but also at channels between SGCC and SM) cannotdeduce the user activities in a day More specifically weformally state the privacy requirement definition as follows

Definition 1 User activities They are the activities thatdamage user privacy and are related to using one or multiplehousehold appliances in a daily life They are denoted as a set119860119862119879 = 119886

1 1198862 119886

119898 where 119886

119894(119894 = 1 119898) is an activity

related to one or multiple appliances

Definition 2 Deduce It means an activity in 119860119862119879 can beinferred by data in119863119860119879119860

119887 If an activity 119886

119895isin 119860119862119879 is inferred

by data 119889119894isin 119863119860119879119860

119887 it is denoted as a relation (119889

119894 119886119895) isin 119877 =

119863119860119879119860119887times 119860119862119879 where 119877 is a deduction relationship set and

defined previously and empirically119863119860119879119860119887is the set of ldquobadrdquo

data that can infer to at least one in 119860119862119879

Definition 3 Perfect full privacy (denoted as Privacy119901

full)

Simply speaking any adversary A cannot deduce fromanyone in119863119860119879119860

119906to one in119860119862119879 after viewing119863119860119879119860

119906More

specifically given anyone 119889119906119894isin 119863119860119879119860

119906 it is impossible for

any adversary A to find 119886119895isin 119860119862119879 such that (119889119906

119894 119886119895) isin 119877

That is

Pr forall119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0

(1)

where Pr119860 119861 denotes after viewing ldquo119861rdquo the probability ofevent ldquo119860rdquo happens ldquolArrrdquo means ldquois selected fromrdquo ldquordquo meanstwo operations happen consequently ldquostrdquo is a shorthand forldquosuch thatrdquo

International Journal of Distributed Sensor Networks 3

Definition 4 Computational full privacy (denoted asPrivacy119888full) Given anyone 119889119906

119894isin 119863119860119879119860

119906 it is computa-

tionally infeasible for any Probabilistic Polynomial TuringMachine (PPTM) adversary A to find 119886

119895isin 119860119862119879 such that

(119889119906119894 119886119895) isin 119877 That is

Pr forall119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

lt negl (119911)

(2)

where negl(119911) is a negligible functionwith security parameter119911

Claim 1 Perfect (computational) full privacy can protect userprivacy on all user activities in a day as no activity can bededuced from data in119863119860119879119860

119906by any (PPTM) adversary

In previous claim the content in ldquo()rdquo is correspondedwith each other Similarly the perfect (computational) partialprivacy can be defined in the following

Definition 5 Perfect (computational) partial privacy denot-ed as Privacy119901(119888)

partial Given at least one 119889119906

119894isin 119863119860119879119860

119906 it is

computationally infeasible for any (PPTM) adversary A tofind 119886

119895isin 119860119862119879 such that (119889119906

119894 119886119895) isin 119877 after viewing 119863119860119879119860

119906

Besides given at least one 119886119895isin 119860119862119879 it is computationally

infeasible for any (PPTM) adversaryA to find 119889119906119894isin 119863119860119879119860

119906

such that (119889119906119894 119886119895) isin 119877 after viewing119863119860119879119860

119906 That is

Pr exist119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0 (lt negl (119911))

Pr exist119886119895isin 119860119862119879 119889119906

119894lArr997904 119863119860119879119860

119906 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0 (lt negl (119911))

(3)

Claim 2 Perfect (computational) partial privacy can protectcertain privacy-sensitive activities as these activities cannotbe deduced by119863119860119879119860

119906by any (PPTM) adversary

Claim 3 Full privacy has stronger strength than partialprivacy in terms of the number of deducible data in119863119860119879119860

119906

Perfect privacy has stronger strength than computationalprivacy due to the adversaryrsquos ability That is

Privacy119888

partical lt Privacy119901

partical lt Privacy119888

full lt Privacy119901

full

(4)

where ldquo119860 lt 119861rdquo means that the privacy protection strength ofldquoArdquo is weaker than that of ldquoBrdquo

Roughly speaking full privacy protects all activities par-tial privacy protects partial activities Perfect privacy defendsagainst any adversary computational privacy defends againstany PPTM adversary As perfect full privacy has the strongestprivacy strength we thus concentrate on the perfect fullprivacy protection in the following

Definition 6 Full privacy attacking experiment on thescheme Π defending against any adversary A-ExpPrivacy

119901AΠ

fullis defined as follows

(1) the scheme Π is executed in the presence of anyadversaryA

(2) A fully accesses 119863119860119879119860119906 119860119862119879 and 119877 Given any

119889119906119894isin 119863119860119879119860

119906 if A can find 119886

119895isin 119860119862119879 such that

(119889119906119894 119886119895) isin 119877A outputs 1 otherwise outputs 0

(3) if and only ifA outputs 1 the experiment outputs 1

Definition 7 The scheme Π that can guarantee the perfectfull privacy in presence of any adversary A (denoted asPrivacy

119901AΠ

full= 1) is defined as follows

For any adversary A that the scheme Π defends againstthe probability that the output of the full privacy attackingexperiment equals one is 0 That is if and only if

Pr [ExpPrivacy119901AΠfull = 1] = 0 (5)

Privacy119901AΠ

full= 1

Therefore the design goal is to propose a scheme Π sat-isfying Privacy

119901AΠ

fulland importantly with ultra-lightweight

computation without any cryptographic computation

3 Proposed Schemes

31 ProblemReduction To protect the privacy of sensing data119863119860119879119860

119904 a naive method is encrypting them at SM and then

uploading them to SGCC As SGCC is untrustworthy SGCCcannot decrypt them and has to consult a TTP The TTPdecrypts the data and the result cannot be sent to SGCCTheTTP should compute accumulative values (or metadata) andsend them to SGCC for further scheduling and charging Itobviously arises multiple overheads a large volume of com-putation overhead at SM extra communication overhead atSM and SGCC extra entity TTP key management overheadbetween SM and TTP

As SM is trustworthy SM is proposed to equip a trustedmixing layer between sensing layer and communication layerThat is SM is modeled as three tuples ⟨119871

119904 119871119898 119871119888⟩ where

119871119904is a sensing layer computing the power consumption

periodically The output of layer 119871119904is 119863119860119879119860

119904 119871119898

is amixing layer that transfers 119863119860119879119860

119904into 119863119860119879119860

119906 119871119888is a

communication layer that uploads119863119860119879119860119906to SGCCThat is

SM = ⟨119871119904 119871119898 119871119888⟩

119871119904997904rArr 119871

119898 119863119860119879119860

119904

119871119898= 119865 119863119860119879119860

119904997888rarr 119863119860119879119860

119906

119871119898997904rArr 119871

119906 119863119860119879119860

119906

(6)

where ldquo=rdquo means ldquois defined asrdquo ldquorArrrdquo means ldquodata trans-ferring between layersrdquo 119865 is a data transforming functionldquorarr rdquo that means the input of the function 119865 is transformedinto the output of the function 119865 Therefore it becomes the

4 International Journal of Distributed Sensor Networks

concentration to search an ultra-lightweight transformationfunction 119865 with Privacy

119901A119865

full= 1 in the rest of the paper

Definition 8 ldquoBadrdquo data set (119863119860119879119860119887) It consists of all

power consumption data that can deduce to one or multipleactivities in119860119862119879119863119860119879119860

119887= 1198891198871 1198891198872 119889119887

119900 where 119900 is the

total number of 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)

The characteristics of 119863119860119879119860119887 119860119862119879 and deduction

relationship set 119877 are as the following

(1) Without loss of generality 119863119860119879119860119887is a sorted set of

positive numbersThat is1198891198871lt 1198891198872lt sdot sdot sdot lt 119889119887

1199001198891198871is

equal to or greater than the power consumption of theminimum power consumption appliance in a period119889119887119900is equal to or less than the power consumption of

all appliances in a period

(2) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may represent the

usage of one appliance in a period For example 1198891198871

(30wh) is the power consumption of a lamp for aperiod 119889119887

1is related to an event (eg 119886

1) that means

the lamp is on in the period

(3) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may also repre-

sent the usage of multiple household appliances Forexample 119889119887

9represents two household appliances

used simultaneously 1198891198879= 1198891198871+ 1198891198872 where 119889119887

1is

the power consumption of the lamp in a period 1198891198872

is the power consumption of the washing machine inthe period Thus 119889119887

9means using lamp and washing

machine simultaneously in the period

(4) Similarly any 119886119895isin 119860119862119879 (119895 = 1 119898)may represent

the usage of one appliance or multiple householdappliances simultaneously

(5) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) is related to at least

one 119886119895isin 119860119862119879 (119895 = 1 119898) any 119886

119895isin 119860119862119879 (119895 =

1 119898) is related to at least one in 119889119887119894isin 119863119860119879119860

119887(119894 =

1 119900)

(6) Different 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) cannot be relat-

ed to the same 119886119895isin 119860119862119879 (119895 = 1 119898) as any 119886

119895isin

119860119862119879 (119895 = 1 119898) has single power consumption ina period

(7) 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)may be related tomultiple

119886119895 because such 119889119887

119894may be the power consumption

for multiple appliances and those appliances mayhave the same power consumption in total Forexample 119889119887

9= 1198891198871+ 1198891198872= 1198891198873+ 1198891198874 1198891198879is related

to 1198865 1198866isin 119860119862119879 where 119886

5means using lamp and

washing machine simultaneously and 1198866means the

usage of the other two appliances

In summary the deduction relationship set119877 = 119863119860119879119860119887times

119860119862119879 can be further refined from a general relationship set toa relationship set with following properties

Pr forall119889119887119894isin 119863119860119879119860

119887 exist119886119895isin 119860119862119879 st (119889119887

119894 119886119895) isin 119877 = 1

Pr forall119886119895isin 119860119862119879 exist119889119887

119894isin 119863119860119879119860

119887 st (119889119887

119894 119886119895) isin 119877 = 1

Pr exist119889119887119894isin 119863119860119879119860

119887 1198861198951isin 119860119862119879 119886

1198952isin 119860119862119879

st (119889119887119894 1198861198951) isin 119877 (119889119887

119894 1198861198952) isin 119877 gt 0

Pr exist1198891198941isin 119863119860119879119860

119887 1198891198942isin 119863119860119879119860

119887 119886119895isin 119860119862119879

st (1198891198941 119886119895) isin 119877 (119889

1198942 119886119895) isin 119877 = 0

(7)

In other words mapping 119863119860119879119860119887rarr 119860119862119879 is not a

function and mapping 119860119862119879 rarr 119863119860119879119860119887is a surjective and

not a injective function

Definition 9 After transformation 119865 the privacy of119863119860119879119860

119906is guaranteed (denoted as Privacy119865

119863119860119879119860119906

= 1)Privacy119865

119863119860119879119860119906

= 1 if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) notin 119863119860119879119860

119887 (8)

where 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

Definition 10 After transformation 119865 the soundness of119863119860119879119860

119906is guaranteed (Soundness119865

119863119860119879119860119906

= 1) The utilitysummation remains unchanged That is

119899

sum

119894=1

119889119904119894lowast 119901119894=

119899

sum

119894=1

119889119906119894lowast 119901119894 (9)

Due to the concentration in the rest of the paper theresearch problem is reduced to as follows given119863119860119879119860

119904 find

an ultra-lightweight transformation 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

such that the privacy and soundness of 119863119860119879119860119906are both

guaranteed That is given 119863119860119879119860119904 find 119865 119863119860119879119860

119904rarr

119863119860119879119860119906 st Privacy119865

119863119860119879119860119906

= 1 and Soundness119865119863119860119879119860

119906

= 1Next we propose a family of schemes to solve the

problem We list all major notations used in the remainderof the paper in Table 1

32 Random Perturbation Scheme (RPS) We firstly proposea basic scheme-random perturbation scheme (RPS) to illus-trate our motivations In RPS any 119889119904

119894isin 119863119860119879119860

119904is perturbed

into a new value in the middle of 119889119887119895and 119889119887

119895minus1or in the

middle of 119889119887119895and 119889119887

119895+1The two cases are selected randomly

A Random Perturbation Algorithm called RPA is proposedfor transformation 119865 as follows

321 Analysis of Algorithm 1

Proposition 11 After the transformation of algorithmRPA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119875119860119863119860119879119860

119906

= 1)

International Journal of Distributed Sensor Networks 5

Table 1 Notation

A Adversary119863119860119879119860

119904= 119889119904

1 119889119904

119899 Sensing power consumption data set

119863119860119879119860119906= 119889119906

1 119889119906

119899 Uploading power consumption data set

119865 Transforming function from119863119860119879119860119904to119863119860119879119860

119906

119863119860119879119860119887= 119889119887

1 119889119887

119900 ldquoBadrdquo power consumption data set

119875119877119868119862119864 = 1199011 1199012 119901

119899 Price set

119860119862119879 = 1198861 1198862 119886

119898 Activity set

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRPA

119863119860119879119860119906

=1 SoundnessRPA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904) Get a data from119863119860119879119860

119904

for 119894 = 1 to 119899 minus 1 doif ((119889119904

119894== 119889119887

1)OR (119889119887

1lt 119889119904119894lt 1198891198872)) then

119889119906119894lArr (119889119887

1+ 1198891198872)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif ((119889119904

119894== 119889119887

119900)OR (119889119887

119900minus1lt 119889119904119894lt 119889119887119900)) then

119889119906119894lArr (119889119887

119900minus1+ 119889119887119900)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end iffor 119895 = 2 to 119900 minus 1 do

if (119889119904119894== 119889119887

119895) then

119889119906119894lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119887

119895+ 119889119887119895+1)2 (119889119887

119895+ 119889119887119895minus1)2)

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif (119889119887

119895lt 119889119904119894lt 119889119887119895+1)then

119889119906119894lArr (119889119887

119895+ 119889119887119895+1)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifend for

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899For soundness

Algorithm 1 Random Perturbation AlgorithmmdashRPA

Proof The biases of 119889119906119894(119894 = 1 119899 minus 1) comparing to

119889119904119894(1 119899minus1) are accumulated into a total value119861119868119860119878119861119868119860119878

is changed into extra power consumption and added to thelast one 119889119906

119899 Thussum119899

119894=1119889119904119894lowast119901119894= sum119899

119894=1119889119906119894lowast119901119894 The total cost

of power consumption in a day maintains the correct valueso SoundnessRPA

119863119860119879119860119906

= 1

Proposition 12 The scheme RPS is ultra-lightweight

Proof As algorithm RPA is ultra-lightweight the number ofloops is (119899 minus 1) lowast (119900 minus 2) The computation in each loop isonly simple operations such asmodulo minus plus divisionandmultiplicationThe computation complexity of algorithmRPA is 119874(119899 lowast 119900)

Proposition 13 The scheme RPS can guarantee the perfect fullprivacy (Privacy119901A119877119875119878

119891119906119897119897= 1)

Proof It is clear that for all 119889119904119894isin 119863119860119879119860

119904 119889119906119894= 119865(119889119904

119894) notin

119863119860119879119860119887 Thus PrivacyRPA

119863119860119879119860119906

= 1 According to the definitionof the perfect full privacy Privacy119901ARPS

full= 1

33 RandomWalk Scheme (RWS) If the gap between 119889119887119895and

119889119887119895+1

(119895 = 1 119900minus1) is small the perturbation (namely 120575) inRPSwill be small It can be proofed as a claim in the following

Claim 4 If the gap between 119889119887119895and 119889119887

119895+1(119895 = 1 119900 minus 1) is

small the perturbation in RPS will be small

Proof Suppose max(|119889119887119895minus 119889119887119895+1|) = 119892(119895 = 1 119899 minus 1) If

119889119904119894= 119889119887119895isin 119863119860119879119860

119887) in RPA max(120575) le 1198922 If 119889119904

119894= 119889119887119895isin

119863119860119879119860119887 max(120575) lt 1198922 Thus the perturbation 120575 is small if 119892

is small

6 International Journal of Distributed Sensor Networks

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRWA

119863119860119879119860119906

= 1 SoundnessRWA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 do119895 lArr (119903119886119899119889119900119898()119900 + 1)119889119906119894lArr 119889119887

119895

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 2 RandomWalk Algorithm (RWA)

If the perturbation is small adversaries may guess the 119889119904119894

correctly and adversaries can guess the activity is either oftwo activities To address this issue we propose a randomwalk scheme called RWS in which 119889119904

119894isin 119863119860119879119860

119904randomly

jumps to a value in119863119860119879119860119887 In this case the privacy definition

is extended to include unlinkability inwhich the possibility of119889119887119895isin 119863119860119879119860

119887for 119889119904

119894is equal Thus the revealed user activity

occurs with equal possibility

Definition 14 After transformation 119865 the privacy of119863119860119879119860119906

is guaranteed (denoted as Privacy119865119863119860119879119860

119906

= 1) if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) isin 119863119860119879119860

119906

forall119889119887119901 119889119887

119902isin 119863119860119879119860

119887 119889119887

119901= 119889119887119902

Pr 119889119906119894= 119889119887119901 = Pr 119889119906

119894= 119889119887119902

(10)

The definition for privacy is thus extended to include thedefinition here and Definition 9

In RWS any 119889119904119894isin 119863119860119879119860

119904(119894 = 1 119899 minus 1) is perturbed

to a value 119889119887119895isin 119863119860119879119860

119887(119895 = 1 119900) which is randomly

selected This algorithm is thus especially ultra-lightweightin terms of computation A randomwalk algorithm (RWA) isproposed for the transformation function 119865 as follows

331 Analysis of Algorithm 2

Proposition 15 After the transformation of algorithmRWA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119882119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Proposition 11As sum119899119894=1119889119904119894lowast 119901119894= sum119899

119894=1119889119906119894lowast 119901119894 the total cost of power

consumption in a day maintains the correct value Thus thesoundness of RWA is guaranteed

Proposition 16 The scheme RWS is ultra-lightweight

Proof The number of loops is 119899 minus 1 so algorithm RPA isultra-lightweight The computations in loops are only simpleoperations such as modulo minus plus and multiplication

Moreover algorithm RWA is more lightweight than algo-rithm RPA Thus scheme RWS is ultra-lightweight

Proposition 17 The scheme RWS can guarantee the perfectfull privacy (Privacy119901A119877119882119878

119891119906119897119897= 1)

Proof According to the algorithm for for all 119889119904119894isin 119863119860119879119860

119904

if 119889119906119894= 119865(119889119904

119894) isin 119863119860119879119860

119906 we have forall119889119887

119901 119889119887119902isin 119863119860119879119860

119887

119889119887119901= 119889119887119902 and Pr119889119906

119894= 119889119887

119901 = Pr119889119906

119894= 119889119887

119902 Thus

PrivacyRWA119863119860119879119860

119906

= 1 According to the definition of the privacyin Definition 14 Privacy119901ARWS

full= 1

34 Distance-Bounded Random Walk with PerturbationScheme (DBS) In smart grid the uploading data will beused as a feedback for future scheduling of distribution andtransmission It thus requires the uploading data can accu-rately present the power consumption (namely sensing data)However thanks to the power distribution and transmissionserve not for a single SM but a large number of SMs (eg acampus a community or a county scale) only the accuracyfor a scale of SMs is sufficient for scheduling

In RPS and RWS although the bias exists (that isuploading data is not equal to sensing data) at single SMthe uploading data for a large number of SMs can stillrepresent power consumption in a scaleMore specifically thedeviation between the summation of uploading data and thesummation of sensing data is randomly positive or negativein one SM thus the overall summation remains almostunchanged in expectation in a large scale It is explained asfollows

Definition 18 After the transformation 119865 the accuracy of119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(denoted as Accuracy119865119863119860119879119860

119906

= 1) The summation of119863119860119879119860119906

equals the summation of 119863119860119879119860119904 in scheduling area and

scheduling period More specifically suppose that eachscheduling period consists of 119909 sensing (uploading) periodand each scheduling area consists of 119910 SMs The uploadingdata for them is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 The

sensing data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894

International Journal of Distributed Sensor Networks 7

Required119863119860119879119860119904 119863119860119879119860

119887 BOUND

Ensure119863119860119879119860119906 PrivacyDBA

119863119860119879119860119906

= 1 SoundnessDBA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 doWHILE (1)

119895 lArr (119903119886119899119889119900119898()(119900 minus 2) + 2)120575 lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119904

119894minus (119889119887119895+ (119889119887119895+1minus 119889119887119895)2)) (119889119904

119894minus (119889119887119895+ (119889119887119895minus 119889119887119895minus1)2)))

if (119886119887119904(120575) le 119861119874119880119873119863) then119889119906119894lArr 119889119904

119894minus 120575

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

EXITelse

CONTINUEend if

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 3 Distance-Bounded Algorithm (DBA)

The accuracy of119863119860119879119860119906is guaranteed if and only if SUM

119904=

SUM119906

Proposition 19 After the transformation 119877119875119860 or 119877119882119860 theaccuracy of119863119860119879119860

119906is guaranteed in expectation for a schedul-

ing area (Accuracy119877119875119860119877119882119860119863119860119879119860

119906

= 1)

Proof In each sensing (uploading) period 119889119904119894is changed into

119889119906119894at single SM 120575 = 119889119904

119894minus 119889119906119894 Suppose that each scheduling

period consists of 119909 sensing (uploading) period and eachscheduling area consists of 119910 SMs The uploading data forthem is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 the sensing

data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894 The

expectation of both is equal as the expectation of 120575 is 0 ina scheduling area That is SUM

119904= SUM

119906 as 120575 = 0 where119867

means the expectation of119867

To further guarantee the scheduling accuracy we proposea distance-bounded scheme in which the perturbation value(ie 120575) is bounded The accuracy is thus guaranteed withina threshold value It takes the advantages of former twoalgorithms RPA and RWA A distance-bounded algorithm(DBA) for the transformation 119865 is proposed as follows

341 Analysis of Algorithm 3

Proposition 20 After the transformation of algorithmDBA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Propositions 11 and15

Proposition 21 The scheme DBS is ultra-lightweight

Proof The proof can be reduced to the proof of Propositions12 and 16

Proposition 22 The scheme DBS can guarantee the perfectfull privacy (Privacy119901A119863119861119878

119891119906119897119897= 1)

Proof Theproof is similar to the proof of Propositions 13 and17

Proposition 23 After the transformation 119863119861119860 the accuracyof 119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(Accuracy119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is reduced to the proof of Proposition 19

Proposition 24 The summation of uploading data equals thesummation of the sensing data with deviation bounded by 120572 lowast120573lowast119861119874119880119873119863 where 120572 is the number of SMs in a schedule area120573 is the number of sensing (uploading) period in a scheduleperiod (That is |119878119880119872

119906minus 119878119880119872

119904| le 120572 lowast 120573 lowast 119861119874119880119873119863)

Proof The schedule accuracy is the deviation between thesummation of uploading data and the summation of sensingdata As it is proofed in Proposition 19 it depends on thenumber of SMs in the schedule area and the number ofsensing (uploading) period in the schedule period Theexpectation value is proofed to be 0 as the expectation of120575 is 0 Concerning the accuracy of one schedule periodthe maximal bias between the summation of uploading dataand the summation of sensing data is bounded by 120572 lowast 120573 lowast119861119874119880119873119863

4 Related Work

The security architectures and overall security requirementsin smart grid were discussed in the recent years [3 7] Cur-rently the privacy issue in smart grid starts to attract moreattentions The requirements of privacy were explored insome previousworks [8ndash11]They pointed out the importance

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

2 International Journal of Distributed Sensor Networks

would be large for a month even at single smart meterMoreover the extra power consumption will be accumulatedto an unsatisfactory waste because the number of smartmeters in smart grid is huge Furthermore the decryptioncomputation at SGCC has to be conducted if the uploadingdata are encrypted at smart meters The energy consumptionof decryption at SGCC will thus extremely increase Lastbut not least the smart meters usually have resource andpower constraints like traditional sensors As the privacyprotection must be conducted at smart meters any com-putation for privacy protection should cost low energy totackle these constraints The frequent encryption operationsare undesirable Even though the encryption is lightweightin certain situations the key management for encryptionis also a difficult issue for deployment Therefore privacyprotection by encryption unfortunately contradicts the inten-tion of smart grid for saving energy an ultra-lightweightmethod without any cryptographic computation for privacyprotection is mandatory for a long run and a large scale

In this paper we propose perturbation-based schemeswith ultra-lightweight computation without any crypto-graphic computation Besides we strictly and formally defineand proof its privacy protection strengthWe adapt a rigorousmethod to state present and analyze the privacy protectionachievements All our presentations strictly follow the formalexpressions for better clarity and generality

The contributions of the paper are listed as follows(i) we propose ultra-lightweight privacy-protection schemesin terms of computation (and thus energy consumption)without any cryptographic computation (ii) we strictly definethe requirements on privacy soundness and accuracy insmart grid and proof the guarantee of those requirements

The rest of the paper is organized as follows In Section 2we discuss the basic assumption andmodels used throughoutthe paper Section 3 provides the detailed description of ourproposedmodels and analysis Section 4 gives an overview onrelevant prior work Finally Section 5 concludes the paper

2 Problem Formulation

21 Network Model Two major entities exist in smart gridsmart meter (denoted by SM hereafter) and SGCC

SM computes power consumption data and uploads themto SGCC periodically The period for computing powerconsumption data at SM is called sensing period The periodfor uploading power consumption data to SGCC is calleduploading period Without loss of generality suppose thesensing period and uploading period are both 119905minutes Thesensing times and uploading times in a day will thus be 119899 =[24 lowast 60119905] The total sensing data for a day are denoted asa set 119863119860119879119860

119904= 1198891199041 119889119904

119899 The total uploading data for a

day are denoted as a set119863119860119879119860119906= 119889119906

1 119889119906

119899 If SM does

not hide119863119860119879119860119904119863119860119879119860

119904will be the same as119863119860119879119860

119906

In smart grid utility price may vary in different timeslotsThe price information is delivered by SGCC in advanceUsers use such information to guide the power consumptionSM receives such information to calculate utility charge in amonth for users Suppose the prices for 119899 uploading periods

in a day are denoted as a set 119875119877119868119862119864 = 1199011 1199012 119901

119899 Thus

the total utility charge for a day issum119899119894=1119889119906119894lowast119901119894The total utility

charge for amonth is the summation of charges for all days inthismonth If the sensing data are changed into the uploadingdata for protecting privacy the total utility charge for a dayshould be remained correct

22 Attack Model and Trust Model Only adversaries whoattack user privacy are considered in this paper Adversariescan eavesdrop the channels between SM and SGCC those aredenoted asA

119888 Adversaries at SGCC can access all uploading

data by SM those are denoted asA119904 Both adversaries desire

to deduce the user behaviors in a day by analyzing theuploading data fromSM namely119863119860119879119860

119906 AsA

119888andA

119904have

the same viewon119863119860119879119860119906 we further do not distinguish those

two adversaries Both are denoted by the same notationASGCC is untrustworthy as we assume adversaries at

SGCC are interested in user privacy SM should be trustwor-thy It is a prerequisite for any further discussion sensing dataare at SM and all possible solutions are conducted at SMBesides if SM is untrustworthy users will not choose themSM can be easily evaluated and authorized by a TrustedThirdParty (TTP)

23 Security Definition and Design Goal Informally speak-ing the privacy is guaranteed if the adversaries (not only atSGCC but also at channels between SGCC and SM) cannotdeduce the user activities in a day More specifically weformally state the privacy requirement definition as follows

Definition 1 User activities They are the activities thatdamage user privacy and are related to using one or multiplehousehold appliances in a daily life They are denoted as a set119860119862119879 = 119886

1 1198862 119886

119898 where 119886

119894(119894 = 1 119898) is an activity

related to one or multiple appliances

Definition 2 Deduce It means an activity in 119860119862119879 can beinferred by data in119863119860119879119860

119887 If an activity 119886

119895isin 119860119862119879 is inferred

by data 119889119894isin 119863119860119879119860

119887 it is denoted as a relation (119889

119894 119886119895) isin 119877 =

119863119860119879119860119887times 119860119862119879 where 119877 is a deduction relationship set and

defined previously and empirically119863119860119879119860119887is the set of ldquobadrdquo

data that can infer to at least one in 119860119862119879

Definition 3 Perfect full privacy (denoted as Privacy119901

full)

Simply speaking any adversary A cannot deduce fromanyone in119863119860119879119860

119906to one in119860119862119879 after viewing119863119860119879119860

119906More

specifically given anyone 119889119906119894isin 119863119860119879119860

119906 it is impossible for

any adversary A to find 119886119895isin 119860119862119879 such that (119889119906

119894 119886119895) isin 119877

That is

Pr forall119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0

(1)

where Pr119860 119861 denotes after viewing ldquo119861rdquo the probability ofevent ldquo119860rdquo happens ldquolArrrdquo means ldquois selected fromrdquo ldquordquo meanstwo operations happen consequently ldquostrdquo is a shorthand forldquosuch thatrdquo

International Journal of Distributed Sensor Networks 3

Definition 4 Computational full privacy (denoted asPrivacy119888full) Given anyone 119889119906

119894isin 119863119860119879119860

119906 it is computa-

tionally infeasible for any Probabilistic Polynomial TuringMachine (PPTM) adversary A to find 119886

119895isin 119860119862119879 such that

(119889119906119894 119886119895) isin 119877 That is

Pr forall119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

lt negl (119911)

(2)

where negl(119911) is a negligible functionwith security parameter119911

Claim 1 Perfect (computational) full privacy can protect userprivacy on all user activities in a day as no activity can bededuced from data in119863119860119879119860

119906by any (PPTM) adversary

In previous claim the content in ldquo()rdquo is correspondedwith each other Similarly the perfect (computational) partialprivacy can be defined in the following

Definition 5 Perfect (computational) partial privacy denot-ed as Privacy119901(119888)

partial Given at least one 119889119906

119894isin 119863119860119879119860

119906 it is

computationally infeasible for any (PPTM) adversary A tofind 119886

119895isin 119860119862119879 such that (119889119906

119894 119886119895) isin 119877 after viewing 119863119860119879119860

119906

Besides given at least one 119886119895isin 119860119862119879 it is computationally

infeasible for any (PPTM) adversaryA to find 119889119906119894isin 119863119860119879119860

119906

such that (119889119906119894 119886119895) isin 119877 after viewing119863119860119879119860

119906 That is

Pr exist119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0 (lt negl (119911))

Pr exist119886119895isin 119860119862119879 119889119906

119894lArr997904 119863119860119879119860

119906 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0 (lt negl (119911))

(3)

Claim 2 Perfect (computational) partial privacy can protectcertain privacy-sensitive activities as these activities cannotbe deduced by119863119860119879119860

119906by any (PPTM) adversary

Claim 3 Full privacy has stronger strength than partialprivacy in terms of the number of deducible data in119863119860119879119860

119906

Perfect privacy has stronger strength than computationalprivacy due to the adversaryrsquos ability That is

Privacy119888

partical lt Privacy119901

partical lt Privacy119888

full lt Privacy119901

full

(4)

where ldquo119860 lt 119861rdquo means that the privacy protection strength ofldquoArdquo is weaker than that of ldquoBrdquo

Roughly speaking full privacy protects all activities par-tial privacy protects partial activities Perfect privacy defendsagainst any adversary computational privacy defends againstany PPTM adversary As perfect full privacy has the strongestprivacy strength we thus concentrate on the perfect fullprivacy protection in the following

Definition 6 Full privacy attacking experiment on thescheme Π defending against any adversary A-ExpPrivacy

119901AΠ

fullis defined as follows

(1) the scheme Π is executed in the presence of anyadversaryA

(2) A fully accesses 119863119860119879119860119906 119860119862119879 and 119877 Given any

119889119906119894isin 119863119860119879119860

119906 if A can find 119886

119895isin 119860119862119879 such that

(119889119906119894 119886119895) isin 119877A outputs 1 otherwise outputs 0

(3) if and only ifA outputs 1 the experiment outputs 1

Definition 7 The scheme Π that can guarantee the perfectfull privacy in presence of any adversary A (denoted asPrivacy

119901AΠ

full= 1) is defined as follows

For any adversary A that the scheme Π defends againstthe probability that the output of the full privacy attackingexperiment equals one is 0 That is if and only if

Pr [ExpPrivacy119901AΠfull = 1] = 0 (5)

Privacy119901AΠ

full= 1

Therefore the design goal is to propose a scheme Π sat-isfying Privacy

119901AΠ

fulland importantly with ultra-lightweight

computation without any cryptographic computation

3 Proposed Schemes

31 ProblemReduction To protect the privacy of sensing data119863119860119879119860

119904 a naive method is encrypting them at SM and then

uploading them to SGCC As SGCC is untrustworthy SGCCcannot decrypt them and has to consult a TTP The TTPdecrypts the data and the result cannot be sent to SGCCTheTTP should compute accumulative values (or metadata) andsend them to SGCC for further scheduling and charging Itobviously arises multiple overheads a large volume of com-putation overhead at SM extra communication overhead atSM and SGCC extra entity TTP key management overheadbetween SM and TTP

As SM is trustworthy SM is proposed to equip a trustedmixing layer between sensing layer and communication layerThat is SM is modeled as three tuples ⟨119871

119904 119871119898 119871119888⟩ where

119871119904is a sensing layer computing the power consumption

periodically The output of layer 119871119904is 119863119860119879119860

119904 119871119898

is amixing layer that transfers 119863119860119879119860

119904into 119863119860119879119860

119906 119871119888is a

communication layer that uploads119863119860119879119860119906to SGCCThat is

SM = ⟨119871119904 119871119898 119871119888⟩

119871119904997904rArr 119871

119898 119863119860119879119860

119904

119871119898= 119865 119863119860119879119860

119904997888rarr 119863119860119879119860

119906

119871119898997904rArr 119871

119906 119863119860119879119860

119906

(6)

where ldquo=rdquo means ldquois defined asrdquo ldquorArrrdquo means ldquodata trans-ferring between layersrdquo 119865 is a data transforming functionldquorarr rdquo that means the input of the function 119865 is transformedinto the output of the function 119865 Therefore it becomes the

4 International Journal of Distributed Sensor Networks

concentration to search an ultra-lightweight transformationfunction 119865 with Privacy

119901A119865

full= 1 in the rest of the paper

Definition 8 ldquoBadrdquo data set (119863119860119879119860119887) It consists of all

power consumption data that can deduce to one or multipleactivities in119860119862119879119863119860119879119860

119887= 1198891198871 1198891198872 119889119887

119900 where 119900 is the

total number of 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)

The characteristics of 119863119860119879119860119887 119860119862119879 and deduction

relationship set 119877 are as the following

(1) Without loss of generality 119863119860119879119860119887is a sorted set of

positive numbersThat is1198891198871lt 1198891198872lt sdot sdot sdot lt 119889119887

1199001198891198871is

equal to or greater than the power consumption of theminimum power consumption appliance in a period119889119887119900is equal to or less than the power consumption of

all appliances in a period

(2) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may represent the

usage of one appliance in a period For example 1198891198871

(30wh) is the power consumption of a lamp for aperiod 119889119887

1is related to an event (eg 119886

1) that means

the lamp is on in the period

(3) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may also repre-

sent the usage of multiple household appliances Forexample 119889119887

9represents two household appliances

used simultaneously 1198891198879= 1198891198871+ 1198891198872 where 119889119887

1is

the power consumption of the lamp in a period 1198891198872

is the power consumption of the washing machine inthe period Thus 119889119887

9means using lamp and washing

machine simultaneously in the period

(4) Similarly any 119886119895isin 119860119862119879 (119895 = 1 119898)may represent

the usage of one appliance or multiple householdappliances simultaneously

(5) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) is related to at least

one 119886119895isin 119860119862119879 (119895 = 1 119898) any 119886

119895isin 119860119862119879 (119895 =

1 119898) is related to at least one in 119889119887119894isin 119863119860119879119860

119887(119894 =

1 119900)

(6) Different 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) cannot be relat-

ed to the same 119886119895isin 119860119862119879 (119895 = 1 119898) as any 119886

119895isin

119860119862119879 (119895 = 1 119898) has single power consumption ina period

(7) 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)may be related tomultiple

119886119895 because such 119889119887

119894may be the power consumption

for multiple appliances and those appliances mayhave the same power consumption in total Forexample 119889119887

9= 1198891198871+ 1198891198872= 1198891198873+ 1198891198874 1198891198879is related

to 1198865 1198866isin 119860119862119879 where 119886

5means using lamp and

washing machine simultaneously and 1198866means the

usage of the other two appliances

In summary the deduction relationship set119877 = 119863119860119879119860119887times

119860119862119879 can be further refined from a general relationship set toa relationship set with following properties

Pr forall119889119887119894isin 119863119860119879119860

119887 exist119886119895isin 119860119862119879 st (119889119887

119894 119886119895) isin 119877 = 1

Pr forall119886119895isin 119860119862119879 exist119889119887

119894isin 119863119860119879119860

119887 st (119889119887

119894 119886119895) isin 119877 = 1

Pr exist119889119887119894isin 119863119860119879119860

119887 1198861198951isin 119860119862119879 119886

1198952isin 119860119862119879

st (119889119887119894 1198861198951) isin 119877 (119889119887

119894 1198861198952) isin 119877 gt 0

Pr exist1198891198941isin 119863119860119879119860

119887 1198891198942isin 119863119860119879119860

119887 119886119895isin 119860119862119879

st (1198891198941 119886119895) isin 119877 (119889

1198942 119886119895) isin 119877 = 0

(7)

In other words mapping 119863119860119879119860119887rarr 119860119862119879 is not a

function and mapping 119860119862119879 rarr 119863119860119879119860119887is a surjective and

not a injective function

Definition 9 After transformation 119865 the privacy of119863119860119879119860

119906is guaranteed (denoted as Privacy119865

119863119860119879119860119906

= 1)Privacy119865

119863119860119879119860119906

= 1 if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) notin 119863119860119879119860

119887 (8)

where 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

Definition 10 After transformation 119865 the soundness of119863119860119879119860

119906is guaranteed (Soundness119865

119863119860119879119860119906

= 1) The utilitysummation remains unchanged That is

119899

sum

119894=1

119889119904119894lowast 119901119894=

119899

sum

119894=1

119889119906119894lowast 119901119894 (9)

Due to the concentration in the rest of the paper theresearch problem is reduced to as follows given119863119860119879119860

119904 find

an ultra-lightweight transformation 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

such that the privacy and soundness of 119863119860119879119860119906are both

guaranteed That is given 119863119860119879119860119904 find 119865 119863119860119879119860

119904rarr

119863119860119879119860119906 st Privacy119865

119863119860119879119860119906

= 1 and Soundness119865119863119860119879119860

119906

= 1Next we propose a family of schemes to solve the

problem We list all major notations used in the remainderof the paper in Table 1

32 Random Perturbation Scheme (RPS) We firstly proposea basic scheme-random perturbation scheme (RPS) to illus-trate our motivations In RPS any 119889119904

119894isin 119863119860119879119860

119904is perturbed

into a new value in the middle of 119889119887119895and 119889119887

119895minus1or in the

middle of 119889119887119895and 119889119887

119895+1The two cases are selected randomly

A Random Perturbation Algorithm called RPA is proposedfor transformation 119865 as follows

321 Analysis of Algorithm 1

Proposition 11 After the transformation of algorithmRPA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119875119860119863119860119879119860

119906

= 1)

International Journal of Distributed Sensor Networks 5

Table 1 Notation

A Adversary119863119860119879119860

119904= 119889119904

1 119889119904

119899 Sensing power consumption data set

119863119860119879119860119906= 119889119906

1 119889119906

119899 Uploading power consumption data set

119865 Transforming function from119863119860119879119860119904to119863119860119879119860

119906

119863119860119879119860119887= 119889119887

1 119889119887

119900 ldquoBadrdquo power consumption data set

119875119877119868119862119864 = 1199011 1199012 119901

119899 Price set

119860119862119879 = 1198861 1198862 119886

119898 Activity set

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRPA

119863119860119879119860119906

=1 SoundnessRPA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904) Get a data from119863119860119879119860

119904

for 119894 = 1 to 119899 minus 1 doif ((119889119904

119894== 119889119887

1)OR (119889119887

1lt 119889119904119894lt 1198891198872)) then

119889119906119894lArr (119889119887

1+ 1198891198872)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif ((119889119904

119894== 119889119887

119900)OR (119889119887

119900minus1lt 119889119904119894lt 119889119887119900)) then

119889119906119894lArr (119889119887

119900minus1+ 119889119887119900)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end iffor 119895 = 2 to 119900 minus 1 do

if (119889119904119894== 119889119887

119895) then

119889119906119894lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119887

119895+ 119889119887119895+1)2 (119889119887

119895+ 119889119887119895minus1)2)

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif (119889119887

119895lt 119889119904119894lt 119889119887119895+1)then

119889119906119894lArr (119889119887

119895+ 119889119887119895+1)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifend for

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899For soundness

Algorithm 1 Random Perturbation AlgorithmmdashRPA

Proof The biases of 119889119906119894(119894 = 1 119899 minus 1) comparing to

119889119904119894(1 119899minus1) are accumulated into a total value119861119868119860119878119861119868119860119878

is changed into extra power consumption and added to thelast one 119889119906

119899 Thussum119899

119894=1119889119904119894lowast119901119894= sum119899

119894=1119889119906119894lowast119901119894 The total cost

of power consumption in a day maintains the correct valueso SoundnessRPA

119863119860119879119860119906

= 1

Proposition 12 The scheme RPS is ultra-lightweight

Proof As algorithm RPA is ultra-lightweight the number ofloops is (119899 minus 1) lowast (119900 minus 2) The computation in each loop isonly simple operations such asmodulo minus plus divisionandmultiplicationThe computation complexity of algorithmRPA is 119874(119899 lowast 119900)

Proposition 13 The scheme RPS can guarantee the perfect fullprivacy (Privacy119901A119877119875119878

119891119906119897119897= 1)

Proof It is clear that for all 119889119904119894isin 119863119860119879119860

119904 119889119906119894= 119865(119889119904

119894) notin

119863119860119879119860119887 Thus PrivacyRPA

119863119860119879119860119906

= 1 According to the definitionof the perfect full privacy Privacy119901ARPS

full= 1

33 RandomWalk Scheme (RWS) If the gap between 119889119887119895and

119889119887119895+1

(119895 = 1 119900minus1) is small the perturbation (namely 120575) inRPSwill be small It can be proofed as a claim in the following

Claim 4 If the gap between 119889119887119895and 119889119887

119895+1(119895 = 1 119900 minus 1) is

small the perturbation in RPS will be small

Proof Suppose max(|119889119887119895minus 119889119887119895+1|) = 119892(119895 = 1 119899 minus 1) If

119889119904119894= 119889119887119895isin 119863119860119879119860

119887) in RPA max(120575) le 1198922 If 119889119904

119894= 119889119887119895isin

119863119860119879119860119887 max(120575) lt 1198922 Thus the perturbation 120575 is small if 119892

is small

6 International Journal of Distributed Sensor Networks

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRWA

119863119860119879119860119906

= 1 SoundnessRWA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 do119895 lArr (119903119886119899119889119900119898()119900 + 1)119889119906119894lArr 119889119887

119895

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 2 RandomWalk Algorithm (RWA)

If the perturbation is small adversaries may guess the 119889119904119894

correctly and adversaries can guess the activity is either oftwo activities To address this issue we propose a randomwalk scheme called RWS in which 119889119904

119894isin 119863119860119879119860

119904randomly

jumps to a value in119863119860119879119860119887 In this case the privacy definition

is extended to include unlinkability inwhich the possibility of119889119887119895isin 119863119860119879119860

119887for 119889119904

119894is equal Thus the revealed user activity

occurs with equal possibility

Definition 14 After transformation 119865 the privacy of119863119860119879119860119906

is guaranteed (denoted as Privacy119865119863119860119879119860

119906

= 1) if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) isin 119863119860119879119860

119906

forall119889119887119901 119889119887

119902isin 119863119860119879119860

119887 119889119887

119901= 119889119887119902

Pr 119889119906119894= 119889119887119901 = Pr 119889119906

119894= 119889119887119902

(10)

The definition for privacy is thus extended to include thedefinition here and Definition 9

In RWS any 119889119904119894isin 119863119860119879119860

119904(119894 = 1 119899 minus 1) is perturbed

to a value 119889119887119895isin 119863119860119879119860

119887(119895 = 1 119900) which is randomly

selected This algorithm is thus especially ultra-lightweightin terms of computation A randomwalk algorithm (RWA) isproposed for the transformation function 119865 as follows

331 Analysis of Algorithm 2

Proposition 15 After the transformation of algorithmRWA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119882119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Proposition 11As sum119899119894=1119889119904119894lowast 119901119894= sum119899

119894=1119889119906119894lowast 119901119894 the total cost of power

consumption in a day maintains the correct value Thus thesoundness of RWA is guaranteed

Proposition 16 The scheme RWS is ultra-lightweight

Proof The number of loops is 119899 minus 1 so algorithm RPA isultra-lightweight The computations in loops are only simpleoperations such as modulo minus plus and multiplication

Moreover algorithm RWA is more lightweight than algo-rithm RPA Thus scheme RWS is ultra-lightweight

Proposition 17 The scheme RWS can guarantee the perfectfull privacy (Privacy119901A119877119882119878

119891119906119897119897= 1)

Proof According to the algorithm for for all 119889119904119894isin 119863119860119879119860

119904

if 119889119906119894= 119865(119889119904

119894) isin 119863119860119879119860

119906 we have forall119889119887

119901 119889119887119902isin 119863119860119879119860

119887

119889119887119901= 119889119887119902 and Pr119889119906

119894= 119889119887

119901 = Pr119889119906

119894= 119889119887

119902 Thus

PrivacyRWA119863119860119879119860

119906

= 1 According to the definition of the privacyin Definition 14 Privacy119901ARWS

full= 1

34 Distance-Bounded Random Walk with PerturbationScheme (DBS) In smart grid the uploading data will beused as a feedback for future scheduling of distribution andtransmission It thus requires the uploading data can accu-rately present the power consumption (namely sensing data)However thanks to the power distribution and transmissionserve not for a single SM but a large number of SMs (eg acampus a community or a county scale) only the accuracyfor a scale of SMs is sufficient for scheduling

In RPS and RWS although the bias exists (that isuploading data is not equal to sensing data) at single SMthe uploading data for a large number of SMs can stillrepresent power consumption in a scaleMore specifically thedeviation between the summation of uploading data and thesummation of sensing data is randomly positive or negativein one SM thus the overall summation remains almostunchanged in expectation in a large scale It is explained asfollows

Definition 18 After the transformation 119865 the accuracy of119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(denoted as Accuracy119865119863119860119879119860

119906

= 1) The summation of119863119860119879119860119906

equals the summation of 119863119860119879119860119904 in scheduling area and

scheduling period More specifically suppose that eachscheduling period consists of 119909 sensing (uploading) periodand each scheduling area consists of 119910 SMs The uploadingdata for them is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 The

sensing data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894

International Journal of Distributed Sensor Networks 7

Required119863119860119879119860119904 119863119860119879119860

119887 BOUND

Ensure119863119860119879119860119906 PrivacyDBA

119863119860119879119860119906

= 1 SoundnessDBA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 doWHILE (1)

119895 lArr (119903119886119899119889119900119898()(119900 minus 2) + 2)120575 lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119904

119894minus (119889119887119895+ (119889119887119895+1minus 119889119887119895)2)) (119889119904

119894minus (119889119887119895+ (119889119887119895minus 119889119887119895minus1)2)))

if (119886119887119904(120575) le 119861119874119880119873119863) then119889119906119894lArr 119889119904

119894minus 120575

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

EXITelse

CONTINUEend if

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 3 Distance-Bounded Algorithm (DBA)

The accuracy of119863119860119879119860119906is guaranteed if and only if SUM

119904=

SUM119906

Proposition 19 After the transformation 119877119875119860 or 119877119882119860 theaccuracy of119863119860119879119860

119906is guaranteed in expectation for a schedul-

ing area (Accuracy119877119875119860119877119882119860119863119860119879119860

119906

= 1)

Proof In each sensing (uploading) period 119889119904119894is changed into

119889119906119894at single SM 120575 = 119889119904

119894minus 119889119906119894 Suppose that each scheduling

period consists of 119909 sensing (uploading) period and eachscheduling area consists of 119910 SMs The uploading data forthem is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 the sensing

data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894 The

expectation of both is equal as the expectation of 120575 is 0 ina scheduling area That is SUM

119904= SUM

119906 as 120575 = 0 where119867

means the expectation of119867

To further guarantee the scheduling accuracy we proposea distance-bounded scheme in which the perturbation value(ie 120575) is bounded The accuracy is thus guaranteed withina threshold value It takes the advantages of former twoalgorithms RPA and RWA A distance-bounded algorithm(DBA) for the transformation 119865 is proposed as follows

341 Analysis of Algorithm 3

Proposition 20 After the transformation of algorithmDBA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Propositions 11 and15

Proposition 21 The scheme DBS is ultra-lightweight

Proof The proof can be reduced to the proof of Propositions12 and 16

Proposition 22 The scheme DBS can guarantee the perfectfull privacy (Privacy119901A119863119861119878

119891119906119897119897= 1)

Proof Theproof is similar to the proof of Propositions 13 and17

Proposition 23 After the transformation 119863119861119860 the accuracyof 119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(Accuracy119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is reduced to the proof of Proposition 19

Proposition 24 The summation of uploading data equals thesummation of the sensing data with deviation bounded by 120572 lowast120573lowast119861119874119880119873119863 where 120572 is the number of SMs in a schedule area120573 is the number of sensing (uploading) period in a scheduleperiod (That is |119878119880119872

119906minus 119878119880119872

119904| le 120572 lowast 120573 lowast 119861119874119880119873119863)

Proof The schedule accuracy is the deviation between thesummation of uploading data and the summation of sensingdata As it is proofed in Proposition 19 it depends on thenumber of SMs in the schedule area and the number ofsensing (uploading) period in the schedule period Theexpectation value is proofed to be 0 as the expectation of120575 is 0 Concerning the accuracy of one schedule periodthe maximal bias between the summation of uploading dataand the summation of sensing data is bounded by 120572 lowast 120573 lowast119861119874119880119873119863

4 Related Work

The security architectures and overall security requirementsin smart grid were discussed in the recent years [3 7] Cur-rently the privacy issue in smart grid starts to attract moreattentions The requirements of privacy were explored insome previousworks [8ndash11]They pointed out the importance

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 3

Definition 4 Computational full privacy (denoted asPrivacy119888full) Given anyone 119889119906

119894isin 119863119860119879119860

119906 it is computa-

tionally infeasible for any Probabilistic Polynomial TuringMachine (PPTM) adversary A to find 119886

119895isin 119860119862119879 such that

(119889119906119894 119886119895) isin 119877 That is

Pr forall119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

lt negl (119911)

(2)

where negl(119911) is a negligible functionwith security parameter119911

Claim 1 Perfect (computational) full privacy can protect userprivacy on all user activities in a day as no activity can bededuced from data in119863119860119879119860

119906by any (PPTM) adversary

In previous claim the content in ldquo()rdquo is correspondedwith each other Similarly the perfect (computational) partialprivacy can be defined in the following

Definition 5 Perfect (computational) partial privacy denot-ed as Privacy119901(119888)

partial Given at least one 119889119906

119894isin 119863119860119879119860

119906 it is

computationally infeasible for any (PPTM) adversary A tofind 119886

119895isin 119860119862119879 such that (119889119906

119894 119886119895) isin 119877 after viewing 119863119860119879119860

119906

Besides given at least one 119886119895isin 119860119862119879 it is computationally

infeasible for any (PPTM) adversaryA to find 119889119906119894isin 119863119860119879119860

119906

such that (119889119906119894 119886119895) isin 119877 after viewing119863119860119879119860

119906 That is

Pr exist119889119906119894isin 119863119860119879119860

119906 119886119895lArr997904 119860119862119879 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0 (lt negl (119911))

Pr exist119886119895isin 119860119862119879 119889119906

119894lArr997904 119863119860119879119860

119906 st (119889119906

119894 119886119895) isin 119877 119863119860119879119860

119906

= 0 (lt negl (119911))

(3)

Claim 2 Perfect (computational) partial privacy can protectcertain privacy-sensitive activities as these activities cannotbe deduced by119863119860119879119860

119906by any (PPTM) adversary

Claim 3 Full privacy has stronger strength than partialprivacy in terms of the number of deducible data in119863119860119879119860

119906

Perfect privacy has stronger strength than computationalprivacy due to the adversaryrsquos ability That is

Privacy119888

partical lt Privacy119901

partical lt Privacy119888

full lt Privacy119901

full

(4)

where ldquo119860 lt 119861rdquo means that the privacy protection strength ofldquoArdquo is weaker than that of ldquoBrdquo

Roughly speaking full privacy protects all activities par-tial privacy protects partial activities Perfect privacy defendsagainst any adversary computational privacy defends againstany PPTM adversary As perfect full privacy has the strongestprivacy strength we thus concentrate on the perfect fullprivacy protection in the following

Definition 6 Full privacy attacking experiment on thescheme Π defending against any adversary A-ExpPrivacy

119901AΠ

fullis defined as follows

(1) the scheme Π is executed in the presence of anyadversaryA

(2) A fully accesses 119863119860119879119860119906 119860119862119879 and 119877 Given any

119889119906119894isin 119863119860119879119860

119906 if A can find 119886

119895isin 119860119862119879 such that

(119889119906119894 119886119895) isin 119877A outputs 1 otherwise outputs 0

(3) if and only ifA outputs 1 the experiment outputs 1

Definition 7 The scheme Π that can guarantee the perfectfull privacy in presence of any adversary A (denoted asPrivacy

119901AΠ

full= 1) is defined as follows

For any adversary A that the scheme Π defends againstthe probability that the output of the full privacy attackingexperiment equals one is 0 That is if and only if

Pr [ExpPrivacy119901AΠfull = 1] = 0 (5)

Privacy119901AΠ

full= 1

Therefore the design goal is to propose a scheme Π sat-isfying Privacy

119901AΠ

fulland importantly with ultra-lightweight

computation without any cryptographic computation

3 Proposed Schemes

31 ProblemReduction To protect the privacy of sensing data119863119860119879119860

119904 a naive method is encrypting them at SM and then

uploading them to SGCC As SGCC is untrustworthy SGCCcannot decrypt them and has to consult a TTP The TTPdecrypts the data and the result cannot be sent to SGCCTheTTP should compute accumulative values (or metadata) andsend them to SGCC for further scheduling and charging Itobviously arises multiple overheads a large volume of com-putation overhead at SM extra communication overhead atSM and SGCC extra entity TTP key management overheadbetween SM and TTP

As SM is trustworthy SM is proposed to equip a trustedmixing layer between sensing layer and communication layerThat is SM is modeled as three tuples ⟨119871

119904 119871119898 119871119888⟩ where

119871119904is a sensing layer computing the power consumption

periodically The output of layer 119871119904is 119863119860119879119860

119904 119871119898

is amixing layer that transfers 119863119860119879119860

119904into 119863119860119879119860

119906 119871119888is a

communication layer that uploads119863119860119879119860119906to SGCCThat is

SM = ⟨119871119904 119871119898 119871119888⟩

119871119904997904rArr 119871

119898 119863119860119879119860

119904

119871119898= 119865 119863119860119879119860

119904997888rarr 119863119860119879119860

119906

119871119898997904rArr 119871

119906 119863119860119879119860

119906

(6)

where ldquo=rdquo means ldquois defined asrdquo ldquorArrrdquo means ldquodata trans-ferring between layersrdquo 119865 is a data transforming functionldquorarr rdquo that means the input of the function 119865 is transformedinto the output of the function 119865 Therefore it becomes the

4 International Journal of Distributed Sensor Networks

concentration to search an ultra-lightweight transformationfunction 119865 with Privacy

119901A119865

full= 1 in the rest of the paper

Definition 8 ldquoBadrdquo data set (119863119860119879119860119887) It consists of all

power consumption data that can deduce to one or multipleactivities in119860119862119879119863119860119879119860

119887= 1198891198871 1198891198872 119889119887

119900 where 119900 is the

total number of 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)

The characteristics of 119863119860119879119860119887 119860119862119879 and deduction

relationship set 119877 are as the following

(1) Without loss of generality 119863119860119879119860119887is a sorted set of

positive numbersThat is1198891198871lt 1198891198872lt sdot sdot sdot lt 119889119887

1199001198891198871is

equal to or greater than the power consumption of theminimum power consumption appliance in a period119889119887119900is equal to or less than the power consumption of

all appliances in a period

(2) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may represent the

usage of one appliance in a period For example 1198891198871

(30wh) is the power consumption of a lamp for aperiod 119889119887

1is related to an event (eg 119886

1) that means

the lamp is on in the period

(3) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may also repre-

sent the usage of multiple household appliances Forexample 119889119887

9represents two household appliances

used simultaneously 1198891198879= 1198891198871+ 1198891198872 where 119889119887

1is

the power consumption of the lamp in a period 1198891198872

is the power consumption of the washing machine inthe period Thus 119889119887

9means using lamp and washing

machine simultaneously in the period

(4) Similarly any 119886119895isin 119860119862119879 (119895 = 1 119898)may represent

the usage of one appliance or multiple householdappliances simultaneously

(5) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) is related to at least

one 119886119895isin 119860119862119879 (119895 = 1 119898) any 119886

119895isin 119860119862119879 (119895 =

1 119898) is related to at least one in 119889119887119894isin 119863119860119879119860

119887(119894 =

1 119900)

(6) Different 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) cannot be relat-

ed to the same 119886119895isin 119860119862119879 (119895 = 1 119898) as any 119886

119895isin

119860119862119879 (119895 = 1 119898) has single power consumption ina period

(7) 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)may be related tomultiple

119886119895 because such 119889119887

119894may be the power consumption

for multiple appliances and those appliances mayhave the same power consumption in total Forexample 119889119887

9= 1198891198871+ 1198891198872= 1198891198873+ 1198891198874 1198891198879is related

to 1198865 1198866isin 119860119862119879 where 119886

5means using lamp and

washing machine simultaneously and 1198866means the

usage of the other two appliances

In summary the deduction relationship set119877 = 119863119860119879119860119887times

119860119862119879 can be further refined from a general relationship set toa relationship set with following properties

Pr forall119889119887119894isin 119863119860119879119860

119887 exist119886119895isin 119860119862119879 st (119889119887

119894 119886119895) isin 119877 = 1

Pr forall119886119895isin 119860119862119879 exist119889119887

119894isin 119863119860119879119860

119887 st (119889119887

119894 119886119895) isin 119877 = 1

Pr exist119889119887119894isin 119863119860119879119860

119887 1198861198951isin 119860119862119879 119886

1198952isin 119860119862119879

st (119889119887119894 1198861198951) isin 119877 (119889119887

119894 1198861198952) isin 119877 gt 0

Pr exist1198891198941isin 119863119860119879119860

119887 1198891198942isin 119863119860119879119860

119887 119886119895isin 119860119862119879

st (1198891198941 119886119895) isin 119877 (119889

1198942 119886119895) isin 119877 = 0

(7)

In other words mapping 119863119860119879119860119887rarr 119860119862119879 is not a

function and mapping 119860119862119879 rarr 119863119860119879119860119887is a surjective and

not a injective function

Definition 9 After transformation 119865 the privacy of119863119860119879119860

119906is guaranteed (denoted as Privacy119865

119863119860119879119860119906

= 1)Privacy119865

119863119860119879119860119906

= 1 if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) notin 119863119860119879119860

119887 (8)

where 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

Definition 10 After transformation 119865 the soundness of119863119860119879119860

119906is guaranteed (Soundness119865

119863119860119879119860119906

= 1) The utilitysummation remains unchanged That is

119899

sum

119894=1

119889119904119894lowast 119901119894=

119899

sum

119894=1

119889119906119894lowast 119901119894 (9)

Due to the concentration in the rest of the paper theresearch problem is reduced to as follows given119863119860119879119860

119904 find

an ultra-lightweight transformation 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

such that the privacy and soundness of 119863119860119879119860119906are both

guaranteed That is given 119863119860119879119860119904 find 119865 119863119860119879119860

119904rarr

119863119860119879119860119906 st Privacy119865

119863119860119879119860119906

= 1 and Soundness119865119863119860119879119860

119906

= 1Next we propose a family of schemes to solve the

problem We list all major notations used in the remainderof the paper in Table 1

32 Random Perturbation Scheme (RPS) We firstly proposea basic scheme-random perturbation scheme (RPS) to illus-trate our motivations In RPS any 119889119904

119894isin 119863119860119879119860

119904is perturbed

into a new value in the middle of 119889119887119895and 119889119887

119895minus1or in the

middle of 119889119887119895and 119889119887

119895+1The two cases are selected randomly

A Random Perturbation Algorithm called RPA is proposedfor transformation 119865 as follows

321 Analysis of Algorithm 1

Proposition 11 After the transformation of algorithmRPA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119875119860119863119860119879119860

119906

= 1)

International Journal of Distributed Sensor Networks 5

Table 1 Notation

A Adversary119863119860119879119860

119904= 119889119904

1 119889119904

119899 Sensing power consumption data set

119863119860119879119860119906= 119889119906

1 119889119906

119899 Uploading power consumption data set

119865 Transforming function from119863119860119879119860119904to119863119860119879119860

119906

119863119860119879119860119887= 119889119887

1 119889119887

119900 ldquoBadrdquo power consumption data set

119875119877119868119862119864 = 1199011 1199012 119901

119899 Price set

119860119862119879 = 1198861 1198862 119886

119898 Activity set

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRPA

119863119860119879119860119906

=1 SoundnessRPA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904) Get a data from119863119860119879119860

119904

for 119894 = 1 to 119899 minus 1 doif ((119889119904

119894== 119889119887

1)OR (119889119887

1lt 119889119904119894lt 1198891198872)) then

119889119906119894lArr (119889119887

1+ 1198891198872)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif ((119889119904

119894== 119889119887

119900)OR (119889119887

119900minus1lt 119889119904119894lt 119889119887119900)) then

119889119906119894lArr (119889119887

119900minus1+ 119889119887119900)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end iffor 119895 = 2 to 119900 minus 1 do

if (119889119904119894== 119889119887

119895) then

119889119906119894lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119887

119895+ 119889119887119895+1)2 (119889119887

119895+ 119889119887119895minus1)2)

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif (119889119887

119895lt 119889119904119894lt 119889119887119895+1)then

119889119906119894lArr (119889119887

119895+ 119889119887119895+1)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifend for

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899For soundness

Algorithm 1 Random Perturbation AlgorithmmdashRPA

Proof The biases of 119889119906119894(119894 = 1 119899 minus 1) comparing to

119889119904119894(1 119899minus1) are accumulated into a total value119861119868119860119878119861119868119860119878

is changed into extra power consumption and added to thelast one 119889119906

119899 Thussum119899

119894=1119889119904119894lowast119901119894= sum119899

119894=1119889119906119894lowast119901119894 The total cost

of power consumption in a day maintains the correct valueso SoundnessRPA

119863119860119879119860119906

= 1

Proposition 12 The scheme RPS is ultra-lightweight

Proof As algorithm RPA is ultra-lightweight the number ofloops is (119899 minus 1) lowast (119900 minus 2) The computation in each loop isonly simple operations such asmodulo minus plus divisionandmultiplicationThe computation complexity of algorithmRPA is 119874(119899 lowast 119900)

Proposition 13 The scheme RPS can guarantee the perfect fullprivacy (Privacy119901A119877119875119878

119891119906119897119897= 1)

Proof It is clear that for all 119889119904119894isin 119863119860119879119860

119904 119889119906119894= 119865(119889119904

119894) notin

119863119860119879119860119887 Thus PrivacyRPA

119863119860119879119860119906

= 1 According to the definitionof the perfect full privacy Privacy119901ARPS

full= 1

33 RandomWalk Scheme (RWS) If the gap between 119889119887119895and

119889119887119895+1

(119895 = 1 119900minus1) is small the perturbation (namely 120575) inRPSwill be small It can be proofed as a claim in the following

Claim 4 If the gap between 119889119887119895and 119889119887

119895+1(119895 = 1 119900 minus 1) is

small the perturbation in RPS will be small

Proof Suppose max(|119889119887119895minus 119889119887119895+1|) = 119892(119895 = 1 119899 minus 1) If

119889119904119894= 119889119887119895isin 119863119860119879119860

119887) in RPA max(120575) le 1198922 If 119889119904

119894= 119889119887119895isin

119863119860119879119860119887 max(120575) lt 1198922 Thus the perturbation 120575 is small if 119892

is small

6 International Journal of Distributed Sensor Networks

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRWA

119863119860119879119860119906

= 1 SoundnessRWA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 do119895 lArr (119903119886119899119889119900119898()119900 + 1)119889119906119894lArr 119889119887

119895

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 2 RandomWalk Algorithm (RWA)

If the perturbation is small adversaries may guess the 119889119904119894

correctly and adversaries can guess the activity is either oftwo activities To address this issue we propose a randomwalk scheme called RWS in which 119889119904

119894isin 119863119860119879119860

119904randomly

jumps to a value in119863119860119879119860119887 In this case the privacy definition

is extended to include unlinkability inwhich the possibility of119889119887119895isin 119863119860119879119860

119887for 119889119904

119894is equal Thus the revealed user activity

occurs with equal possibility

Definition 14 After transformation 119865 the privacy of119863119860119879119860119906

is guaranteed (denoted as Privacy119865119863119860119879119860

119906

= 1) if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) isin 119863119860119879119860

119906

forall119889119887119901 119889119887

119902isin 119863119860119879119860

119887 119889119887

119901= 119889119887119902

Pr 119889119906119894= 119889119887119901 = Pr 119889119906

119894= 119889119887119902

(10)

The definition for privacy is thus extended to include thedefinition here and Definition 9

In RWS any 119889119904119894isin 119863119860119879119860

119904(119894 = 1 119899 minus 1) is perturbed

to a value 119889119887119895isin 119863119860119879119860

119887(119895 = 1 119900) which is randomly

selected This algorithm is thus especially ultra-lightweightin terms of computation A randomwalk algorithm (RWA) isproposed for the transformation function 119865 as follows

331 Analysis of Algorithm 2

Proposition 15 After the transformation of algorithmRWA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119882119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Proposition 11As sum119899119894=1119889119904119894lowast 119901119894= sum119899

119894=1119889119906119894lowast 119901119894 the total cost of power

consumption in a day maintains the correct value Thus thesoundness of RWA is guaranteed

Proposition 16 The scheme RWS is ultra-lightweight

Proof The number of loops is 119899 minus 1 so algorithm RPA isultra-lightweight The computations in loops are only simpleoperations such as modulo minus plus and multiplication

Moreover algorithm RWA is more lightweight than algo-rithm RPA Thus scheme RWS is ultra-lightweight

Proposition 17 The scheme RWS can guarantee the perfectfull privacy (Privacy119901A119877119882119878

119891119906119897119897= 1)

Proof According to the algorithm for for all 119889119904119894isin 119863119860119879119860

119904

if 119889119906119894= 119865(119889119904

119894) isin 119863119860119879119860

119906 we have forall119889119887

119901 119889119887119902isin 119863119860119879119860

119887

119889119887119901= 119889119887119902 and Pr119889119906

119894= 119889119887

119901 = Pr119889119906

119894= 119889119887

119902 Thus

PrivacyRWA119863119860119879119860

119906

= 1 According to the definition of the privacyin Definition 14 Privacy119901ARWS

full= 1

34 Distance-Bounded Random Walk with PerturbationScheme (DBS) In smart grid the uploading data will beused as a feedback for future scheduling of distribution andtransmission It thus requires the uploading data can accu-rately present the power consumption (namely sensing data)However thanks to the power distribution and transmissionserve not for a single SM but a large number of SMs (eg acampus a community or a county scale) only the accuracyfor a scale of SMs is sufficient for scheduling

In RPS and RWS although the bias exists (that isuploading data is not equal to sensing data) at single SMthe uploading data for a large number of SMs can stillrepresent power consumption in a scaleMore specifically thedeviation between the summation of uploading data and thesummation of sensing data is randomly positive or negativein one SM thus the overall summation remains almostunchanged in expectation in a large scale It is explained asfollows

Definition 18 After the transformation 119865 the accuracy of119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(denoted as Accuracy119865119863119860119879119860

119906

= 1) The summation of119863119860119879119860119906

equals the summation of 119863119860119879119860119904 in scheduling area and

scheduling period More specifically suppose that eachscheduling period consists of 119909 sensing (uploading) periodand each scheduling area consists of 119910 SMs The uploadingdata for them is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 The

sensing data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894

International Journal of Distributed Sensor Networks 7

Required119863119860119879119860119904 119863119860119879119860

119887 BOUND

Ensure119863119860119879119860119906 PrivacyDBA

119863119860119879119860119906

= 1 SoundnessDBA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 doWHILE (1)

119895 lArr (119903119886119899119889119900119898()(119900 minus 2) + 2)120575 lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119904

119894minus (119889119887119895+ (119889119887119895+1minus 119889119887119895)2)) (119889119904

119894minus (119889119887119895+ (119889119887119895minus 119889119887119895minus1)2)))

if (119886119887119904(120575) le 119861119874119880119873119863) then119889119906119894lArr 119889119904

119894minus 120575

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

EXITelse

CONTINUEend if

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 3 Distance-Bounded Algorithm (DBA)

The accuracy of119863119860119879119860119906is guaranteed if and only if SUM

119904=

SUM119906

Proposition 19 After the transformation 119877119875119860 or 119877119882119860 theaccuracy of119863119860119879119860

119906is guaranteed in expectation for a schedul-

ing area (Accuracy119877119875119860119877119882119860119863119860119879119860

119906

= 1)

Proof In each sensing (uploading) period 119889119904119894is changed into

119889119906119894at single SM 120575 = 119889119904

119894minus 119889119906119894 Suppose that each scheduling

period consists of 119909 sensing (uploading) period and eachscheduling area consists of 119910 SMs The uploading data forthem is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 the sensing

data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894 The

expectation of both is equal as the expectation of 120575 is 0 ina scheduling area That is SUM

119904= SUM

119906 as 120575 = 0 where119867

means the expectation of119867

To further guarantee the scheduling accuracy we proposea distance-bounded scheme in which the perturbation value(ie 120575) is bounded The accuracy is thus guaranteed withina threshold value It takes the advantages of former twoalgorithms RPA and RWA A distance-bounded algorithm(DBA) for the transformation 119865 is proposed as follows

341 Analysis of Algorithm 3

Proposition 20 After the transformation of algorithmDBA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Propositions 11 and15

Proposition 21 The scheme DBS is ultra-lightweight

Proof The proof can be reduced to the proof of Propositions12 and 16

Proposition 22 The scheme DBS can guarantee the perfectfull privacy (Privacy119901A119863119861119878

119891119906119897119897= 1)

Proof Theproof is similar to the proof of Propositions 13 and17

Proposition 23 After the transformation 119863119861119860 the accuracyof 119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(Accuracy119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is reduced to the proof of Proposition 19

Proposition 24 The summation of uploading data equals thesummation of the sensing data with deviation bounded by 120572 lowast120573lowast119861119874119880119873119863 where 120572 is the number of SMs in a schedule area120573 is the number of sensing (uploading) period in a scheduleperiod (That is |119878119880119872

119906minus 119878119880119872

119904| le 120572 lowast 120573 lowast 119861119874119880119873119863)

Proof The schedule accuracy is the deviation between thesummation of uploading data and the summation of sensingdata As it is proofed in Proposition 19 it depends on thenumber of SMs in the schedule area and the number ofsensing (uploading) period in the schedule period Theexpectation value is proofed to be 0 as the expectation of120575 is 0 Concerning the accuracy of one schedule periodthe maximal bias between the summation of uploading dataand the summation of sensing data is bounded by 120572 lowast 120573 lowast119861119874119880119873119863

4 Related Work

The security architectures and overall security requirementsin smart grid were discussed in the recent years [3 7] Cur-rently the privacy issue in smart grid starts to attract moreattentions The requirements of privacy were explored insome previousworks [8ndash11]They pointed out the importance

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

4 International Journal of Distributed Sensor Networks

concentration to search an ultra-lightweight transformationfunction 119865 with Privacy

119901A119865

full= 1 in the rest of the paper

Definition 8 ldquoBadrdquo data set (119863119860119879119860119887) It consists of all

power consumption data that can deduce to one or multipleactivities in119860119862119879119863119860119879119860

119887= 1198891198871 1198891198872 119889119887

119900 where 119900 is the

total number of 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)

The characteristics of 119863119860119879119860119887 119860119862119879 and deduction

relationship set 119877 are as the following

(1) Without loss of generality 119863119860119879119860119887is a sorted set of

positive numbersThat is1198891198871lt 1198891198872lt sdot sdot sdot lt 119889119887

1199001198891198871is

equal to or greater than the power consumption of theminimum power consumption appliance in a period119889119887119900is equal to or less than the power consumption of

all appliances in a period

(2) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may represent the

usage of one appliance in a period For example 1198891198871

(30wh) is the power consumption of a lamp for aperiod 119889119887

1is related to an event (eg 119886

1) that means

the lamp is on in the period

(3) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) may also repre-

sent the usage of multiple household appliances Forexample 119889119887

9represents two household appliances

used simultaneously 1198891198879= 1198891198871+ 1198891198872 where 119889119887

1is

the power consumption of the lamp in a period 1198891198872

is the power consumption of the washing machine inthe period Thus 119889119887

9means using lamp and washing

machine simultaneously in the period

(4) Similarly any 119886119895isin 119860119862119879 (119895 = 1 119898)may represent

the usage of one appliance or multiple householdappliances simultaneously

(5) Any 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) is related to at least

one 119886119895isin 119860119862119879 (119895 = 1 119898) any 119886

119895isin 119860119862119879 (119895 =

1 119898) is related to at least one in 119889119887119894isin 119863119860119879119860

119887(119894 =

1 119900)

(6) Different 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900) cannot be relat-

ed to the same 119886119895isin 119860119862119879 (119895 = 1 119898) as any 119886

119895isin

119860119862119879 (119895 = 1 119898) has single power consumption ina period

(7) 119889119887119894isin 119863119860119879119860

119887(119894 = 1 119900)may be related tomultiple

119886119895 because such 119889119887

119894may be the power consumption

for multiple appliances and those appliances mayhave the same power consumption in total Forexample 119889119887

9= 1198891198871+ 1198891198872= 1198891198873+ 1198891198874 1198891198879is related

to 1198865 1198866isin 119860119862119879 where 119886

5means using lamp and

washing machine simultaneously and 1198866means the

usage of the other two appliances

In summary the deduction relationship set119877 = 119863119860119879119860119887times

119860119862119879 can be further refined from a general relationship set toa relationship set with following properties

Pr forall119889119887119894isin 119863119860119879119860

119887 exist119886119895isin 119860119862119879 st (119889119887

119894 119886119895) isin 119877 = 1

Pr forall119886119895isin 119860119862119879 exist119889119887

119894isin 119863119860119879119860

119887 st (119889119887

119894 119886119895) isin 119877 = 1

Pr exist119889119887119894isin 119863119860119879119860

119887 1198861198951isin 119860119862119879 119886

1198952isin 119860119862119879

st (119889119887119894 1198861198951) isin 119877 (119889119887

119894 1198861198952) isin 119877 gt 0

Pr exist1198891198941isin 119863119860119879119860

119887 1198891198942isin 119863119860119879119860

119887 119886119895isin 119860119862119879

st (1198891198941 119886119895) isin 119877 (119889

1198942 119886119895) isin 119877 = 0

(7)

In other words mapping 119863119860119879119860119887rarr 119860119862119879 is not a

function and mapping 119860119862119879 rarr 119863119860119879119860119887is a surjective and

not a injective function

Definition 9 After transformation 119865 the privacy of119863119860119879119860

119906is guaranteed (denoted as Privacy119865

119863119860119879119860119906

= 1)Privacy119865

119863119860119879119860119906

= 1 if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) notin 119863119860119879119860

119887 (8)

where 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

Definition 10 After transformation 119865 the soundness of119863119860119879119860

119906is guaranteed (Soundness119865

119863119860119879119860119906

= 1) The utilitysummation remains unchanged That is

119899

sum

119894=1

119889119904119894lowast 119901119894=

119899

sum

119894=1

119889119906119894lowast 119901119894 (9)

Due to the concentration in the rest of the paper theresearch problem is reduced to as follows given119863119860119879119860

119904 find

an ultra-lightweight transformation 119865 119863119860119879119860119904rarr 119863119860119879119860

119906

such that the privacy and soundness of 119863119860119879119860119906are both

guaranteed That is given 119863119860119879119860119904 find 119865 119863119860119879119860

119904rarr

119863119860119879119860119906 st Privacy119865

119863119860119879119860119906

= 1 and Soundness119865119863119860119879119860

119906

= 1Next we propose a family of schemes to solve the

problem We list all major notations used in the remainderof the paper in Table 1

32 Random Perturbation Scheme (RPS) We firstly proposea basic scheme-random perturbation scheme (RPS) to illus-trate our motivations In RPS any 119889119904

119894isin 119863119860119879119860

119904is perturbed

into a new value in the middle of 119889119887119895and 119889119887

119895minus1or in the

middle of 119889119887119895and 119889119887

119895+1The two cases are selected randomly

A Random Perturbation Algorithm called RPA is proposedfor transformation 119865 as follows

321 Analysis of Algorithm 1

Proposition 11 After the transformation of algorithmRPA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119875119860119863119860119879119860

119906

= 1)

International Journal of Distributed Sensor Networks 5

Table 1 Notation

A Adversary119863119860119879119860

119904= 119889119904

1 119889119904

119899 Sensing power consumption data set

119863119860119879119860119906= 119889119906

1 119889119906

119899 Uploading power consumption data set

119865 Transforming function from119863119860119879119860119904to119863119860119879119860

119906

119863119860119879119860119887= 119889119887

1 119889119887

119900 ldquoBadrdquo power consumption data set

119875119877119868119862119864 = 1199011 1199012 119901

119899 Price set

119860119862119879 = 1198861 1198862 119886

119898 Activity set

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRPA

119863119860119879119860119906

=1 SoundnessRPA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904) Get a data from119863119860119879119860

119904

for 119894 = 1 to 119899 minus 1 doif ((119889119904

119894== 119889119887

1)OR (119889119887

1lt 119889119904119894lt 1198891198872)) then

119889119906119894lArr (119889119887

1+ 1198891198872)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif ((119889119904

119894== 119889119887

119900)OR (119889119887

119900minus1lt 119889119904119894lt 119889119887119900)) then

119889119906119894lArr (119889119887

119900minus1+ 119889119887119900)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end iffor 119895 = 2 to 119900 minus 1 do

if (119889119904119894== 119889119887

119895) then

119889119906119894lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119887

119895+ 119889119887119895+1)2 (119889119887

119895+ 119889119887119895minus1)2)

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif (119889119887

119895lt 119889119904119894lt 119889119887119895+1)then

119889119906119894lArr (119889119887

119895+ 119889119887119895+1)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifend for

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899For soundness

Algorithm 1 Random Perturbation AlgorithmmdashRPA

Proof The biases of 119889119906119894(119894 = 1 119899 minus 1) comparing to

119889119904119894(1 119899minus1) are accumulated into a total value119861119868119860119878119861119868119860119878

is changed into extra power consumption and added to thelast one 119889119906

119899 Thussum119899

119894=1119889119904119894lowast119901119894= sum119899

119894=1119889119906119894lowast119901119894 The total cost

of power consumption in a day maintains the correct valueso SoundnessRPA

119863119860119879119860119906

= 1

Proposition 12 The scheme RPS is ultra-lightweight

Proof As algorithm RPA is ultra-lightweight the number ofloops is (119899 minus 1) lowast (119900 minus 2) The computation in each loop isonly simple operations such asmodulo minus plus divisionandmultiplicationThe computation complexity of algorithmRPA is 119874(119899 lowast 119900)

Proposition 13 The scheme RPS can guarantee the perfect fullprivacy (Privacy119901A119877119875119878

119891119906119897119897= 1)

Proof It is clear that for all 119889119904119894isin 119863119860119879119860

119904 119889119906119894= 119865(119889119904

119894) notin

119863119860119879119860119887 Thus PrivacyRPA

119863119860119879119860119906

= 1 According to the definitionof the perfect full privacy Privacy119901ARPS

full= 1

33 RandomWalk Scheme (RWS) If the gap between 119889119887119895and

119889119887119895+1

(119895 = 1 119900minus1) is small the perturbation (namely 120575) inRPSwill be small It can be proofed as a claim in the following

Claim 4 If the gap between 119889119887119895and 119889119887

119895+1(119895 = 1 119900 minus 1) is

small the perturbation in RPS will be small

Proof Suppose max(|119889119887119895minus 119889119887119895+1|) = 119892(119895 = 1 119899 minus 1) If

119889119904119894= 119889119887119895isin 119863119860119879119860

119887) in RPA max(120575) le 1198922 If 119889119904

119894= 119889119887119895isin

119863119860119879119860119887 max(120575) lt 1198922 Thus the perturbation 120575 is small if 119892

is small

6 International Journal of Distributed Sensor Networks

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRWA

119863119860119879119860119906

= 1 SoundnessRWA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 do119895 lArr (119903119886119899119889119900119898()119900 + 1)119889119906119894lArr 119889119887

119895

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 2 RandomWalk Algorithm (RWA)

If the perturbation is small adversaries may guess the 119889119904119894

correctly and adversaries can guess the activity is either oftwo activities To address this issue we propose a randomwalk scheme called RWS in which 119889119904

119894isin 119863119860119879119860

119904randomly

jumps to a value in119863119860119879119860119887 In this case the privacy definition

is extended to include unlinkability inwhich the possibility of119889119887119895isin 119863119860119879119860

119887for 119889119904

119894is equal Thus the revealed user activity

occurs with equal possibility

Definition 14 After transformation 119865 the privacy of119863119860119879119860119906

is guaranteed (denoted as Privacy119865119863119860119879119860

119906

= 1) if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) isin 119863119860119879119860

119906

forall119889119887119901 119889119887

119902isin 119863119860119879119860

119887 119889119887

119901= 119889119887119902

Pr 119889119906119894= 119889119887119901 = Pr 119889119906

119894= 119889119887119902

(10)

The definition for privacy is thus extended to include thedefinition here and Definition 9

In RWS any 119889119904119894isin 119863119860119879119860

119904(119894 = 1 119899 minus 1) is perturbed

to a value 119889119887119895isin 119863119860119879119860

119887(119895 = 1 119900) which is randomly

selected This algorithm is thus especially ultra-lightweightin terms of computation A randomwalk algorithm (RWA) isproposed for the transformation function 119865 as follows

331 Analysis of Algorithm 2

Proposition 15 After the transformation of algorithmRWA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119882119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Proposition 11As sum119899119894=1119889119904119894lowast 119901119894= sum119899

119894=1119889119906119894lowast 119901119894 the total cost of power

consumption in a day maintains the correct value Thus thesoundness of RWA is guaranteed

Proposition 16 The scheme RWS is ultra-lightweight

Proof The number of loops is 119899 minus 1 so algorithm RPA isultra-lightweight The computations in loops are only simpleoperations such as modulo minus plus and multiplication

Moreover algorithm RWA is more lightweight than algo-rithm RPA Thus scheme RWS is ultra-lightweight

Proposition 17 The scheme RWS can guarantee the perfectfull privacy (Privacy119901A119877119882119878

119891119906119897119897= 1)

Proof According to the algorithm for for all 119889119904119894isin 119863119860119879119860

119904

if 119889119906119894= 119865(119889119904

119894) isin 119863119860119879119860

119906 we have forall119889119887

119901 119889119887119902isin 119863119860119879119860

119887

119889119887119901= 119889119887119902 and Pr119889119906

119894= 119889119887

119901 = Pr119889119906

119894= 119889119887

119902 Thus

PrivacyRWA119863119860119879119860

119906

= 1 According to the definition of the privacyin Definition 14 Privacy119901ARWS

full= 1

34 Distance-Bounded Random Walk with PerturbationScheme (DBS) In smart grid the uploading data will beused as a feedback for future scheduling of distribution andtransmission It thus requires the uploading data can accu-rately present the power consumption (namely sensing data)However thanks to the power distribution and transmissionserve not for a single SM but a large number of SMs (eg acampus a community or a county scale) only the accuracyfor a scale of SMs is sufficient for scheduling

In RPS and RWS although the bias exists (that isuploading data is not equal to sensing data) at single SMthe uploading data for a large number of SMs can stillrepresent power consumption in a scaleMore specifically thedeviation between the summation of uploading data and thesummation of sensing data is randomly positive or negativein one SM thus the overall summation remains almostunchanged in expectation in a large scale It is explained asfollows

Definition 18 After the transformation 119865 the accuracy of119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(denoted as Accuracy119865119863119860119879119860

119906

= 1) The summation of119863119860119879119860119906

equals the summation of 119863119860119879119860119904 in scheduling area and

scheduling period More specifically suppose that eachscheduling period consists of 119909 sensing (uploading) periodand each scheduling area consists of 119910 SMs The uploadingdata for them is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 The

sensing data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894

International Journal of Distributed Sensor Networks 7

Required119863119860119879119860119904 119863119860119879119860

119887 BOUND

Ensure119863119860119879119860119906 PrivacyDBA

119863119860119879119860119906

= 1 SoundnessDBA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 doWHILE (1)

119895 lArr (119903119886119899119889119900119898()(119900 minus 2) + 2)120575 lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119904

119894minus (119889119887119895+ (119889119887119895+1minus 119889119887119895)2)) (119889119904

119894minus (119889119887119895+ (119889119887119895minus 119889119887119895minus1)2)))

if (119886119887119904(120575) le 119861119874119880119873119863) then119889119906119894lArr 119889119904

119894minus 120575

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

EXITelse

CONTINUEend if

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 3 Distance-Bounded Algorithm (DBA)

The accuracy of119863119860119879119860119906is guaranteed if and only if SUM

119904=

SUM119906

Proposition 19 After the transformation 119877119875119860 or 119877119882119860 theaccuracy of119863119860119879119860

119906is guaranteed in expectation for a schedul-

ing area (Accuracy119877119875119860119877119882119860119863119860119879119860

119906

= 1)

Proof In each sensing (uploading) period 119889119904119894is changed into

119889119906119894at single SM 120575 = 119889119904

119894minus 119889119906119894 Suppose that each scheduling

period consists of 119909 sensing (uploading) period and eachscheduling area consists of 119910 SMs The uploading data forthem is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 the sensing

data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894 The

expectation of both is equal as the expectation of 120575 is 0 ina scheduling area That is SUM

119904= SUM

119906 as 120575 = 0 where119867

means the expectation of119867

To further guarantee the scheduling accuracy we proposea distance-bounded scheme in which the perturbation value(ie 120575) is bounded The accuracy is thus guaranteed withina threshold value It takes the advantages of former twoalgorithms RPA and RWA A distance-bounded algorithm(DBA) for the transformation 119865 is proposed as follows

341 Analysis of Algorithm 3

Proposition 20 After the transformation of algorithmDBA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Propositions 11 and15

Proposition 21 The scheme DBS is ultra-lightweight

Proof The proof can be reduced to the proof of Propositions12 and 16

Proposition 22 The scheme DBS can guarantee the perfectfull privacy (Privacy119901A119863119861119878

119891119906119897119897= 1)

Proof Theproof is similar to the proof of Propositions 13 and17

Proposition 23 After the transformation 119863119861119860 the accuracyof 119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(Accuracy119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is reduced to the proof of Proposition 19

Proposition 24 The summation of uploading data equals thesummation of the sensing data with deviation bounded by 120572 lowast120573lowast119861119874119880119873119863 where 120572 is the number of SMs in a schedule area120573 is the number of sensing (uploading) period in a scheduleperiod (That is |119878119880119872

119906minus 119878119880119872

119904| le 120572 lowast 120573 lowast 119861119874119880119873119863)

Proof The schedule accuracy is the deviation between thesummation of uploading data and the summation of sensingdata As it is proofed in Proposition 19 it depends on thenumber of SMs in the schedule area and the number ofsensing (uploading) period in the schedule period Theexpectation value is proofed to be 0 as the expectation of120575 is 0 Concerning the accuracy of one schedule periodthe maximal bias between the summation of uploading dataand the summation of sensing data is bounded by 120572 lowast 120573 lowast119861119874119880119873119863

4 Related Work

The security architectures and overall security requirementsin smart grid were discussed in the recent years [3 7] Cur-rently the privacy issue in smart grid starts to attract moreattentions The requirements of privacy were explored insome previousworks [8ndash11]They pointed out the importance

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 5

Table 1 Notation

A Adversary119863119860119879119860

119904= 119889119904

1 119889119904

119899 Sensing power consumption data set

119863119860119879119860119906= 119889119906

1 119889119906

119899 Uploading power consumption data set

119865 Transforming function from119863119860119879119860119904to119863119860119879119860

119906

119863119860119879119860119887= 119889119887

1 119889119887

119900 ldquoBadrdquo power consumption data set

119875119877119868119862119864 = 1199011 1199012 119901

119899 Price set

119860119862119879 = 1198861 1198862 119886

119898 Activity set

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRPA

119863119860119879119860119906

=1 SoundnessRPA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904) Get a data from119863119860119879119860

119904

for 119894 = 1 to 119899 minus 1 doif ((119889119904

119894== 119889119887

1)OR (119889119887

1lt 119889119904119894lt 1198891198872)) then

119889119906119894lArr (119889119887

1+ 1198891198872)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif ((119889119904

119894== 119889119887

119900)OR (119889119887

119900minus1lt 119889119904119894lt 119889119887119900)) then

119889119906119894lArr (119889119887

119900minus1+ 119889119887119900)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end iffor 119895 = 2 to 119900 minus 1 do

if (119889119904119894== 119889119887

119895) then

119889119906119894lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119887

119895+ 119889119887119895+1)2 (119889119887

119895+ 119889119887119895minus1)2)

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifif (119889119887

119895lt 119889119904119894lt 119889119887119895+1)then

119889119906119894lArr (119889119887

119895+ 119889119887119895+1)2

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end ifend for

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899For soundness

Algorithm 1 Random Perturbation AlgorithmmdashRPA

Proof The biases of 119889119906119894(119894 = 1 119899 minus 1) comparing to

119889119904119894(1 119899minus1) are accumulated into a total value119861119868119860119878119861119868119860119878

is changed into extra power consumption and added to thelast one 119889119906

119899 Thussum119899

119894=1119889119904119894lowast119901119894= sum119899

119894=1119889119906119894lowast119901119894 The total cost

of power consumption in a day maintains the correct valueso SoundnessRPA

119863119860119879119860119906

= 1

Proposition 12 The scheme RPS is ultra-lightweight

Proof As algorithm RPA is ultra-lightweight the number ofloops is (119899 minus 1) lowast (119900 minus 2) The computation in each loop isonly simple operations such asmodulo minus plus divisionandmultiplicationThe computation complexity of algorithmRPA is 119874(119899 lowast 119900)

Proposition 13 The scheme RPS can guarantee the perfect fullprivacy (Privacy119901A119877119875119878

119891119906119897119897= 1)

Proof It is clear that for all 119889119904119894isin 119863119860119879119860

119904 119889119906119894= 119865(119889119904

119894) notin

119863119860119879119860119887 Thus PrivacyRPA

119863119860119879119860119906

= 1 According to the definitionof the perfect full privacy Privacy119901ARPS

full= 1

33 RandomWalk Scheme (RWS) If the gap between 119889119887119895and

119889119887119895+1

(119895 = 1 119900minus1) is small the perturbation (namely 120575) inRPSwill be small It can be proofed as a claim in the following

Claim 4 If the gap between 119889119887119895and 119889119887

119895+1(119895 = 1 119900 minus 1) is

small the perturbation in RPS will be small

Proof Suppose max(|119889119887119895minus 119889119887119895+1|) = 119892(119895 = 1 119899 minus 1) If

119889119904119894= 119889119887119895isin 119863119860119879119860

119887) in RPA max(120575) le 1198922 If 119889119904

119894= 119889119887119895isin

119863119860119879119860119887 max(120575) lt 1198922 Thus the perturbation 120575 is small if 119892

is small

6 International Journal of Distributed Sensor Networks

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRWA

119863119860119879119860119906

= 1 SoundnessRWA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 do119895 lArr (119903119886119899119889119900119898()119900 + 1)119889119906119894lArr 119889119887

119895

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 2 RandomWalk Algorithm (RWA)

If the perturbation is small adversaries may guess the 119889119904119894

correctly and adversaries can guess the activity is either oftwo activities To address this issue we propose a randomwalk scheme called RWS in which 119889119904

119894isin 119863119860119879119860

119904randomly

jumps to a value in119863119860119879119860119887 In this case the privacy definition

is extended to include unlinkability inwhich the possibility of119889119887119895isin 119863119860119879119860

119887for 119889119904

119894is equal Thus the revealed user activity

occurs with equal possibility

Definition 14 After transformation 119865 the privacy of119863119860119879119860119906

is guaranteed (denoted as Privacy119865119863119860119879119860

119906

= 1) if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) isin 119863119860119879119860

119906

forall119889119887119901 119889119887

119902isin 119863119860119879119860

119887 119889119887

119901= 119889119887119902

Pr 119889119906119894= 119889119887119901 = Pr 119889119906

119894= 119889119887119902

(10)

The definition for privacy is thus extended to include thedefinition here and Definition 9

In RWS any 119889119904119894isin 119863119860119879119860

119904(119894 = 1 119899 minus 1) is perturbed

to a value 119889119887119895isin 119863119860119879119860

119887(119895 = 1 119900) which is randomly

selected This algorithm is thus especially ultra-lightweightin terms of computation A randomwalk algorithm (RWA) isproposed for the transformation function 119865 as follows

331 Analysis of Algorithm 2

Proposition 15 After the transformation of algorithmRWA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119882119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Proposition 11As sum119899119894=1119889119904119894lowast 119901119894= sum119899

119894=1119889119906119894lowast 119901119894 the total cost of power

consumption in a day maintains the correct value Thus thesoundness of RWA is guaranteed

Proposition 16 The scheme RWS is ultra-lightweight

Proof The number of loops is 119899 minus 1 so algorithm RPA isultra-lightweight The computations in loops are only simpleoperations such as modulo minus plus and multiplication

Moreover algorithm RWA is more lightweight than algo-rithm RPA Thus scheme RWS is ultra-lightweight

Proposition 17 The scheme RWS can guarantee the perfectfull privacy (Privacy119901A119877119882119878

119891119906119897119897= 1)

Proof According to the algorithm for for all 119889119904119894isin 119863119860119879119860

119904

if 119889119906119894= 119865(119889119904

119894) isin 119863119860119879119860

119906 we have forall119889119887

119901 119889119887119902isin 119863119860119879119860

119887

119889119887119901= 119889119887119902 and Pr119889119906

119894= 119889119887

119901 = Pr119889119906

119894= 119889119887

119902 Thus

PrivacyRWA119863119860119879119860

119906

= 1 According to the definition of the privacyin Definition 14 Privacy119901ARWS

full= 1

34 Distance-Bounded Random Walk with PerturbationScheme (DBS) In smart grid the uploading data will beused as a feedback for future scheduling of distribution andtransmission It thus requires the uploading data can accu-rately present the power consumption (namely sensing data)However thanks to the power distribution and transmissionserve not for a single SM but a large number of SMs (eg acampus a community or a county scale) only the accuracyfor a scale of SMs is sufficient for scheduling

In RPS and RWS although the bias exists (that isuploading data is not equal to sensing data) at single SMthe uploading data for a large number of SMs can stillrepresent power consumption in a scaleMore specifically thedeviation between the summation of uploading data and thesummation of sensing data is randomly positive or negativein one SM thus the overall summation remains almostunchanged in expectation in a large scale It is explained asfollows

Definition 18 After the transformation 119865 the accuracy of119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(denoted as Accuracy119865119863119860119879119860

119906

= 1) The summation of119863119860119879119860119906

equals the summation of 119863119860119879119860119904 in scheduling area and

scheduling period More specifically suppose that eachscheduling period consists of 119909 sensing (uploading) periodand each scheduling area consists of 119910 SMs The uploadingdata for them is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 The

sensing data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894

International Journal of Distributed Sensor Networks 7

Required119863119860119879119860119904 119863119860119879119860

119887 BOUND

Ensure119863119860119879119860119906 PrivacyDBA

119863119860119879119860119906

= 1 SoundnessDBA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 doWHILE (1)

119895 lArr (119903119886119899119889119900119898()(119900 minus 2) + 2)120575 lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119904

119894minus (119889119887119895+ (119889119887119895+1minus 119889119887119895)2)) (119889119904

119894minus (119889119887119895+ (119889119887119895minus 119889119887119895minus1)2)))

if (119886119887119904(120575) le 119861119874119880119873119863) then119889119906119894lArr 119889119904

119894minus 120575

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

EXITelse

CONTINUEend if

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 3 Distance-Bounded Algorithm (DBA)

The accuracy of119863119860119879119860119906is guaranteed if and only if SUM

119904=

SUM119906

Proposition 19 After the transformation 119877119875119860 or 119877119882119860 theaccuracy of119863119860119879119860

119906is guaranteed in expectation for a schedul-

ing area (Accuracy119877119875119860119877119882119860119863119860119879119860

119906

= 1)

Proof In each sensing (uploading) period 119889119904119894is changed into

119889119906119894at single SM 120575 = 119889119904

119894minus 119889119906119894 Suppose that each scheduling

period consists of 119909 sensing (uploading) period and eachscheduling area consists of 119910 SMs The uploading data forthem is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 the sensing

data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894 The

expectation of both is equal as the expectation of 120575 is 0 ina scheduling area That is SUM

119904= SUM

119906 as 120575 = 0 where119867

means the expectation of119867

To further guarantee the scheduling accuracy we proposea distance-bounded scheme in which the perturbation value(ie 120575) is bounded The accuracy is thus guaranteed withina threshold value It takes the advantages of former twoalgorithms RPA and RWA A distance-bounded algorithm(DBA) for the transformation 119865 is proposed as follows

341 Analysis of Algorithm 3

Proposition 20 After the transformation of algorithmDBA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Propositions 11 and15

Proposition 21 The scheme DBS is ultra-lightweight

Proof The proof can be reduced to the proof of Propositions12 and 16

Proposition 22 The scheme DBS can guarantee the perfectfull privacy (Privacy119901A119863119861119878

119891119906119897119897= 1)

Proof Theproof is similar to the proof of Propositions 13 and17

Proposition 23 After the transformation 119863119861119860 the accuracyof 119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(Accuracy119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is reduced to the proof of Proposition 19

Proposition 24 The summation of uploading data equals thesummation of the sensing data with deviation bounded by 120572 lowast120573lowast119861119874119880119873119863 where 120572 is the number of SMs in a schedule area120573 is the number of sensing (uploading) period in a scheduleperiod (That is |119878119880119872

119906minus 119878119880119872

119904| le 120572 lowast 120573 lowast 119861119874119880119873119863)

Proof The schedule accuracy is the deviation between thesummation of uploading data and the summation of sensingdata As it is proofed in Proposition 19 it depends on thenumber of SMs in the schedule area and the number ofsensing (uploading) period in the schedule period Theexpectation value is proofed to be 0 as the expectation of120575 is 0 Concerning the accuracy of one schedule periodthe maximal bias between the summation of uploading dataand the summation of sensing data is bounded by 120572 lowast 120573 lowast119861119874119880119873119863

4 Related Work

The security architectures and overall security requirementsin smart grid were discussed in the recent years [3 7] Cur-rently the privacy issue in smart grid starts to attract moreattentions The requirements of privacy were explored insome previousworks [8ndash11]They pointed out the importance

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Distributed Sensor Networks

Required119863119860119879119860119904119863119860119879119860

119887

Ensure119863119860119879119860119906 PrivacyRWA

119863119860119879119860119906

= 1 SoundnessRWA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 do119895 lArr (119903119886119899119889119900119898()119900 + 1)119889119906119894lArr 119889119887

119895

120575 lArr 119889119904119894minus 119889119906119894

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 2 RandomWalk Algorithm (RWA)

If the perturbation is small adversaries may guess the 119889119904119894

correctly and adversaries can guess the activity is either oftwo activities To address this issue we propose a randomwalk scheme called RWS in which 119889119904

119894isin 119863119860119879119860

119904randomly

jumps to a value in119863119860119879119860119887 In this case the privacy definition

is extended to include unlinkability inwhich the possibility of119889119887119895isin 119863119860119879119860

119887for 119889119904

119894is equal Thus the revealed user activity

occurs with equal possibility

Definition 14 After transformation 119865 the privacy of119863119860119879119860119906

is guaranteed (denoted as Privacy119865119863119860119879119860

119906

= 1) if

forall119889119904119894isin 119863119860119879119860

119904 119889119906

119894= 119865 (119889119904

119894) isin 119863119860119879119860

119906

forall119889119887119901 119889119887

119902isin 119863119860119879119860

119887 119889119887

119901= 119889119887119902

Pr 119889119906119894= 119889119887119901 = Pr 119889119906

119894= 119889119887119902

(10)

The definition for privacy is thus extended to include thedefinition here and Definition 9

In RWS any 119889119904119894isin 119863119860119879119860

119904(119894 = 1 119899 minus 1) is perturbed

to a value 119889119887119895isin 119863119860119879119860

119887(119895 = 1 119900) which is randomly

selected This algorithm is thus especially ultra-lightweightin terms of computation A randomwalk algorithm (RWA) isproposed for the transformation function 119865 as follows

331 Analysis of Algorithm 2

Proposition 15 After the transformation of algorithmRWA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119877119882119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Proposition 11As sum119899119894=1119889119904119894lowast 119901119894= sum119899

119894=1119889119906119894lowast 119901119894 the total cost of power

consumption in a day maintains the correct value Thus thesoundness of RWA is guaranteed

Proposition 16 The scheme RWS is ultra-lightweight

Proof The number of loops is 119899 minus 1 so algorithm RPA isultra-lightweight The computations in loops are only simpleoperations such as modulo minus plus and multiplication

Moreover algorithm RWA is more lightweight than algo-rithm RPA Thus scheme RWS is ultra-lightweight

Proposition 17 The scheme RWS can guarantee the perfectfull privacy (Privacy119901A119877119882119878

119891119906119897119897= 1)

Proof According to the algorithm for for all 119889119904119894isin 119863119860119879119860

119904

if 119889119906119894= 119865(119889119904

119894) isin 119863119860119879119860

119906 we have forall119889119887

119901 119889119887119902isin 119863119860119879119860

119887

119889119887119901= 119889119887119902 and Pr119889119906

119894= 119889119887

119901 = Pr119889119906

119894= 119889119887

119902 Thus

PrivacyRWA119863119860119879119860

119906

= 1 According to the definition of the privacyin Definition 14 Privacy119901ARWS

full= 1

34 Distance-Bounded Random Walk with PerturbationScheme (DBS) In smart grid the uploading data will beused as a feedback for future scheduling of distribution andtransmission It thus requires the uploading data can accu-rately present the power consumption (namely sensing data)However thanks to the power distribution and transmissionserve not for a single SM but a large number of SMs (eg acampus a community or a county scale) only the accuracyfor a scale of SMs is sufficient for scheduling

In RPS and RWS although the bias exists (that isuploading data is not equal to sensing data) at single SMthe uploading data for a large number of SMs can stillrepresent power consumption in a scaleMore specifically thedeviation between the summation of uploading data and thesummation of sensing data is randomly positive or negativein one SM thus the overall summation remains almostunchanged in expectation in a large scale It is explained asfollows

Definition 18 After the transformation 119865 the accuracy of119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(denoted as Accuracy119865119863119860119879119860

119906

= 1) The summation of119863119860119879119860119906

equals the summation of 119863119860119879119860119904 in scheduling area and

scheduling period More specifically suppose that eachscheduling period consists of 119909 sensing (uploading) periodand each scheduling area consists of 119910 SMs The uploadingdata for them is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 The

sensing data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894

International Journal of Distributed Sensor Networks 7

Required119863119860119879119860119904 119863119860119879119860

119887 BOUND

Ensure119863119860119879119860119906 PrivacyDBA

119863119860119879119860119906

= 1 SoundnessDBA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 doWHILE (1)

119895 lArr (119903119886119899119889119900119898()(119900 minus 2) + 2)120575 lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119904

119894minus (119889119887119895+ (119889119887119895+1minus 119889119887119895)2)) (119889119904

119894minus (119889119887119895+ (119889119887119895minus 119889119887119895minus1)2)))

if (119886119887119904(120575) le 119861119874119880119873119863) then119889119906119894lArr 119889119904

119894minus 120575

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

EXITelse

CONTINUEend if

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 3 Distance-Bounded Algorithm (DBA)

The accuracy of119863119860119879119860119906is guaranteed if and only if SUM

119904=

SUM119906

Proposition 19 After the transformation 119877119875119860 or 119877119882119860 theaccuracy of119863119860119879119860

119906is guaranteed in expectation for a schedul-

ing area (Accuracy119877119875119860119877119882119860119863119860119879119860

119906

= 1)

Proof In each sensing (uploading) period 119889119904119894is changed into

119889119906119894at single SM 120575 = 119889119904

119894minus 119889119906119894 Suppose that each scheduling

period consists of 119909 sensing (uploading) period and eachscheduling area consists of 119910 SMs The uploading data forthem is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 the sensing

data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894 The

expectation of both is equal as the expectation of 120575 is 0 ina scheduling area That is SUM

119904= SUM

119906 as 120575 = 0 where119867

means the expectation of119867

To further guarantee the scheduling accuracy we proposea distance-bounded scheme in which the perturbation value(ie 120575) is bounded The accuracy is thus guaranteed withina threshold value It takes the advantages of former twoalgorithms RPA and RWA A distance-bounded algorithm(DBA) for the transformation 119865 is proposed as follows

341 Analysis of Algorithm 3

Proposition 20 After the transformation of algorithmDBA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Propositions 11 and15

Proposition 21 The scheme DBS is ultra-lightweight

Proof The proof can be reduced to the proof of Propositions12 and 16

Proposition 22 The scheme DBS can guarantee the perfectfull privacy (Privacy119901A119863119861119878

119891119906119897119897= 1)

Proof Theproof is similar to the proof of Propositions 13 and17

Proposition 23 After the transformation 119863119861119860 the accuracyof 119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(Accuracy119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is reduced to the proof of Proposition 19

Proposition 24 The summation of uploading data equals thesummation of the sensing data with deviation bounded by 120572 lowast120573lowast119861119874119880119873119863 where 120572 is the number of SMs in a schedule area120573 is the number of sensing (uploading) period in a scheduleperiod (That is |119878119880119872

119906minus 119878119880119872

119904| le 120572 lowast 120573 lowast 119861119874119880119873119863)

Proof The schedule accuracy is the deviation between thesummation of uploading data and the summation of sensingdata As it is proofed in Proposition 19 it depends on thenumber of SMs in the schedule area and the number ofsensing (uploading) period in the schedule period Theexpectation value is proofed to be 0 as the expectation of120575 is 0 Concerning the accuracy of one schedule periodthe maximal bias between the summation of uploading dataand the summation of sensing data is bounded by 120572 lowast 120573 lowast119861119874119880119873119863

4 Related Work

The security architectures and overall security requirementsin smart grid were discussed in the recent years [3 7] Cur-rently the privacy issue in smart grid starts to attract moreattentions The requirements of privacy were explored insome previousworks [8ndash11]They pointed out the importance

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 7

Required119863119860119879119860119904 119863119860119879119860

119887 BOUND

Ensure119863119860119879119860119906 PrivacyDBA

119863119860119879119860119906

= 1 SoundnessDBA119863119860119879119860

119906

= 1119889119904119894lArr 119866119890119905119863119886119905119886(119863119860119879119860

119904)

for 119894 = 1 to 119899 minus 1 doWHILE (1)

119895 lArr (119903119886119899119889119900119898()(119900 minus 2) + 2)120575 lArr 119894119891119891(119903119886119899119889119900119898()2 (119889119904

119894minus (119889119887119895+ (119889119887119895+1minus 119889119887119895)2)) (119889119904

119894minus (119889119887119895+ (119889119887119895minus 119889119887119895minus1)2)))

if (119886119887119904(120575) le 119861119874119880119873119863) then119889119906119894lArr 119889119904

119894minus 120575

119861119868119860119878 lArr 119861119868119860119878 + 120575 lowast 119901119894

EXITelse

CONTINUEend if

end for119889119906119899lArr 119889119904

119899+ 119861119868119860119878119901

119899

Algorithm 3 Distance-Bounded Algorithm (DBA)

The accuracy of119863119860119879119860119906is guaranteed if and only if SUM

119904=

SUM119906

Proposition 19 After the transformation 119877119875119860 or 119877119882119860 theaccuracy of119863119860119879119860

119906is guaranteed in expectation for a schedul-

ing area (Accuracy119877119875119860119877119882119860119863119860119879119860

119906

= 1)

Proof In each sensing (uploading) period 119889119904119894is changed into

119889119906119894at single SM 120575 = 119889119904

119894minus 119889119906119894 Suppose that each scheduling

period consists of 119909 sensing (uploading) period and eachscheduling area consists of 119910 SMs The uploading data forthem is SUM

119906= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119906119894 the sensing

data for them is SUM119904= sum119910

119905=1SM119905 SM119905= sum119909

119894=1119889119904119894 The

expectation of both is equal as the expectation of 120575 is 0 ina scheduling area That is SUM

119904= SUM

119906 as 120575 = 0 where119867

means the expectation of119867

To further guarantee the scheduling accuracy we proposea distance-bounded scheme in which the perturbation value(ie 120575) is bounded The accuracy is thus guaranteed withina threshold value It takes the advantages of former twoalgorithms RPA and RWA A distance-bounded algorithm(DBA) for the transformation 119865 is proposed as follows

341 Analysis of Algorithm 3

Proposition 20 After the transformation of algorithmDBA the soundness of 119863119860119879119860

119906is guaranteed

(Soundness119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is similar to the proof of Propositions 11 and15

Proposition 21 The scheme DBS is ultra-lightweight

Proof The proof can be reduced to the proof of Propositions12 and 16

Proposition 22 The scheme DBS can guarantee the perfectfull privacy (Privacy119901A119863119861119878

119891119906119897119897= 1)

Proof Theproof is similar to the proof of Propositions 13 and17

Proposition 23 After the transformation 119863119861119860 the accuracyof 119863119860119879119860

119906is guaranteed in expectation for a scheduling area

(Accuracy119863119861119860119863119860119879119860

119906

= 1)

Proof The proof is reduced to the proof of Proposition 19

Proposition 24 The summation of uploading data equals thesummation of the sensing data with deviation bounded by 120572 lowast120573lowast119861119874119880119873119863 where 120572 is the number of SMs in a schedule area120573 is the number of sensing (uploading) period in a scheduleperiod (That is |119878119880119872

119906minus 119878119880119872

119904| le 120572 lowast 120573 lowast 119861119874119880119873119863)

Proof The schedule accuracy is the deviation between thesummation of uploading data and the summation of sensingdata As it is proofed in Proposition 19 it depends on thenumber of SMs in the schedule area and the number ofsensing (uploading) period in the schedule period Theexpectation value is proofed to be 0 as the expectation of120575 is 0 Concerning the accuracy of one schedule periodthe maximal bias between the summation of uploading dataand the summation of sensing data is bounded by 120572 lowast 120573 lowast119861119874119880119873119863

4 Related Work

The security architectures and overall security requirementsin smart grid were discussed in the recent years [3 7] Cur-rently the privacy issue in smart grid starts to attract moreattentions The requirements of privacy were explored insome previousworks [8ndash11]They pointed out the importance

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Distributed Sensor Networks

and urgency of privacy issues Efthymiou and Kalogridisproposed a privacy protection scheme via anonymizationof data [12] Their work relied on Escrow and Public KeyInfrastructure (PKI) thus the flexibility and scalability maybe tampered Tomosada and Sinohara proposed to use virtualenergy demand to estimate the energy load and protectingconsumer privacy [13] but the estimation may take muchcomputation overhead and accuracy may be damaged Lu etal [10] proposed an efficient and privacy-preserving aggrega-tion scheme (EPPA) Their scheme relied on homomorphicPaillier cryptosystem and induces much computation over-head Cheung et al [14] proposed a credential-based privacy-preserving power request scheme for smart grid which reliedon an advanced cryptographic primitive-blind signature Heet al [15] proposed to use homomorphic encryption for smartgrid communications Comparing with all aforementionedrelated work our final scheme does not rely on any crypto-graphic primitive but fulfils provable privacy and restrainsultra-lightweight in computation

5 Conclusions

In this paper we proposed three schemes to protect user pri-vacy in smart grid without any cryptographic primitive andwith ultra-lightweight computation They are random per-turbation scheme (RPS) random walk scheme (RWS) anddistance-bounded random walk with perturbation scheme(DBS) We also proposed three algorithms for three schemesrespectively Our schemes do not rely on any cryptographiccomputations are sound in terms of maintaining the correctutility charge can guarantee the privacy that were strictlyproofed and can ensure the scheduling accuracy in powertransmission and distribution All proposed schemes andalgorithms were extensively analyzed which justified theirapplicability

Acknowledgments

W Renrsquos research was financially supported by NationalNatural Science Foundation of China (61170217) the OpenResearch Fund from Shandong provincial Key Laboratoryof Computer Network (SDKLCN-2011-01) and FundamentalResearch Funds for the Central Universities (CUG110109) YRenrsquos research was sponsored in part by the ldquoAim for the TopUniversity Projectrdquo of the National Chiao Tung Universityand the Ministry of Education Taiwan

References

[1] The Smart Grid Interoperability Panel Cyber Security Work-ing Group ldquoNistir 7628 guidelines for smart grid cybersecurityrdquo in Privacy and the smart grid vol 2 2010 httpcsrcnistgovpublicationsnistirir7628nistir-7628 vol2pdf

[2] H Khurana M Hadley N Lu and D A Frincke ldquoSmart-gridsecurity issuesrdquo IEEE Security and Privacy vol 8 no 1 pp 81ndash85 2010

[3] P McDaniel and S McLaughlin ldquoSecurity and privacy chal-lenges in the smart gridrdquo IEEE Security and Privacy vol 7 no3 pp 75ndash77 2009

[4] A R Metke and R L Ekl ldquoSecurity technology for smart gridnetworksrdquo IEEE Transactions on Smart Grid vol 1 no 1 pp99ndash107 2010

[5] G N Ericsson ldquoCyber security and power system commu-nicationessential parts of a smart grid infrastructurerdquo IEEETransactions on Power Delivery vol 25 no 3 pp 1501ndash15072010

[6] A Vaccaro M Popov D Villacci and V Terzija ldquoAn integratedframework for smart microgrids modeling monitoring con-trol communication and verificationrdquo Proceedings of the IEEEvol 99 no 1 pp 119ndash132 2010

[7] T M Overman R W Sackman T L Davis and B S CohenldquoHigh-assurance smart grid a three-part model for smart gridcontrol systemsrdquo Proceedings of the IEEE vol 99 no 6 pp1046ndash1062 2011

[8] J Liu Y Xiao S Li W Liang and C Chen ldquoCyber security andprivacy issues in smart gridsrdquo IEEE Communications SurveysTutorials vol 99 pp 1ndash17 2012

[9] F Maandrmol C Sorge O Ugus and G Peandrez ldquoDo notsnoop my habits preserving privacy in the smart gridrdquo IEEECommunications Magazine vol 50 no 5 pp 166ndash172 2012

[10] R Lu X Liang X Li X Lin and X Shen ldquoEppa anefficient and privacypreserving aggregation scheme for securesmart grid communicationsrdquo IEEE Transactions on Parallel andDistributed Systems vol 23 no 9 pp 1621ndash1631 2012

[11] S Wang L Cui J Que et al ldquoA randomized response modelfor privacy preserving smart meteringrdquo IEEE Transactions onSmart Grid vol 3 no 3 pp 1317ndash1324 2012

[12] C Efthymiou and G Kalogridis ldquoSmart grid privacy viaanonymization of smart metering datardquo in Proceedings of the 1stIEEE International Conference on Smart Grid Communications(SmartGridComm rsquo10) pp 238ndash243 October 2010

[13] M Tomosada and Y Sinohara ldquoVirtual energy demand dataestimating energy load and protecting consumersrsquo privacyrdquo inProceedings of the IEEE PES Innovative Smart Grid Technologies(ISGT rsquo11) pp 1ndash8 January 2011

[14] J Cheung T Chim S Yiu L Hui and V Li ldquoCredential-based privacy-preserving power request scheme for smart gridnetworkrdquo in Proceedings of the IEEE Global TelecommunicationsConference (GLOBECOM rsquo11) pp 1ndash5 December 2011

[15] X He M Pun and C Kuo ldquoSecure and efficient cryptosystemfor smart grid using homomorphic encryptionrdquo in Proceedingsof the IEEE PES Innovative Smart Grid Technologies (ISGT rsquo12)pp 1ndash8 January 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of