ResearchGate

Seediscussions,stats,andauthorprofilesforthispublicationat:

/publication/339860852

Quantumkeydistributionsolutionoverindoorvisiblelightcommunication

networks

ConferencePaper·March2020DOI:10.1117/12.2552987

CITATIONS2

READS

460

5authors,including:

NgocDang

PostsandTelecommunicationsInstituteofTechnology

114PUBLICATIONS948CITATIONS

SEEPROFILE

HienT.T.Pham

PostsandTelecommunicationsInstituteofTechnology

52PUBLICATIONS564CITATIONS

SEEPROFILE

VuongMai

UniversityofBradford

82PUBLICATIONS775CITATIONS

SEEPROFILE

Allcontentfollowingthispagewasuploadedby

NgocDang

on05June2020.Theuserhasrequestedenhancementofthedownloadedfile.

PROCEEDINGSOFSPIE

SPIEDigitalL/conference-proceedings-of-spie

Quantumkeydistributionsolution

overindoorvisiblelight

communicationnetworks

Dang,Ngoc,Vu,Minh,Pham,Thu,Pham,HienT.,Mai,Vuong

NgocT.Dang,MinhB.Vu,ThuA.Pham,HienT.T.Pham,VuongV.Mai,

"Quantumkeydistributionsolutionoverindoorvisiblelightcommunication

networks,"Proc.SPIE11331,FourthInternationalConferenceonPhotonics

Solutions(ICPS2019),113310A(11March2020);doi:10.1117/12.2552987

SPIE。

Event:FourthInternationalConferenceonPhotonicSolutions(ICPS2019),

2019,ChiangMai,Thailand

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020TermsofUse:/terms-of-use

Quantumkeydistributionsolutionoverindoorvisiblelightcommunicationnetworks

NgocT.Dang*a,MinhB.Vua,ThuA.Phama,HienT.T.Phama,VuongV.Maib,

aPostsandTelecommunicationsInstituteofTechnology,122HoangQuocViet,HaN?i,VietNam

bPhotonicsSystemsResearchLaboratory,SchoolofElectricalEngineering,KAIST,Korea

ABSTRACT

Inthispaper,westudyanapplicationofquantumkeydistribution(QKD)forindoorvisiblelightcommunication(VLC)networks.ContinuousvariableQKD(CV-QKD)isusedduetothefactthatitislessexpensive,workingatroomtemperature,andmucheasiertoimplement.WedesignandanalyzethesecurityperformanceoftheCV-QKDprotocolbasedonsub-carrierintensitymodulation(SIM)overindoorVLCsystemstakingintoaccounttheeffectsofVLCchannelandotherphysicallayerimpairments.Themathematicalexpressionsforquantumbit-errorrate(QBER)andsecret-keyratearederived.Basedonthemathematicalexpressions,varioussystems’metrics,includingthemodulationdepthandthedual-thresholdscalecoefficient,canbedeterminedsoastoQBERandsecret-keyratemeetthedesigncriteria.

Keywords:Quantumkeydistribution(QKD),visiblelightcommunications(VLC),quantumbit-errorrate(QBER),secret-keyrate.

1.INTRODUCTION

Visiblelightcommunication(VLC)usinglightemittingdiodes(LEDs)inilluminationinfrastructurehasbeenattractedalotofscientificresearchinterest[1].ThemainadvantagesofVLCareenergyefficient,reliable,andeco-friendly[2].Besides,duetothescarcewirelessresource,VLChasbecomeafavorablecomplementarytechnologytoRFcommunicationinshort-rangecommunicationscenariosforfuture5Gnetworks.Especiallyfor5Gindoorapplications,VLChasdevelopedrapidlyinthelastfewyears[3,4].Whiletheprogressofthismagnitudeisintriguing,thehyper-indoorconnectivitythat5GnetworksenablewillexacerbatesecurityissuesinVLCnetworks.Althoughsecurityissueshavebeenmentionedinseveralsurveypapers[5]-[8],thereisstillalackofintensivestudiesontheissues.TheIEEE

802.15.7VLCstandardalsomentionedabouttheuseofsymmetric-keycryptographyforimprovingthesecurityofVLCnetworks.However,themethodsofkeygenerationandmanagementarenotdetailedinthestandard[9].

Onepotentialsolutionforsecuringcommunicationsacross5Gnetworksistheuseofquantumkeydistribution(QKD).Thisisthemethodofdistributingsymmetricsecretkeyswithinformation-theoreticsecurity(ITS).AccordingtoShannontheoryofITS,theunconditional(i.e.,perfect)securitycanbeachievedwhenalong-symmetricalkeyisusedanditisusedonlyonce(i.e.,one-timepad).Dependingonhowthekey(formedbyagroupofbinarybits)isencoded,QKDcanbeclassifiedintotwomajorkeydistributionmethods,namelydiscretevariable(DV)andcontinuousvariable(CV).Intheformer,binarybitsareencodedbyquantumstatesoflight,whichisphysicallyimpossibletobecompromisedbyanyeavesdroppingmeans.However,thismethodisexpensiveandnotfeasibleatroomtemperature.Thelatterenablesbinarybitstobeencodedontoopticalwavesbyasimilarwayofopticalmodulationtechniques.Thismethodislessexpensive,workingatroomtemperature,andmucheasiertoimplementasitiscompatiblewiththestandardopticalcommunicationtechnologies[10,11].

Motivatedbytheabovediscussion,weinvestigateinthisstudyanapplicationofQKDasasecurecommunicationmethodforVLCnetworks.ThisstudyistheoutcomeofourASEANIVOproject“SmartLightingforInternetofThingsandSmartHomes”,inwhichweproposeanddevelopnovelvisiblelighttechnologiesanditssystemsforIoTapplicationsandhigh-speedindoorcommunications.WhileanumberofstudiesaboutQKDthroughopticalfiberorfree-spaceopticalsystemshavebeendonesofar[12]-[15],tothebestofourknowledge,thisisthefirststudyofQKDinVLCnetworks.Morespecifically,thecontributionsofthispapercanbesummarizedasfollows:

FourthInternationalConferenceonPhotonicsSolutions(ICPS2019),editedbyTetsuyaKawanishi,

SurachetKanprachar,WaranontAnukool,UkritMankong,Proc.ofSPIEVol.11331,113310A

?2020SPIE·CCCcode:0277-786X/20/$21·doi:10.1117/12.2552987

Proc.ofSPIEVol.11331113310A-1

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

Proc.ofSPIEVol.11331113310A-2

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

DesignofCV-QKD/VLCsystems:wepresenttheCV-QKDprotocoloperationoveraVLClink.Also,weprovideaguidancefortherealizationofCV-QKD/VLCusingsubcarrierintensitymodulation(SIM)binaryphase-shift-keying(BPSK)anddualthreshold/direct-detection(DT/DD)receiver.

PerformanceanalysisofCV-QKD/VLCsystems:asthemaincontributionofthisstudy,wederivemathematicalexpressionsforquantumbit-errorrate(QBER)andsecret-keyrate,takingintoaccountvariouseffectsofVLCchannelandsystemimpairments.Theseexpressionscouldbehelpfulinpracticefordesignerstodeterminethesystemparameters.Theimportanceisshownthroughselectionsofmodulationdepthanddual-thresholdscalecoefficientbasedonadesigncriterionofQBERandsecret-keyrate.

2.CV-QKD/VLCSYSTEM

Alice

VLCchannel

Bob

PD

OBPF

LEDarray

(t)

0

X

1

1X0X00...

DC

bias

d(t)

110100...

FilterCircuit

—學(xué):Opticalsignal

:Electricalsignal

cos(2πfct)

g(t)

cos(2πfct)

BPSKmodulatorofQKD-VLCBPSKdemodulatorofQKD-VLC

t0,t2,t4,t5,...

1000...1000...

Classicalpublicchannel

Figure1.BlockdiagramofCV/QKD-VLCsystem.

PresentedinthissectionareoperationandmodelingofCV-QKD/VLCsystemsusingSIM/BPSKandDT/DD.Detailsareasfollows:

Step1:AtthesourceAlicehasasecretkeythatisformedbyagroupofbinarybits,asshowninFig.1.Theywillbeencodedontoopticalwaves.Todoso,Alicerandomlychoosestwodifferentphasesπapartinlinearphasebases.ThebinarybitsaremodulatedintoRFsubcarriersignalsbySIM/BPSKscheme,inwhichbits“1”andbit“0”arerepresentedbythechosenphases.Sincethesubcarriersignals(t)consistsofbothpositiveandnegativevalues,aDCbiasisaddedwiths(t)beforeconvertingitformelectricaldomainintoopticaldomainviaLEDarray.Thesubcarriersignalisgivenby

s(t)=a(t)r(t)cos(2πfct+siπ),(1)

wherea(t)isthesubcarrieramplitude,r(t)istherectangularpulsefunction,fcissubcarrierfrequencyandsipresentstheithbinarybit.Afterthat,theopticalsignalwillbepropagatedtoBobthroughtheVLClink,wheretheopticaloutputsignalisgivenby

(2)

wherePisthepeaktransmittedpower,ρisthemodulationdepth(0<ρ<1)topreventtheover-modulation(-1<ρs(t)<1).AssumingthatthetransmittedpowerofallLEDsarethesame,PiswrittenasP=PLED×nLED,wherePLEDisthetransmittedpowerofaLEDandnLEDisthenumberofLEDsintheLEDarray.

Step2:Atthedestination,theopticalsignalisfilteredbyanopticalband-passfilter(OBPF)beforebeingconvertedintotheelectricaldomainbyusingaphotodetector(PD).TheopticalgainofPDusingnon-imagingconcentratorcanbeexpressedas

Proc.ofSPIEVol.11331113310A-3

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

wherenistherefractiveindexandΨcistheFOV.ChannelcoefficientofVLCchannelcanbepresentedasfollows

whereA,d,φandΨarethephysicaldetectorarea,thechanneldistance,theirradiationangleandtheincidentangle,respectively.mlistheorderofLambertianemission,whichcanbeexpressedas

ml=,(5)

whereΦ1/2isthehalfpowersemi-angle.Theoutputelectricalsignalcanbepresentedas

I(t)=g(Ψ)Ts(Ψ)H(Ψ)1+Ps(t)+n(t),(6)

whereistheresponsivityofthePD,Ts(Ψ)isthegainofopticalband-passfilterandn(t)isthereceivernoise.TheelectricalsignalthenpassedthroughtheBPSKdemodulator,whereitcombinedwiththereferencesignalcos(2πfct).Thedemodulatedsignalscorrespondingbits“1”and“0”aregivenby

Afterthat,thedemodulatedelectricalsignalisbeingsampledandthenusedtorecoverbinarybitsofthesecretkeybasedondualthresholds.

Probabilitydensityfunction(PDF)

bit1bitXbit0

d10d0

Bob’sreceivedcurrentsignal

Figure2.PDFofBob’sreceivedsignaloverVLCchannel,d1

anddoaretwolevelsofthedualthresholds.

Probabilitydensityfunction(PDF)

bit1bit0

dE=0

Eve’sreceivedcurrentsignal

Figure3.PDFofEve’sreceivedsignaloverVLCchannelwith

theoptimalthresholddE

Fig.2showstwopeaksofreceivedsignalcorrespondingtoAlice’stransmittedbit“1”andbit“0”.Here,twothresholds,

i.e.,d1andd0,aresymmetricoverthe“zero”leverforbitdetections.Thedetectionruleispresentedasfollows

〔0

Decision={1

lX

,

if(x≥d0)if(x≤d1)

otherwise.

(8)

whereXrepresentsthecaseofnobitdetected,andxisBob’sreceivedcurrentsignal.

Proc.ofSPIEVol.11331113310A-4

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

Step3:Usingatraditionalchannel,Alicebroadcastsherphasechoiceforeachbitofherrawkey,butnotthebitvalue.BobrevealsAlicethetimeinstantsthatthesamephasewasusedtodetectbits“0”and“1”.TheybothdiscardtheunidentifiedbitswhereBobusedadifferentphase.Theremainingbitsinthebitsequence(i.e.50%remainingbitsinthesequence)willbeusedtocreatethenewbitsequencesharedbetweenAliceandBod,namelyasthesiftedkeys.

Step4:Bob’ssiftedkeysmayhappenerrorsduetotheunwantedeffects.Therefore,informationreconciliationcanbeperformedoverthepublicchanneltocorrecttheseerrorsandobtaintheerror-freesecretkey.

Itisimportanttonotethat,therecouldexistaneavesdropper(namelyasEve)inthesystem.Toimprovethesecurity,themodulatedsignalusingSIM/BPSKschemewithsmallmodulationdepthcouldbeused.AsillustratedinFig.3,whenEvetriestodecodethekeyusingtheoptimalthresholddE(at“zero”),shewillsufferfromahigherrorrate.Withapropersettingofmodulationdepthatthetransmitter,wecanguaranteethatEve’serrorratecanbeclosetoprobabilitythatEvechoosestheincorrectbasic.

3.PERFORMANCEANALYSIS

3.1QuantumBitErrorRate

FortheperformanceevaluationoftheCV-QKD/VLCsystem,weinvestigatethequantumbit-errorrate(thepercentageofbiterrorsinthesiftedkey).Itisgivenby

(9)

Here,PsiftrepresentstheprobabilitythatBob’schoosebasesandAlice’schoosebasesisthesameandhecandetectbits“0”and“1”basedonthecorrectbases:Psift=PA,B(0,0)+PA,B(0,1)+PA,B(1,0)+PA,B(1,1);PerrorisdenotedastheprobabilitythatBobwronglydecides“0”whenAlicesent“1”andconversely:Perror=PA,B(0,1)+PA,B(1,0).Intheseprobabilities,PA,B(a,b),wherea,b∈{0,1},isthejointprobabilitythatAlicesendsbit“a”andBobdetectsbit“b”,definedas

PA,B(a,b)=PA(a)PBA(ba),(10)

wherePA(a)=1/2istheprobabilitythatAlicesendsbit“0”orbit“1”,whichisassumedtobeequallylikely.PB,A(b|a)istheconditionalprobabilitythatAlice’sbit“a”coincideswithBob’sbit“b”.

Weassumethatthenoisecomponentsconsistofshortnoise,thermalnoise,andbackgroundnoise.TheycanbemodeledasGaussianrandomvariableswithzeromean.Therefore,thefollowingjointprobabilitiescanbecomputedviathetotalnoisevarianceandthedual-thresholdrule,

(11)

(12)

withδisthresholdscalecoefficient.Q(.)istheGaussianQ-function,wherethetotalnoisevarianceisgivenby

σ=σ+σ+σ,(13)

Whereσ,σ,andσtarerespectivelythevariancesofshotnoise,backgroundnoiseandthermalnoise,

σ=2qIBI2B,(15)

Proc.ofSPIEVol.11331113310A-5

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

?hereq,I2andIBaretheelectroniccharge,thesecondpersonnickintegralandthebackgroundcurrent,respectively.TheequivalentnoisebandwidthB=Rbisset,withRbistheVLCchanneldatarate.kistheBoltzmann’sconstant,Tkistheabsolutetemperature,Golistheopen-loopvoltagegain,Cpdisthefixedcapacitanceofphotodetectorperunitarea,Γisthefieldeffectstransistors(FET)channelnoisefactor,gmistheFETtransconductance,andI3isthethirdpersonnickintegral.

3.2ErgodicSecret-KeyRate

WealsoinvestigatethesecurityoftheCV-QKD/VLCsystemwiththepresenceofaneavesdropperEve.Toevaluatethesecurityperformance,weanalyzetheergodicsecret-keyrateoverindoorVLCchannels.First,wedenoteH(B)andH(E)astheinformationentropyofBobandEve,respectively.TheconditionalentropiesofBob-AliceandEve-AlicearedenotedasH(B|A)andH(E|A),respectively.Thus,I(A,B)=H(B)-H(B|A)andI(A,E)=H(E)-H(E|A),inwhichthekeyissaidtobesecureifI(A,B)ishigherthanI(A,E).Asaresult,wepresenttheergodicsecret-keyrateasthemaximumtransmissionrateatwhichtheeavesdropperisunabletodecodeanyinformation,

ESKR=I(A;B)-I(A;E).(17)

a.MutualinformationbetweenAliceandBob

P(x1)=α

P(x2)=1-α

x1

x2

p

q

q

p

y1

y2

y3

Figure4.Diagramofthebinaryerasurechannel(BEC)witherrorsbetweenAliceandBob.

AsdepictedinFig.4,AliceandBobshareinformationovertheindoorVLCchannel,wherexi(i∈{1,2})respectivelyrepresentsbits“0”and“1”,andyj(j∈{1,2,3})respectivelyrepresentsbits“0”,X,and“1”.pandqrepresentthechanneltransitionprobabilities.αand1-αaretheprobabilitiesoftransmittingbits“0”and“1”.Wedefinethisnewtypeofchannelasthebinaryerasurechannel(BEC)witherrors.Hence,themutualinformationcanbederivedas

I(A;B)=plog2(p)+(1-p-q)log2(1-p-q)

-(ap+(1-a)(1-p-q))log2(ap+(1-a)(1-p-q)).(18)

-(a(1-p-q)+(1-a)p)log2(a(1-p-q)+(1-a)p)

Detailsoftheproofofaboveexpressionareomittedduetospacelimitation.Inoursystem,wehaveα=0.5,andvaluesofp,qcanbededucedfromthejointprobabilitiesderivedinSect.3.1.

b.MutualinformationbetweenAliceandEve

Inoursystem,EvecreatesabitstringthrougheavesdroppinginformationbetweenAliceandBob,wherebitvaluesarepartiallyidenticaltoAlice’sbitvalues.Thus,wecanconsiderthatAliceandEvesharesomeinformationviabinarysymmetricchannel(BSC).So,themutualinformationcanbegivenas

I(A;E)=1+elog2(e)+(1-e)log2(1-e),(19)

whereeisEve’sprobabilityoferror,definedase=PA,E(0,1)+PA,E(1,0).Here,PA,E(0,1)andPA,E(1,0)arethejointprobabilitiesthatEvedetectsthebitwrongversusAlice’stransmittedbitusingthresholddetectiondE,

Proc.ofSPIEVol.11331113310A-6

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

(20)

(21)

whereI1eandIoearetheEve’sreceivedcurrentsignalscorrespondingtobit“1”andbit“0”,respectively.SinceEvedoesnotknowthephasesthatAliceselectstodistributethesecret-key,Evemayusewrongphaseindetectingbits.Therefore,theEve’sreceivedcurrentsignalcanbecomputedasfollows

I1e=-Pg(Ψ)Ts(Ψ)H(Ψ)cos(Δφe),(23)

whereΔφeisthevalueoftheEve’sphaseerror,i.e.,thedifferencebetweenthephaseofthereceivedsignalandthephaseofthelocaloscillatoratEve’sreceiver.

4.NUMERICALRESULTS

Basedonepreviouslyderivedequation,weinvestigatetheselectionsofdesignparametersfortransmitterandreceivertomaintainthesecurityundereavesdropper’sattacking.WeassumethattheVLCnetworkisdeployedinthetypical(5m×5m×3m)roomsize.Alice’stransmitterislocatedintheceilingcenter,whileBob’sreceiverandEve’sreceiverarelocatedonaplaneof0.75mabovetheground.TheparametersofthetransmitterandthereceiveraswellastheconstantsareshowninTable1.

Table1.Parametersandconstants.

Name

Symbol

Value

Modulationindex

ml

0.8

PDresponsivity

0.54A/W

Detectorarea

A

1cm2

RefractiveindexoflensatPD

n

1.5

Halfpowersemi-angle

Φ1/2

600

Gainofopticalfilter

Ts(Ψ)

1

WidthofFOV

Ψc

600

NumberofLEDsinanarray

nLED

60×60

Backgroundcurrent

IB

5100μA

Equivalentnoisebandwidth

B

150Mbit/s

Open-loopvoltagegain

Gol

10

FETchannelnoisefactor

Γ

1.5

FETtransconductance

gm

30mS

PDcapacitance

Cpd

112pF/cm2

Secondpersonnickintegral

I2

0.562

Thirdpersonnickintegral

I3

0.0868

Electronicchargeconstant

q

1.6×10-19C

Boltzmann’sconstant

K

1.38×10-23WHz-1K-1

InFig.5,wefirstinvestigateQBERatBob’sreceiverfordifferentlocationsintheroomwiththeintensitymodulationdepthρ=0.25,thedual-thresholdscalecoefficientδ=1.5,andthetransmittedpowerperLEDPLED=-3dBm.Itisclearthat,whentheBob’slocationisintheroomcenter,BobcanreceivethekeywiththesmallestvalueofQBERduetotheshortesttransmissiondistancefromthetransmittertothereceiver.Whenthedistanceislarge,e.g.,Bobisnearthecornersoftheroom,QBERincreasessignificantlythusitmaynotmeettherequirementthatQBERislowerthanor

Proc.ofSPIEVol.11331113310A-7

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

equalto10-3,atwhichbiterrorsareabletobecorrectedthankstoerrorcorrectioncodes.ThisproblemcanbesolvedbyincreasingthetransmittedpowerperLEDorthenumberofLEDsintheLEDarray.

Figure5.QBERversusdifferentBob’slocationswhenthedual-

thresholdscalecoefficientδ=1.5,theintensitymodulationdepth

ρ=0.25andPLED=-3dBm

Figure7.ESKRversusthephaseerror(Δφe)forthedifferent

intensitymodulationdepth(ρ)withδ=1,PLED=-10dBm,

(xB,yB,zB)=(2.0,2.0,2.15),(xE,yE,zE)=(2.0,-2.0,2.15).

Figure6.QBERandPsiftversusthedual-thresholdscale

coefficient(δ)fordifferentvaluesofthetransmittedpowerwith

ρ=0.5andBob’slocation(xB,yB,zB)=(2.5,2.5,2.15).

Figure8.ESKRversustheintensitymodulationdepth(ρ)forthe

differentdual-thresholdscalecoefficient(δ)withΔφe=π/4,

(xB,yB,zB)=(0.5,0.5,2.15),(xE,yE,zE)=(1.5,1.5,2.15),PLED=-8

dBm.

InFig.6,weshowQBERandPsiftversusthedual-thresholdscalecoefficientwiththedifferentvaluesofthetransmittedpoweratPLED=0dBm,PLED=1dBm.Theintensitymodulationdepthis0.5andtheBob’sreceiverislocatedat(xB,yB,zB)=(5,5,2.15).Fromthisfigure,wecandeterminethedual-thresholdscalecoefficientforthedesignofCV-QKD/VLCsystemthatsatisfiestherequirementsofbothQBERandPsift.Morespecifically,itisnecessarytokeepQBER≤10-3andPsift≥10-2toguaranteethesifted-keyrateatMbps.Accordingly,thevalueofthedual-thresholdscalecoefficientshouldbeintherangeof1.1≤δ≤1.65and0.4≤δ≤1.65whenPLED=0dBmandPLED=1dBm,respectively.Itisclearthat,whenPLEDincreases,probabilitiesthatBobwronglydecidesbit“1”andbit“0”decreasethustheQBERreduces.Consequently,therangeofdual-thresholdscalecoefficientisextendedtothelowvalues.

Next,wevalidatethesecurityofCV-QKD/VLCsysteminFig.7,wheretheergodicsecret-keyrateisinvestigatedversusthephaseerroratEve’sreceiver.ThelocationsofBob’sreceiverandEve’sreceiverarefixedat(xB,yB,zB)=(2.0,2.0,2.15),(xE,yE,zE)=(2.0,-2.0,2.15),respectively.Inthiscase,thedistanceforBob’sreceiverandEve’sreceiverto

Proc.ofSPIEVol.11331113310A-8

DownloadedFrom:

/conference-proceedings-of-spieon29Mar2020

TermsofUse:

/terms-of-use

Alice’stransmitterarethesame.ItisseenthattheESKRchangesperiodicallywiththephaseerrorandreachesthepeakatthephaseerrorofπ/2intheperiodofπ.Withphaseerrorofπ/2,thereceivedsignalandthelocaloscillatorsignalatEve’sreceiverareorthogonal.Thisfigurealsohelpstodeterminetherangeofphaseerror,wheretheCV-QKD/VLCsystemissecured(i.e.,ESKR>0).Forinstance,therangeofphaseerrorshouldbefrom0.5radto2.6radwhenρ=0.4.Whentheintensitymodulationdepthincreases,theESKRpeakalsoincreases,howevertherangeofphaseerroratwhichESKR>0isnarrowed.ThisisduetoEve’sreceiverobtainsmorepowerwhenρincreases.

Finally,weshowthedependenceoftheergodicsecret-keyrateontheintensitymodulationdepthwithdifferentvaluesofdual-thresholdscalecoefficients.Similarly,thelocationsofBobandEvearefixedandPLEDissetto-8dBm.Inaddition,Eve’sphaseerrorissettoπ/4.ThefigureshowsthatESKRcurvesconsistoftwoparts.Atthefirstpartthatiscorrespondingtothesmallvaluesofρ,ESKRincreaseswiththeincreaseofρ.However,inthesecondpart,ESKRreduceswhenρincreases.ThisisbecauselargevalueofρcausestheincreaseofthemutualinformationbetweenAliceandEve.

5.CONCLUSION

WehavestudiedthesecurityperformanceofCV-QKD/VLCsystemusingsubcarrierintensitymodulationwithbinaryphase-shift-keyinganddualthreshold/direct-detection.WederivethemathematicalexpressionsforQBERandESKRofthesystemconsideringtheimpactofindoorVLCchannelandreceivernoise,

weretheoreticallyderivedinclosed-formexpressions.Theselectionsofdesignparametersfortransmitterandreceiver,suchasthemodulationdepthandthedual-thresholdscalecoefficient,werestudied.

ACKNOWLEDGEMENT

ThisworkistheoutputoftheASEANIVO(

http://www.nict.go.jp/en/asean_ivo/index.html

)projectSmartLightingforInternetofThingsandSmartHomesandfinanciallysupportedbyNICT(

http://www.nict.go.jp/en/index.html

).

REFERENCES

[1]D.Karunatilaka,F.Zafar,V.Kalavally,andR.Parthiban,“LEDbasedindoorvisiblelightcommunications:stateoftheart,”IEEECommunicationsSurveys&Tutorials,vol.17,no.3,pp.1649-1678,Mar.2015.

[2]Z.Ghassemlooy,L.Alves,S.S.Zvanovec,andM.M.A.Khalighi.Visiblelightcommunications:theoryandapplications.NewYork:CRCPress,2017.

[3]L.Feng