混沌通信中周期信号的破译与密钥提取(1)

太原理工大学硕士学位论文混沌通信中周期信号的破译与密钥提取姓名：赵清春申请学位级别：硕士专业：@指导教师：王云才@I1.2.DuffingDuffingLorenzDuffing3.KerckhoffIIDuffing,,IIIEXTRACTIONOFPERIODICMESSAGEANDKEYINCHAOTICCOMMUNICATIONABSTRACTChaosisapseudo-random,long-timeunpredictablesignalgeneratedbydeterminedsystems.Becauseofthetwoproperties,chaosisverysuitableforcarrierincommunicationsattemptingtotransmitmessagessecurely.Chaoticcommunicationhasbeendevelopedrapidlyduringthelasttwodecades,anditismaturinggradually.Soonafterchaoscommunicationwasproposed,someresearchershavebeguntostudyitssecurityperformance.Themainworksofthisdissertationaresummarizedasfollows:1.Wehavereviewedthecurrentresearchstatusonsecurityperformanceofchaoticcommunication.Tochaoticcommunicationsystemsusingcircuits,weanalyzesomemessageeavesdroppingmethodsbasedonnonlineardynamicalforecasting,returnmaps,andparameterestimationindetail.Besides,wealsopointouttheadvantagesanddisadvantagesofthesemethods.Theirpropertiesformessageeavesdroppingarealsoexamined.Tochaoticopticalcommunicationsystem,weanalyzethemethodsandIVproceduresforextractionoftimedelayandmessages.2.WeutilizetheDuffingoscillatorstoextractmessagesinchaoticcommunicationusingcircuitsandpresentapracticalsetupforextractingtheperiodicsignalsmaskedbyachaoticcommunicationsystem.Thenumericalsimulationsverifythefeasibilityofthissetup.WeapprovethatthedrivenDuffingoscillatorisimmunetothechaoticcarrierandsensitivetocertainperiodicsignals.Accordingtothisfact,asinusoidalmessageinLorenzchaoticcommunicationsystemisextracted.OurresultsindicatethatthehiddenmessagesinchaoticsecurecommunicationcanbeeavesdroppedutilizingDuffingoscillators.3.External-cavitylasersarethecommontransmittersinchaoticcommunication.Thefeedbacklength(FL),playinganessentialroleforchaoticstate,isusuallyusedasanadditionalkeytoenhancethesecurityofsystems.Ithasbeenapprobatedasakeyinshort-cavitysystems.Forthepracticallong-cavitycase,basingontheKerckhoffs’principleofmoderncryptography,wenumericallyexaminethesecuritywhentheFLisutilizedasakey.Forthestaticanddynamickeys,theeavesdroppercanobtaintheFLoftransmitterbyscanning,andthenextractthehiddennonreturn-to-zeromessages.TheresultsshowthatthesecurityofchaoticcommunicationsystemusingexternalcavitylaserscannotbeenhancedwhentheFLisutilizedasakey.VKEYWORDS:chaoticcommunication,security,Duffingoscillator,externalcavitylaser,key,feedbacklength11.120[1][2,3][4][5][6-8]1.2Lyapunov[9]1990L.M.PecoraT.L.Carroll[10]GHzYong-Silva2200MHz[11]1994R.RoyNd:YAG[12]1996C.R.Mirasso[13]1998R.Roy10MHz[14]2002J.Ohtsubo780nm1.5GHz[15]2004K.A.ShoreDFB[16]2005A.Argyris120km1Gbit/s10-7[17]V.Annovazzi-Lodi[18]2006K.A.Shore[19]2007C.R.Mirasso[20]J.M.Buldú[21]/1.36077704120070810191.2.DuffingDuffing3Lorenz3.Kerckhoff4.42.1L.M.PecotaT.L.Carroll[10](Eavesdropper)[22](Nonlineardynamicalforecasting,NLDF)[23-28](Returnmaps)[29-32][33-39]2.1.1NLDF(+)K.M.Short[23-26][26]NLDF(Phase5spacereconstruction)(AMI)Xφ{Xi}F{Xi}F(Xi)=Xi+1F(Least-squaresminimization)FF(Xφ)=Xφ+12.1.2G.PérezH.A.CerdeiraLorenz(Chaoticmasking)(Chaoticswitching,binaryparametermodulation)[29]Chua(Nonautonomousmodulation)[30](Discrete-timechaoticmap)DCSK[31][32]tnx(t)Xnxumx(t)YmxAn=(Xn+Yn)/2,Bn=Xn-Yn,-AnBn3kHz[29]GHz2.1.3()[40][41]6[33][34]/[35,36][37][38]2.2R.Roy[14]GHz[42][42]Gbit/s[17]2.2.1Lang-Kobayashi[43](Delaydifferentialequation,DDE)()()(),,ytTFxtT=(2-1)x(t)T[44]1.(Returnmaps)x(t)x(t-t0)t0t0=T72.(Autocorrelationfunction,ACF)*()()()xRtxxtdτττ∞−∞=−∫(2-2)Rx(t)T3.(Averagemutualinformationtechnique,AMItechnique)AMI(),()((),())I()((),())log(())(())ItItpItItpItItpItpItθθθθθ−−=−−∑(2-3)p(I(t),I(t-θ))p(I(t)),p(I(t-θ))x(t)x(t-t0)t0=T4.(Timedistributionofextrema)10t=T5.(Locallinearfitsinalow-dimensionalspace)M.J.Bünner[45]C.ZhouC.-H.Lai[46][dx(t)/dt,x(t),x(t-T)]i,M.J.Bünner^0iiiiiitxabxcx•−=++(2-4)^ix•t0bici{xi}σt0TσT8M.W.Lee[47]D.Rontani[48]2.2.21.R.J.Jones[49]2-1PD1PD2PD12-1[49]Fig.2-1Schematicdiagramoftheexperimentalarrangement(Figurefromreference[49])9S.Sivaprakasam[50]2-2[49]MBS2T2-2[50]Fig.2-2Experimentalsetup(Figurefromreference[50])2.J.B.Geddes[37]2-31200()[()]nmnmnmnHttmTnmTmαβδ∞−===−−−∑∑(2-5)10α,β,T1,T2(Partialauto-correlationfunction)Im(t)It(t)H(t)2-3Im(t)It(t)Ir(t)[37]Fig.2-3Schematicofthetransmitterandreceiver.ThemessagebitstreamIm(t)issentthroughthedelayloopsofthetransmittertoproducethetransmittedsignalIt(t).ThereceiversignalIr(t)isgeneratedbypassingthetransmittedsignalthroughareceiver.Properdelaytimesandamplificationfactorsallowrecoveryofthemessage.(Figurefromreference[37])11DBR[51-52]V.S.Udaltsov[53]S.Ortín(Artificialneuralnetworks)[54][55]2.312Duffing3.1Duffing[56-60]DuffingDuffingLorenz3.2LorenzDuffingLorenzE.N.Lorenz[61]()d,dd20,dd5,duvutvruvutuvbtσωωω=−=−−=−(3-1)u,v,ωσ,r,bσ=16,b=4,r=45.92(3-2)3-1(a)u(t)ω(t)(b)(3-2)133-1Lorenz(a)(b)Fig.3-1AttractorsoftheLorenzsystem:(a)double-attractor,(b)three-dimensionattractorDuffing()()0300d,ddcos,dxytyyxxtinputtωωδγω==−+−++(3-3)x,yδ0.5γcos(ω0t)inputDuffing3-2x(t)γx(t)γx(t)γ(0.828)x(t)3-2Duffingx(t)γFig.3-2Bifurcationdiagramofthevariablex(t)ofDuffingoscillatorasafunction