新的量子代理多重签名方案New-Quantum-Proxy-Multi-signature-Sche

IntJTheorPhysDOI10.1007/s10773-015-2715-yANewQuantumProxyMulti-signatureSchemeUsingMaximallyEntangledSeven-QubitStatesHai-JingCao1·Jia-FuZhang1·JianLiu1·Zeng-YouLi1Received:4March2015/Accepted:3June2015©SpringerScience+BusinessMediaNewYork2015AbstractInthispaper,weproposeanewsecurequantumproxymulti-signatureschemeusingseven-qubitentangledquantumstateasquantumchannels,whichmayhaveappli-cationsine-paymentsystem,e-government,e-business,etc.Thisschemeisbasedoncontrolledquantumteleportation.Theschemeusesthephysicalcharacteristicsofquan-tummechanicstoguaranteeitsanonymity,verifiability,traceability,unforgetabilityandundeniability.KeywordsProxysignature·Controlledquantumteleportation·Seven-qubitentanglementstate1IntroductionDigitalsignature,whichisanimportantbranchofcryptography,hasbeenwidelyusedinpracticalapplications.Unfortunately,mostexistingclassicalsignatureschemeswhosesecuritydependsonthedifficultyofsolvingsomehardmathematicalproblemswerethreatenedbyquantumcomputation.Therefore,researchersturntoinvestigateitsquantumcounterpartwiththehopethatquantumsignaturecanbecomeanalternativetoclassicalsignatureandprovideunconditionalsecurity.In1996,Mambo,Usuda,andOkamotointro-ducedtheconceptofaproxysignaturescheme[1].Itallowsadesignatedperson,calledaproxysigner,tosignonbehalfofanoriginalsigner,incaseofsay,temporalabsence,lackoftimeorcomputationalpower,etc.ProxysignaturesareusefulconstructionsingridProjectsupportedbytheNationalNaturalScienceFoundationofChina(GrantNo11305100)[e-mail]1PhysicsDepartment,ShanghaiUniversityofElectricPower,Shanghai201300,ChinaIntJTheorPhyscomputing,mobileagent,mobilecommunications,e-commerceetc.Then,Barnumetal.[2]pointedoutano-gotheoremfortheapplicationofthequantumsignaturein2002.AlthoughBarnumetal.’sconclusioncreatedaseriousobstacleforquantumsignature,thestudyofthequantumsignatureschemehasnotstopped.In2002,ZengandKeitel[3]firstproposedanarbitratedquantumsignature(AQS)protocol,whichiscalledtheZKprotocol,tosignaquantummessage.ThisworkgaveanelementarymodeltoovercomeBarnumetal.’sno-gotheoremforquantumsignature[2].Afterwards,Lietal.foundthatthearbitra-torisunnecessarytoentanglewiththeothertwoparticipantsintheAQSschemepresentedinRef.[4],andthusthethree-particleentangledGHZstatesusedintheschemecanbereplacedwithtwo-particleentangledBellstates.Wenetal.[5,6]proposedsomemulti-signatureschemes.Besides,manyquantumsignatureschemesbasedonquantummechanicsorquantumcomputingalgorithmwereproposed[7–12].Quantumentanglementisakeyelementforapplicationsofquantumcommunicationsandquantuminformation.Inparticular,theentanglementcanbeusedasaquantumresourcetocarryoutanumberofcomputationalandinformationprocessingtasks.Duetoitsgreatrelevance,fromboththetheoreticalandthepracticalpointsofview,itisimperativetoexploreandcharacterizeallaspectsofthequantumentanglementofmultipartitequantumsystems.Inthispaperwepresentaquantumproxymulti-signatureschemebasedoncon-trolledquantumteleportation.Ahighlyentangledseven-qubitstatefunctionsasquantumchannels.Inourscheme,oneparticleoftheentangledseven-qubitstateisdeliveredtotheproxysignerAlice,andtheoriginalsignersCharlieandDavidholdfiveparticles,whileoneparticletotheverifierBob.AliceperformsBell-statemeasurement(BM)onparticle1andtheparticleMcarryingmessage,andthenCharlieperformssingleparticlemea-surementonherparticlesandDavidperformBMontheirparticles.Bobcouldverifythesignatureaccordingtothecorrelationoftheentangledseven-qubitstate.Ifsomedisagree-menthappens,themessageownerAlicecouldbetraced.Weusequantumkeydistributionandone-timepadtoguaranteetheunconditionalsecurityandsignatureanonymity.Itisshowntobeunconditionallysecure,i.e.,maynotbeforgedormodifiedinanywaybythereceiverorattacker.Inaddition,itmayneitherbedisavowedbythesignatory,norbedeniablebythereceiver.2PreliminaryTheoryThequantumproxymulti-signatureschemeisbasedoncontrolledquantumteleportation.Inthissection,wewillintroducethecontrolledteleportationschemeusingseven-qubitentan-glementstates[13]asquantumchannel.Maximallymulti-qubitentangledstates(MMES)[14]arestateswhoseentanglementismaximalforevery(balanced)bipartition.Inmaxi-mallyentangledseven-qubitstates,marginaldensitymatricesforsubsystemsofoneandtwoqubitsarecompletelymixedandmost,butnotall,ofthemarginaldensitymatricesofthreequbitsarecompletelymixed.Thehighlyentangledseven-qubitstateplaysakeyroleinquantuminformationprocessingtasksandturnsouttobeanimportantresourceinquantumcommunication.Thishastheform:|ξ1234567=14√2[(|0000000+|0000011+|0001101+|0001110)(1)+(|0010001−|0010010+|0011100−|0011111)+(−|0100101−|0100110+|0101000+|0101011)IntJTheorPhys+(|0110100−|0110111−|0111001+|0111010)+(−|1000100−|1000111+|1001001+|1001010)+(|1010101−|1010110−|1011000+|1011011)+(|1100001+|1100010+|1101100+|1101111)+(|1110000−|1110011+|1111101−|1111110)]1234567.Inthequantumproxysignature,theproxysignerAliceownsparticle1.Particles(2,5,7)and(3,4)arebelongtotheoriginalsignersCharlieandDavid,respectively.TheverifierBobholdsparticle6.Supposethatthequantumstateof