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1、ShortsignaturesfromtheWeilpairingDanBoneh?,BenLynn,andHovavShachamComputerScienceDepartment,StanfordUniversityfdabo,blynn,hovavg@cs.stanford.eduAbstract.WeintroduceashortsignatureschemebasedontheCompu-tationalDi±e-Hellmanassumptiononcertainelliptican
2、dhyper-ellipticcurves.ThesignaturelengthishalfthesizeofaDSAsignatureforasimilarlevelofsecurity.Ourshortsignatureschemeisdesignedforsys-temswheresignaturesaretypedinbyahumanorsignaturesaresentoveralow-bandwidthchannel.1IntroductionShortdigitalsignatur
3、esareneededinenvironmentswhereahumanisaskedtomanuallykeyinthesignature.Forexample,productregistrationsystemsoftenaskuserstokeyinasignatureprovidedonaCDlabel.Moregenerally,shortsig-naturesareneededinlow-bandwidthcommunicationenvironments.Forexample,sh
4、ortsignaturesareneededwhenprintingasignatureonapostagestamp[21,19].Currently,thetwomostfrequentlyusedsignaturesschemes,RSAandDSA,providerelativelylongsignaturescomparedtothesecuritytheyprovide.Forexample,whenoneusesa1024-bitmodulus,RSAsignaturesare10
5、24bitslong.Similarly,whenoneusesa1024-bitmodulus,standardDSAsignaturesare320bitslong.EllipticcurvevariantsofDSA,suchasECDSA,arealso320bitslong[1].A320-bitsignatureistoolongtobekeyedinbyahuman.Weproposeasignatureschemewhoselengthisapproximately160bits
6、andprovidesalevelofsecuritysimilarto320-bitDSAsignatures.Oursignatureschemeissecureagainstexistentialforgeryunderachosenmessageattack(intherandomoraclemodel)assumingtheComputationalDi±e-Hellmanproblem(CDH)ishardoncertainellipticcurvesovera¯nite¯eldof
7、characteristicthree.Generatingasignatureisasimplemultiplicationonthecurve.Verifyingthesignatureisdoneusingabilinearpairingonthecurve.Oursignatureschemeinherentlyusespropertiesofellipticcurves.Consequently,thereisnoequivalentofourschemeinF¤.pDuetothep
8、ropertiesofthecurvesweuse,currentlywecanonlyprovidesignaturesofthelengthsgivenbelow.ThebestknownalgorithmforsolvingtheCDHprobleminthesegroupsrequiresadiscrete-logona¯nite¯eldofcharacteristicthree.Thesizeofthis¯eldisgiven(inbits)intherightmostcolumnof
