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A forward-secure public-key encryption scheme

Abstract Cryptographic computations are often carried out on insecure devices for which the threatof key exposure represents a serious and realistic concern. In an effort to mitigate the damage

AForward-SecurePublic-KeyEncryptionScheme

RanCanetti ShaiHalevi

December23,2003JonathanKatz

Abstract

Cryptographiccomputationsareoftencarriedoutoninsecuredevicesforwhichthethreatofkeyexposurerepresentsaseriousandrealisticconcern.Inane orttomitigatethedamagecausedbyexposureofsecretkeysstoredonsuchdevices,theparadigmofforwardsecuritywasintroduced.Inaforward-securescheme,secretkeysareupdatedatregularperiodsoftime;exposureofthesecretkeycorrespondingtoagiventimeperioddoesnotenableanadversaryto“break”thescheme(intheappropriatesense)foranypriortimeperiod.Anumberofconstructionsofforward-securedigitalsignatureschemes,key-exchangeprotocols,andsymmetric-keyschemesareknown.

Wepresentthe rstnon-trivialconstructionsof(non-interactive)forward-securepublic-keyencryptionschemes.Ourmainconstructionachievessecurityagainstchosen-plaintextattacksunderthedecisionalbilinearDi e-Hellmanassumptioninthestandardmodel.Thisschemeispractical,andallparametersgrowatmostlogarithmicallywiththetotalnumberoftimeperiods.Wealsogiveaslightlymoree cientschemeintherandomoraclemodel.Bothourschemescanbeextendedtoachievesecurityagainstchosen-ciphertextattacksandtosupportanunboundednumberoftimeperiods.

Towardourgoal,weintroducethenotionofbinarytreeencryptionandshowhowtocon-structabinarytreeencryptionschemeinthestandardmodel.Thisnewprimitivemaybeofindependentinterest.Inparticular,weuseittoconstructthe rstknownexampleofa(hierar-chical)identity-basedencryptionschemethatissecureinthestandardmodel.(Here,however,thenotionofsecurityweachieveisslightlyweakerthanwhatisachievedinsomepreviousconstructionsintherandomoraclemodel.)

Keywords:BilinearDi e-Hellman,Encryption,Binary-treeencryption,Identity-basedencryp-tion,Forwardsecurity,Keyexposure.

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