Functional encryption Definitions and challenges

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1、FunctionalEncryption:DefinitionsandChallengesDanBonehAmitSahaiBrentWatersyStanfordUniversityUCLAUniversityofTexasatAustinAbstractWeinitiatetheformalstudyoffunctionalencryptionbygivingprecisedefinitionsoftheconceptanditssecurity.Roughlyspeaking,functionalencryptionsupportsrestrictedsecretkeyst

2、hatenableakeyholdertolearnaspecificfunctionofencrypteddata,butlearnnothingelseaboutthedata.Forexample,givenanencryptedprogramthesecretkeymayenablethekeyholdertolearntheoutputoftheprogramonaspecificinputwithoutlearninganythingelseabouttheprogram.Weshowthatdefiningsecurityforfunctionalencryptioni

3、snon-trivial.First,weshowthatanaturalgame-baseddefinitionisinadequateforsomefunctionalities.Wethenpresentanaturalsimulation-baseddefinitionandshowthatit(provably)cannotbesatisfiedinthestandardmodel,butcanbesatisfiedintherandomoraclemodel.Weshowhowtomapmanyexistingconceptstoourformalizationoffunc

4、tionalencryptionandconcludewithseveralinterestingopenproblemsinthisyoungarea.SupportedbyNSF,MURI,andthePackardfoundation.ySupportedbyNSFCNS-0716199,CNS-0915361,andCNS-0952692,AirForceOfficeofScientificResearch(AFOSR)undertheMURIawardfor“Collaborativepoliciesandassuredinformationsharing”(Proje

5、ctPRESIDIO),DepartmentofHomelandSecurityGrant2006-CS-001-000001-02(subaward641),andtheAlfredP.SloanFoundation.1IntroductionEncryptionisamethodforausertosecurelysharedataoveraninsecurenetworkorstoragesite.Beforetheadventofpublickeycryptography,awidelyheldviewwasthatfortwouserstocommunicatedat

6、aconfiden-tiallytheywouldneedtoaprioriestablishamutuallyheldsecretkeyk.Whilethismightbeacceptableforsomesmallortightlyknitorganizations,suchasolutionwasclearlyinfeasibleforlargernetworkssuchastoday’sInternetconsistingofbillionsofusers.Overthirtyyearsago,DiffieandHellman[DH76a,DH76b]putforthara

7、dicallynewideaintheconceptofpublickeycryptography,wheretwopartiescansecurelycom-municatewitheachotherwithouthavinganapriormutualsecret—radicallychallengingtheconventionalwisdomofthetime.Todaypublickeyencryptionisaninvaluabletoolanditsuseisubiquitou