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1、Lecture19
2、HomomorphicEncryption1:De nitionandApplicationtoPrivateInformationRetrieval,Zeroknowledge.BoazBarakApril12,2010HomomorphicencryptionWestressedthatCPAsecuritydoesnotpreventanattackerfromtamperingwiththeencryptedmessage,changingforexampleanen
3、cryptionofthemessagexintoanencryptionofxwithitslastbit
ipped.Homomorphicencryptiontakesthistoanextremeandactuallyrequiresthatitispossibletotamperwiththeencryptioninanarbitraryway(whilestillmaintainingCPAsecurity!).Thequestionifthisispossiblewas rstra
4、isedin1978byRivest,Adleman,andDertouzos,andovertheyearsmanyconjecturedthatthisisinfactimpossible.LastyearGentrygaveverystrongevidencethatsuchencryptionsexist,byconstructingsuchaschemethatissecureunderrelativelyreasonablecomputationalassumptions.De ni
5、tionWesaythataCPA-securepublickeyencryptionscheme(G;E;D)withonebitmes-sagesisfullyhomomorphicifthereexistsanalgorithmNANDsuchthatforevery(e;d)G(1n),a;b2f0;1g,and^aEe(a),^bEe(b),NANDe(^a;^b)Ee(aNANDb)wheredenotesstatisticalindistinguishability(i.e.,
6、n
