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1、CanHomomorphicEncryptionbePractical?KristinLauterMichaelNaehrigVinodVaikuntanathanMicrosoftResearchMicrosoftResearchMicrosoftResearchklauter@microsoft.commnaehrig@microsoft.comvinod@microsoft.comABSTRACT1.INTRODUCTIONTheprospectofoutsourcinganincreasingamountofdataThedevelopmentofcloudstorag
2、eandcomputingplat-storageandmanagementtocloudservicesraisesmanynewformsallowsuserstooutsourcestorageandcomputationsprivacyconcernsforindividualsandbusinessesalike.Theontheirdata,andallowsbusinessestoooadthetaskofprivacyconcernscanbesatisfactorilyaddressedifusersen-maintainingdata-centers.Ho
3、wever,concernsoverlossofcryptthedatatheysendtothecloud.Iftheencryptionprivacyandbusinessvalueofprivatedataisanoverwhelm-schemeishomomorphic,thecloudcanstillperformmean-ingbarriertotheadoptionofcloudservicesbyconsumersingfulcomputationsonthedata,eventhoughitisencrypted.andbusinessesalike.Anex
4、cellentwaytoassuagethesepri-vacyconcernsistostorealldatainthecloudencrypted,andInfact,wenowknowanumberofconstructionsoffullyho-performcomputationsonencrypteddata.Tothisend,wemomorphicencryptionschemesthatallowarbitrarycompu-needanencryptionschemethatallowsmeaningfulcomputa-tationonencryptedd
5、ata.Inthelasttwoyears,solutionsfortiononencrypteddata,namelyahomomorphicencryptionfullyhomomorphicencryptionschemeshavebeenproposedscheme.andimprovedupon,butitishardtoignoretheelephantinHomomorphicencryptionschemesthatallowsimplecom-theroom,namelyeciency{canhomomorphicencryptionputationsone
6、ncrypteddatahavebeenknownforalongeverbeecientenoughtobepractical?Certainly,itseemstime.Forexample,theencryptionsystemsofGoldwasserthatallknownfullyhomomorphicencryptionschemeshaveandMicali[GM82],ElGamal[El-84]andPaillier[Pai99]alongwaytogobeforetheycanbeusedinpractice.Givensupporteitheraddi
7、ngormultiplyingencryptedciphertexts,thisstateofa airs,ourcontributionistwo-fold.butnotbothoperationsatthesametime.Boneh,GohandNissim[BGN05]werethe rsttoconstructaschemecapa-First,weexhibitanumberofreal-worldapplications,inbleofperformingbothoperati
