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1、ComputingBlindfolded:NewDevelopmentsinFullyHomomorphicEncryptionVinodVaikuntanathanUniversityofTorontoAbstract—Afullyhomomorphicencryptionschemeen-arbitrarycomputationstothe“cloud”andtheabilitytoablescomputationofarbitraryfunctionsonencrypteddata.storealldataencryptedandperf
2、ormcomputationsonFullyhomomorphicencryptionhaslongbeenregardedasencrypteddata,decryptingonlywhennecessary.cryptography’sprized“holygrail”–extremelyusefulyetratherelusive.StartingwiththegroundbreakingworkofFullyHomomorphicencryptionisaspecialtypeofGentryin2009,thelastthreeyea
3、rshavewitnessednumer-encryptionsystemthatpermitsarbitrarilycomplexcom-ousconstructionsoffullyhomomorphicencryptioninvolvingputationonencrypteddata.Longregardedasa“holynovelmathematicaltechniques,andanumberofexcitinggrail”ofcryptography,fullyhomomorphicencryptionapplications.
4、Wewilltakethereaderthroughajourneyofwas?rstshowntobepossibleintherecent,break-thesedevelopmentsandprovideaglimpseoftheexcitingresearchdirectionsthatlieahead.throughworkofGentry.Wewilltakethereaderthroughajourneyofthefascinatingmathematicaltechniquesunderlyingthesedevelopment
5、s,whichinturnraisea1.INTRODUCTIONnumberofexcitingnewquestionsincryptography.Encryptionhastraditionallybeenviewedasamech-OrganizationofthisSurvey.Startingwithabriefhistory,anismthatenablessecurecommunication,namelythewegoontoformallyde?nehomomorphicencryptionproblemoftransmit
6、tingamessagefromAlicetoBobanditsvarioususefulproperties,andthendescribetheoverapublicchannelwhilekeepingithiddenfromideasbehindGentry’sconstruction.Wethendescribeaneavesdropper.Inparticular,Public-keyEncryptiontherecentworksinthisareathatsigni?cantlydiffer–conceivedinthesemi
7、nalworkofDif?eandHell-fromGentry’sblueprintandresultinsimplerconstruc-man[24]and?rstconstructedbyRivest,Shamirandtions,betteref?ciencyandbetterassumptions–allinAdleman[68]–providesawayforAlicetoencryptaone.Weconcludewithadiscussionoftheapplicationsmessageintoaciphertextusing
8、Bob’spublickey,andoffullyhomomorphicencryptionanda(highlyincom-forBobtodecr
