Computing Blindfolded New Developments in Fully Homomorphic Encryption

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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、Wewilltakethereaderthroughajourneyofwasfirstshowntobepossibleintherecent,break-thesedevelopmentsandprovideaglimpseoftheexcitingresearchdirectionsthatlieahead.throughworkofGentry.Wewilltakethereaderthroughajourneyofthefascinatingmathematicaltechniquesunderlyingthesedevelopment

5、s,whichinturnraisea1.INTRODUCTIONnumberofexcitingnewquestionsincryptography.Encryptionhastraditionallybeenviewedasamech-OrganizationofthisSurvey.Startingwithabriefhistory,anismthatenablessecurecommunication,namelythewegoontoformallydefinehomomorphicencryptionproblemoftransmit

6、tingamessagefromAlicetoBobanditsvarioususefulproperties,andthendescribetheoverapublicchannelwhilekeepingithiddenfromideasbehindGentry’sconstruction.Wethendescribeaneavesdropper.Inparticular,Public-keyEncryptiontherecentworksinthisareathatsignificantlydiffer–conceivedinthesemi

7、nalworkofDiffieandHell-fromGentry’sblueprintandresultinsimplerconstruc-man[24]andfirstconstructedbyRivest,Shamirandtions,betterefficiencyandbetterassumptions–allinAdleman[68]–providesawayforAlicetoencryptaone.Weconcludewithadiscussionoftheapplicationsmessageintoaciphertextusing

8、Bob’spublickey,andoffullyhomomorphicencryptionanda(highlyincom-forBobtodecr