MSnookThesisInteger-Based Fully Homomorphic Encryption

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1、RochesterInstituteofTechnologyCollegeofScienceSchoolofMathematicalSciencesInteger-BasedFullyHomomorphicEncryptionbyMichaelSnookThesissubmittedinpartialfulllmentoftherequirementsforthedegreeofMasterofScienceinAppliedandComputationalMathematics17June2011C

2、ommitteeSignaturesDr.AnuragAgarwalDr.StanislawRadziszowskiProf.DavidBarth-HartiiAbstractTheconceptoffullyhomomorphicencryptionhasbeenconsideredtheholygrail"ofcryptographysincethediscoveryofsecurepublickeycryptographyinthe1970s.Fullyhomomorphicencryption

3、allowsarbi-trarycomputationonencrypteddatatobeperformedsecurely.CraigGentry'snewmethodofbootstrappingintroducedin2009providesatechniqueforconstructingfullyhomomorphiccryptosystems.Inthispaperweexploreonesuchbootstrappablesystembasedonsim-pleintegerarithm

4、eticinamannerthatsomeonewithoutahighlevelofexperienceinhomomorphicencryptioncanreadilyunderstand.Fur-ther,wepresentanimplementationofthesystemaswellasalattice-basedattack.Wepresentperformanceresultsofourimplementationundervariousparameterchoicesandtheres

5、istanceofthesystemtothelattice-basedattackunderthoseparameters.Unfortunately,whilethesystemisveryinterestingfromatheoreticalpointofview,theresultsshowthatitisstillnotfeasibleforuse.iiiContents1Background11.1Requirements...........................11.1.1Bo

6、otstrapping.......................31.2Applications............................41.2.1Multi-PartyCommunication...............51.2.2Zero-KnowledgeProofs..................81.2.3SecurityinCloudComputing..............91.3ABriefHistory..........................

7、112UnderlyingHomomorphicSystem132.1Description............................132.1.1Correctness........................142.1.2Completeness.......................162.2PublicKeyVersion........................172.2.1Security..........................182.2.2Com

8、plexity........................192.3Bootstrapping...........................212.4ApproximateGCD........................222.4.1Example..........................233IntegerLattices243.1Properties.............................2