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1、FullyHomomorphicEncryptionUsingIdealLatticesCraigGentryStanfordUniversity,IBMFieldsInstitute,05/11/09Wouldn’titbeneatifyoucould…Queryencrypteddata?•Storeyourencrypteddataonanuntrustedserver•Querythedata–i.e.,makebooleanqueriesonthedata•Getausefulrespon
2、sefromtheserver,withouttheserverjustsendingallofthedatatoyouFullyHomomorphicEncryptionUsingIdealLattices5/14/2009CraigGentryWouldn’titbeneatifyoucould…Queryencrypteddata?•Storeyourencrypteddataonanuntrustedserver•Querythedata–i.e.,makebooleanqueriesont
3、hedata•Getausefulresponsefromtheserver,withouttheserverjustsendingallofthedatatoyouQuerydataprivately?•Sendanencryptedqueryregardingstoreddata(e.g.,onGoogle’sservers)•GetausefulconciseresponseFullyHomomorphicEncryptionUsingIdealLattices5/14/2009CraigGe
4、ntryWouldn’titbeneatifyoucould…Queryencrypteddata?•Storeyourencrypteddataonanuntrustedserver•Querythedata–i.e.,makebooleanqueriesonthedata•Getausefulresponsefromtheserver,withouttheserverjustsendingallofthedatatoyouQuerydataprivately?•Sendanencryptedqu
5、eryregardingstoreddata(e.g.,onGoogle’sservers)•GetausefulconciseresponseDobothsimultaneously?FullyHomomorphicEncryptionUsingIdealLattices5/14/2009CraigGentryPrivacyHomomorphism(a.k.a.FullyHomomorphicEncryption)Well,here’show:•Privacyhomomorphism:Rivest
6、,AdlemanandDertouzosproposedtheconceptin1978.(Rivest,Shamir,andAdlemanproposedRSAin1977,publishedin1978.)•Assumeyouhavepublic-keyencryptionschemethat,inadditiontoalgorithms(KeyGen,Enc,Dec),hasanefficientalgorithm“Evaluate”,suchthat:Evaluate(pk,C,ψ,…,ψ)
7、≈Enc(pk,C(π,…,π))1t1tforallpk,allcircuitsC,allψ=Encrypt(pk,π).iiFullyHomomorphicEncryptionUsingIdealLattices5/14/2009CraigGentryPrivacyHomomorphismWell,here’show:•Assumeyouhavepublic-keyencryptionschemethat,inadditiontoalgorithms(KeyGen,Enc,Dec),hasane
8、fficientalgorithm“Evaluate”,suchthat:Evaluate(pk,C,ψ,…,ψ)≈Enc(pk,C(π,…,π))1t1tforallpk,allcircuitsC,allψ=Encrypt(pk,π).iiQueryencrypteddata:ØEncryptstoreddata:ψ,…,ψ1tØQuery:sendyourcircuitCØResponse:Eval(pk,C,ψ,…,ψ)1tØDecryptresponse→C(
