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nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyHomomorphicEncryptionovertheIntegerswithShorterPublicKeysJean-Se´bastienCoron,AvradipMandal,DavidNaccacheandMehdiTibouchiUniversityofLuxembourg&ENSCRYPTO,2011-08-17oCcnulisno
nIrtoudcitnorPveoisuowkrOutlineIntroductionFullyhomomorphicencryptionTheoryandpracticeuOroctnirubPreviousworkBuildingFHEwithbootstrappingTheDGHVsomewhathomomorphicschemeOurcontributionShorteningthesomewhathomomorphicPKCompressingthesquashedschemeSettingparametersitnooCcnulisno
nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyhomomorphicencryptionHomomorphicencryption:Anencryptionschemeishomomorphicwhenitsupportsoperationsonencrypteddata.Multiplicativelyhomomorphic:RSA.Givenc1=m1emodN,c2=m2emodN,wehave(c1c2)=(m1m2)emodNAdditivelyhomomorphic:Paillier.Paillier:givenc1=gm1rNmodN2,c2=gm2sNmodN2,wehavec1c2=gm1+m2(rs)NmodN2.Fullyhomomorphic:homomorphicforbothadditionandmultiplicationOpenproblemuntilGentry’sbreakthroughin2009.oCcnulisno
nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyhomomorphicencryptionHomomorphicencryption:Anencryptionschemeishomomorphicwhenitsupportsoperationsonencrypteddata.Multiplicativelyhomomorphic:RSA.Givenc1=m1emodN,c2=m2emodN,wehave(c1c2)=(m1m2)emodNAdditivelyhomomorphic:Paillier.Paillier:givenc1=gm1rNmodN2,c2=gm2sNmodN2,wehavec1c2=gm1+m2(rs)NmodN2.Fullyhomomorphic:homomorphicforbothadditionandmultiplicationOpenproblemuntilGentry’sbreakthroughin2009.oCcnulisno
nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyhomomorphicencryptionHomomorphicencryption:Anencryptionschemeishomomorphicwhenitsupportsoperationsonencrypteddata.Multiplicativelyhomomorphic:RSA.Givenc1=m1emodN,c2=m2emodN,wehave(c1c2)=(m1m2)emodNAdditivelyhomomorphic:Paillier.Paillier:givenc1=gm1rNmodN2,c2=gm2sNmodN2,wehavec1c2=gm1+m2(rs)NmodN2.Fullyhomomorphic:homomorphicforbothadditionandmultiplicationOpenproblemuntilGentry’sbreakthroughin2009.oCcnulisno
nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyhomomorphicencryptionHomomorphicencryption:Anencryptionschemeishomomorphicwhenitsupportsoperationsonencrypteddata.Multiplicativelyhomomorphic:RSA.Givenc1=m1emodN,c2=m2emodN,wehave(c1c2)=(m1m2)emodNAdditivelyhomomorphic:Paillier.Paillier:givenc1=gm1rNmodN2,c2=gm2sNmodN2,wehavec1c2=gm1+m2(rs)NmodN2.Fullyhomomorphic:homomorphicforbothadditionandmultiplicationOpenproblemuntilGentry’sbreakthroughin2009.oCcnulisno