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Introduction Previous work Our contribution Conclusion

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Introduction Previous work Our contribution Conclusion Fully Homomorphic Encryption over the Integers with Shorter Public Keys Jean-Sebastien Coron, Avradip Mandal, David Naccache and Mehdi Tibouchi University of Luxembourg & ENS CRYPTO, 2011-08-17

  • avradip mandal

  • fully homomorphic

  • homomorphic encryption

  • open problem until

  • introduction fully

  • setting parameters

  • gm1rn mod


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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
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