Introduction Previous work Our contribution Conclusion

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Publié par

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


Publié le : mardi 19 juin 2012
Lecture(s) : 29
Source : di.ens.fr
Nombre de pages : 60
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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
nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyhomomorphicpublic-keyencryptionoCWerestrictourselvestopublic-keyencryptionofasinglebit:0203ef6124...23ab87161b327653c1...db326516FullyhomomorphicpropertyGivenE(b0)andE(b1),onecancomputeE(b0b1)andE(b0b1)withoutknowingtheprivate-key.Computingoveraring:Givenacircuitwithxorsandands,andencryptedinputbits,onecancomputetheoutputinencryptedform,withoutknowingtheprivatekey.Asaresult:publiclycomputeanyfunctiononencrypteddata(oratleastanyfunctionthatcanberepresentedasabooleancircuitwithpolynomiallymanygates).cnulisno
nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyhomomorphicpublic-keyencryptionoCWerestrictourselvestopublic-keyencryptionofasinglebit:0203ef6124...23ab87161b327653c1...db326516FullyhomomorphicpropertyGivenE(b0)andE(b1),onecancomputeE(b0b1)andE(b0b1)withoutknowingtheprivate-key.Computingoveraring:Givenacircuitwithxorsandands,andencryptedinputbits,onecancomputetheoutputinencryptedform,withoutknowingtheprivatekey.Asaresult:publiclycomputeanyfunctiononencrypteddata(oratleastanyfunctionthatcanberepresentedasabooleancircuitwithpolynomiallymanygates).cnulisno
nIrtoudcitnorPveoisuowkruOroctnirubitnoFullyhomomorphicpublic-keyencryptionoCWerestrictourselvestopublic-keyencryptionofasinglebit:0203ef6124...23ab87161b327653c1...db326516FullyhomomorphicpropertyGivenE(b0)andE(b1),onecancomputeE(b0b1)andE(b0b1)withoutknowingtheprivate-key.Computingoveraring:Givenacircuitwithxorsandands,andencryptedinputbits,onecancomputetheoutputinencryptedform,withoutknowingtheprivatekey.Asaresult:publiclycomputeanyfunctiononencrypteddata(oratleastanyfunctionthatcanberepresentedasabooleancircuitwithpolynomiallymanygates).cnulisno
nIrtoudcitnorPveoisuowkruOroctnirubitnoWhatfullyhomomorphicencryptionbringsyouoCnYouhaveasoftwarethatgiventherevenue,pastincome,headcount,etc.,ofacompanycanpredictitsfuturestockprice.Iwanttoknowthefuturestockpriceofmycompany,butIdon’twanttodiscloseconfidentialinformation.Andyoudon’twanttogivemeyoursoftwarecontainingsecretformulas.Usinghomomorphicencryption:Iencryptalltheinputsusingfullyhomomorphicencryptionandsendthemtoyouinencryptedform.Youprocessallmyinputs,viewingyoursoftwareasacircuit.Yousendmetheresult,stillencrypted.Idecrypttheresultandgetthepredictedstockprice.Youdidn’tlearnanyinformationaboutmycompany.Moregenerally:Coolbuzzwordslikesecurecloudcomputing.Coolmathematicalchallenges.lcsuoin
nIrtoudcitnorPveoisuowkruOroctnirubitnoWhatfullyhomomorphicencryptionbringsyouoCnYouhaveasoftwarethatgiventherevenue,pastincome,headcount,etc.,ofacompanycanpredictitsfuturestockprice.Iwanttoknowthefuturestockpriceofmycompany,butIdon’twanttodiscloseconfidentialinformation.Andyoudon’twanttogivemeyoursoftwarecontainingsecretformulas.Usinghomomorphicencryption:Iencryptalltheinputsusingfullyhomomorphicencryptionandsendthemtoyouinencryptedform.Youprocessallmyinputs,viewingyoursoftwareasacircuit.Yousendmetheresult,stillencrypted.Idecrypttheresultandgetthepredictedstockprice.Youdidn’tlearnanyinformationaboutmycompany.Moregenerally:Coolbuzzwordslikesecurecloudcomputing.Coolmathematicalchallenges.lcsuoin
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