Introduction Previous work Our contribution Conclusion

Jean - Sebastien Coron

Description

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

Sujets

• Naccache
• Homomorphic encryption

Informations

• Publié par: pefav
• Nombre de lectures: 31

Extrait

nIrtoudcitnorPveoisuowkruOroctnirubitno FullyHomomorphicEncryptionovertheIntegers withShorterPublicKeys Jean-Se´bastienCoron,AvradipMandal, DavidNaccacheandMehdiTibouchi UniversityofLuxembourg&ENS CRYPTO,2011-08-17 oCcnulisno

nIrtoudcitnorPveoisuowkr Outline Introduction Fullyhomomorphicencryption Theoryandpractice uOroctnirub Previouswork BuildingFHEwithbootstrapping TheDGHVsomewhathomomorphicscheme Ourcontribution ShorteningthesomewhathomomorphicPK Compressingthesquashedscheme Settingparameters itnooCcnulisno

nIrtoudcitnorPveoisuowkruOroctnirubitno Fullyhomomorphicencryption • Homomorphicencryption: •Anencryptionschemeishomomorphicwhenitsupports operationsonencrypteddata. • Multiplicativelyhomomorphic:RSA. • Givenc 1 =m 1 e modN,c 2 =m 2 e modN,wehave (c 1 ∙ c 2 )=(m 1 ∙ m 2 ) e modN •Additivelyhomomorphic:Paillier. • Paillier:givenc 1 =g m 1 r N modN 2 ,c 2 =g m 2 s N modN 2 , wehavec 1 ∙ c 2 =g m 1 +m 2 ∙ (rs) N modN 2 . • Fullyhomomorphic:homomorphicforbothadditionand multiplication •OpenproblemuntilGentry’sbreakthroughin2009. oCcnulisno

nIrtoudcitnorPveoisuowkruOroctnirubitno Fullyhomomorphicencryption • Homomorphicencryption: •Anencryptionschemeishomomorphicwhenitsupports operationsonencrypteddata. • Multiplicativelyhomomorphic:RSA. • Givenc 1 =m 1 e modN,c 2 =m 2 e modN,wehave (c 1 ∙ c 2 )=(m 1 ∙ m 2 ) e modN •Additivelyhomomorphic:Paillier. • Paillier:givenc 1 =g m 1 r N modN 2 ,c 2 =g m 2 s N modN 2 , wehavec 1 ∙ c 2 =g m 1 +m 2 ∙ (rs) N modN 2 . • Fullyhomomorphic:homomorphicforbothadditionand multiplication •OpenproblemuntilGentry’sbreakthroughin2009. oCcnulisno

nIrtoudcitnorPveoisuowkruOroctnirubitno Fullyhomomorphicencryption • Homomorphicencryption: •Anencryptionschemeishomomorphicwhenitsupports operationsonencrypteddata. • Multiplicativelyhomomorphic:RSA. • Givenc 1 =m 1 e modN,c 2 =m 2 e modN,wehave (c 1 ∙ c 2 )=(m 1 ∙ m 2 ) e modN •Additivelyhomomorphic:Paillier. • Paillier:givenc 1 =g m 1 r N modN 2 ,c 2 =g m 2 s N modN 2 , wehavec 1 ∙ c 2 =g m 1 +m 2 ∙ (rs) N modN 2 . • Fullyhomomorphic:homomorphicforbothadditionand multiplication •OpenproblemuntilGentry’sbreakthroughin2009. oCcnulisno

nIrtoudcitnorPveoisuowkruOroctnirubitno Fullyhomomorphicencryption • Homomorphicencryption: •Anencryptionschemeishomomorphicwhenitsupports operationsonencrypteddata. • Multiplicativelyhomomorphic:RSA. • Givenc 1 =m 1 e modN,c 2 =m 2 e modN,wehave (c 1 ∙ c 2 )=(m 1 ∙ m 2 ) e modN •Additivelyhomomorphic:Paillier. • Paillier:givenc 1 =g m 1 r N modN 2 ,c 2 =g m 2 s N modN 2 , wehavec 1 ∙ c 2 =g m 1 +m 2 ∙ (rs) N modN 2 . • Fullyhomomorphic:homomorphicforbothadditionand multiplication •OpenproblemuntilGentry’sbreakthroughin2009. oCcnulisno