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Homomorphic Encryption for Multiplications and Pairing Evaluation

hal.structure.identifierArithmetic and Computing [ARIC]
dc.contributor.authorLAGUILLAUMIE, Fabien
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCASTAGNOS, Guilhem
dc.contributor.editorIvan Visconti and Roberto De Prisco
dc.date.accessioned2024-04-04T02:23:42Z
dc.date.available2024-04-04T02:23:42Z
dc.date.issued2012
dc.date.conference2012-09
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189756
dc.description.abstractEnWe propose a generic approach to design homomorphic encryption schemes, which extends Gj\o steen's framework. From this generic method, we deduce a new homomorphic encryption scheme in a com\-posite-order subgroup of points of an elliptic curve which admits a pairing $e: \G\times \G \rightarrow \G_t$. This scheme has some interesting theoretical and practical properties: it allows an arbitrary number of multiplications in the groups $\G$ \emph{and} $\G_t$, \emph{as well as} a pairing evaluation on the underlying plaintexts. We prove the semantic security under chosen plaintext attack of our scheme under a generalized subgroup membership assumption, and we also prove that it \emph{cannot} achieve {\sf ind-cca1} security. We eventually propose an original application to shared decryption. On the theoretical side, this scheme is an example of cryptosystem which can be naturally implemented with groups of prime order, as the homomorphic properties require only a \emph{projecting} pairing using Freeman's terminology. However the application to shared decryption also relies on the fact that the pairing is \emph{cancelling} and therefore does not survive this conversion.
dc.language.isoen
dc.title.enHomomorphic Encryption for Multiplications and Pairing Evaluation
dc.typeCommunication dans un congrès
dc.subject.halInformatique [cs]/Cryptographie et sécurité [cs.CR]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleSecurity and Cryptography for Networks - 8th International Conference, SCN 2012
bordeaux.countryIT
bordeaux.conference.cityAmalfi
bordeaux.peerReviewedoui
hal.identifierhal-00763110
hal.version1
hal.invitednon
hal.proceedingsoui
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00763110v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2012&rft.au=LAGUILLAUMIE,%20Fabien&CASTAGNOS,%20Guilhem&rft.genre=unknown


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