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Homomorphic Encryption for Multiplications and Pairing Evaluation

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCASTAGNOS, Guilhem
hal.structure.identifierEquipe AMACC - Laboratoire GREYC - UMR6072
dc.contributor.authorLAGUILLAUMIE, Fabien
dc.date.accessioned2024-04-04T03:20:07Z
dc.date.available2024-04-04T03:20:07Z
dc.date.issued2012
dc.date.conference2012-09-05
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194565
dc.description.abstractEnWe propose a generic approach to design homomorphic en-cryption schemes, which extends Gjøsteen'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 pair-ing e : G × G → Gt. This scheme has some interesting theoretical and practical properties: it allows an arbitrary number of multiplications in the groups G and Gt, 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 cannot achieve 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 projecting pairing using Freeman's terminology. However the application to shared decryption also relies on the fact that the pair-ing is cancelling and therefore does not survive this conversion.
dc.language.isoen
dc.publisherSpringer LNCS
dc.title.enHomomorphic Encryption for Multiplications and Pairing Evaluation
dc.typeCommunication dans un congrès
dc.identifier.doi10.1007/978-3-642-32928-9_21
dc.subject.halInformatique [cs]
dc.subject.halInformatique [cs]/Cryptographie et sécurité [cs.CR]
bordeaux.page374 - 392
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleProceedings of SCN 2012
bordeaux.countryIT
bordeaux.conference.cityAmalfi
bordeaux.peerReviewedoui
hal.identifierhal-01084946
hal.version1
hal.invitednon
hal.proceedingsoui
hal.conference.end2012-09-07
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01084946v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2012&rft.spage=374%20-%20392&rft.epage=374%20-%20392&rft.au=CASTAGNOS,%20Guilhem&LAGUILLAUMIE,%20Fabien&rft.genre=unknown


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