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dc.contributor.authorKarabina, K.en_US
dc.contributor.authorKnapp, E.en_US
dc.contributor.authorMenezes, A.en_US
dc.date.accessioned2016-02-08T09:41:11Z
dc.date.available2016-02-08T09:41:11Z
dc.date.issued2013en_US
dc.identifier.issn19305346
dc.identifier.urihttp://hdl.handle.net/11693/21101
dc.description.abstractFor symmetric pairings e: G × G → GT, Verheul proved that the existence of an efficiently-computable isomorphism Φ: GT → G implies that the Diffie-Hellman problems in G and GT can be efficiently solved. In this paper, we explore the implications of the existence of efficiently-computable isomorphisms Φ1: GT →G1 and Φ2: GT →G2 for asymmetric pairings e: G1 × G2 → GT. We also give a simplified proof of Verheul's theorem. © 2013 AIMS.en_US
dc.language.isoEnglishen_US
dc.source.titleAdvances in Mathematics of Communicationsen_US
dc.relation.isversionofhttp://dx.doi.org/10.3934/amc.2013.7.103en_US
dc.subjectAsymmetric pairingsen_US
dc.subjectCryptographyen_US
dc.subjectDiscrete logarithm problemen_US
dc.subjectVerheul's theoremen_US
dc.titleGeneralizations of verheul's theorem to asymmetric pairingsen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematics
dc.citation.spage103en_US
dc.citation.epage111en_US
dc.citation.volumeNumber7en_US
dc.citation.issueNumber1en_US
dc.identifier.doi10.3934/amc.2013.7.103en_US


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