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The Kernel Matrix Diffie-Hellman Assumption
dc.contributor.author | Morillo Bosch, M. Paz |
dc.contributor.author | Ràfols Salvador, Carla |
dc.contributor.author | Villar Santos, Jorge Luis |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-03-28T09:12:06Z |
dc.date.available | 2017-03-28T09:12:06Z |
dc.date.issued | 2016-12 |
dc.identifier.citation | Morillo, M., Rafols, C., Villar, J. The Kernel Matrix Diffie-Hellman Assumption. "Lecture notes in computer science", Desembre 2016, vol. 10031, p. 729-758. |
dc.identifier.issn | 0302-9743 |
dc.identifier.uri | http://hdl.handle.net/2117/102936 |
dc.description | The final publication is available at link.springer.com |
dc.description.abstract | We put forward a new family of computational assumptions, the Kernel Matrix Diffie-Hellman Assumption. Given some matrix A sampled from some distribution D, the kernel assumption says that it is hard to find “in the exponent” a nonzero vector in the kernel of A>. This family is a natural computational analogue of the Matrix Decisional Diffie-Hellman Assumption (MDDH), proposed by Escala et al. As such it allows to extend the advantages of their algebraic framework to computational assumptions. The k-Decisional Linear Assumption is an example of a family of decisional assumptions of strictly increasing hardness when k grows. We show that for any such family of MDDH assumptions, the corresponding Kernel assumptions are also strictly increasingly weaker. This requires ruling out the existence of some black-box reductions between flexible problems (i.e., computational problems with a non unique solution). |
dc.format.extent | 30 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional |
dc.subject.lcsh | Geometry, Algebraic |
dc.subject.other | Matrix Assumptions |
dc.subject.other | Computational Problems |
dc.subject.other | Black-Box Reductions |
dc.subject.other | Structure Preserving Cryptography |
dc.title | The Kernel Matrix Diffie-Hellman Assumption |
dc.type | Article |
dc.subject.lemac | Geometria algèbrica |
dc.contributor.group | Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
dc.identifier.doi | 10.1007/978-3-662-53887-6_27 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry |
dc.relation.publisherversion | http://link.springer.com/chapter/10.1007/978-3-662-53887-6_27 |
dc.rights.access | Open Access |
local.identifier.drac | 19721958 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Morillo, M.; Rafols, C.; Villar, J. |
local.citation.publicationName | Lecture notes in computer science |
local.citation.volume | 10031 |
local.citation.startingPage | 729 |
local.citation.endingPage | 758 |
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