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dc.contributor.authorEscala Ribas, Alex
dc.contributor.authorHerold, Gottfried
dc.contributor.authorKiltz, Eike
dc.contributor.authorRàfols Salvador, Carla
dc.contributor.authorVillar Santos, Jorge Luis
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2016-10-25T09:11:30Z
dc.date.available2017-10-03T00:30:33Z
dc.date.issued2015-10-22
dc.identifier.citationEscala, A., Herold, G., Kiltz, E., Rafols, C., Villar, J. An algebraic framework for Diffie–Hellman assumptions. "Journal of cryptology", 2017, vol. 30, núm. 1, p. 242-288.
dc.identifier.issn0933-2790
dc.identifier.urihttp://hdl.handle.net/2117/91050
dc.description.abstractWe put forward a new algebraic framework to generalize and analyze Diffie-Hellman like Decisional Assumptions which allows us to argue about security and applications by considering only algebraic properties. Our D`,k-MDDH assumption states that it is hard to decide whether a vector in ¿ìs linearly dependent of the columns of some matrix in ¿`×k sampled according to distribution D`,k. It covers known assumptions such as DDH, 2-Lin (linear assumption), and k-Lin (the k-linear assumption). Using our algebraic viewpoint, we can relate the generic hardness of our assumptions in m-linear groups to the irreducibility of certain polynomials which describe the output of D`,k. We use the hardness results to find new distributions for which the D`,k-MDDH-Assumption holds generically in m-linear groups. In particular, our new assumptions 2-SCasc and 2-ILin are generically hard in bilinear groups and, compared to 2-Lin, have shorter description size, which is a relevant parameter for efficiency in many applications. These results support using our new assumptions as natural replacements for the 2-Lin Assumption which was already used in a large number of applications. To illustrate the conceptual advantages of our algebraic framework, we construct several fundamental primitives based on any MDDH-Assumption. In particular, we can give many instantiations of a primitive in a compact way, including public-key encryption, hash-proof systems, pseudo-random functions, and Groth-Sahai NIZK and NIWI proofs. As an independent contribution we give more efficient NIZK and NIWI proofs for membership in a subgroup of ¿` . The results imply very significant efficiency improvements for a large number of schemes.
dc.format.extent46 p.
dc.language.isoeng
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
dc.subject.lcshNumber theory
dc.subject.otherDiffie-Hellman Assumption
dc.subject.otherGeneric Hardness
dc.subject.otherGroth-Sahai proofs
dc.subject.otherHash Proof Systems
dc.subject.otherPublic-key Encryption
dc.titleAn algebraic framework for Diffie–Hellman assumptions
dc.typeArticle
dc.subject.lemacNombres, Teoria dels
dc.contributor.groupUniversitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.identifier.doi10.1007/s00145-015-9220-6
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::11 Number theory::11Y Computational number theory
dc.relation.publisherversionhttp://link.springer.com/article/10.1007%2Fs00145-015-9220-6
dc.rights.accessOpen Access
local.identifier.drac17502631
dc.description.versionPostprint (author's final draft)
local.citation.authorEscala, A.; Herold, G.; Kiltz, E.; Rafols, C.; Villar, J.
local.citation.publicationNameJournal of cryptology
local.citation.volume30
local.citation.number1
local.citation.startingPage242
local.citation.endingPage288


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