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dc.contributor.authorVillar Santos, Jorge Luis
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationVillar, J. Equivalences and black-box separations of Matrix Diffie-Hellman problems. "Lecture notes in computer science", Febrer 2017, vol. 10174, p. 435-464.
dc.descriptionThe final publication is available at
dc.description.abstractIn this paper we provide new algebraic tools to study the relationship between different Matrix Diffie-Hellman (MDDH) Problems, which are recently introduced as a natural generalization of the so-called Linear Problem. Namely, we provide an algebraic criterion to decide whether there exists a generic black-box reduction, and in many cases, when the answer is positive we also build an explicit reduction with the following properties: it only makes a single oracle call, it is tight and it makes use only of operations in the base group. It is well known that two MDDH problems described by matrices with a different number of rows are separated by an oracle computing cer- tain multilinear map. Thus, we put the focus on MDDH problems of the same size. Then, we show that MDDH problems described with a different number of parameters are also separated (meaning that a suc- cessful reduction cannot decrease the amount of randomness used in the problem instance description). When comparing MDDH problems of the same size and number of pa- rameters, we show that they are either equivalent or incomparable. This suggests that a complete classification into equivalence classes could be done in the future. In this paper we give some positive and negative par- tial results about equivalence, in particular solving the open problem of whether the Linear and the Cascade MDDH problems are reducible to each other. The results given in the paper are limited by some technical restrictions in the shape of the matrices and in the degree of the polynomials defining them. However, these restrictions are also present in most of the work dealing with MDDH Problems. Therefore, our results apply to all known instances of practical interest.
dc.format.extent30 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica
dc.subject.lcshProgramming (Mathematics)
dc.subject.lcshNumerical analysis
dc.subject.otherMatrix Diffie-Hellman problems
dc.subject.otherBlack-box reductions
dc.subject.otherDecisional linear assumption
dc.subject.otherBlack-box separations
dc.titleEquivalences and black-box separations of Matrix Diffie-Hellman problems
dc.subject.lemacProgramació (Matemàtica)
dc.subject.lemacAnàlisi numèrica
dc.contributor.groupUniversitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
dc.subject.amsClassificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorVillar, J.
upcommons.citation.publicationNameLecture notes in computer science

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