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Title:
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The Kernel Matrix Diffie-Hellman Assumption
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Author:
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Morillo Bosch, M. Paz; Ràfols Salvador, Carla; Villar Santos, Jorge Luis
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
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Abstract:
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The final publication is available at link.springer.com |
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Abstract:
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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). |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
-Geometry, Algebraic
-Matrix Assumptions
-Computational Problems
-Black-Box Reductions
-Structure Preserving Cryptography
-Geometria algèbrica
-Classificació AMS::14 Algebraic geometry::14Q Computational aspects in algebraic geometry |
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Rights:
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Document type:
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Article - Submitted version
Article |
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