Title:
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The Kernel Matrix Diffie-Hellman assumption
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Author:
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Morillo, Paz; Ràfols, Carla; Villar, Jorge L.
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Abstract:
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Comunicació presentada a: ASIACRYPT 2016, celebrat a Hanoi, Vietnam, del 4 al 6 de desembre de 2016. |
Abstract:
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We put forward a new family of computational assumptions,
the Kernel Matrix Diffi-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 com-
putational assumptions.
The k-Decisional Linear Assumption is an example of a family of de-
cisional 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
exible
problems (i.e., computational problems with a non unique solution). |
Subject(s):
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-Matrix assumptions -Computational problems -Black-box reductions -Structure preserving cryptography |
Rights:
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© International Association for Cryptologic Research 2016
The final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-662-53887-6_27 |
Document type:
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Conference Object Article - Accepted version |
Published by:
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Springer
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