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Disjunctions for Hash Proof Systems: New Constructions and Applications

Michel Abdalla 1, 2, 3 Fabrice Benhamouda 2, 3, 1 David Pointcheval 3, 2, 1
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : Hash Proof Systems were first introduced by Cramer and Shoup (Eurocrypt’02) as a tool to construct efficient chosen-ciphertext-secure encryption schemes. Since then, they have found many other applications, including password authenticated key exchange, oblivious transfer, and zero-knowledge arguments. One of the aspects that makes hash proof systems so interesting and powerful is that they can be seen as implicit proofs of membership for certain languages. As a result, by extending the family of languages that they can handle, one often obtains new applications or new ways to understand existing schemes. In this paper, we show how to construct hash proof systems for the disjunction of languages defined generically over cyclic, bilinear, and multilinear groups. Among other applications, this enables us to construct the most efficient one-time simulation-sound (quasi-adaptive) non-interactive zero-knowledge arguments for linear languages over cyclic groups, the first one-round group password-authenticated key exchange without random oracles, the most efficient threshold structure-preserving chosen-ciphertext-secure encryption scheme, and the most efficient one-round password authenticated key exchange in the UC framework.
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Contributor : Michel Abdalla <>
Submitted on : Monday, March 16, 2015 - 2:57:20 PM
Last modification on : Tuesday, May 4, 2021 - 2:06:02 PM

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Michel Abdalla, Fabrice Benhamouda, David Pointcheval. Disjunctions for Hash Proof Systems: New Constructions and Applications. EUROCRYPT 2015, Apr 2015, Sofia, Bulgaria. pp.69-100, ⟨10.1007/978-3-662-46803-6_3⟩. ⟨hal-01131994⟩



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