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Removing Erasures with Explainable Hash Proof Systems

Michel Abdalla 1, 2 Fabrice Benhamouda 3 David Pointcheval 1, 2
1 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 : An important problem in secure multi-party computation is the design of protocols that can tolerate adversaries that are capable of corrupting parties dynamically and learning their internal states. In this paper, we make significant progress in this area in the context of password-authenticated key exchange (PAKE) and oblivious transfer (OT) protocols. More precisely, we first revisit the notion of projective hash proofs and introduce a new feature that allows us to explain any message sent by the simulator in case of corruption, hence the notion of Explainable Projective Hashing. Next, we demonstrate that this new tool generically leads to efficient PAKE and OT protocols that are secure against semi-adaptive adversaries without erasures in the Universal Composability (UC) framework. We then show how to make these protocols secure even against adaptive adversaries, using \emph{non-committing encryption}, in a much more efficient way than generic conversions from semi-adaptive to adaptive security. Finally, we provide concrete instantiations of explainable projective hash functions that lead to the most efficient PAKE and OT protocols known so far, with UC-security against adaptive adversaries, with or without erasures, in the single global CRS setting. As an important side contribution, we also propose a new commitment scheme based on DDH, which leads to the construction of the first one-round PAKE adaptively secure under plain DDH without pairing, assuming reliable erasures, and also improves previous constructions of OT and two- or three-round PAKE schemes.
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https://hal.inria.fr/hal-01471896
Contributor : David Pointcheval <>
Submitted on : Monday, February 20, 2017 - 12:59:37 PM
Last modification on : Tuesday, May 4, 2021 - 2:06:02 PM

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Michel Abdalla, Fabrice Benhamouda, David Pointcheval. Removing Erasures with Explainable Hash Proof Systems. Public-Key Cryptography - PKC 2017 - 20th International Conference on Practice and Theory in Public-Key Cryptography, Mar 2017, Amsterdam, Netherlands. pp.151-174, ⟨10.1007/978-3-662-54365-8_7⟩. ⟨hal-01471896⟩

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