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Post-Quantum and UC-secure Oblivious Transfer from SPHF with Grey Zone

Slim Bettaieb 1 Loïc Bidoux 2 Olivier Blazy 3 Baptiste Cottier 4, 5 David Pointcheval 4, 5 
3 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
4 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique - ENS Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : Oblivious Transfer (OT) is a major primitive for secure multiparty computation. Indeed, combined with symmetric primitives along with garbled circuits, it allows any secure function evaluation between two parties. In this paper, we propose a new approach to build OT protocols. Interestingly, our new paradigm features a security analysis in the Universal Composability (UC) framework and may be instantiated from post-quantum primitives. In order to do so, we define a new primitive named Smooth Projective Hash Function with Grey Zone (SPHFwGZ) which can be seen as a relaxation of the classical Smooth Projective Hash Functions, with a subset of the words for which one cannot claim correctness nor smoothness: the grey zone. As a concrete application, we provide two instantiations of SPHFwGZ respectively based on the Diffie-Hellman and the Learning With Errors (LWE) problems. Hence, we propose a quantum-resistant OT protocol with UC-security in the random oracle model.
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https://hal.archives-ouvertes.fr/hal-03772089
Contributor : Baptiste Cottier Connect in order to contact the contributor
Submitted on : Wednesday, November 23, 2022 - 12:36:42 PM
Last modification on : Thursday, November 24, 2022 - 3:57:35 AM

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  • HAL Id : hal-03772089, version 2
  • ARXIV : 2209.04149

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Slim Bettaieb, Loïc Bidoux, Olivier Blazy, Baptiste Cottier, David Pointcheval. Post-Quantum and UC-secure Oblivious Transfer from SPHF with Grey Zone. 15th International Symposium on Foundations & Practice of Security (FPS – 2022)., Dec 2022, Ottawa, Canada. ⟨hal-03772089v2⟩

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