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arXiv · 2209.04149

Post-Quantum Oblivious Transfer from Smooth Projective Hash Functions with Grey Zone

Slim Bettaieb·Loïc Bidoux·Olivier Blazy·Baptiste Cottier·David Pointcheval
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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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Slim Bettaieb, Loïc Bidoux, Olivier Blazy, Baptiste Cottier, David Pointcheval. 2022-09-09. Post-Quantum Oblivious Transfer from Smooth Projective Hash Functions with Grey Zone. https://arxiv.org/abs/2209.04149

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