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

Slim Bettaieb (1) , Loïc Bidoux (2) , Olivier Blazy (3) , Baptiste Cottier (4, 5) , David Pointcheval (4, 5)

1 Worldline France
2 TII - Technology Innovation Institute
3 GRACE - Geometry, arithmetic, algorithms, codes and encryption
4 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
5 DI-ENS - Département d'informatique - ENS Paris

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.

Mots clés: Smooth projective hash function; Oblivious transfer; Post quantum cryptography

Domaines: Cryptographie et sécurité [cs.CR]

Slim Bettaieb, Loïc Bidoux, Olivier Blazy, Baptiste Cottier, David Pointcheval. Post-Quantum Oblivious Transfer from Smooth Projective Hash Functions with Grey Zone. 2022. ⟨hal-03772089v1⟩