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

Oblivious Transfer (OT) is a major primitive for secure multiparty\ncomputation. Indeed, combined with symmetric primitives along with garbled\ncircuits, it allows any secure function evaluation between two parties. In this\npaper, we propose a new approach to build OT protocols. Interestingly, our new\nparadigm features a security analysis in the Universal Composability (UC)\nframework and may be instantiated from post-quantum primitives. In order to do\nso, we define a new primitive named Smooth Projective Hash Function with Grey\nZone (SPHFwGZ) which can be seen as a relaxation of the classical Smooth\nProjective Hash Functions, with a subset of the words for which one cannot\nclaim correctness nor smoothness: the grey zone. As a concrete application, we\nprovide two instantiations of SPHFwGZ respectively based on the Diffie-Hellman\nand the Learning With Errors (LWE) problems. Hence, we propose a\nquantum-resistant OT protocol with UC-security in the random oracle model.\n