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.

翻译：显而易见的转移(OT)是安全的多方计算的主要原始数据。 事实上,它与对称原始数据以及混凝土电路一起,允许双方进行任何安全功能评估。 在本文中,我们提出了建立OT协议的新办法。 有趣的是,我们的新范式在通用合成框架(UC)中包含安全分析,并可能从后夸特原始数据中即刻产生。 为了做到这一点,我们定义了一个名为“与灰色区(SPHFwGZ)一起的滑动投影散射函数”的新原始数据,它可以被视为古典的光滑投影散列函数的松散,其中一部分是无法声称正确或顺畅的词:灰色区域。作为一个具体应用,我们提供了基于Diffie-Hellman和“有错误的学习”问题的两种SPHFHWGZ的即时空。 因此,我们提出了一种在随机或触控模型中具有UC安全的量抗量性OT协议。