带灰区的光滑投影Hash函数的后量子不经意传输
Post-Quantum Oblivious Transfer from Smooth Projective Hash Functions with Grey Zone
摘要：
不经意传输（OT）是安全多方计算的一个主要原语。事实上，结合对称原语和乱码电路，它允许双方之间的任何安全函数评估。在本文中，我们提出了一种新的方法来建立OT协议。有趣的是，我们的新范式在通用可组合性（UC）框架中进行了安全分析，并且可以从后量子原语中实例化。为了做到这一点，我们定义了一个新的原语，称为带灰色区域的平滑投影哈希函数（SPHFwGZ），它可以被看作是经典平滑投影哈希函数的放松，其中包含一个不能声称正确性或平滑性的词的子集：灰色区域。作为具体的应用，我们分别基于Diffie-Hellman和带错误学习（LWE）问题给出了SPHFwGZ的两个实例。因此，我们在随机预言模型下提出了一个具有UC-安全性的抗量子OT协议。
英文摘要：
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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