Private set intersection (PSI) is a cryptographic primitive that allows two or more parties to learn the intersection of their input sets and nothing else. In this paper, we present a private set intersection protocol based on a new secure multi-party quantum protocol for greatest common divisor (GCD). The protocol is mainly inspired by the recent quantum private set union protocol based on least common multiple by Li, Yang, and Liu. Performance analysis guarantees the correctness and it also shows that the proposed protocols are completely secure in semi-honest model. Moreover, the complexity is proven to be efficient in the size of the input sets.

翻译：私有集合交集（PSI）是一种加密原语，允许两个或多个方了解它们输入集合的交集以及其他任何信息。在本文中，我们提出了一种基于新的安全多方量子GCD协议的私有集合交集协议。该协议主要受到Li，Yang和Liu提出的基于最小公倍数的量子私有集合并协议的启发。性能分析保证了正确性，并证明了在半诚实模型下，所提出的协议是完全安全的。此外，复杂度证明对于输入集合大小是有效的。