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）是一种密码学原语，允许多方在不泄露其他信息的情况下获取其输入集合的交集。本文提出了一种基于新型安全多方量子最大公约数（GCD）协议的私有集合交集协议。该协议主要受Li、Yang和Liu近期提出的基于最小公倍数的量子私有集合并集协议启发。性能分析保证了协议的正确性，同时表明所提协议在半诚实模型下是完全安全的。此外，协议复杂度被证明在输入集合规模上是高效的。