Privacy-preserving geometric intersection (PGI) is an important issue in Secure multiparty computation (SMC). The existing quantum PGI protocols are mainly based on grid coding, which requires a lot of computational complexity. The phase-encoded query method which has been used in some Quantum SMC protocols is suitable to solve the decision problem, but it needs to apply high dimensional Oracle operators. In this paper, we use the principle of phase-encoded query to solve an important PGI problem, namely privacy-preserving two-party circle intersection. We study the implementation of Oracle operator in detail, and achieve polynomial computational complexity by decompsing it into quantum arithmetic operations. Performance analysis shows that our protocol is correct and efficient, and can protect the privacy of all participants against internal and external attacks.

翻译：隐私保护几何相交（PGI）是安全多方计算（SMC）中的重要问题。现有量子PGI协议主要基于网格编码，需要较高的计算复杂度。已应用于部分量子SMC协议的相位编码查询方法适用于解决判定性问题，但需应用高维Oracle算子。本文利用相位编码查询原理解决一个重要的PGI问题——隐私保护两方圆相交。我们详细研究了Oracle算子的实现方式，通过将其分解为量子算术运算，实现了多项式计算复杂度。性能分析表明，该协议正确且高效，能够保护所有参与方的隐私免受内部和外部攻击。