Quantum Privacy-preserving Two-party Circle Intersection Protocol Based on Phase-encoded Query

TL;DR

This paper introduces a quantum protocol for privacy-preserving two-party circle intersection that reduces computational complexity using phase-encoded queries and quantum arithmetic, ensuring security and efficiency.

Contribution

It presents a novel quantum protocol for circle intersection that simplifies Oracle implementation and lowers computational complexity compared to grid coding methods.

Findings

Protocol is correct and efficient

Achieves polynomial computational complexity

Protects privacy against internal and external attacks

Abstract

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.