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

TL;DR

This work tackles privacy-preserving two-party circle intersection (P2CI) in quantum secure multiparty computation by recasting the decision as a phase-encoded query. It develops a polynomial-time Oracle by decomposing the phase-encoded query into quantum arithmetic (modular adders and multipliers) and a carefully constructed phase flip on $D-R$, where $D=(x_1-x_2)^2+(y_1-y_2)^2$ and $R=(r_1+r_2)^2$. The protocol combines a preparation, operation, and output stage with a Shi honesty test to deter cheating, achieving correctness and privacy against internal and external threats. This approach provides a scalable alternative to grid-based QPGI methods and advances quantum PGI for regular geometric shapes like circles.

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.

Figures (3)

• Figure 1: A diagrammatic sketch of phase-encoded query.
• Figure 2: A diagrammatic sketch of P2CI problem.
• Figure 3: The circuit implementation of the Oracle operator.

Theorems & Definitions (1)

• Definition 1: Privacy-preserving two-party circle intersection, P2CI