Abstract: The secure two-party line segment intersection is an important branch of computational geometry in multi-party safe computation, with high research and practical value as it can be extended to applications such as privacy computation for polygon area and convex hull intersection. In classical computation, various solutions have been proposed based on the principles of computational complexity, yet they are unable to withstand potential quantum attacks in the future. To address the issue, a secure two-party line segment intersection protocol based on quantum homomorphic encryption is proposed. In this protocol, the computation process is completed by a semi-trusted third-party computing center. Throughout the entire protocol, the privacy of the two-party line segments is protected. Finally, the protocol was applied to specific instances and security analysis was conducted against external and internal attacks. Experimental results demonstrated the security and reliability of the protocol.

Key words: quantum homomorphic encryption, computational geometry, secure multi-party computing；two-party line segment intersection