An Enhanced QFT‐Based Quantum‐Secure Multi‐Party Protocol for Geometric Relation Determination Involving Ellipses

ABSTRACT

Quantum‐secure multi‐party computational geometry (QSMCG) aims to determine geometric relations without revealing the private spatial parameters of the participants. Existing QFT‐based secure multiparty quantum summation and multiplication protocols provide useful arithmetic primitives, but they still involve single‐initiator trust dependence and insufficient protocol‐level verification of channel disturbance and abnormal quantum‐state evolution. This paper proposes enhanced QFT‐based secure multi‐party summation and multiplication protocols. The protocols combine ‐threshold secret sharing with two complementary verification layers. Decoy‐particle detection monitors the quantum channel during transmission and is designed to catch eavesdropping, interception‐resend, delayed‐photon, invisible‐photon, or other transmission disturbances. Zero‐check verification is executed after the accumulated state is disentangled; it checks whether the target register returns to , so it tests whether the internal computation flow is consistent with the intended protocol. Based on these protocols, three modular QSMCG protocols are constructed for point‐ellipse, line‐ellipse, and circle‐ellipse relation determination under a TP‐assisted blinded‐comparison architecture. Correctness and security analyses show that the proposed protocols obtain the intended arithmetic and geometric results while improving resistance to representative external and internal attacks. Moreover, Qiskit simulations further verify the correctness and circuit‐level feasibility of the core quantum operations.