The emergence of sixth-generation (6G) wireless networks is driving the need for secure group key generation mechanisms resilient to quantum-computing attacks. Conventional quantum key distribution (QKD) protocols are designed for point-to-point communication and are therefore not directly applicable to group key establishment. To address this limitation, this paper proposes a scalable High-Altitude Platform (HAP)-assisted multipartite QKD network architecture that integrates $N$-GHZ-state protocols with a Time Division Multiple Access (TDMA) scheme over free-space optical (FSO) channels. The performance of the proposed system is evaluated using a Qiskit-based simulation framework that incorporates realistic physical-layer impairments of FSO links. Simulation results demonstrate that the proposed architecture significantly improves the group secret key rate (SKR) compared to conventional bipartite approaches, while effectively reducing overall network execution delay. In addition, the analysis reveals the impact of channel impairments and provides practical design insights, such as optimal beam-waist control. The proposed framework demonstrates the potential of HAP-assisted multipartite QKD as an effective security solution for future large-scale 6G wireless networks supporting secure group communications.

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