Hamza Sohail, Burhan Ul Islam Khan, Nur Fatin Liyana Mohd Rosely, Khang Wen Goh, Dwi Sudarno Putra, Abdul Raouf Khan, Mesith Chaimanee
Multi-party quantum key agreement (MQKA) enables a group of mutually untrusted users to jointly establish a secret key with equal influence, a capability not provided by two-party quantum key distribution (QKD) and increasingly relevant for securing resilient infrastructure such as quantum-enabled smart grid networks and distributed cyber-physical systems. We present a high-dimensional Greenberger-Horne-Zeilinger (GHZ)-based MQKA that simultaneously targets rigorous security, provable fairness, and practical loss tolerance. The protocol distributes an N-partite d-level GHZ state in a star (with an optional star-of-stars hierarchy for large N) and maps each user’s contribution to local XdaZdb operations. A commit-then-reveal layer makes inputs binding and hiding, yielding equal influence fairness over Zd with a strict fair-abort guarantee. Composable secrecy is established via entropy bounds and a Devetak-Winter-style key rate analysis, strengthened by test-round statistics; we connect Mermin/Svetlichny-type correlators to min-entropy lower bounds and incorporate full leakage accounting and finite-key penalties. We model depolarizing, shift/phase (Weyl), amplitude-damping, erasures, detector efficiency, and dark counts, and derive closed-form mappings from device parameters to symbol/phase errors. Monte Carlo studies confirm that d>2 expands the positive-rate region and reduces the global survival required for a given throughput compared with qubit GHZ MQKA under identical conditions. We discuss potential photonic realizations (time-bin or frequency-bin encoding, discrete Fourier transform networks, and superconducting nanowire detectors) and architectural pathways toward larger N via hierarchical clustering, while acknowledging the significant technological challenges that would need to be overcome to realize high-dimensional multipartite entanglement experimentally. Overall, the scheme delivers higher efficiency per entangled state, rigorous fairness, and composable security with realistic noise and loss, addressing key gaps in current MQKA designs for resilient infrastructure. © The Author(s) 2026.
Pak-Austria Fachhochschule Institute of Applied Sciences and Technology, Haripur, 22620, Pakistan; Faculty of Computer Science and Information Technology, Universiti Malaya, Kuala Lumpur, 50603, Malaysia; School of Computing Science, Taylor’s University, Selangor, 47500, Malaysia; Faculty of Data Science and Information Technology, INTI International University, Nilai, 71800, Malaysia; Fakultas Teknik, Universitas Negeri Padang, Padang, 25132, Indonesia; Department of Computer Sciences, King Faisal University, Al-Ahsa, 31982, Saudi Arabia; Faculty of Engineering and Technology, Shinawatra University, Pathum Thani, 12160, Thailand
