Group Secret-Key Generation using Algebraic Rings in Three-User Wireless Networks
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Physical-layer Group Secret-Key (GSK) generation is an effective way of synthesizing symmetric keys across multiple nodes in wireless networks. Unlike the case of two-user key generation, GSK generation necessitates some nodes to act as facilitators, which broadcast linear combinations of the channel realizations thereby assisting all the nodes to witness the intended common source of randomness. However, in practice, radio devices are designed to transmit symbols from finite complex constellations, and as a result, the channel realizations are typically quantized by the facilitator which in turn impacts the overall secret-key rate. Identifying this issue, we propose a class of GSK generation protocols, called Symmetrically Quantized GSK (SQGSK) protocols, in a network of three nodes. In the proposed protocols, due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately to generate the keys. Under special conditions, we analytically show that the SQGSK protocols provide higher key-rate than the baselines wherein only the facilitator quantizes the channel realizations. We use extensive simulations to demonstrate the benefits of the proposed protocols when the facilitator employs finite constellations such as 4-, 16-, and 64-QAM.
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