Low-Latency Exchange of Common Randomness for Group-Key Generation

In physical-layer Group Secret-Key (GSK) generation, multiple nodes of a wireless network synthesize symmetric keys by observing a subset of their channel realizations, referred to as the common source of randomness (CSR). Unlike the case of two-user key generation, exchanging pilot symbols within the coherence-block is not sufficient to arrive at a CSR. In addition, some nodes must act as facilitators by broadcasting linear combinations of the channel realizations within the coherence-block, thereby giving rise to low-latency requirement for sharing the CSR. To assist the latency constraint, practical radio devices are forced to quantize the linear combination of channel realizations directly to finite complex constellations before broadcasting them to the other nodes. First, we show that this direct quantization at the facilitator results in asymmetric noise levels at the nodes, which in turn impacts the overall key-rate. Identifying the above issue, we propose a practical GSK generation protocol, referred to as Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol, in a network of three nodes. In the proposed protocol, due to quantization of symbols at the facilitator, the other two nodes also quantize their channel realizations, and use them appropriately over algebraic rings to generate the keys. Under special conditions, we analytically show that the A-SQGSK protocol provides higher key-rate than the baselines, and also prove that the proposed protocol incurs zero leakage to an external eavesdropper. We also use extensive simulation results to demonstrate the benefits of the proposed protocol at different regimes of signal-to-noise-ratios.