Group Secret-Key Generation Using Algebraic Rings in Wireless Networks

It is well known that physical-layer Group Secret-Key (GSK) generation techniques allow multiple nodes of a wireless network to synthesize common secret-key, which can be subsequently used keep their group messages confidential. As one its salient features, the involved in GSK extract randomness from subset channels, referred as source (CSR). Unlike two-user key generation, some must act facilitators by broadcasting quantized versions linear combinations channel realizations, so assist all observe CSR. However, we note combination realizations incurs non-zero leakage CSR an eavesdropper, and moreover, quantizing also reduces overall key-rate. Identifying these issues, propose practical protocol, Algebraic Symmetrically Quantized (A-SQGSK) three nodes, wherein due quantization symbols at facilitator, other two quantize use them appropriately over algebraic rings generate keys. First, prove A-SQGSK protocol zero eavesdropper. Subsequently, on provided consensus algorithm among called Entropy-Maximization Error-Minimization (EM-EM) algorithm, maximizes entropy secret-key subject upper-bound mismatch-rate. We extensive analysis simulation results lay out guidelines jointly choose parameters EM-EM algorithm.