On Opportunistic Selection of Common Randomness and LLR generation for Algebraic Group Secret-Key Generation

It is well known that physical-layer key generation methods enable wireless devices to harvest symmetric keys by accessing the randomness offered by the wireless channels. Although two-user key generation is well understood, group secret-key (GSK) generation, wherein more than two nodes in a network generate secret-keys, still poses open problems. Recently, Manish Rao et al., have proposed the Algebraic Symmetrically Quantized GSK (A-SQGSK) protocol for a network of three nodes wherein the nodes share quantized versions of the channel realizations over algebraic rings, and then harvest a GSK. Although A-SQGSK protocol guarantees confidentiality of common randomness to an eavesdropper, we observe that the key-rate of the protocol is poor since only one channel in the network is used to harvest GSK. Identifying this limitation, in this paper, we propose an opportunistic selection method wherein more than one wireless channel is used to harvest GSKs without compromising the confidentiality feature, thereby resulting in remarkable improvements in the key-rate. Furthermore, we also propose a log-likelihood ratio (LLR) generation method for the common randomness observed at various nodes, so that the soft-values are applied to execute LDPC codes based reconciliation to reduce the bit mismatches among the nodes.