  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.
