In this work, we discuss key generation problems under the Pairwise Independent
Network (PIN) model. Under this model, we construct two-step low-complexity key
generation schemes: local key generation + global key propagation. The local key
generation step uses only point-to-point source codes, while the global key
propagation step can be modeled as a linear programming problem. Two different
scenarios will be discussed. In the first scenario, a single group key
generation needs to be generated. We show that the global key propagation step
of this scenario can be solved using network coding technique. In the second
scenario, multiple keys need to be generated. We model the global key
propagation step as a multi-commodity flows over network problem.