Abstract-This paper investigates group secret key generation problems for different types of wireless networks, by exploiting physical layer characteristics of wireless channels. A new group key generation strategy with low-complexity is proposed, which combines the well established point-to-point pairwise key generation technique, the multi-segment scheme, and the onetime pad. In particular, this group key generation process is studied for three types of communication networks: 1) the threenode network, 2) the multi-node ring network and 3) the multinode mesh network. Three group key generation algorithms are developed for these communication networks, respectively. The analysis shows that the first two algorithms yield optimal group key rates, whereas the third algorithm achieves the optimal multiplexing gain. Next, for the first two types of networks, we address the time allocation problem in the channel estimation step to maximize the group key rates. This non-convex maxmin time allocation problem is first reformulated into a series of geometric programming, and then a single-condensation-method based iterative algorithm is proposed. Numerical results are also provided to validate the performance of the proposed key generation algorithms and the time allocation algorithm.