Group Secret Key Generation in Wireless Networks: Algorithms and Rate Optimization

A group key generation algorithm 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 wellestablished point-to-point pair wise key generation technique, the multisegment scheme, and the onetime pad. In particular, this group key generation process is studied for three types of communication networks: 1) A three-node network; 2) A multi node ring network; and 3) A multi node mesh network. Three group key generation algorithms are developed for these communication networks, respectively. The analysis8 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 nonconvex max – min 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