Wireless key establishment with asynchronous clocks

Recently, there has been great research interest in utilizing the phase response of multipath fading channels as sources of common randomness to achieve information-theoretic key establishment. Previous work along this direction assume a common time reference is shared among the keying nodes such that each node can obtain absolute phase estimations. However, such assumption is impractical in some scenarios where common time reference is not available. Without the common time reference, each keying node in the system has to estimate the channel phase based on its own independent and imperfect local clock, resulting in a phase offset between its local estimates and the absolute estimates. In this paper, we study the effect of clock deviations among keying nodes and propose a novel key generation protocol with asynchronous clocks among the keying nodes. Our contributions include: 1) Mitigate the reliance on common time reference to get a desired key agreement probability; 2) Improve the key generation rate by utilizing additional randomness provided by the relay nodes. Numerical and simulation results show that a desired estimation accuracy and key generation rate could be achieved with the help of a rely node.