  A novel framework for sharing common randomness and generating secret keys in
wireless networks is considered. In particular, a network of users equipped
with pulse oscillators (POs) and coupling mechanisms in between is considered.
Such mechanisms exist in synchronized biological and natural systems, and have
been exploited to provide synchronization in distributed networks. We show that
naturally-existing initial random phase differences between the POs in the
network can be utilized to provide almost identical common randomness to the
users. This randomness is extracted from the synchronization time in the
network. Bounds on the entropy of such randomness are derived for a two-user
system and a conjecture is made for a general $n$-user system. Then, a
three-terminal scenario is considered including two legitimate users and a
passive eavesdropper, referred to as Eve. Since in a practical setting Eve
receives pulses with propagation delays, she can not identify the exact
synchronization time. A simplified model is then considered for Eve's receiver
and then a bound on the rate of secret key generation is derived. Also, it is
shown, under certain conditions, that the proposed protocol is resilient to an
active jammer equipped with a similar pulse generation mechanism.
