  Information theoretic secrecy is combined with cryptographic secrecy to
create a secret-key exchange protocol for wireless networks. A network of
transmitters, which already have cryptographically secured channels between
them, cooperate to exchange a secret key with a new receiver at a random
location, in the presence of passive eavesdroppers at unknown locations. Two
spatial point processes: homogeneous Poisson process and independent uniformly
distributed points are used for the spatial distributions of transmitters and
eavesdroppers. We analyse the impact of the number of cooperating transmitters
and the number of eavesdroppers on the area fraction where secure communication
is possible. Upper bounds on the probability of existence of positive secrecy
between the cooperating transmitters and the receiver are derived. The
closeness of the upper bounds to the real value is then estimated by means of
numerical simulations. Simulations also indicate that a deterministic spatial
distribution for the transmitters e.g. hexagonal and square lattices, increases
the probability of existence of positive secrecy capacity compared to the
random spatial distributions. For the same number of friendly nodes,
cooperative transmitting provides a dramatically larger secrecy region than
cooperative jamming and cooperative relaying.
