The secure transmission of information in wireless networks without knowledge of eavesdropper channels or locations is considered. Two key mechanisms are employed: artificial noise generation from system nodes other than the transmitter and receiver, and a form of multi-user diversity that allows message reception in the presence of the artificial noise. We determine the maximum number of independently-operating and uniformly distributed eavesdroppers that can be present while the desired secrecy is achieved with high probability in the limit of a large number of system nodes. While our main motivation is considering eavesdroppers of unknown location, we first consider the case where the path-loss is identical between all pairs of nodes. In this case, a number of eavesdroppers that is exponential in the number of systems nodes can be tolerated. In the case of uniformly distributed eavesdroppers of unknown location, any number of eavesdroppers whose growth is sub-linear in the number of system nodes can be tolerated. The proposed approach significantly outperforms a power control approach based on standard multi-user diversity.