Security is becoming an increasingly important issue in wireless communications, to which physical layer approaches can contribute by providing addition resources for securing confidential messages. In this paper, the resilience of multi-user networks to passive and active eavesdropping is investigated. In particular, average secrecy capacities are evaluated in scenarios involving a base station and several terminals, some of which constitute passive or active eavesdroppers. Network resources (e.g. power) are allocated by the base station based on the available channel state information. The average secrecy capacity of such a network is evaluated in the following cases: (i) in the presence of passive eavesdroppers when no side information is available to the base station; (ii) in the presence of passive eavesdroppers with side information available; and (iii) in the presence of a single active eavesdropper with side information available. This investigation demonstrates that substantial secrecy rates are attainable in the presence of passive eavesdroppers as long as minimal side information, e.g. a statistical characterization of the number of potential eavesdroppers, is available to the base station. On the other hand, it is further found that active eavesdroppers can potentially compromise such networks unless statistical inference is employed to restrict their ability to attack.