We consider the problem of cross-layer resource allocation in time-varying cellular wireless networks and incorporate information theoretic secrecy as a quality-of-service constraint. Specifically, each node in the network injects two types of traffic, private and open, at rates chosen in order to maximize a global utility function, subject to network stability and secrecy constraints. The secrecy constraint enforces an arbitrarily low mutual information leakage from the source to every node in the network, except for the sink node. We first obtain the achievable rate region for the problem for single- and multiuser systems assuming that the nodes have full channel state information (CSI) of their neighbors. Then, we provide a joint flow control, scheduling, and private encoding scheme, which does not rely on the knowledge of the prior distribution of the gain of any channel. We prove that our scheme achieves a utility arbitrarily close to the maximum achievable utility. Numerical experiments are performed to verify the analytical results and to show the efficacy of the dynamic control algorithm.