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In this paper, resource allocation for energy-efficient secure communication in an orthogonal frequency-division multiple-access (OFDMA) downlink network is studied. The considered problem is modeled as a nonconvex optimization problem that takes into account the sum-rate-dependent circuit power consumption, multiple-antenna eavesdropper, artificial noise generation, and different quality-of-service (QoS) requirements, including a minimum required secrecy sum rate and a maximum tolerable secrecy outage probability. The power, secrecy data rate, and subcarrier allocation policies are optimized for maximization of the energy efficiency of secure data transmission (bit/joule securely delivered to the users). The considered nonconvex optimization problem is transformed into a convex optimization problem by exploiting the properties of fractional programming, which results in an efficient iterative resource allocation algorithm. In each iteration, the transformed problem is solved by using dual decomposition. Simulation results illustrate that the proposed iterative resource allocation algorithm not only converges in a small number of iterations but maximizes the system energy efficiency and guarantees a nonzero secrecy data rate for the desired users as well. In addition, the obtained results unveil a tradeoff between energy efficiency and secure communication.