In integrated sensing and communication (ISAC) systems, the target of interest may \textit{intentionally disguise itself as an eavesdropper}, enabling it to intercept and tap into the communication data embedded in the ISAC waveform. The following paper considers a full duplex (FD)-ISAC system, which involves multiple malicious targets attempting to intercept both uplink (UL) and downlink (DL) communications between the dual-functional radar and communication (DFRC) base station (BS) and legitimate UL/DL communication users (CUs). For this, we formulate an optimization framework that allows maximization of both UL and DL sum secrecy rates, under various power budget constraints for sensing and communications. As the proposed optimization problem is non-convex, we develop a method called Iterative Joint Taylor-Block cyclic coordinate descent (IJTB) by proving essential lemmas that transform the original problem into a more manageable form. In essence, IJTB alternates between two sub-problems: one yields UL beamformers in closed-form, while the other approximates the solution for UL power allocation, artificial noise covariance, and DL beamforming vectors. This is achieved through a series of Taylor approximations that effectively \textit{"convexify"} the problem, enabling efficient optimization. Simulation results demonstrate the effectiveness of the proposed solver when compared with benchmarking ones. Our findings reveal that the IJTB algorithm shows fast convergence, reaching stability within approximately $10$ iterations. In addition, all benchmarks reveal a substantial decline in the sum secrecy rate, approaching zero as the eavesdropper distance reaches $17$ meters, underscoring their vulnerability in comparison to IJTB.