In this paper, we investigate physical layer security (PLS) for full-duplex (FD) multi-user systems. We consider a base station (BS) that operates in FD mode and transmits artificial noise (AN) to simultaneously protect uplink (UL) and downlink (DL) transmissions. Conventional fixed-position antennas (FPAs) at the FD BS struggle to fully exploit spatial degrees of freedom (DoFs) to improve signal reception and suppress interference. To overcome this limitation, we propose a novel FD BS architecture equipped with multiple transmit and receive movable antennas (MAs). The MAs introduce the DoFs in antenna position optimization, which can improve the performance of secure communication systems. To serve users and counter the cooperative interception of multiple eavesdroppers (Eves), we formulate a sum of secrecy rates (SSR) maximization problem to jointly optimize the MA positions, the transmit, receive, and AN beamformers at the BS, and the UL powers. We propose an alternating optimization (AO) algorithm, which decomposes the original problem into three sub-problems, to solve the challenging non-convex optimization problem with highly coupled variables. Specifically, we propose the multi-velocity particle swarm optimization (MVPSO), which is an improved version of the standard particle swarm optimization (PSO), to simultaneously optimize all MA positions. The transmit/AN beamformers and the UL powers are solved by successive convex approximation (SCA). The optimal receive beamformer is derived as a closed-form solution. Simulation results demonstrate the effectiveness of the proposed algorithms and the advantages of MAs over conventional FPAs in enhancing the security of FD multi-user systems.