In this paper, we investigate physical layer security (PLS) for full-duplex (FD) multi-user systems. To simultaneously protect uplink (UL) and downlink (DL) transmissions and ensure efficient use of time-frequency resources, we consider a base station (BS) that operates in FD mode and enables to emit the artificial noise (AN). Conventional fixed-position antennas (FPAs) at the BS struggle to fully exploit spatial degrees of freedom (DoFs). Therefore, we propose a new paradigm for secure FD multi-user systems, where multiple transmit and receive movable antennas (MAs) are deployed at the BS to serve UL and DL users and effectively counter the cooperative interception by multiple eavesdroppers (Eves). Specifically, the MA positions, the transmit, receive, and AN beamformers at the BS, and the UL powers are jointly optimized to maximize the sum of secrecy rates (SSR). To solve the challenging non-convex optimization problem with highly coupled variables, we propose an alternating optimization (AO) algorithm. This algorithm decomposes the original problem into three sub-problems, which are iteratively solved by the proposed multi-velocity particle swarm optimization (MVPSO) and successive convex approximation (SCA). Simulation results demonstrate that the proposed scheme for MA-aided secure FD multi-user systems can significantly enhance security performance compared to conventional FPA systems.