This letter proposes a low-latency secure mobile edge computing (MEC) system where multiple users offload computing tasks to a base station in the presence of an eavesdropper. We jointly optimize the users' transmit power, computing capacity allocation, and user association to minimize the computing and transmission latencies over all users subject to security and computing resource constraints. Numerical results show that our proposed algorithm outperforms baseline strategies. Furthermore, we highlight a novel trade-off between the latency and security of MEC systems.