Secure federated learning is a privacy-preserving framework to improve machine learning models by training over large volumes of data collected by mobile users. This is achieved through an iterative process where, at each iteration, users update a global model using their local datasets. Each user then masks its local model via random keys, and the masked models are aggregated at a central server to compute the global model for the next iteration. As the local models are protected by random masks, the server cannot observe their true values. This presents a major challenge for the resilience of the model against adversarial (Byzantine) users, who can manipulate the global model by modifying their local models or datasets. Towards addressing this challenge, this paper presents the first single-server Byzantine-resilient secure aggregation framework (BREA) for secure federated learning. BREA is based on an integrated stochastic quantization, verifiable outlier detection, and secure model aggregation approach to guarantee Byzantine-resilience, privacy, and convergence simultaneously. We provide theoretical convergence and privacy guarantees and characterize the fundamental trade-offs in terms of the network size, user dropouts, and privacy protection. Our experiments demonstrate convergence in the presence of Byzantine users, and comparable accuracy to conventional federated learning benchmarks.