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Federated recommender system (FRS), which enables many local devices to train a shared model jointly without transmitting local raw data, has become a prevalent recommendation paradigm with privacy-preserving advantages. However, previous work on FRS performs similarity search via inner product in continuous embedding space, which causes an efficiency bottleneck when the scale of items is extremely large. We argue that such a scheme in federated settings ignores the limited capacities in resource-constrained user devices (i.e., storage space, computational overhead, and communication bandwidth), and makes it harder to be deployed in large-scale recommender systems. Besides, it has been shown that transmitting local gradients in real-valued form between server and clients may leak users' private information. To this end, we propose a lightweight federated recommendation framework with privacy-preserving matrix factorization, LightFR, that is able to generate high-quality binary codes by exploiting learning to hash technique under federated settings, and thus enjoys both fast online inference and economic memory consumption. Moreover, we devise an efficient federated discrete optimization algorithm to collaboratively train model parameters between the server and clients, which can effectively prevent real-valued gradient attacks from malicious parties. Through extensive experiments on four real-world datasets, we show that our LightFR model outperforms several state-of-the-art FRS methods in terms of recommendation accuracy, inference efficiency and data privacy.