Recent advances in recommender systems have shown that relying on graph filters, such as the normalized item-item adjacency matrix and the ideal low-pass filter yields competitive performance and scales better than Graph Convolutional Networks-based solutions. However, these solutions require centralizing user data, which raises concerns over data privacy, security, and the monopolization of user data by a few actors. To address those concerns, we propose PriviRec and PriviRec-k, two complementary recommendation frameworks. In PriviRec, we show that it is possible to decompose widely used filters so that they can be computed in a distributed setting using Secure Aggregation and a distributed version of the Randomized Power Method, without revealing individual users contributions. PriviRec-k extends this approach by having users securely aggregate low-rank projections of their contributions, enabling a tunable balance between communication overhead and recommendation accuracy. We demonstrate theoretically as well as experimentally on Gowalla, Yelp2018, and Amazon-Book that our methods achieve performance comparable to centralized state-of-the-art recommender systems and superior to decentralized ones, while preserving confidentiality and low communication and computational overheads.