We consider the problem of training User Verification (UV) models in federated setup, where each user has access to the data of only one class and user embeddings cannot be shared with the server or other users. To address this problem, we propose Federated User Verification (FedUV), a framework in which users jointly learn a set of vectors and maximize the correlation of their instance embeddings with a secret linear combination of those vectors. We show that choosing the linear combinations from the codewords of an error-correcting code allows users to collaboratively train the model without revealing their embedding vectors. We present the experimental results for user verification with voice, face, and handwriting data and show that FedUV is on par with existing approaches, while not sharing the embeddings with other users or the server.