||Advances in Federated Learning and an abundance of user data have enabled rich collaborative learning between multiple clients, without sharing user data. This is done via a central server that aggregates learning in the form of weight updates. However, this comes at the cost of repeated expensive communication between the clients and the server, and concerns about compromised user privacy. The inversion of gradients into the data that generated them is termed data leakage. Encryption techniques can be used to counter this leakage, but at added expense. To address these challenges of communication efficiency and privacy, we propose TOFU, a novel algorithm which generates proxy data that encodes the weight updates for each client in its gradients. Instead of weight updates, this proxy data is now shared. Since input data is far lower in dimensional complexity than weights, this encoding allows us to send much lesser data per communication round. Additionally, the proxy data resembles noise, and even perfect reconstruction from data leakage attacks would invert the decoded gradients into unrecognizable noise, enhancing privacy. We show that TOFU enables learning with less than 1% and 7% accuracy drops on MNIST and on CIFAR-10 datasets, respectively. This drop can be recovered via a few rounds of expensive encrypted gradient exchange. This enables us to learn to near-full accuracy in a federated setup, while being 4x and 6.6x more communication efficient than the standard Federated Averaging algorithm on MNIST and CIFAR-10, respectively.