Recently, an increasing number of work discusses the use of multi-input functional encryption in privacy preserving machine learning as it provides a number of unique advantages. For example, the computational effort is completely outsourced to the analyst, while still maintaining control over the type of computation. However, almost all efficient schemes are restricted to linear functions and/or one data source only, substantially limiting their usability. We introduce a new quadratic noisy multi-input functional encryption scheme which is more efficient than comparable schemes. We show that supporting quadratic functions allows for privacy preserving training of machine learning models on encrypted data. We use iterative techniques from federated learning and operate over hybrid split data. Moreover, our scheme also supports noisy outputs which in turn allows for making the learning process differentially private. Our experiments demonstrate the applicability of the method in practice while its security is proven secure under the widely used decisional Diffie-Hellman assumption.