Crypto-biometric schemes, such as fuzzy commitment, require binary sources. A novel approach to binarising biometric data using Deep Neural Networks applied to facial biometric data is introduced. The binary representations are evaluated on the MOBIO and the Labelled Faces in the Wild databases, where their biometric recognition performance and entropy are measured. The proposed binary embeddings give a state-ofthe-art performance on both databases with almost negligible degradation compared to the baseline. The representations' length can be controlled. Using a pretrained convolutional neural network and training the model on a cleaned version of the MS-celeb-1M database, binary representations of length 4096 bits and 3300 bits of entropy are obtained. The extracted representations have high entropy and are long enough to be used in crypto-biometric systems, such as fuzzy commitment. Furthermore, the proposed approach is data-driven and constitutes a locality preserving hashing that can be leveraged for data clustering and similarity searches. As a use case of the binary representations, a cancellable system is created based on the binary embeddings using a shuffling transformation with a randomisation key as a second factor. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.