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Deep neural networks (DNNs) can be attacked by adversarial examples, e.g., images that are misclassified because of just a few tweaked pixel values. White-box attacks (WBA) are based on complete knowledge of the DNN's internal parameters (i.e., weights and biases). In this talk, the concept of grey-box attacks (GBA) and a method of their a-priori evaluation is proposed. GBAs are only based on knowledge about the DNN's training method and data. Small standard benchmark images show how robustness concepts based on two metric spaces of DNNs lead to different GBAs with substantially differing success levels. This is joint work with my doctoral student Ronan Richter.