Deep neural networks, like many other machine learning models, have recently been shown to lack robustness against adversarially crafted inputs. These inputs are derived from regular inputs by minor yet carefully selected perturbations that deceive machine learning models into desired misclassifications. Existing work in this emerging field was largely specific to the domain of image classification, since the high-entropy of images can be conveniently manipulated without changing the images' overall visual appearance. Yet, it remains unclear how such attacks translate to more security-sensitive applications such as malware detection - which may pose significant challenges in sample generation and arguably grave consequences for failure. In this paper, we show how to construct highly-effective adversarial sample crafting attacks for neural networks used as malware classifiers. The application domain of malware classification introduces additional constraints in the adversarial sample crafting problem when compared to the computer vision domain: (i) continuous, differentiable input domains are replaced by discrete, often binary inputs; and (ii) the loose condition of leaving visual appearance unchanged is replaced by requiring equivalent functional behavior. We demonstrate the feasibility of these attacks on many different instances of malware classifiers that we trained using the DREBIN Android malware data set. We furthermore evaluate to which extent potential defensive mechanisms against adversarial crafting can be leveraged to the setting of malware classification. While feature reduction did not prove to have a positive impact, distillation and re-training on adversarially crafted samples show promising results.